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UNIVERSITÉ MOHAMMED V – AGDAL FACULTÉ DES SCIENCES Rabat N° d’ordre : 2660 THESE DE DOCTORAT Présentée par ABDELJALIL LBADAOUI Discipline : PHYSIQUE Spécialité : SISMOLOGIE BODY WAVES TOMOGRAPHY FROM OBS-RECORDED EARTHQUAKES IN THE GULF OF CADIZ Soutenue le 8 Juillet 2013 Devant le jury Président : Mohammed Ouadi BENSALAH P.E.S Faculté des Sciences, Rabat P.E.S P.H P.E.S P.E.S Faculté des Sciences, Rabat Faculté des Sciences, Rabat CNRST Rabat CNRST Rabat Examinateurs : Abdallah EL HAMMOUMI Hamid BOUABID Aomar IBEN BRAHIM Azelarab EL MOURAOUAH Faculté des Sciences, 4 Avenue Ibn Battouta B.P. 1014 RP, Rabat – Maroc Tel +212 (0) 37 77 18 34/35/38, Fax : +212 (0) 37 77 42 61, http://www.fsr.ac.ma ACKNOWLEDGEMENTS This work was carried out in the Mechanics Laboratory under the direction of Professor Abdallah EL HAMMOUMI of the Faculty of Sciences of Rabat and in the National Institute of Geophysics in the National Centre for Scientific and Technical Research of Rabat, under supervision of Professor Aomar IBEN BRAHIM. First and foremost, I want to thank my advisor professor Abdallah EL HAMMOUMI of the faculty of sciences of Rabat, who guided me through all the difficulties in my research and provided me huge supports and several ideas about how to thinks and to solve scientific problems and how to be a real researcher. My thank goes also to all members of the dissertation committee, professors Mohammed Ouadi BENSALAH and Hamid BOUABID of the faculty of sciences of Rabat. Special thank for Professors Aomar IBEN BRAHIM and Azelarab EL MOURAOUAH, for their assistance and moral support, and encouragements for challenges. I learned from them a great knowledge and patience. Their passion and persistence in science imprint in my mind and will inspire me in the future. 2 TITLE BODY WAVES TOMOGRAPHY FROM OBS-RECORDED EARTHQUAKES IN THE GULF OF CADIZ ABSTRACT The gulf of Cadiz is a region considered as a complex seismic area, where strong earthquakes occur and where the plate boundary between the African and Eurasian plates is not exactly known. we use high resolution seismic data recorded by a network of ocean bottom seismometers stations in the Gulf of Cadiz as well as eight Portugal land seismic stations. The OBS network was deployed within an experiment of the NEAREST project. Nearly 600 seismic events are extracted from the recorded data set and their analysis revealed that most of them occur at 20 to 80 km depths, with clusters of seismicity that occur mainly at the Gorringe Bank, within the SW segment of the Horseshoe fault and the Marques de Pombal Plateau and the S. Vicente Fault. A new NW-SE trend of seismicity has been revealed with depths that extend from 35 to 80 km. This seismicity trend is close and nearly parallel to the SWIM faults lineament. We present the first regional-scale high resolution P- and S-velocity distributions across the Gulf of Cadiz region. These velocity models are obtained using 3D seismic tomography to invert the OBS data-set. The results show that the patterns of anomalies in the Gulf of Cadiz are in general, oriented in NE-SW and NW-SE directions. They also show the presence of a low velocity zone (LVZ) to the SE of our study area. At shallow depth, this LVZ is interpreted as due to a large accumulation of sediments within the accretionary wedge, while at a greater crustal depth, it may reflect a continental crustal composition rather than an oceanic crust. Moreover, seismic velocity profiles show that under this region of the Gulf of Cadiz, the Moho averages a 30-km depth. The Gorringe Bank and the Marquise de Pombal plateau are found to be deeply rooted features and represent expressions of mantle uplifting. KEYWORDS Seismic tomography, inversion, body wave, Gulf of Cadiz. 3 TITRE TOMOGRAPHIE DES ONDES DE VOLUME DEPUIS DES TREMBLEMENTS DE TERRE ENREGISTRES PAR DES OBS DANS LE GOLFE DE CADIX RESUME Le golfe de Cadix est une région considérée comme une zone sismique complexe. Dans ce travail, nous utilisons les données sismiques enregistrées par un réseau de stations OBS déployées dans cette région et par huit stations sismiques portugaises. 600 événements sont détectés et analysés. La sismicité est principalement remarquée au Banc de Gorringe au sud ouest de la faille Horseshoe, au niveau du plateau Marques de Pombal et de la faille Sao Vicente. Une orientation nord-ouest/sud-est de la sismicité a été révélée avec des profondeurs qui s'étendent de 35 à 80 km. Nous avons présenté des modèles tomographiques des ondes de volume. Ces modèles de vitesses sont obtenus en utilisant la tomographie sismique 3D par inversion de l'ensemble des données enregistrées. Les résultats montrent que les anomalies sont orientées dans des directions nord-ouest/sud-est et nordest/sud-ouest. Ils montrent également la présence d'une zone de faibles vitesses (LVZ) au sud-est de la région étudiée. Les profils des vitesses obtenus montrent un soulèvement du manteau au niveau de la faille Sâo Vicente coïncidant avec le plateau Marques de Pombal. Ils montrent de plus que le Moho sous le golfe de Cadix est plutôt profond, avec une profondeur moyenne d'environ 30 km en aval de la surface de l’océan. En outre, une zone nord-ouest/sud-est de grandes vitesses est localisée au sud-ouest de notre zone d'étude. MOTS CLEFS Tomographie sismique, inversion, ondes de volume, Golfe de Cadix. 4 RESUME DETAILLE Depuis une dizaine d'années, de nombreuses études ont été menées en tomographie sismique pour établir une image de l'intérieur de la Terre et de comprendre la structure géologique de certaines régions parmi les plus complexes du monde. Cependant, aucune étude d'imagerie tomographique à base des ondes de volume avec des données OBS n’a été réalisée dans le golfe de Cadix. Le principal objectif du travail présenté dans cette thèse est de mener une étude détaillée permettant de déterminer un modèle de tomographie sismique locale dans le golfe de Cadix. La zone étudiée est caractérisée par un aspect géologique très complexe, résultant de la convergence des plaques africaine et eurasienne, où de violents séismes se produisent et où la limite entre les plaques africaine et eurasienne n'est pas toujours exactement connue. Ce travail a été réalisé en utilisant des données sismiques de très haute résolution obtenues par un réseau sous-marin de stations OBS déployées dans le golfe de Cadix ainsi que par huit stations sismiques terrestres situées au Portugal. Le réseau OBS a été déployé dans le cadre du projet NEAREST. Les images tomographiques des perturbations de vitesse en trois dimensions ont été réalisées par inversion des temps d’arrivée des ondes sismiques de volume élaborées à partir de sismogrammes, par détermination des différentes phases. Le système d'analyse sismologique SEISAN a été utilisé pour localiser plus de 600 événements survenus pendant cette période. Parmi lesquels le ML = 4.8 du 1er Janvier 2008 ,événement sismique qui présente la plus grande magnitude enregistrée par le réseau OBS et les stations sismiques Portugaises considérée durant cette période d'observation .Grace au réseau OBS, nous avons détecté un nombre important d'événements locaux qui n'ont pas pu être identifiés précédemment avec les réseaux sismiques Marocain, Espagnol et Portugais. Le grand nombre de tremblements de terre enregistrés au cours de cette période d'une année montre que le golfe de Cadix est une zone très active, en raison de la convergence entre les plaques et parce qu’il est réparti sur une vaste zone de déformation. Dans notre cas, la sismicité se situe au nord de la zone des failles SWIM ; elle est concentrée au niveau de trois principaux blocs : au sud du banc de Gorringe, la partie sud de 5 la plaine abyssale de Horseshoe, et au nord,nord-ouest de la faille de Horseshoe, le long du plateau Marques de Pombal et la faille Sâo Vicente. Quelques tremblements de terre se sont produits dans la zone du prisme d'accrétion, et une sismicité dispersée est observée au sud du bassin d'Algarve et du banc de Portimâo. La distribution en profondeur des hypocentres varie entre les catégories peu profonds et profondeur intermédiaire ; la majorité des événements enregistrés ont entre 20 et 80 km de profondeur. Nos résultats montrent une orientation NW-SE de la sismicité qui traverse la faille du Horseshoe. Cette sismicité observée au sud de notre zone d'étude, parallèlement à la SFZ peut donc être corrélée à l’ensemble des failles SWIM. La première section verticale montre trois principaux blocs de tremblements de terre : le long du banc de Gorringe, la faille de Sao Vicente et le sud du banc de Potimâo, tandis que le second profil montre que la sismicité se concentre dans deux principaux domaines : au niveau banc de Gorringe et de la faille du Horseshoe. La faille inverse du Horseshoe présente une pente d’environ 50 km de longueur. L'inversion des temps d’arrivée est un processus itératif qui requiert un modèle de référence. Dans ce travail, nous l’avons initialisé à l’aide du modèle proposé par l’équipe de recherche du projet NEAREST , 2008. Ce modèle a été, par la suite, amélioré (Matias, et al., 2009). Tous les événements enregistrés sont, ensuite, localisés par ce modèle de vitesse initiale avec une amélioration en utilisant l’algorithme VELEST (Kissling, et al., 1994). Ce dernier est constitué d'une croûte comportant trois couches avec une interface à environ 6 km de profondeur, et la discontinuité du Moho à environ 26 km de profondeur. L’algorithme tomographique LOTOS-10 conçu pour l'inversion simultanée des ondes P et S, a été utilisé dans ce travail. Nous avons défini les paramètres de l’amortissement et de l’effet du bruit de fond en effectuant une série de tests synthétiques. De plus, un réglage sélectif des données a été effectué, dans certaines régions. Ce test montre une excellente zone de couverture entre 15 et 45 km de profondeur. Le paramétrage du domaine a été réalisé avec la construction du maillage par le réglage de la distance entre les nœuds à 5 km. Cet algorithme utilise la méthode dite de pseudo-bending pour le traçage des rais. Elle permet l’estimation de la trajectoire la plus courte des rais : le rai initial est perturbé alors que les points source et récepteur sont maintenus fixes (Nolet,. 2008). Le code LOTOS 6 utilise cette approche pour le traçage des rais avec une légère modification (Koulakov, 2009). Les rais construits de cette manière ont tendance à voyager à travers les anomalies de grandes vitesses et éviter les modèles à faibles vitesses. Avant l’inversion, nous avons effectué plusieurs séries de tests synthétiques afin d'obtenir un paramétrage optimal et d'évaluer la fiabilité des modèles tomographiques. Le test synthétique est une technique qui permet d'examiner la résolution des données utilisées, le test montre que les anomalies périodiques sont reconstruites dans la plupart des régions de la zone d'étude, et la résolution est beaucoup plus élevée dans la zone délimitée par le banc de Gorringe à l'ouest du Cap Sao Vicente au nord, du banc de Portimao à l'Est et la ligne dorsale du Coral dans le sud. En plus du test du damier, nous avons effectué le test odd/even pour donner plus de crédibilité aux résultats tomographiques. Cet essai montre une bonne corrélation des résultats dans la plupart des zones du golfe de Cadix. Les structures tridimensionnelles y révèlent une limite marquante entre les différentes anomalies de haute et basse distribution de vitesse, soit dans une direction NE-SO ou dans des directions NW-SE. Nous remarquons, en outre que les tomogrammes des ondes P et S montrent une distribution de vitesses plus ou moins semblables. Délimitée en latitudes par 35,1 ° N et 37 ° N et en longitudes par 8 ° W et 10 ° W, une grande anomalie négative dans la direction SE est mise en évidence. Elle peut être expliquée par la présence d'une zone à forte concentration de sédiments. A de grandes profondeurs, cette anomalie pourrait être interprétée comme une zone de forte réflexion. Cette partie du golfe de Cadix est plutôt faite de la croûte continentale et donc, sa partie nord délimite plus ou moins la limite entre les croûtes océanique et continentale. Nos résultats montrent une ceinture NW-SE des anomalies de grande vitesse s'étendant à partir du banc de Gorringe jusqu’au prisme d'accrétion traversant la plaine abyssale de Horseshoe. Cette ceinture suit environ le SWIM (SFZ), présentant un ensemble de failles de décrochement comme il a été prouvé précédemment. On constate en plus une zone de transition qui présente une séparation claire de deux structures. Cela peut être interprété comme le résultat d'une déformation de compression oblique de l’Ibérie par rapport à la plaque Nubie. Notre modèle montre aussi une large anomalie positive, s'étendant sur 50 km à l'ouest de la profondeur du Cap Sao Vicente. Cette anomalie est assez claire, la distribution des anomalies de vitesse des 7 ondes S y est presque similaire à celle des ondes P. Elle peut être associée à un soulèvement du manteau profond. Des profils tomographiques verticaux ont été réalisés dans lesquels nous présentons les vitesses réelles au lieu des leurs perturbations. Ces profils montrent un soulèvement du manteau au niveau de la faille Sâo Vicente coïncidant avec le plateau Marquis de Pombal. Ils montrent de plus que le Moho sous le golfe de Cadix est plutôt profond, avec une profondeur moyenne d'environ 26 km en aval de la surface de l’océan. Au NW de la zone d'étude, une anomalie distincte de grande vitesse s'étend à partir de 10 km à 35 km de profondeur et coïncide à peu près avec le soulèvement du banc de Gorringe. En dessous de ces profondeurs, cette anomalie à grande vitesse continue à apparaitre mais semble plutôt atténuée, ce qui confirme les résultats d’une récente étude (Jiménez, Munt et al 2010), En outre, la coupe verticale de tomographie montre clairement que le banc de Gorringe est une anomalie qui implique un soulèvement du manteau et que cette caractéristique topographique émerge d’une profondeur considérable à partir du manteau. L’orientation W-E du banc de Portimao où une anomalie de grande vitesse est observée, est expliquée à la fois, par la convergence oblique des plaques et par l’existence d'une activité sismique récente. La partie de la plaine abyssale Horseshoe que nous étudions est proche de la frontière entre l’Eurasie et la plaque africaine. Cette région est fortement influencée par un mouvement de compression. Les images tomographiques de la partie nord de la plaine abyssale Horseshoe montrent une anomalie de faible vitesse séparant deux blocs d’anomalie positive le long de l’alignement SWIM où l'activité sismique est faible. Cette anomalie peut, sans aucun doute, être interprétée comme la zone de contact entre la faille Horseshoe et les failles de l’alignement SWIM. Certains auteurs soutiennent l'existence d'une zone de subduction active sous le golfe de Cadix, les données GPS n'ont, par contre, montré aucun mouvement différentiel à travers le détroit de Gibraltar (Stich et al, 2006; Serpelloni et al, 2007). En fait, pour des profondeurs inférieures 50 kilomètres, nos profils de vitesse ne montrent aucune indication de la zone de subduction au SE de la zone d'étude. 8 TABLE OF CONTENT Acknowledgements ................................................................................................................................................. 3 abstract.................................................................................................................................................................... 4 Resumé .................................................................................................................................................................... 5 Résumé détaillé ....................................................................................................................................................... 6 Liste of figures ....................................................................................................................................................... 13 List of tables .......................................................................................................................................................... 18 General introduction ............................................................................................................................................. 19 PART 1 LITERATURE REVIEW 1. Introduction ....................................................................................................................................................... 22 2. THEORY OF ELASTICITY ...............................................................................................................................23 2.1 Displacement vector ........................................................................................................................................ 24 2.2 Strain tensor .................................................................................................................................................... 25 2.3 Stress tensor .................................................................................................................................................... 26 2.4 Equation of motion .......................................................................................................................................... 28 2.5 Stress strain relation ........................................................................................................................................ 29 2.5.1 Fluid material (zero viscosity) ....................................................................................................................... 29 2.5.2 Elastic material ............................................................................................................................................. 29 2.6 Wave equations ............................................................................................................................................... 30 2.7 Body waves ...................................................................................................................................................... 31 2.7.1 Longitudinal waves ....................................................................................................................................... 31 2.7.2 Transverse Waves ......................................................................................................................................... 32 2.8 Surface waves .................................................................................................................................................. 33 2.8.1 Rayleigh Waves ........................................................................................................................................... 35 2.8.2 Love waves ................................................................................................................................................... 41 2.8.3 Love waves in a layer on a half space ......................................................................................................... 41 2.7.4 Boundary conditions..................................................................................................................................... 43 3. EARTH STRUCTURE......................................................................................................................................45 3.1 The crust .......................................................................................................................................................... 47 3.2 The mantle....................................................................................................................................................... 48 3.3 The core ........................................................................................................................................................... 49 3.4 Tectonic plates................................................................................................................................................. 50 3.5 Convection and the earth’s mantle ................................................................................................................. 53 3.5.1 Where tectonic plates meet ......................................................................................................................... 54 4. EARTHQUAKES ............................................................................................................................................56 4.1 Where do earthquakes happen ? .................................................................................................................... 59 4.2 Seismographs .................................................................................................................................................. 61 4.3 Seismograms ................................................................................................................................................... 62 4.4 Phase nomenclature ........................................................................................................................................ 64 4.5 Teleseismic, Regional and Local earthquakes ................................................................................................. 66 9 4.5.1 Teleseismic earthquakes .............................................................................................................................. 66 4.5.2 Regional earthquakes ................................................................................................................................... 67 4.5.3 Local earthquakes ....................................................................................................................................... 68 5. WHAT IS SEISMIC TOMOGRAPHY? ..............................................................................................................69 5.1 The main steps to image earth interior ........................................................................................................... 72 5.2 Imaging the earth with seismic data ............................................................................................................... 74 5.2.1 Travel time tomography ............................................................................................................................... 74 5.2.2 Example of travel time tomography ............................................................................................................. 80 6. INVERSE PROBLEM ......................................................................................................................................82 6.1 Travel time inverse .......................................................................................................................................... 83 6.2 Why inverse problems are hard? .................................................................................................................... 87 6.3 Earthquakes location ....................................................................................................................................... 87 6.2.1 Example location of earthquake in homogenous medium .......................................................................... 92 7. CONCLUSION...............................................................................................................................................95 PART 2 BODY WAVES TOMOGRAPHY IN THE GULF OF CADIZ 1. INTRODUCTION ...........................................................................................................................................97 2. MOTIVATION AND RESEARCH OBJECTIVES..................................................................................................99 3. THE GULF OF CADIZ STUDY AREA ..............................................................................................................100 4. RAY TRACING AND TRAVEL-TIMES INVERSION ..........................................................................................105 4.1 The Eikonal equation ..................................................................................................................................... 106 4.1.1 Eikonal equation for fluid mediums ......................................................................................................... 106 4.1.2 Eikonal Equations in Isotropic Elastic Mediums ....................................................................................... 108 4.2 Ray geometry ............................................................................................................................................... 111 4.2.1 Ray solution in layered mediums ............................................................................................................... 112 4.2.2 Inversion of travel time .............................................................................................................................. 118 4.2.3 Shortest travel-time path ......................................................................................................................... 121 4.3 Bending method ............................................................................................................................................ 123 4.3.1 Pseudo bending method ............................................................................................................................ 125 5. SEISMICITY OF THE GULF OF CADIZ ................................................................................................................ 129 5.1 Nearest Project .............................................................................................................................................. 129 5.2 Data format ................................................................................................................................................... 134 5.3 Seisan analysis software ................................................................................................................................ 134 5.4 Seismicity ....................................................................................................................................................... 136 5.5 Inversion method and procedure .................................................................................................................. 140 6.5.1 Using the LOTOS code ................................................................................................................................ 145 5.5.2 One dimensional velocity optimization and preliminary source location algorithm ................................. 146 5.6 Starting velocity model .................................................................................................................................. 148 6. SYNTHETIC TESTS ............................................................................................................................................ 152 7. RESULTS AND DISCUSSION ............................................................................................................................. 158 7.1 Swim lineaments (SFZ) ................................................................................................................................. 165 7.2 Sâo Vicente Canyon ...................................................................................................................................... 167 7.3 Gorringe Bank ............................................................................................................................................... 172 10 7.4 Portimao-Bank............................................................................................................................................... 175 7.5 Horseshoe Abyssal Plain ............................................................................................................................... 176 8. conclusion ....................................................................................................................................................... 178 9. References ...................................................................................................................................................... 180 APPENDIX 1. Least squares method ...................................................................................................................................... 188 2. Snell’s law ....................................................................................................................................................... 192 3. Pane wave ........................................................................................................................................................ 194 4. Conversion of format seisan to lotos ............................................................................................................... 196 5. Surface waves tomography.............................................................................................................................. 200 11 LITERATURE REVIEW LISTE OF FIGURES Figure Figure Figure Figure Figure 1.1 1.2 1.3 1.4 1.5 Figure 1.6 Figure 1.7 Figure 1.8 Figure 1.9 Figure 1.10 Figure 1.11 Figure 1.12 Figure 1.13 Figure 1.14 Figure 1.15 Figure 1.16 Figure 1.17 Figure 1.18 Figure 1.19 Figure 1.20 Figure 1.21 Displacement of two neighboring point P and Q Stress tensor Displacement shape produced by compressional waves propagation. Displacement shape produced by shear waves propagation. Three component seismogram showing the surface waves phases, of earthquake , Rayleigh wave are observed in vertical and radial component, whereas Love waves are shown in transverse component. The particle motion for surface waves (Rayleigh waves), (P. Shearer, 2009). The shape of displacement variation with depth shows that displacement is exponentially decreasing with depth. The particle motion for surface waves (Love waves), (P. Shearer, 2009). Love waves in a half space. A cross section through earth, showing the thicknesses of each layer, dividing the earth in three main layers ( the crust, the mantle and the core). A cross section through earth , showing detailed earth structure, (1) Continental crust, (2) Oceanic Crust , (3) Subduction Zone, (4) Upper Mantle, (5) Volcanic Eruption, (6) Lower Mantle ,(7) Panache Material Warmer ,(8)Outer Core, (9) Inner Core, (10) Cells Mantle Convection, (11) Lithosphere, (12) Asthenosphere, (13) Discontinuity Gutenberg, (14) Discontinuity Mohorovicic. Map show the crustal plates boundary (Stein and Wysession, 2003). Picture shows the process of the Sea floor spreading. Convection in the mantle drives plate tectonics .(www.geo .m tu. edu/~hamorgan/ bigideas welc-o me.html). Stress builds until it exceeds rock strength. Agadir earthquake February 29, 1960, killed some 12,000 people and injured 12,000 others. Destruction of the old part of the city was complete, and some 70% of the new structures in the city were destroyed (http://mimoun1.forumavie.com). Comparison of frequency, magnitude, and energy release of earthquakes. (Stein and Wysession., 2003). 30 years seismicity map of earthquakes magnitude greater than four, shows that most events occur along the boundaries between tectonic plates, (Stein and Wysession, 2003). First teleseismic record of earthquake of April 17 1889 in Japan , enregistred by the Geodetic institute Potsdam (http://www.gfz-potsdam.de/portal/gfz). Three component seismogram showing the body and the surface waves phases of the earthquake occurred in Gulf of cadiz in August 1 , OBS 1. Seismograms showing the differences in amplitudes and frequencies between an earthquake occurred in India in April 4, 1995 of magnitude 4.8 (bleu signal) and an nuclear test occurred again in Indian in may 11, 1998 ,magnitude 5.1 ( red signal), data are recorded at Nilore, Pakistan (Stein and Wysession, 2003). 12 LITERATURE REVIEW Figure 1.22 The 1994 Northridge earthquake recorded at station OBN in Russia. Some of the visible phases are labeled (Shearer, 2010). Figure 1.23 Examples of seismic rays and their nomenclature. The most commonly identified phases used in earthquake location are the first arriving phases: P and PKIKP (Stein and Wysession, 2003). Figure 1.24 Teleseismic earthquake of may 2008 (China), M= 8.0, recorded by OBS 12 (all components). The seismic phases continued for more than 6000 Seconds. Long period surface waves (Rayleigh & Love) are also recorded. Figure 1.25 Part of seismogram showing a regional earthquake of june 8/ 2008 (Greece) recorded by OBS 12 (all components), M= 6.5. Figure 1.26 Part of seismogram showing a local earthquake (all OBS’s vertical components) of November 1st, 2008 (Greece), M=4.8 (SW Iberia). Figure 1.27 Global Seismographic Network (IRIS). Figure 1.28 Travel time picks for various body waves phases and travel time curves, the data are 57655 travel times from 104 sources (earthquakes and explosions). ( Kennett and Engdahl, 1991). Figure 1.29 An example ray path in a 3-D block velocity perturbation for Tomography problems. Figure 1.30 Travel time plot of the P seismic waves of the events occurred in morocco between 1993 to 2003 recorded by Moroccan seismic station networks. Figure 1.31 An example ray path and cell numbering scheme for a simple 2-D tomography problem. Figure 1.32 An example ray path and in 2-D dimension showing the blocs where the basis function is none zero. Figure 1.33 2-D block geometry velocity perturbation for an idealized tomography problem, the model consists on identical blocks , traversed by 13 ray paths. Figure 1.34 Chart showing the differences between the inverse and forward problem. Figure 1.35 Geometry for an earthquake location in earth with variance change in velocity with depth. Figure 2.1 Plate tectonic interactions between the southern Eurasia and the North Africa plates with the main elements of plate boundaries superimposed: AGL: Azores–Gibraltar Line; GC: Gulf of Cadiz; GF: Gloria Fault; MAR: Mid-Atlantic Ridge; TR: Terceira Ridge. Solid yellow line: plate boundaries (Zitellini et al 2009). Figure 2.2 Gulf of Cadiz region offshore SW Iberia, showing the bathymetry map and existing faults, SWIM is South West Iberian Margin faults lineament (Duarte, et al 2009). Figure 2.3 Geometry of the ray segment along a path from a surface source to a surface receiver Figure 2.4 Incidence angle of a ray Figure 2.5 Incidence angle of a ray Figure 2.6 Polar coordinate system for a ray in equatorial plan Figure 2.7 Ray path in spherical earth model. Figure 2.8 Ray and wavefront geometry. 13 LITERATURE REVIEW Figure 2.9 An example of a shortest path followed by a seismic ray traveling from a source S to receiver R. Figure 2.10 Piece of the path shown in Figure (2.17). Figure 2.11 Process of bending algorithm used to determinate the shortest path. Hatched light grey patterns represent negative anomalies of -30%; dark grey patterns are positive anomalies of +30%. (Koulakov, 2009). Figure 2.12 Tangential, normal and anti-normal unit vectors along the ray path (Kazuki et al,. 1997) Figure 2.13 Three point perturbation scheme used in pseudo bending method, Um & Thurber (1987). Figure 2.14 Seismicity of the Gulf of Cadiz as recorded between august 2007 and July 2008 as shown by the red dots;, GB : Gorringe Bank , CP: Coral Pach, , SVC: Sâo vicente Canyon, RV : Rharb Valley , PB: Portimâo Bank, AB: Algarve Bassin, AJB: Alentijo Bassin , Ocean Bottom Seismometers (OBS) blue triangles and Portugal Land stations green triangles. Figure 2.15 Ocean Bottom Seismometer’s on board, (Zitellini N., Carrara G. & NEAREST Team. - ISMAR Bologna Technical Report, June 2009). Figure 2.16 Location of the broad band stations used in this study, ocean Bottom Seismometers (OBS) blue triangles and Portugal Land stations green triangles. Figure 2.17 Seismicity of the Gulf of Cadiz as recorded between august 2007 and July 2008 as shown by the black circles; AB: Algarve Bassin, AJB: Alentijo Bassin the inclined blue line represents the SWIM faults zone (SFZ), and red lines are the possible faults.CP: Coral Pach, GB : Gorringe Bank , GF : Gorringe fault , HsF : horseshoe fault ,MPF : Marques de Pombal fault , PB: Portimâo Bank, PSF: Pereira de Sousa fault, RV : Rharb Valley , SVC: Sâo vicente Canyon, SVF: Sâo vicente fault, Figure 2.18 Seismic profiles shown in the map Figure (2.9), showing events that occurred within 40 km distance from the profile. This profile indicates a more continuous pattern of seismicity. HsF: Horseshoe fault, GB: Gorring Bank. Figure 2.19 Seismic profiles shown in the map Figure (2.26), showing events that occurred within 40 km distance from the profile, this shows three separate clusters of seismicity. AW: Accretionary wedge, GB: Gorring Bank , SVF: Sao Vicente fault. Figure 2.20 Seismic profiles shown in the map Figure (2.26), showing events that occurred within 40 km distance from the profile, this shows three separate clusters of seismicity. AW: Accretionary wedge, GB: Gorring Bank , HsF: horsechoe Fault. Figure 2.21 Chart showing the General structure of the LOTOS code working process. Figure 2.22 Ray paths in the map view at depth of 20, 40, 60 and 80 Km showing the coverage paths, purple point are the stations. Figure 2.23 Ray paths in the map view in a vertical cross section shown by grey dots. Blue triangles are the stations. Figure 2.24 Earthquakes location of more than 600 events recorded during NEAREST 14 LITERATURE REVIEW Figure 2.25.a Figure 2.25.b Figure 2.26 Figure 2.27 Figure 2.28 Figure 2.29 Figure 2.30 Figure 2.31 Figure 2.32 Figure 2.33 Figure 2.34 Figure 2.35 Figure 2.36 Figure 2.37 Figure 2.38 cruise survey. Velocity model obtained by the VELEST algorithm , the black line plot represent the model given by OBS location , the red line represent the model given using both OBS’s and Portugal land station and the blue model is given using only the Portugal land stations. Different starting P-velocity models used for optimization of the initial velocity model; model 1 is the velocity model proposed in the NEAREST2008 cruise report, model 3 is the model derived using VELEST, while models 2,4,5,6 and 7 are initial-velocity models with slight modifications of the previous ones. Checkerboard test performed for P and S waves in horizontals sections. Synthetic test performed for P and S waves in horizontals sections at 35 Km depth. Checkerboard test performed for P waves in vertical sections, AA’ and BB’ shown in Figure below. Checkerboard test performed for S waves in vertical sections, AA’ and BB’ shown in Figure below. Anomalies of P velocities distribution, test with inversion of two independent data subsets (with odd/even numbers of events). Anomalies of P velocities distribution, test with inversion of two independent data subsets (with odd/even numbers of events). P-velocity distribution at 10 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). P-velocity distribution at 15 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). P-velocity distribution at 25 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). P-velocity distribution at 35 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). P-velocity distribution at 50 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). S-velocity distribution anomalies at 10 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ) S-velocity distribution anomalies at 15 km. Solid lines show the existing 15 LITERATURE REVIEW Figure 2.39 Figure 2.40 Figure 2.41 Figure 2.42 Figure 2.43 Figure 2.44 faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). S-velocity distribution anomalies at 25 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ) S-velocity distribution anomalies at 35 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ) S-velocity distribution anomalies at 50 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ) Horizontal sections of P-velocity anomalies at 15,25,35,50 km depth. (perspective view) Horizontal sections of P-velocity anomalies at 15,25,35,50 km depth. (perspective view) NW-SE belt of high velocity anomaly (SWIM lineament) Figure 2.45 Horizontal P-velocity distribution at 25, 35 and 50 km, showing high velocity anomaly southwest Portuguese Margin. Figure 2.46 Positions of the vertical cross-sections velocity profiles 1 and 2 Figure 2.47 P velocity distribution in vertical cross-sections 1, the position of vertical section is shown in the Figure (2.39)., GB: Gorringe Bank. HsF: Horseshoe Fault Figure 2.48 P velocity distribution in vertical cross-sections 2, the position of vertical section is shown in the Figure (2.39), SVF : Sao Vicente Fault, AW : Accretionary wedge. Figure 2.49 Horizontal P-velocity distribution at 25, 35 and 50 km, showing the attenuation of anomaly A between the Gorringe bank and horsechoe abyssal plain. Figure 2.50 Density and temperature depth profiles at four positions identified in Fig (2.26): Tagus Abyssal Plain (profile a), Gorringe Bank (profile b), and Horseshoe Abyssal Plain (profiles c and d), (Jiménez, Munt et al 2010). Figure 2.51 Figure (3.5) Anomalies of P velocities distribution, test with inversion of two independent data subsets (with odd/even numbers of events). Figure 2.52 Figure (3.4) Checkerboard test performed for S waves in vertical sections, AA’ and BB’ shown in Figure below. Figure 2.53 Model results showing the lithosphere structure. The map above show the position of the profile. White dots are earthquake hypocenters, (Jiménez, Munt et al 2010). Figure 2.54 P- velocity distribution in vertical cross-sections 1, shows the layers going to 50 km depth , precising the direction in which the African oceanic lithosphere thrust Eurasian plate. 16 LITERATURE REVIEW Figure 2.55 Horizontal P-velocity distribution at 25, 35 and 50 km, showing high velocity anomaly in the Porimaô Bank. Figure 2.56 Horizontal P-velocity distribution at 25, 35 and 50 km, showing low velocity anomaly in the N-W of the horseshoe Abyssal Plain. Figure 3.1 a projection in subspace, p is the projection in column space, d is the data vector and e is the error vector. b) Illustrate the projection of the data vector in terms of components, showing the error quantities and is an outlier. Figure 3.2 A plane wave incident on a horizontal surface, is the incidence angle, denote the length of the ray. Figure 3.3 A plane wave crossing a horizontal interface between two homogeneous half-spaces. Figure 3.4 Propagation of plane wave. Figure 3.5 Chart of processing method Figure 3.6 Resolution Kernel (Badal et al 2003). LISTE OF TABLE Table 1.1 Earthquakes with 70 000 or more deaths (http://earthquake .usgs.gov). Table 1. Table 1.1 2 P and S velocities in the reference 1-d model after optimization by the Lotos software. 17 LITERATURE REVIEW GENERAL INTRODUCTION Nowadays, the plate tectonics theory provides several models trying to explain the major geological features of the present structure of our planet. This theory proposes that the current deformation of the lithosphere is related to several internal processes inside the earth. For few a decades, many research studies have been conducted in seismic tomography to image the interior of the Earth and to understand the most complex geological structure of the globe. Recently, the development and improvement of equipments in several domains, as well as advances in computer studies (processing power, memory capacity), in electronic (more sensitive sensors) have contributed significantly to obtain more explicit models of the earth. However, it is known that the resolution of tomographic models is limited by a number of factors, including the distribution of seismogenic zones and seismological networks scattered around the world. The seismotectonic context does not always allow the investigation of some complex areas by non-destructive methods. Before that, it was too difficult to investigate the oceans underground, since the sensors are often located only on the continental zones; the nonuniform distribution location of these sensors makes the ray tracing to be a difficult task. The direct result of these limitations is that the regions of low coverage have often lower resolution models. Seismic tomography is a still widely used method of exploring the earth interior, although the gravimetric measurements and morphological studies of bathymetry (Zitellini et al, 2009), (Gutscher et al, 2002), (Gracia et al, 2010) begin to show their importance, and the international community is naturally oriented towards tomographic techniques for determining the basement velocity structure. These techniques have been field proven in the continental, and marine seismic application did not require major changes. The main objective of the work presented in this thesis is to undertake a detailed study that will help produce a local seismic tomography model of the south West region of the Gulf of Cadiz, which is an area characterized by a complex geology, resulting from the convergence of the African and Eurasian plates. 18 LITERATURE REVIEW The local seismic tomography studies of this offshore zone requires in general that the stations must be in the same study area, thus, achieving a tomographic studies based on the data collected by land stations can never reveal the detailed structure of the region. In August 2007, a European research consortium team decided to make detailed studies of the western zone of the Gulf of Cadiz, in the project nearest (integrated observations from near shore sources of tsunamis: towards an early warning system) which is an eu-funded project (goce, contract n. 037110) mainly addressed to the identification and characterisation of large potential tsunami sources located near shore in the Gulf of Cadiz, and to realize a quantitative understanding of lithosphere processes. Since, it was necessary to carry out seismic measurements at sea; the broad band seismic stations have been installed in the Atlantic Ocean, since, a glimmer of hope will begin to emerge, then we were assured that we will use a worthwhile quality feedstock, the National Center for Scientific and Technical Research (CNRST) in Rabat, participated to this project by accomplishing a tomographic study of the region by exploiting the data collected in the ocean. A tremendous amount of work was made, and incredible patience is needed to extract all the seismic events that occurred in this period, thorough job was carried out when analyzing earthquakes, knowing that good location leads to successful tomographic models. Often seismic tomography need a large database to get an excellent coverage, however, having a huge amount of data can be misleading sometimes about the reality reality of the earth interior. We have exploited more than 600 events in this study, which is an enormous database for an excellent coverage. After that, our database is prepared for inversion process, containing all the epicenters and arrival times of all recorded earthquakes; we examined several inversion methods, to choose the adapted method for our data inversion and to avoid accumulation of errors by applying appropriate algorithms, the most recent methods and systems have been used, for example we have chosen ray tracing algorithms that use methods of integration instead of differentiation. We showed results from 10 km depth, as we will see after, from this depth rays coverage begin to be excellent, it means that there are still 5.2 km of the crust needs to be investigated, because of deepest station is in about 4.8 km deep, we plan to study this layer 19 LITERATURE REVIEW applying a surface wave tomography rather than body waves, by determination of velocity models for shallow structure, using the Rayleigh waveforms which depend strongly on the shallow velocity structure of the medium, which is used to obtain the group-velocity dispersion curve (Dziewonski et al., 1969), and applying the digital filtering with a combination of Multiple Filter Technique (Dziewonski et al 1969), (Badal et al, 1992), (Chourak et al, 2003). 20 LITERATURE REVIEW Part 1 Literature review CHAPTER OUTLINE 1. Introduction 2. Theory of elasticity 3. Earth structure 4. Earthquakes 5. What is seismic tomography? 6. Inverse problem 7. Conclusion 21 LITERATURE REVIEW 1. Introduction Seismology is the multi-variant discipline that can never be understood without dealing with the theory of elasticity. During the Master studies we have carried out several notions to deeply understand this theory, which allows me to penetrate in theoretical concepts of seismology. The theory of elasticity solved several seismological problems even if approximations are sometime needed for simplifying. Accordingly, basic concepts and principles, dealing with stresses and strains were used to establish relationships applicable to different types of mediums; however, they do not allow the resolution of complex problems. That is why scientists introduce other concepts to define cases of the ideal material, so even if the continuum mechanics are not able to examine the true nature of matter, it’s still establishing different laws of behavior of real materials. We know that the surface of the earth, where we are living is constantly shaken, because of the movement of the plates, sometimes is violently shaken during earthquakes, causes then a human disaster. We describe in this thesis the main processes of the dynamics of the planet consists of various internal layers that are in constant motion, and the causes of these disasters. Great progress for the development of seismic instrumentation in recent years has greatly helped geophysicists to perform great tomographic models. But it’s not always easy to estimate the parameters of inverse problems, seismic tomography models are mainly resolved by inverting the travel time of the different phases, and they need often a great effort in the estimation of parameters, and powerful algorithms for matrix inversion, because often the amount of data exceeds the number of model parameters, we are dealing here with an inverse problem which consists of determining the internal state of unknown system, based on a given quantities of observations, knowing the structure of the system. Inverse problems are present in almost sciences and engineering, and they are applied when you search for information on a system without being able to measure directly. In this part we will explain how we can solve an inverse problem using a mathematical approach. 22 LITERATURE REVIEW 2. Theory of elasticity The theory of seismic waves is based on the theory of elasticity. This theory is closely related to the development of the seismology. Regarded on Hook’s discovery, Navier was the first how present the equations for equilibrium and motion of elastic solid, and investigate the general equations of the theory of elasticity. Development of theory of elasticity was largely due to the work of Cauchy and Poisson when they worked on the propagation of light, in 1831 Poisson found that, at large distance from source of disturbance (not the case at the present with sophisticated instruments) the motion transmitted by the fast wave was longitudinal, followed by a transverse wave that is the slowest one. After that Stokes demonstrate in 1845 that the displacement of matter was irrotational dilatation, and the slower wave was a wave of equivoluminal distortion with elements rotations, he made the observation that resistance to compression and resistance to shearing are the two fundamental kinds of elastic resistance by introducing the modulus of compressibility and rigidity. Forty two years later, Lord Rayleigh discovered that a specific wave can be formed near the free surface of homogeneous body propagating along the surface with a different velocity, and decay with a depth, he found that this wave is elliptically polarized in the plane determined by the normal to the surface and by the direction of propagation. Since, it is the discovery of Rayleigh waves; 24 years later Love called them “Rayleigh waves” after he discovered them theoretically. This entire exploit, has been discovered by several mathematicians and scientists long before any seismic records were obtained, in this thesis we will develop the theory for more understanding the process of wave propagation, and the elastic constitutive equations and equations of motion in Cartesian coordinates. All these results can be found in several textbooks, (Love 1944), (Fung 1965), (Takeuchi and Saito, 1972), (Aki and Richard, 1980), (Thorne lay terry c. Wallace, 1995), (Seth Stein and Michael Wysession, 2003), (P. Shearer, 2009) and (Novotny, 1999). 23 LITERATURE REVIEW 2.1 Displacement vector Consider a particle at point P (original state) , which is moved to point P’ (deformed state, the position of the vector y depends on the one of x, therefore (1,1) Under the condition of continuity, we notice the existence of the inverse function According to Lagrange description of motion, the displacement is given by – In a neighborhood of the P point, let's consider another point Q, displaced to the point Q’ in the deformed state Figure (1.1) Figure 1.1 Displacement of two neighboring point P and Q. 24 LITERATURE REVIEW Using the Taylor expansion we obtain , Where (1.4) and using the Einstein’s summation convention So, we can get 2.2 Strain tensor From the displacement field we can derive the strain field; we take the straightforward approach, assuming that if only the small strains are considered (Ewing et al 1957). The distance between P and Q is and the square of this distance can be expressed as From the quadrangle (PP’QQ’) and Equation (1.6) 25 LITERATURE REVIEW Can be expressed in term of components Consequently We consider: with and the quantity S and we introduce , the strain tensor can be expressed as Strain is the formal description of the change in shape of a material, if we neglect the nonlinear terms we get the Cauchy’s infinitesimal strain tensor 2.3 Stress tensor The stress vector is defined by 26 LITERATURE REVIEW Figure 1.2 Stress tensor. Where is the effect of all surface forces exerted across the element of surface . Let be the stress vector acting on this element, this vector can be expressed on tensor notation as where , are the components of the stress tensor. Applying the condition of equilibrium yield Using the Cauchy’s formula Applying the Gauss theorem And putting , where A is a continuous vector with continuous derivatives and v is the unit outward normal, may be expressed as a volume integral 27 LITERATURE REVIEW If the integral assumed to be equal to zero, this yield Eq. is known as the equation of the equilibrium. 2.4 Equation of motion The equation of motion can be obtained by adding the inertial force , we define is the density, v the velocity and t is the time, the total derivative with respect to time is equal to the corresponding partial derivative where u is the displacement. The equation of motion of a continuum mechanics can be expressed in this form Taking in account the approximation assuming that the products of the derivatives are small we get 28 LITERATURE REVIEW 2.5 Stress strain relation 2.5.1 Fluid material (zero viscosity) The stress tensor is defined in a fluid material of zero viscosity as 2.5.2 Elastic material The stress tensor is defined in elastic material of zero viscosity as is the material constant. In an isotropic Earth the elasticity tensor involves only two constants, the bulk modulus and the shear modulus where where (Nolet 2008). so, is the volume dilatation, is the shear modulus and has no immediate physical interpretation. Such laws can be very complicated, but are greatly simplified when we ignore the hysteresis caused by anelastic effects and when we confine ourselves to very small displacements. In that case the medium deforms approximately linearly with the applied stress. We replace (1.22) into the Equation of motion (1.18) For a homogeneous isotropic medium, the elastic coefficients are constant, than (1.23) can be written as 29 LITERATURE REVIEW It is known that So (1.23) become Representing the equation of motion in terms of components of displacement vector Finally, if we replace we deduce the equation of motion well-known in seismology, from which we shall derive the wave equations 2.6 Wave equations From the previous equation , than we neglect the body forces F, this equation can take the form Applying the divergence operator yield and , equation (1.29), become 30 LITERATURE REVIEW Where is the velocity of compressional waves, and if we applying the curl operator to the equation (1.28), we get the vector wave equation Where is the velocity of shear waves. The purpose of the following is to give a precise explanation of the theory of propagation of elastic waves, it also defines essential mathematical formulas for understanding the physics of waves propagations, and we will deal with the different types of waves that propagate in different elastic media. 2.7 Body waves It follows from the theory of elasticity that there are two principal types of elastic body waves, Includes the P and S waves, and the wavefront makes a spherical shape when the body waves propagate in elastic medium. 2.7.1 Longitudinal waves Also called compressional or irrotational waves; in seismology we call them the primary waves or just P waves, because they are the fastest waves, so they are the first appearing on seismograms, longitudinal waves undergo an volume change, as the waves propagates, the displacements in the direction of waves propagation cause material to be alternately compressed and expanded. The irrotational waves are thus generated by a scalar potential. The solutions for P and S waves like those given in equation and give the locations of wave-fronts, when P-wave emerges from deep in the Earth to the surface, a fraction of it is transmitted into atmosphere as sound waves. Such sounds, if frequency is greater than 15 cycles per second, are audible to animals or human beings. These are known 31 LITERATURE REVIEW as earthquake sound (J.R. Kayal, 2008), for it cannot describe all wave phenomena. These approximations are collectively known as geometric ray theory and are the standard basis for seismic body-wave interpretation. Figure 1.3 Displacement shape produced by compressional waves propagation. 2.7.2 Transverse Waves also called shear, rotational or secondary waves (S waves), when these waves pass through elastic medium they involve shearing and rotation of material without any volume changes, the displacement associated with propagating shear wave is perpendicular to the direction of wave propagation. Figure 1.4 Displacement shape produced by shear waves propagation. 32 LITERATURE REVIEW The velocities of longitudinal waves and the transverse waves in homogeneous and isotropic medium, satisfy the Hook’s law, are given by the formulas , where is the shear modulus, is the Lamé coefficient, and relation assumes the fact where the coefficients are equals, is the density. Poisson this relation is often used in seismology to describe many elastic materials, involve that Both longitudinal and transverse waves can propagate in solid media, but only primary waves can propagate in fluid medium when . Elastic body waves are reflected and transmitted at the discontinuities of elastic parameters; in fact we observe increases the number of waves on seismograms. 2.8 Surface waves We have seen that the body waves can propagate in a homogeneous, isotropic and unbounded medium. If the medium is bounded, another kind of waves can be guided along the surface of the medium. The Surface waves are the waves that propagate along a boundary and whose amplitudes go to zero as the distance from the boundary goes to infinity. There are two basic types of surface waves, Love and Rayleigh waves, named after the scientists who studied them first. Love’s work was directed to the explanation of waves observed in horizontal seismographs, while Rayleigh predicted the existence of the waves with his name. The main difference between the two types of waves is that the motion is of SH type for Love waves, and of P–SV types for Rayleigh waves. Love and Rayleigh waves show a large surface wave train arriving on a seismometer’s Figure (1.5); transverse component shows the arrival of Love waves, followed by Rayleigh waves on a vertical and radial component, which are distinguished from each other by the types of particle motion in their wave fronts. In the description of body waves, the motion of particles in the wavefront was resolved into three orthogonal components – a longitudinal vibration parallel to the ray 33 LITERATURE REVIEW path (the P-wave motion), a transverse vibration in the vertical plane containing the ray path (the vertical shear or SV-wave) and a horizontal transverse vibration (the horizontal shear or SH-wave). These components of motion, restricted to surface layers, also determine the particle motion Figure (1.6) and Figure (1.8) and character of these two types of surface waves. Figure 1.5 Three component seismogram showing the surface waves phases, of earthquake , Rayleigh wave are observed in vertical and radial component, whereas Love waves are shown in transverse component. After a large earthquake, contrary to the body waves whose energy spreads three dimensionally, the surface waves can circle the globe many times, and their energy spreads tow dimensionally and it’s concentrated near the earth surface. 34 LITERATURE REVIEW 2.8.1 Rayleigh Waves In 1885 Lord Rayleigh described the propagation of a surface wave along the free surface of a semi-infinite elastic half-space. The particles in the wavefront of the Rayleigh wave are polarized to vibrate in the vertical plane Figure (1.6). The resulting particle motion can be regarded as a combination of the P- and SV-vibrations Figure 1.6 The particle motion for surface waves (Rayleigh waves), (Adapted from , Shearer, 2009). It is well known that a general transient wave can be expressed as a superposition of harmonic waves by means of the Fourier integral (Novotny, 1999). And by the superposition of harmonic waves of different amplitude and frequencies, we can construct rather complicated wave shapes as well as seismic surface waves. If we consider a wave field in term of potential component, from the equation of motion for a homogeneous isotropic 35 LITERATURE REVIEW medium equation , the displacement field can be decomposed into scalar potential and vector potential . And express components of displacement vector in terms of potentials In the case of the wave field independent of the y-coordinate On the other hand we can obtain from 1 and 1 22 the components of the stresses acting in the perpendicular plan of z axis are And from the components of displacement vector of propagating plan contains and we see that the perpendicular plan , whereas is in can be decomposed into two parts, and express the vector potential 36 thus, the wave field as LITERATURE REVIEW where represent the displacement in represent the displacement in plan and plan. Consider the potential for longitudinal waves, , and the potential for transverse waves, , in the form of plane harmonic waves, moving with constant velocity and without change of shape, propagating in the -direction. The displacement vector can then be decomposed as Where and and , for part of wave the components equals zero, hence the displacement is where and can be defined as where is a given angular frequency, and depth-dependent amplitudes, we now replace are unknown functions, describing the in the wave equations and we get These two equations represent the equations of harmonic oscillator, which can be easily resolved, the solutions take the form , where , , So, equations 37 can be written as LITERATURE REVIEW Can be decomposed into, Where and is the wave number. Or in the this form In witch and describes the decomposition of surface wave into two body waves, (Novotny, 1999), ( C. A. Coulson, 1977), replacing into and we can now express the stress components by inserting the displacement components into stress formula , the stress components can then be written as follow We have calculated the stress component to use them, for those further boundary conditions, the stress components equals zero in the free surface of 38 LITERATURE REVIEW The amplitudes diminish with the depth increase for If the apparent velocity (see plane waves in the Appendix) , are real, thus and the goes to infinity, which no agree with the second boundary condition, we have to consider the case to avoid this problem and take the imaginary part of and . The amplitudes now take the form Or in this simple form for that and increase to infinity for infinite depth, this terms doesn’t represent any physical meaning, so we keep The terms for putting Become now These equations show that the waves are exponentially decreasing with depth increase. Figure (1.47) represents the vertical and horizontal displacements calculated for a given value of poison coefficient, these displacements are normalized with respect to the vertical displacement of the particle motion in the surface. 39 LITERATURE REVIEW Figure 1.7 The shape of displacement variation with depth shows that displacement is exponentially decreasing with depth. Now shall we determine the quantities the equations and, from the displacement expression given by , displacement vector can take the form And the stress component become Inserting expressions of and into , when the boundary conditions are satisfied for stresses , we finally arrive at system of linear equations where and 40 with unknowns and , LITERATURE REVIEW The solution of this system of linear equation yield the Rayleigh velocity For typical values of Poisson solid, for more details see (Novotny, 1999) and (Stein and Wysession, 2003). 2.8.2 Love waves The boundary conditions which govern the components of stress at the free surface of a semi-infinite elastic half space prohibit the propagation of SH-waves along the surface. However, A.E.H. Love showed in 1911 that if a horizontal layer lies between the free surface and the semi-infinite half-space. Figure 1.8 The particle motion for surface waves ( Love waves), (P. Shearer, 2009). 2.8.3 Love waves in a layer on a half space Love wave are a surface waves result from interaction of SH waves, this type of waves require an increasing velocity with depth, if not the case Love waves cannot exist. 41 LITERATURE REVIEW Figure 1.9 Love waves in a half space. The displacement of the particle motion associated with propagation of Love waves can be expressed as where 42 LITERATURE REVIEW Where , and is the wave number. 2.7.4 Boundary conditions We consider the following boundary conditions, the stress components equals zero in the free surface of in when , all stresses and displacements are continuous; the displacement go to zero is real, thus , if the apparent velocity go to infinity, which no agree with the boundary condition, we have to consider the case to avoid this problem and take the imaginary part and where 43 . LITERATURE REVIEW The first boundary condition is satisfied when So, The second and third boundary conditions yield again a system of linear equations with unknowns and . where and 44 LITERATURE REVIEW 3. Earth structure The earth is composed of several layers. The inner core in the extreme center is a solid iron and nickel ball located about 6370 km from the surface of the earth. And outer core in form of the ring, formed of a fluid mixture of molten iron and nickel. The core is surrounded by the asthenospher composed of a portion of the mantle and the crust (oceanic or continental) Figure (1.10). It is well known that the Earth has a molten core, what is now general knowledge was slow to develop. In order to explain the existence of volcanoes, some nineteenth century scientists postulated that the Earth must consist of a rigid outer crust around a molten interior. It was also known in the last century that the mean density of the Earth is about 5.5 times that of water (Lowrie, 2007). From this it was inferred that density increased towards the Earth’s center under the effect of gravitational pressure. Figure 1.10 A cross section through earth, showing the thicknesses of each layer, dividing the earth in three main layers ( the crust , the mantle and the core ) 45 LITERATURE REVIEW The key to modern understanding of the interior of the Earth is density, pressure and elasticity was provided by the invention and improvements of sensitive seismographs. The progressive refinement of this instrument and its systematic employment world-wide led to the rapid development of the modern science of seismology. Important results were obtained early in the twentieth century. The Earth’s fluid core was first detected seismologically in 1906 by R. D. Oldham. Resent geophysical studies have revealed that the Earth has several distinct layers. Each of these layers has its own properties Figure (1.11). Figure 1.11 A cross section through earth , showing detailed earth structure, (1) Continental crust, (2) Oceanic Crust , (3) Subduction Zone, ,(4) Upper Mantle, (5) Volcanic Eruption. , (6) Lower Mantle ,(7) Panache Material Warmer ,(8) Outer Core, (9) Inner Core, (10) Cells Mantle Convection, (11) Lithosphere , (12) Asthenosphere, (13) Discontinuity Gutenberg , (14) Discontinuity Mohorovicic. (Wikipedia). 46 LITERATURE REVIEW 3.1 The crust Earth outermost layer, the crust preserves a memory of the Earth’s evolution that extends back more than 3.4 Gy, while today it is well established that silicic material extracted from the mantle forms an outer crust and it’s well documented now a compromise aspects of the physical state of the planet and its evolution and the Earth's crust when many seismological studies performed early from the beginning of the last century brought important elements of the overall appearance and global view of the structure of the crust. Recently, using high frequency resolutions of deep seismic reflection profiling (Meissner,1973. Oliver et al, 1976, Clemperer 1989) and wide-angle reflection profiling investigations (Healy et al., 1982, W.D. Mooney, 1985) understanding the crustal structure began to change radically when all studies showed that the crust is highly heterogeneous in composition and physical properties, furthermore, the large number of collected data and the increasing improvements of seismic station network in the last 40 years played a key role in determining the first model of the crust, an important works mentioning soil crusts have made, and regional crustal thickness models were created by several scientists (Mohorovicic, 1910), (Conrad 1925), (Byerly 1926), (Byerly and Dyk, 1932), (Gutenberg 1932), (DeGolyer, 1935), (Heiland, 1935), (Press, 1964), (Crampin, 1964), (Kovach and Anderson, 1964), (Christensen, 1965), (Dix, 1965), (Audry and Rossetti, 1962), (Aubert and Maignien, 1948), (Leprun, 1978), (Pindell 1985)… Seismology began to have several successful discovery, for example when has succeed to discern the petrological boundary between ultramafic and silicic rocks, where the wave velocity increases by about 6.5 km/s (in the lower crust) to more than 7.7 km/s (upper mantle), (James and Steinhart, 1966). The crust varies in thickness. It is thin (about 7 km) under oceans, thicker (about 40 km) under continents, and thickest (as much as 70 km) under high mountains. The continental crust is made up mostly of low-density granitic rocks and that no granite exists on the floor of the deep ocean, the crust there consists entirely of basalt and gabbro overlay by sediments (Grotzinger et al., 2007). As a result of plate tectonics Figure (1.12), the oceanic crust and continental crust differ systematically in their main physical properties, including density, thickness, age and composition. Continental crust has an average thickness of , and an average age of , the density of , whereas the oceanic crust has an average 47 LITERATURE REVIEW thickness of about 6 km, the density of . Is everywhere younger than , oceanic crust composed mainly of basalt theoleiitic, which has a dark and fin grain texture as consequence of rapid cooling magma, by contrast, the continental crust has a felsic composition than oceanic crust (Dziewonski and Romanowicz,. 2007). 3.2 The mantle The mantle is the layer between the crust and the core, is the widest section of the Earth. The most volume of the earth is taken by the mantle, and it has a thickness of approximately 2,900 km. The mantle is made up of semi-molten rock called magma. In the upper parts of the mantle the rock is hard, but lower down the rock is soft and beginning to melt, made of magma (melted rocks) and is around 3000 °C. The mantle is fundamentally different than the crust based on its composition that it’s made up , the mantle itself can be subdivided into tow layers, upper mantle and lower mantle, Upper part of the mantle is called lithosphere , is the highest part of the earth, and is cooling enough to be solid ( it’s the solid portion of the mantle). From 40 to 400 km depth there consists of the upper mantle, containing the olivine and pyroxene (iron, magnesium and silicate) as well as calcium and aluminum. The upper mantle is divided into three parts: the hydrosphere, is all the compartments containing water on Earth (lakes, rivers, seas, oceans), the lithosphere is the group consisting of the crust and the upper part of the mantle, is between 0 and 100 to 200 km, and Asthenosphere located between 200 and 400 km depth is in the viscous state, with an average temperature would be of the order of 1500 °C; the Transition Area ranges from about 400 to 670 km, basaltic magma source; From 670 to 2960 km the lower mantle there is probably consisting of silicon, magnesium and oxygen with iron, calcium and aluminum. The crust is divided into several plates which float on the liquid upper mantle. They are called tectonic plates. They reflect the current liquid mantle convection: from the deepest parts of the mantle magma rising currents pushing his way to the surface. These currents have broken the solid crust of the earth into several large plates that move slowly separate from each other transported by movements of the mantle. This is what is known as continental drift. It is characterized by two processes: dislocation and wrinkling. Dislocation occurs when two plates move away from each other, allowing the new crust from forming through magma mantle. The folding 48 LITERATURE REVIEW occurs when two plates move towards the edge and that one of the plates immersed below the other features to merge into the mantle. There are also transverse movements between two plates like San Andreas Fault in California. 3.3 The core The deep interior of the earth is currently inaccessible and perhaps would be forever. However, through a large quantity of data collected at the surface, and contains information of inside the earth transported to the surface, by several way, such as seismic waves and free oscillations, topography and of gravity, magnetic and electric fields, heat fluxes and hydrothermal circulation and chemical and isotopic variations in volcanic rocks, geophysicists interpret as they can what earth interior looks like. But until now, they know quite a bit about the composition of the core. Seismology tells us that the core below the mantle is a fluid, but it is much fluid in the center of the earth when the pressure are immense, over 4 million times the atmospheric pressure (Grotzinger et al., 2007), and temperature; The Models produced up to date are consistent and provides a probable picture of the core and lower mantle, although a number of questions remain unanswered, the thermal history calculations for the earth were based upon the assumption that heat is transported radially outward by conduction (Lubimova, 1969). However, with the guidance of (Tozer 1965), opinion shifted to the view that thermal convection is the dominant mechanism of heat transport in the interior of the earth, since that time, the model of thermal convection has been adopted for a long time, recently, it has become clear that the best model for the energy source is gravitational energy released by the growth of the solid inner core, (Braginsky, 1963), (Gubbins, 1976), (Loper, 1978), ( Gubbins et al, 1979), (Gubbins and Masters, 1979), (Loper and Roberts, 1983), the central feature of the gravitationally powered dynamo is that the inner core is growing by freezing of outer-core material as the earth gradually cools (Barry Saltzman, 1984), both seismic and theoretical studies indicate a complicated structure for the inner core. First, the inner core is not completely solid, but is an intimate mixture of solid and liquid, with the mass fraction of solid increasing monotonically with depth. It was also demonstrated, that by the effect of the decreasing of the radioactivity (released from the inside) with time, the earth cannot remain at a constant temperature, and so that the earth is cooling at a given rate, and it can be related to the 49 LITERATURE REVIEW growth of the inner core (Gubbins et al. 1979), and the growth of the solid inner core is caused by the cooling of the core from above, with the core coolest at the top, freezing occurs first at the bottom provided the liquidus gradient with pressure, finally some discovers said that the earth's core is composed principally of iron, with a small but significant percentage of some light constituent. The nature and amount of this constituent are uncertain, (Brett, 1976), (Ringwood, 1977), (Stevenson, 1981), (Brown and McQueen, 1982). 3.4 Tectonic plates The mantle can be divided into three subsections; the Mesosphere, Asthenosphere and Lithosphere. The Mesosphere or lower mantle is a thick liquid, it’s the closest one to the core, the Asthenosphere is a plastic like consistency, it’s a kind of rock not quite solid, but it’s not quite liquid to, this is the cooling part of the mantle, and it’s basically the substances that move very slowly. And finally, the Lithosphere is the upper most part of the mantle, and it’s very rigid and divided into pieces of plates. Figure 1.12 Map shows the crustal plates boundary (Adapted from Michael Allaby, (2009)). 50 LITERATURE REVIEW In 1910, Alfred Wegener published his works where he proposed some of the core ideas of the modern plate tectonic concept, Wegener proposed that the continents were drifting about on the surface of the planet, and that they once fit together to form one great supercontinent, known as Pangaea. After that a revolution shook up the Earth sciences that result in the acceptance of the plate tectonic model which states that the Earth’s outer shell, or lithosphere, is broken into several rigid pieces, called tectonic plates Figure (1.12). The lithosphere is divided then into tectonic plates, the lithosphere is the part of the earth that is basically all cracked and divided into deferent sections. Figure shows the pieces of the lithosphere broken down into pieces, and they float on top of the Asthenosphere, so, they move. But! How they all this giant pieces of floating rocks move? The tectonic plates move because the Sea- floor spreading, see below the Figure (1.13) where two plates separated by ocean, the red dark color indicate a blend of molten and semimolten rock called a magma, and what happen exactly ? the magma pushes up creating under water a mountain ranges, called ridges, when the magma come up in top reaching the bottom of the oceans, its cooling carrying out a new rocks forming, and going to push the two older rocks, there is three ways allowing tectonic plates moving A. Ridge push The ridges formed during sea-floor spreading are higher than where it sinks into the mantle, These are the areas from which the earth breathes, they Spanning about 70,000 km, the oceanic ridges are the largest geological structure of the globe. These are huge relief elongated submarine can reach a height of 3000 m and 2500 m wide. B. Convection Inside the earth, radioactive elements provides some of the thermal energy that causes convection, the convection currents form in the mantle when thermal energy transfers from the core to the mantle; Hotter magma closer to the core rises because it is less dense as the 51 LITERATURE REVIEW denser cooler magma closer to the crust, this creates a current., the same thing can happen in the ocean, the warmer water go to the top of the ocean towards the surface and a cold water on the bottom and push the plates. C. Slab pull Oceanic crust denser than the continental crust sinks and pulls the rest of the plate with it. The slab pull is a direct phenomenon result of the subduction process driving a tectonic plate under another plate of lower density, usually an oceanic plate under a continental plate or in a more recent oceanic plate. In the oceanic divergence oceanic lithosphere, its when two plates collide, the most common to this detachment is when oceanic plate sink into continental plates (driven by its own weight), then the convergence begins to characterized by appearance of slabs. Figure 1.13 Picture shows the process of the Sea floor spreading spreading involving the upwelling and melting of the underlying mantle. 52 LITERATURE REVIEW 3.5 Convection and the earth’s mantle The main heat transfer mechanism in the Earth’s mantle is convection. It is a thermally driven process in which heating at depth causes material to expand and become less dense, causing it to rise while being replaced by complementary cool material that sinks. This moves heat from depth to the surface in a very efficient cycle since the material that rises gives off heat as it rises and cools, and the material that sinks gets heated only to eventually rise again. Convection is the most important mechanism by which the Earth is losing heat, with other mechanisms including conduction, radiation, and advection. However, many of these mechanisms work together in the plate tectonic cycle. Mantle convection brings heat from deep in the mantle to the surface where the heat release forms magmas that generate the oceanic crust. The midocean ridge axis is the site of active hydrothermal circulation and heat loss, forming black smoker chimneys and other vents. As the crust and lithosphere move away from the midocean ridges, it cools by conduction, gradually subsiding (according to the square root of its age) from about 1.5–2.5 miles (2.5–4.0 km) below sea level. Heat loss by mantle convection is therefore the main driving mechanism of plate tectonics, and the moving plates can be thought of as the conductively cooling boundary layer for large-scale mantle convection systems. Very early in the history of the planet at least part of the mantle was molten, and the Earth has been cooling by convection ever since. It is difficult to estimate how much the mantle has cooled with time, but reasonable estimates suggest that the mantle may have been up to a couple of hundred degrees hotter in the earliest Archean. The rate of mantle convection is dependent on the ability of the material to flow. The resistance to flow is a quantity measured as viscosity, defined as the ratio of shear stress to strain rate. Fluids with high viscosity are more resistant to flow than materials with low viscosity. The present viscosity of the mantle is estimated to be 1020–1021 Pascal seconds (Pa/s) in the upper mantle, and 1021–1023 Pa/s in the lower mantle, which are sufficient to allow the mantle to convect and complete an overturn cycle once every 100 million years. The viscosity of the mantle is temperature dependent, so it is possible that in early Earth history the mantle may have been able to flow and convectively overturn much more quickly, making convection an even more efficient process and speeding the rate of plate tectonic processes (T. Kusky, 2005). 53 LITERATURE REVIEW Figure 1.14 Convection in the mantle drives plate tectonics. (www.geo.mtu.edu/~hamorgan/ bigideas welc-o me.html) 3.5.1 Where tectonic plates meet When they are moving, the plates are always bumping into each other, pulling away from each other, or past each other. The plates usually move at about the same speed that your fingernails grow. They run into each other or sliding past each other, at present, we know how this plates are actually moving and how fast (GPS data measurements), we have three main types of plate’s boundary. A. Divergent boundaries It’s where we have the plates moving away from each other, they correspond to the axis of mid-ocean ridges, African plates and South American plate are example of this boundaries. 54 LITERATURE REVIEW B. Convergent boundaries It’s where we have the plates converge upon each other, they can correspond to the subduction zones characterized by the presence of slabs, when oceanic – continental crusts convergence, the Himalaya’s mountain is an example of convergence between two plates in continental domain. C. Transform boundaries (horizontal sliding) They are characterized by transform faults which are breaks in the plates and which allow sliding between two plate portions, San Andreas Fault in California is a result of horizontal sliding of two boundaries. 55 LITERATURE REVIEW 4. Earthquakes Although seismology is a science with a long history, earthquakes were not understood in their original. The Chinese were the first to ask questions related to the origin of earthquakes, Chang Heng invent in 132 AD, the first functional Seismoscope, it was an primitive device, of not characterized by the delicacy and sensitivity of instruments of our day, but a beautiful design able to detected the arrival of seismic waves, when the origins of earthquakes were not at all understood. In 1892, seismologists can finally make a quantitative description of earthquakes at great distances due to a revolutionary invention of a sensitive seismograph by John Milne. Did you know that thousands of earthquakes occur every day? Fortunately, most are very small and cannot be felt. Earthquakes occur when tectonic plates push, pull or slip past each other, But this is not a fast process, this can take a million of years for plates to move centimeters even millimeters of the movement every years, but as they are moving, a lot of stress built up, it’s the stress increases near the plate’s edges, resulting an elastic deformation of the rocks, when the stress exceeds the strength of the rocks along the fault, the fault slips, releasing the stress suddenly and causing an earthquakes, Figure (1.15), big earthquakes are not nearly so common, but when one strikes, it can bring real disaster. Earthquakes can originate from sudden motion along a fault, from a volcanic eruption, or from bomb blasts. (T. Kusky, 2005). Figure 1.15 Stress builds until it exceeds rock strength 56 LITERATURE REVIEW Earthquakes cause many problems; ground shaking can knock buildings down and destroy roads and bridges, vibrating earth can cause entire mountainsides to give way, creating landslides that destroy everything in their paths, Figure (1.16). Undersea earthquakes sometimes bring about monster waves called tsunamis, Tsunamis can travel over the ocean for thousands of miles causing death and destruction far from the earthquake, therefore seismological studies based on the observation of significant effects, concentrated in areas in a big frequency occurrence, where these effects are most intense. Figure 1.16 Agadir earthquake February 29, 1960, killed some 12,000 people and injured 12,000 others. Destruction of the old part of the city was complete, and some 70% of the new structures in the city were destroyed. (http://mimoun1.forumavie.com) When an earthquake occurs releasing enormous energy (the same as millions of explosives being set off at the same time) causes the ground to shake and vibrate, associated with passage of waves of energy released at its source. Earthquakes can be extremely devastating 57 LITERATURE REVIEW and costly events, sometimes killing tens or even hundreds of thousands of people and leveling entire cities in a matter of a few seconds or minutes. Recent earthquakes have been covered in detail by the news media and the destruction and trauma of those affected is immediately apparent. A single earthquake may release the energy equivalent to hundreds or thousands of nuclear blasts Figure (1.17), and may cost billions of dollars in damage. Figure 1.17 Comparison of frequency, magnitude, and energy release of earthquakes. (Stein and Wysession., 2003) Earth’s surface is always on the move. Earth’s crust is broken into tectonic plates, these are large pieces of crust that shift and move. They are always joining together and pulling apart. When tectonic plates move, the edges grate or scrape against each other. This movement causes Earth to tremble and the place where tectonic plates meet is called a fault line. Scientists begin with an understanding of how the planet Earth formed and how its internal heat engine drives tectonic plates to move around on the surface. Geologists and natural philosophers have speculated on the origin of continents, oceans, mountain ranges, and 58 LITERATURE REVIEW earthquakes for hundreds of years. Early geologists recognized and classified many of the major surface and tectonic features of the continents and oceans (T. Kusky,. 2008). 4.1 Where do earthquakes happen ? Most earthquakes occur along the edge of the oceanic and continental plates. The seismicity of the world Figure (1.18) tracks the boundary of the plates Figure (1.12), we see that most earthquakes occur along the plate’s boundary, and the largest earthquakes occur along the Pacific Ocean with 80% of the annual recent seismic activity, each year, one or two earthquakes of magnitude greater than 8 take place somewhere in the world. We note for example that some regions were shaken several times during the last century; this is the case for example in Chile, Mexico, and Japan, it's important to know that more than 90% of earthquakes in the world occur at shallow depth less than 60 km, when the plates move against each other three types of boundaries that are the seat of an intense seismic world activity. Figure 1.18 30 years seismicity map of earthquakes magnitude greater than four, shows that most events occur along the boundaries between tectonic plates, (Stein and Wysession, 2003). 59 LITERATURE REVIEW We then notice that epicenters are distributed along closed curves which divide the world into large oceanic and continental regions, more or less devoid of seismic activity, or "plates", thus satisfying the theory of plate tectonics. There is a diffuse seismicity outside these limits (inter plate seismicity), but as much volcanic activity, almost all earthquakes occur at the boundaries of these plates, and his is called tectonic earthquakes. Because catastrophic earthquakes occur rarely in any particular region, humanity often forgets how devastating these events can be. However, history should remind us of their power to suddenly kill tens of thousands of people Tab (1.1). Table ( 1.1) Earthquakes with 70 000 or more deaths (http://earthquake.usgs.gov) YEAR LOCATION MAG DEATHS 893 Ardabil, Iran --------- 150 000 1138 Aleppo, Syria --------- 230 000 1290 Chihli, China --------- 100 000 1667 Shemakha,Caucasia --------- 80 000 1755 Lisbon, Portugal 8.7 70 000 1920 Gansu,China 7.8 200 000 1923 Kanto, Japan 7.9 143 000 1927 Tsinghai, China 7.9 200 000 1932 Gansu,China 7.6 70 000 1948 Ashgabat,Turkmenistan 7.3 110 000 1976 Tangshan, China 7.5 255 000 2004 Sumatra 9.1 283 106 2005 Pakistan 7.6 86 000 2008 Eastern Sichuan, China 7.9 87 652 60 LITERATURE REVIEW 4.2 Seismographs The first seismological instrument was constructed in second century AD by a Chinese philosopher Chian-hen, but the really big development increase in seismology happened from around 1900 and onwards and was mainly due to improvement in making more sensitive seismographs, to detect even small earthquakes magnitude. Later, the measurement of the ground motion allows studying seismic wave attenuation. in 1750 scientist began to use pendulums to make more sensitive instruments, however, in 1889 in Potsdam (Germany), Ernst von Rebeur-Paschwitz invented the first instrument able to record signal from a teleseismic event from an earthquake in Japan Figure (1.19), in 1915 Shaw and Milan produced Milan-Shaw long period seismograph, it was characterized by his low weight, after that a significant progress in seismological instrument was made and several seismographs were created in Japan, Russia, and Italy. In 1922 Wood Anderson created an instrument records on photographic paper, after that, several electromagnetic seismographs were developed, and since 1970, a new generation of seismographs appeared with electronic amplification of the electric signal. Figure 1.19 first teleseismic record of earthquake of April 17 1889 in Japan , recorded by the Geodetic institute Potsdam (http://www.gfz-potsdam.de/portal/gfz). Nowadays, sophisticated seismological instrument created in particular for the purpose of detecting ground motion and nuclear explosions, able to record the very small movements of the soil. "Networks survey". The development of networks of seismographs around the world quickly showed that the seismicity was not randomly distributed, but it was structured along major seismic continuous lines on the surface of the globe; installation of broadband world network stations, and Ocean Bottom Seismometer, have strongly promote recovery 61 LITERATURE REVIEW and collection of a huge quantities of seismic data in both regional and global scale, we can now use a hard disks with a larger memory storage can be used for recording, the recorder memory is not a problem today and recording is easy and a easy to share, the control of different acquisition parameters become easy and it’s mostly done with development of computational techniques , this instrumental progress helped many geophysicists to study several area that were mysterious. Since, the seismic instrumentation has contributed significantly to saving lives around the world, and helped to investigate the earth interior. 4.3 Seismograms When an earthquake happened, its recorded by a different sensors, and graphical recording is called seismogram, thus, the record signal can be analogical on smoked photographic, or plain paper, in as digital data stored in hard discs. The velocities of seismic waves is big, several kilometers per second, sensors coupled with very accurate clocks are used and perfectly synchronized to the position of the ground return in time with a precision of a few milliseconds, The sensors must record the signal, and the time of the signal, and time, it was difficult to get a good external time reference, availability of GPS (Global Positioning System) signals make the end of all timing problems, the movements of the Earth are continuously recorded. Thus, seismograph records background noise generated by atmospheric changes, marine activity, humane activities, and microseismic, as P-waves are faster than S-waves on the seismogram they appear at first, followed by the S wave and surface waves at the end Figure (1.20). 62 LITERATURE REVIEW Figure 1.20 Three component seismogram showing the body and the surface waves phases of the earthquake occurred in Gulf of cadiz in August 1 , OBS 1. Figure 1.21 Seismograms showing the differences in amplitudes and frequencies between an earthquake occurred in India in April 4, 1995 of magnitude 4.8 ( bleu signal) and an nuclear test occurred again in Indian in may 11, 1998 , magnitude 5.1 ( red signal), data are recorded at Nilore, Pakistan (Stein and Wysession, 2003). 63 LITERATURE REVIEW Seismograms exhibit a number of wave trains some of which travel into the globe completely before arriving at a station, examining seismograms is a very important step in tomographic studies of any region in the globe. Excellent analysis of seismograms often leads to a good resolution of a tomographic problem often solved by inverse methods; indeed, data comes from seismograms and data are treasure of seismologists, data are the key contribute answers to fundamental questions in geophysics. Permanently seismograms are recordings ground motion, recordings made by seismometers, and it is easy to identify from signal the differences between earthquakes and nuclear test Figure (1.21). 4.4 Phase nomenclature The different layers in the Earth (e.g., crust, mantle, outer core, and inner core), combined with the two different body-wave types (P, S), result in a large number of possible ray geometries, termed seismic phases. The following naming scheme has achieved general acceptance in seismology. Earthquakes causes propagation of seismic body and surface waves, these waves travel with different velocities, the time taken by each wave to reach the station is different from other waves, on seismograms, we see different phases, each distinct phase can be associated with a certain travel path “Travel of certain seismic phases” Each distinct phase has a certain travel time, Figure (1.22). Figure 1.22 The 1994 Northridge earthquake recorded at station OBN in Russia. Some of the visible phases are labeled (Shearer, 2010). 64 LITERATURE REVIEW Seismic-wave energy can travel multiple paths from a source to a receiver at a given distance Figure (1.23), to help sort out the various phases, seismologists have developed a nomenclature to describe each phase in terms of its general ray path. The various portions of the path a ray takes, for example, between the source and the free surface, are known as legs. Each leg of a ray is designated with a letter indicating the mode of propagation as a P or S wave, and the phase is designated by stringing together the names of legs. Thus, there are four possible depth phases that have a single leg from the surface reflection point to the receiver: pP, sS, pS, and sP. The main layers constricting earth are the mantle, the fluid outer core, and the solid inner core. P- and S-wave legs in the mantle and core are labeled as follows Some examples of these ray paths and their names are shown in Figure (1.23). Notice that surface multiple phases are denoted by PP, PPP, SS, SP, and so on. For deep focus earthquakes, the up going branch in surface reflections is denoted by a lowercase p or s; this defines pP, sS, sP , etc. (see Figure. (3.8)). These are termed depth phases, and the time separation between a direct arrival and a depth phase is one of the best ways to constrain the depth of distant earthquakes. P-to-S conversions can also occur at the CMB; this provides for phases such as PcS and SKS. Ray paths for the core phase PKP are complicated by the Earth's spherical geometry, leading to several triplications in the travel time curve for this phase. Often the inner-core P phase PKIKP is labeled as the df branch of PKP. Because of the sharp drop in P velocity at the CMB, PKP does not turn in the outer third of the outer core. However, S-to-P converted phases, such as SKS and SKKS, can be used to sample this region, (Shearer, 2010). 65 LITERATURE REVIEW Figure 1.23 Examples of seismic rays and their nomenclature. The most commonly identified phases used in earthquake location are the first arriving phases: P and PKIKP. (Stein and Wysession, 2003). 4.5 Teleseismic, Regional and Local earthquakes Earthquakes may be further classified into three types depending on the distance from source to the seismograph station. Since the character of seismograms depends on epicentral distance, the nomenclature for seismic phases is also distant dependent. 4.5.1 Teleseismic earthquakes The earthquakes, which are recorded by a seismograph station at a greater distance, are called teleseismic earthquakes. These are very often called teleseisms. By international convention the epicentral distance is required to be more than 1000 km for a teleseism. Lay 66 LITERATURE REVIEW and Wallace (1995), however, define teleseismic distance as . An example of a tele- seismogram is shown in Figure (1.24). Depending on the magnitude of the earthquake, teleseismic amplitudes can range from barely perceptible to those that saturate the instrument. These earthquakes provide very useful seismic phases for the crust as well as for the interior of the Earth. The direct P and S-wave arrivals recorded at teleseismic distances between 30° and 95° are relatively simple. Figure 1.24 Teleseismic earthquake of may 2008 (china), M= 8.0, recorded by OBS 12 (all components). The seismic phases continued for more than 6000 Seconds. Long period surface waves (Rayleigh & Love) are also recorded. 4.5.2 Regional earthquakes The earthquakes, which occur beyond say 500 km but within 1000 km of a seismograph station, are called regional earthquakes. An example of a regional earthquake, recorded by a micro earthquake recorder at a distance of about 700 km, is shown in Figure (1.25). Like teleseismic events, amplitudes of regional earthquakes can range from barely perceptible to large, but their periods are less than those of the teleseismic events. These earthquakes also provide seismic wave data for the Earth’s crust and mantle. 67 LITERATURE REVIEW Figure 1.25 Part of seismogram showing a regional earthquake of june 8/ 2008 (Greece), recorded by OBS 12 (all components), M= 6.5. 4.5.3 Local earthquakes Earthquakes occurring within a distance of few hundred km, say 500 km, from a seismic station are called local earthquakes. Local earthquakes are often characterized by impulsive onsets and high frequencies. A seismogram showing local earthquakes recorded by a microearthquake station at a distance ranging from 50 to 250 km is illustrated in Figure (1.26). The local earthquake signal has typically an exponential decreasing tail. The seismic-wave data are very useful to study the local geological structure/velocity structure of the Earth’s crust and upper mantle. Figure 1.26 Part of seismogram showing a local earthquake (all OBS’s vertical components) of November 1st, 2008 (Greece), M=4.8 (SW Iberia). 68 LITERATURE REVIEW 5. What is seismic tomography? Tomography is a name that comes from the Greek word TOMOS meaning slice or section and, graph meaning drawing or imaging. Tomography now is used in different areas, in geophysics to investigate the earth’s interior in many different directions and construct a tree-dimensional image of what’s inside, in medicine to sweep human body in many directions. Nowadays we know that the principles of tomography are applicable to seismology, as well. For example, earthquake seismologists applied tomographic methods to produce a velocity model for the earth’s mantle. But how is this done with earthquakes? , in this case we call it seismic tomography and it represent a data inference technique that exploits information contained in seismic records to constrain 2D or 3D models of earth interior (Rawlinson et al, 2010). Seismic tomography can be designed as a powerful process of estimating the properties of a medium from measurements of sound energy propagating inside the earth. The Progress in seismic tomography has been growing up rapidly during the last 25 years, and substantial numbers of review papers have been published, nevertheless, Imaging of the Earth’s interior based on seismological observation goes back to the beginning of the 20th century. Recently, geophysicists have successfully used seismic tomography to image velocity variations of the earth, the Moho discontinuity (Mohorovicic, 1909) and the existence of the inner core (Lehmann, 1936) were rapidly identified, the body wave travel-times were tabulated by Jeffreys and Bullen (1940). In the following years, Keiiti Aki published a seminal paper in 1976 on 3D velocity determination beneath California from local earthquakes (Aki and Lee, 1976). (Aki et al., 1977; Dziewonski et al., 1977) have solved for 3-dimentional velocity structure under the NORSAR array, (Dziewonski et al. 1977) derive a low resolution model of 3-D velocity perturbations, when he succeed to show a significant correlation between velocity anomalies in the lowermost mantle. Ellsworth and Koyagani imaged the structure beneath the Kilauea volcano on Hawaii in 1977, in this same year, the first attempts to retrieve the lateral variations in the Earth’s structure were done again by Aki et al. (1977), four years later, Dziewonski & Anderson (1981) constructed an average model, known as preliminary Reference Earth Model. In 1984, (Thurber et al,. 1984) imaged velocities at Kilauea that were low enough to be interpreted as the underlying magma complex. Recently, seismic tomography has 69 LITERATURE REVIEW revealed features in the mantle clearly associated with mantle convection. Researchers succeed to construct a tomographic model of S-wave velocity variation in the mantle that shows clearly the structure of the plate tectonics. Before less than forty years, observing the internal structure of the Earth was impossible, now seismology is a scientific branch which is only at the beginning stage of progress, seismologists know well that they can never determine the structure of the earth with absolute precision, even if, at present they are applying the most powerful principles of seismic tomography to construct the underground structure. But, the development of powerful computer technology and sensitive sophisticate instruments helped a lot in improving earthquake location and in more precise determination of travel-times of seismic body waves, giving more credibility to tomographic models recently determined. Figure 1.27 Global Seismographic Network (IRIS). 70 LITERATURE REVIEW The biggest seismology feat is to produce the first maps of the interior of the Earth through the establishment of global seismological networks Figure (1.27) , to develop images of individual slices through the deep Earth, understand the composition of Earth’s interior, and explain geologic mysteries along the world, it has the major advantage of not needing to destroy the earth, this technique need only Sources (data) and receivers (seismometers placed on the Earth’s surface), these sources are either explosions (active) or earthquakes (passive). The technique is to visualize the changes in seismic velocity (expressed in percentage) called seismic velocity anomalies. These abnormalities are related to speed of temperature variations rocks. If a seismic wave travel through a medium whose physical properties (density, elastic modulus) are different from those of the average model, those waves arrive late or ahead of the predictions of this model, we then deduce a map variations of different kinds of seismic wave from the model, the establishment of these maps requires the data of a large number of travel time, we retrieve the records provided by each station, seismic station recorded the arrival of different seismic waves over time as a time series called seismogram, after that seismologist, can operate using a several methods to analyze the data. All require some knowledge of the physics of waves and their propagation. These data can be processed by an optimization process also called inverse problem (see the next section) to recover the properties of the basement. Inverse modeling or inversion is a method of estimating propagation or interval velocities from seismic data. It uses ray tracing over finite depth intervals and to simulate the actual travel path of waves by updating a readably starting velocity earth models, seismic data acquisition parameters, and theoretical models of physical processes to generate synthetic data that match actual seismic data. Inversion is a process used to predict observed data. By contrast, the direct problem (modeling) associated with this inverse problem is when calculate the travel time of seismic waves in a priori known model. These travel times are the solution of the eikonal equation (expressing the equality of the squared modulus of the gradient of the travel time and the square of the slowness). It is the use of these two problems which will optimize the model established by the least squares method, in the most case the method of tomographic inversion of travel time is used to obtain three-dimensional velocity perturbations in the Earth's, travel time of 71 LITERATURE REVIEW seismic waves can be determined from seismograms, is a graph of the time that it takes for seismic waves to travel from the epicenter of an earthquake seismograph stations varying distances away. 5.1 The main steps to image earth interior The first main step is to acquire the observations, although either their nature, they may come from natural origin (faulting, volcanic eruption, landslide) as they can also be of artificial origin (mine collapse, burst, excavation, shooting exploration or nuclear test), differences in their origin can be identified from signal records Figure (1.21). In which there are differences in the frequencies and amplitudes. Numerous seismologists have compiled large arrival-time data sets like that shown in Figure (1.28). Average fits to the various families of arrivals are known as travel-time curves or charts, these represented painstaking data-collection efforts over the first four decades of the century, curves that seismologists are trying to inverse to get the velocities variances in deep structure, Tomography of first arrival seeks to estimate velocity model wave propagation from seismic first arrival times picked on seismograms. The velocity model obtained can then allow a structural interpretation of the environment or serve as a model for other initial treatment imaging seismic. The areas of application of this method lie in different scales of the geotechnical seismology through petroleum geophysics. 72 LITERATURE REVIEW Figure 1.28 Travel time picks for various body waves phases and travel time curves, the data are 57655 travel times from 104 sources (earthquakes and explosions), ( Kennett and Engdahl, 1991). The theory of ray tracing (see chapter 2) is the theoretical concept used to infer the seismic waves travel time, is one of the powerful mathematics tool needed to get help calculating travel time curves, expressions for ray tracing are determined from a known velocity structure in a one-dimensional (1-D) velocity model in which velocity varies only with depth. For three-dimensional (3-D) structures the ray theory is more complex even if follows similar principles. Studding structure of the earth began with examining seismograms and calculating travel time curves, the case where we are given travel times obtained from observations and wish to invert for a velocity structure that can explain the data. In general, the inversion is much more complicate than the forward problem. The inversion for travel time is often an iterative process where a reference model is needed to start inversion, in this stage, travel time residuals are computed for each datum by subtracting the predicted time from the observed time, then we change the model to minimize the difference between observed and computed travel times. After minimizing all the differences error between 73 LITERATURE REVIEW predicted and observed travel time, a 3-D model is obtained by inverting the travel time residuals for velocity perturbations relative to the reference model; this is the main basis for tomographic inversion techniques, we can also look at the surface waves tomography using harmonic modes of Rayleigh waves and love waves, this type of imaging of earth interior at shallow depth level, however, the surface wave tomography is part of another theory process. It is not easy to combine with that of the body waves, the assumptions are different in each case, and they are generally treated separately. 5.2 Imaging the earth with seismic data 5.2.1 Travel time tomography Travel time Tomography seeks to estimate velocity propagation of seismic waves from the time of first arrivals, generally, data rarely fit a straight line exactly. Usually, we must be satisfied with rough predictions. Typically, we have a set of data whose scatter plot appears to "fit" a straight line; this is called a line of best fit. It is important to fit the data to have an initial velocity model of wave propagation, which can then allow preliminary structural interpretation of the environment and serve as initial velocity model to use for inversion. When the 1-D model is available, the next step is to parameterize the 3-D velocity perturbations into uniform blocks velocity perturbations, we illustrate the block parameterization considering a three dimension geometry with the model divided into similar blocks Figure (1.29), the model contain in general all paths connecting the sources and receiver, The next challenge is to find the exact ray path, and it is not always straightforward to do so, there is several methods for solving the tow point ray tracing, the most known one is shooting method, in which slightly the source are sampled in order to converge on the correct receiver location and bending method, where the source and receiver are kept fixed and try to bend the ray, or finite difference or graph theory techniques that require a grid of points. 74 LITERATURE REVIEW Figure 1.29 An example ray path in a 3-D block velocity perturbation for Tomography problems From seismograms we obtain the observations Figure (1.30) by picking different arriving waves, at least P and S phases, at this stage we have to generate linear regression to fit the observations data and use an inversion technique to derive an initial velocity model. Obviously the observed data can not exactly looks like the predicted one, due to the errors in picking phases, effect of instruments measurements and site, we define the travel time residual as the sum of three terms 75 LITERATURE REVIEW Temps de parcours (secondes ) 120 100 80 60 40 20 0 0 100 200 300 400 500 600 700 800 900 1000 Distance (kilomètres ) Figure 1.30 Travel time plot of the P seismic waves of the events occurred in morocco between 1993 to 2003 recorded by Moroccan seismic station networks (Lbadaoui Master thesis, 2008) Almost all seismic tomography methods involve subdividing the medium into blocks or other spatial functions, such as spherical harmonic expansions, and solving for slowness perturbations that cause predicted times to match observed times better than an initial (usually homogeneous or one-dimensional) model. The idea is that the path integral through the medium perturbations should equal the observed travel-time residual. The objective is to seek for a model that minimize the travel time residual , before we have to compute the observed travel time for each ray path. The tomographic process in a nonlinear inverse problem, for which the travel time for the where represent the observations, ray can be expressed by the vector equation is the model parameter and is the frechet derivatives. The travel time tomography is an iterative process, so, an initial model parameter must be used, and is can be created from the best fit of the travel time curve. we make than a little change in the initial model parameter the get a new model, expected to looks like our observations when we will proceed to inversion. 76 LITERATURE REVIEW where represent the perturbation in model parameter and is the new model, then we compute the Taylor expansion of Where are the Freshet derivatives, ( represent the number of the rays and represent the number of cells), the little change in the model (slowness), we’ll end up with a small change in travel time, according to the Fermat’s principal we ignore the change in ray path, thus the observations can be expressed as and where represent the length of the perturbation. Equation ray path in the block and is the slowness is in the form of a linear system of equation which can be solved by the matrix inversion methods, in this case, the path length of each ray in corresponding block, is the partial derivatives of the travel time with respect to the slowness of that block, in general we have more raypaths than model parameters, yielding an over determined system of equation, so, the generalized inverse solution is where , , , (see the inverse theory in the next chapter). the Figure below chow a seismic ray path passing through a medium divided one similar blocs, with small red segment we define the length cover by the path in each bloc, obviously the majority of the segment are not cover by this path, set to zero elements in operator matrix (see the following example), and the geometry of the ray is determined using ray tracing methods, in this work , we have used the bending method (see ray tracing in Part 2). 77 LITERATURE REVIEW Figure 1.31 An example ray path and cell numbering scheme for a simple 2-D tomography problem. To solve the tomographic problem we have to liberalize about the reference model, the relationship between the observation and model parameter is given by where is the sensitivity kernel and where is the model perturbation; is defined by denote the basis function and Figure (1.32). 78 is the weight LITERATURE REVIEW Figure 1.32 An example ray path and in 2-D dimension showing the blocs where the basis function is none zero. by replacing Where in the equation we get is the sensitivity matrix kernel, projected on the basis functions and the value of the weight is length of the . The element of the basis function represent the ray in the block, with these element we construct the matrix . In general, the number of observation is deferent than the number of blocs, so, the operator matrix is not square, in this case we get the solution by applying the generalized least square (see Appendix). 79 LITERATURE REVIEW 5.2.2 Example of travel time tomography To illustrate this idea, we consider the ideal case model consisting on a number of blocks of unit length in tow dimension case Figure (1.33), in which 13 ray paths traverse the model in different directions. Figure 1.33 2-D block geometry velocity perturbation for an idealized tomography problem, the model consists on identical blocks , traversed by 13 ray paths. The travel time perturbation along the ray path is then given by the sum of the product of each block travel time with the fractional velocity perturbation and can be expressed as All the blocks not encountered by the ray are set to zero in the operator matrix, so, for the ray path the travel time residual can be expressed as 80 LITERATURE REVIEW and The reference slowness model is assumed to be appropriate outside the blocks, so the entire travel time residual for each path is attributed to slowness perturbations in the blocks. Thus the problem looks like Where denotes the total number of blocks in the given model. To reach the receiver, it is known that the rays pass through only some blocks of the setting model, so most of the elements of the operator matrix are set to zero. For measurements it can be written in matrix notation as where is a vector of observations or differences between observations and predictions, is a matrix of partial derivatives In our case we have determined problem and , and observations and has rank , finding generalized inverse solution in the next section). 81 model is the vector of model parameters. model unknowns, is an over is dealing with an inverse problem (see the LITERATURE REVIEW 6. Inverse problem In seismology a known incident wave is given and it’s perturbed by a variation of the nominal features of the medium, if these variations are known, the calculation of the perturbation undergone by the incident wave (forward problem) represent a classic methods. Reciprocally, the measure of the perturbation of signal (seismograms) provides the supplementary data permitting reconstruction of an unknown variation of the nominal features (inverse problem). In general inverse problems are hard to solve, we need to be concerned with far more than simply finding mathematically acceptable answers to parameter estimation, One reason is that there may be many models that adequately fit the data, and the process of computing an inverse solution can be, and often is, extremely unstable in that a small change in measurement then can lead to an enormous change in the estimated model. From the mathematical point of view we can represent many physical experiments with a model space consisting of model parameters a data space with data and Both the model parameters and the data are physical magnitudes whose functional relationship are given by a set of computational rules (the function f). If we assume that the fundamental physics are adequately understood, so a function may be specified relating and as Inverse problem cannot solve the system exactly, but have to minimize the misfit between data and model parameter . Generally formulated, the data are a series of observations in the form of measured values, whereas the model parameters stand for the physical properties of the research object. The latter are not necessarily directly measurable. The function stands for a method (usually a mathematical representation of a physical theory), which relate the model parameters data to . If the model parameters are given and the accompanying data calculated, then we speak of a forward problem (unique solution), on the other hand if we want to determine unknown model parameters based on the data (for example, physical measurements, then we speak of the inverse problem (not unique solution). 82 LITERATURE REVIEW Figure 1.34 Chart showing the differences between the inverse and forward problem. In geophysics the term inversion usually refers to making inferences from observations (mainly on the Earth's surface) about the material parameters (density, wave velocity, etc.) and geometric parameters (depth, earthquake parameters, etc.) in the subsurface. 6.1 Travel time inverse The travel time for a given ray can be expressed as The travel time changes with a small perturbation in the path 83 LITERATURE REVIEW Discrete form of the travel time perturbation where is the distance the ray and is the slowness in block or node. Observations of properties integrated along the number of paths through the medium are used to infer the distribution of the physical property within a medium. Is the expression for estimating slowness perturbation from observed travel time perturbation and denote the partial derivative of the rays travel time with respect to the slowness in the block, it is an operator relating the data and model vectors, the dimension of the model vectors is the same as the number of blocks or nodes elements, and the data vector has the dimension of the number of the ray paths. The operator the data function with respect to the model parameters is also the partial derivative of , can be expressed as In general, the system of equation is over-determined because in the most cases we have more equation (ray paths, or observations) than the number of the blocks (model parameter), 84 LITERATURE REVIEW the travel time thus, is predicted using an appropriate starting model, and travel time residuals are computed for each ray using the error vector The error vector illustrates the quality of initial model, where is the observed data and denote the predicted, in most cases, the error vector magnitude is defined by the normalized term called Euclidian length The inverse problem for estimating slowness perturbation from observed travel time perturbation can be expressed in the form is in general not square matrix, so, we form Where is transpose, to get the generalized inverse solution, we invert operator, and the analysis of the inverse problem use the decomposition in singular values of one matrix. See (Marc Bonnet, 2008) for more detail. Where , used in specific case when we need not to apply Lanczos decomposition. The model parameter because, , so the inversion correctly resolve the inversion, likewise when one has the same quantity of the data as for blocks (vector parameter), and linearly independent. In general case when can be solved easily if the rows of is not square matrix, then will be square symmetric Matrix that can be decomposed using its eigenvectors and eigenvalues. 85 are LITERATURE REVIEW where comprise the eigenvectors of eigenvalues of the matrix matrix, and diagonal matrix contains all the . The eigenvalues are distinct, so the eigenvectors are orthogonal Similarly and and it’s possible to decompose can be decomposed as only eigenvectors with non zero-eigenvalues, where eigenvectors associated with non-zero eigenvalues, and using is the matrix is the matrix with with eigenvectors associated with zero eigenvalues. So known as Lanczos decomposition, (Stein and Wysession,.2003), generalized inverse is rather than who can then be written as So the solution to the inverse problem is Finally we find that, and , where is the true model for which we are seeking is called the resolution matrix. The columns of the resolution matrix indicate how much the true model is smeared into the various parameters of the inversion model. Ideally, one would obtain a diagonal resolution matrix, recovering the full model. Calculation of the resolution matrix is essential for assessing an inversion result. We define also the information density matrix given by And the covariance matrix is given by 86 LITERATURE REVIEW These equations give us physical insight into the inversion solution, for a perfect model matrix is equal to identity matrix, diagonal elements that are close to one correspond to parameters for which we can claim good resolution, it happen when all the model parameters are associated with nonzero singular values. Conversely, if any of the diagonal elements are small, then the corresponding model parameters will be poorly resolved. The resolution and stability can be controlled by using the catoff on the ratio of a given eigenvalue to the largest eigenvalue, the cutoff condition number to determine the number of singular values to retain is defined by : See the example of locating an earthquake by using the generalized inversion. 6.2 Why inverse problems are hard? The difficulty of the inverse problem is a combination of several factors; In general the Goal function is not convex, so this leads to the existence of local minima, and process of the convergence does not stop at the right target. The inverse problem can be ill-conditioned problem, because of a big quantity of data, which makes the existence of multiple solutions, ie several parameters producing the same observations, leads to a non uniqueness of the solution. Discontinuity producing instability in inversion process, Even if you can (in theory) solve the problem for accurate observations. 6.3 Earthquakes location One of the most important tasks in observational seismology is locating seismic sources. The location of an earthquake is among the one of the classic inverse problems in seismology, involving determination of both the hypocentral coordinates and the source origin time. In addition, improving the accuracy of localization is one of the major concerns of seismologists, were believes that clearly identified structure can be derived from well 87 LITERATURE REVIEW localized earthquakes, this requires identification of seismic phases and measuring their arrival times. Currently sensitive seismographs help scientists to determine the arrival times of the different seismic phases, nearly 3000 seismic stations distributed worldwide have been systematically reporting major seismic phase arrival times to the International Seismological Centre (ISC) since 1964 (Lay and Wallace,1995). Thus the travel time of the wave is evaluated using these arrival times at several stations. An earthquake happened generally at unknown time caused by a fault rupture, the waves propagate in all directions and travel long enough distances before they are detected by seismometers scattered across the globe. The hypocenter, Figure (1.35), or focus, is the breaking point or point source, this is the point where the seismic waves begins to spread, the projection of the point source on the surface of the earth when is called epicenter. Figure 1.35 Geometry for an earthquake location in earth with variance change in velocity with depth. earthquakes are usually detected by relatively dozens or hundreds of stations of coordinates , each station specifies the arrival time of the earthquake, hence there is 88 LITERATURE REVIEW record for stations, so arrival times for an earthquake occurs at time Arrival time which depends only on the travel time in a position x. can be expressed according to travel time and origin time as Knowledge of the structure, allows knowledge of both, information source coordinates and origin time , this can plays a crucial role in determining data, this is the forward problem, however seismologists are much more interested in inverse problems since the main goal is estimation of model parameter and not the data. or The inverse problem is then to find a model that "looks like" real model, ie find the particular model for which the predicted and observed data were in best agreement. The perfect model which reflects the reality of the structure can never be determined because the inverse problem cannot led to a unique solution, in fact the inverse problem can be seen as a process of elimination of any information that cannot deal with corresponding observed data. After collection of a large number of data, the first step that must begin with is to estimate an initial model (see chapter). Note that even the perfect model can not reflect the data observed in seismograms, because there are always errors in reading the various phases. Estimated data often do not reflect the observed data, an explanation of the observed data then require an initial model preferably close to real model to satisfy the linear approximation (Stein and Wysession, 2003), it is then a temptation to predict what we have observed, it can lead by effecting a little change of in the initial model The vector data do not depend linearly on the model, we have to linearize of , the model can be written as: 89 . in the vicinity LITERATURE REVIEW The difference between the predicted and observed data is given by which can also be written as a system of linear equations: where , is the operator matrix that contains all the partial derivatives of the vector data times model vector , an application of the operator after perturbation of model parameter leads to a change in the vector data, the simplest case to solve is when we have when operator is a square matrix. But in general this is not the case, because we often have a large amount of data, thus characterizing an overdetermined problem, in this case the operator is not square matrix, hence it require the generalized inverse solution. In practice, the arrival time of a wave still contains errors, uncertainties in instrumental measurements or errors reading phases, choosing a simple problem with only four observations cannot reach as well the reality of the structure, it is the fact that the model itself contains errors and is laterally discontinuous, thereby seismologists solve the problem by taking into account a plenty of data, they are carried to solve over-determined and inconsistent problems, and try to minimize the quantity , One of the most common ways to do this is to write an equation for the squared error 90 LITERATURE REVIEW and force to be a minimum by taking the derivative of parameters where quantity with respect to the model and setting it equal to zero is the standard deviations which describe how widely the data is spread. The represents the prediction errors and the determination of the partial derivatives of the equation with respect to a small perturbation lead to minimize the misfit. where where Or collecting terms In the case of equal variance for all data (Stein and Wysession, 2003), in matrix notation as 91 can be written LITERATURE REVIEW This is very useful form called the normal equations. take the form of a square matrix, thus can easily be inversed (as long as it is not singular!). Furthermore, is symmetric operator, which means that its eigenvalues are all real and nonnegative values. Therefore, by inverting we can write a system of linear equation of the form Where is the generalized inverse of, the will only serve as a correction to a starting model, and we must repeat the inverse as an iterative process, with updated for the new model. 6.2.1 Example location of earthquake in homogenous medium Locating earthquake with consideration of an homogenous media is straightforward, because the velocity is constant, thus the ray paths connecting the source and receiver are just a straight lines, when an event is occurred at time at location stations of coordinates the arrival time at the , Let and , it’s recorded by a be the origin time of the earthquake and station, respectively. Then Where denote the travel time and the velocity of wave propagation in the medium. For the land stations we set Ocean Bottom Seismometers , and the equation become (not that in the case of the is always a negative number, because the elevation is taken from the sea level). 92 LITERATURE REVIEW If we clearly see this expression, we infer that related with model represent an element of the data vector by the equation Where x, y, z, and are the elements of the model vector m that we wish to determine. Now we have to form the matrix respect to the model parameter , and calculate all of its elements by referencing . And for the fourth unknown t we have For example, the first element of the operator is Represent the first observation given by the first station. And, Represent the second observation given by the first station. 93 With LITERATURE REVIEW Not that, determination of operator and which is the diagonal matrix with the eigenvalues of the the operator containing the eigenvectors (see inversion theory section in chapter I) can provide precious information about stability of our inversion process, thus, inversion estimates for the change in are most stable for the large values of Wallace, 1995), this is best illustrated by an example, If we consider example of (Lay and operator with or nonzero singular values. For this example the inversion process estimates for the change in elevation associated with the parameter are the most stable, and estimate of changes to the travel time are the least stable part of the inversion process, so we have tactfully determining true travel time given the starting model we have chosen. To start the inversion process, we "guess" a solution from which we can calculate an estimated or predicted data vector. If the initial guess is not very good, which quickly resulted from the travel time residuals a priori computed for each observation using the error vector The process is repeated making a little change in the initial model, and so on until is minimized. The process of the inversion for location earthquakes for more complex geometries is obtained from the follow of proceeding along similar method, with the only real differences being in the calculation of the partial derivatives needed to constrain the different operators required for inversion. 94 LITERATURE REVIEW 7. Conclusion In this chapter we have given an overview of the structure of the earth and the mathematical background necessary to solve inverse problems. In Seismology the problems are often are characterized by their large size due to huge quantity of data. , we often need to use powerful algorithms and simple examples for a perfect homogeneous structure are introduced. We are dealing with a passive seismic tomography, which is based on the joint inversion of the earthquake location and difference waves arrival times of the seismic body waves. An effort is made to use the waveform and in particular, the seismic rays tracing, to build a model of the corresponding interfaces with adequate methods. In Chapter II we explained the choice of optimization algorithms and how to use it, we will give the general formulation of the ray theory that characterizes the path followed by the seismic waves from the source to reach a receiver, These waves undergo multiple reflections or refractions by discontinuity surfaces, the determination of the parameters of our model were determined rigorously, for inversion of the data collected by the stations. We have also well seen the literature and the research work that have been madepreviously for a good choice of the initial model used in the conversion process. 95 LITERATURE REVIEW Part 2 CHAPTER OUTLINE Body waves tomography of the Gulf of Cadiz 1. Introduction 2. Motivation and research objectives 3. The Gulf of Cadiz study area 4. Ray tracing and travel-times inversion 5. Seismicity of the Gulf of Cadiz 6. Synthetic tests 7. Results and discussion 8. Conclusion 9. References 96 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 1. Introduction The gulf of Cadiz region connects the Betic-Rif orogenic arc to the oceanic plate boundary between the Africa and Eurasia plates and the Gloria Fault (Zitellini et al , 200). The nature and exact location of this plate boundary are still uncertain. It is a large area, with complex deformations and diffuse seismicity that extends over 200 km from north to south (JimenezMunt et al, 2004), (Sartori et al, 1994), ( Tortella et al , 1997). The 1755 Lisbon earthquake is still considered the most destructive event in the western Mediterranean. This event was followed by a large tsunami that caused several thousand deaths and many localities were largely destroyed. In particular, all localities on the Atlantic coast of Morocco from Tangier to Agadir, were severely affected by the combined effects of the earthquake and the tsunami that followed (Kaabouben et al, 2009). The tsunami flooded about 2 km inland along the coast of El Jadida, Safi and Essaouira (El Hammoumi et al, 2009), It is worth noting that this event occurred in the Atlantic Ocean, but its precise location is still a matter of debate (El Mrabet et al, 2005),(Baptista et al, 1998), (Zitellini et al , 2000). Some authors attempted to explain the tectonics and the formation of this zone by suggesting a delamination of the continental lithosphere (Buforn et al, 1998), (Platt et al, 1989), while others suggested an oceanic subduction (Calvert et al, 2000), (Duggen et al, 2004), (Gutscher et al , 2002) that led to the formation of an accretionary wedge to the west of the Gibraltar arc. Some of these studies used data recorded by seismic reflection or refraction surveys. However, such studies usually have a limited depth penetration, which limits their tectonic interpretations, especially that most of the seismic activity in the Gulf of Cadiz occurs at more than 20 km depth as will be shown in this work. Other studies used data recorded by land stations in Morocco and Iberia to invert for the three-dimensional velocities underneath the Gulf of Cadiz. However, since the used stations are far away from the Gulf of Cadiz, the results are not quite reliable and remain of limited resolution. 97 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ In this work, we show the results of a body-waves seismic tomography study based on local earthquakes recorded by a network of 24 broadband ocean bottom seismometers (OBS) deployed directly on top of the sea floor of the Gulf of Cadiz. The data used were collected within the framework of the European project NEAREST (Integrated observation from NEAR shore sourcES of Tsunamis: towards an early warning system), in which the 24 OBSs were deployed by the German DEPAS instrument pool coordinated by the Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, and the GeoForschungsZentrum, Potsdam, Germany. The data were collected during one year of recording, beginning August 2007, and augmented by seismic data recorded by eight land seismic stations that belong to the Portugal permanent seismic network. The objective of this work is thus, to use these high quality data to help constrain a 3D velocity model of the earth interior beneath the Gulf of Cadiz and to draw implications for the tectonics of the region. 98 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 2. Motivation and research objectives Seismology is at an extreme of the whole spectrum of earth sciences, first it is concerned only with mechanical properties and dynamics of the earth, and second, it offers a means by which investigation of the earth’s interior can be carried out to the greatest depths, with resolution and accuracy higher than are attainable in any other branch of geophysics. Using the Nearest Network, it was possible to detect a large number of local earthquakes with small magnitudes that we could not otherwise be detected using the existing land stations network. These data will certainly help to improve both the geological and the geophysical knowledge of the tectonic architecture of the area which is presumed to be the source of the great 1755 Lisbon Earthquake which caused several thousand of deaths. A large effort has been made in the last decade to determine the shallow and deep crustal structure of the Atlantic margins of SW Iberia and NW Africa (e.g., Maldonado et al., 1999; Gràcia et al., 2003; Medialdea et al., 2004;, zitellini et al 2009, Gutsher et al 2004, Stich et al, 2006, Terrinha et al, 2009 ). The research subjects in seismic tomography have been strongly associated with the emergence and progress of deep seismic imaging since the first applications of this approach in three dimensional scales. Today, it become a part of the "toolbox" of petroleum geophysics Offshore, and is used almost routine for exploring parts of the world. In this thesis the work is focused on two main steps: Study of the seismicity of the region of the Gulf of Cadiz throughout analyzing the seismic NEAREST network records (all local earthquakes, even small ones) that will allow us to better assess the seismic activity in this region, as well as the maximum possible magnitude, recurrence of earthquakes, and tsunami risk, etc.. Second step is a construction of three dimensional models which describes the velocities of the waves in the subsurface using the arrival times of body seismic waves, and after achieving this work, we will focusing on construction of model velocity using surface waves to better investigate the earth interior at shallow depth. 99 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 3. The Gulf of Cadiz study area The Gulf of Cadiz is located in the eastern part of the Atlantic Ocean between Africa and Europe. It extends from the Strait of Gibraltar (Spain) to Sâo Vicente Cap (Portugal) with an orientation NW / SE controlled by recently active tectonic pattern (Maldonado et al., 1999). This region undergoes complex deformations due to plate tectonic interactions between the southern Eurasia and the North Africa plates; Figure (2.1) shows the displacement these different plates, due to its complex geology it is characterized by irregular bathymetry and concave morphology towards the SW. The plate boundary is still poorly defined until recent day, and the convergence between the African and Eurasian plates is accommodated by a zone of active extensive deformation (Sartori et al., 1994). The Gulf of Cadiz had a complex geological history in response to changes in the location and movement of the plate boundary (Srivastava et al., 1990). Figure 2.1 plate tectonic interactions between the southern Eurasia and the North Africa plates with the main elements of plate boundaries superimposed: AGL: Azores–Gibraltar Line; GC: Gulf of Cadiz; GF: Gloria Fault; MAR: Mid-Atlantic Ridge; , SVC: Sao Vicente Cap. TR: Terceira Ridge. Solid yellow line: plate boundaries (Zitellini et al 2009). In the last decade, several geophysical studies have been undertaken in the Gulf of Cadiz, since this region is a source of many earthquakes and the historical devastating tsunami that 100 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ followed the great Lisbon earthquake of 1st November 1755th with an estimated M=8.5 to 8.7 magnitude (Solares, et al ,2004). The evolution this area is associated with the collision between the Iberian Peninsula and northwest Africa (Nubia) tectonic plates. This collision is the main cause of the formation of the Betic Rif orogenic arc in the Miocene epoch and the formation of submarine accretionary wedge in the Gulf of Cadiz. The Iberian margin area is more complex than most of the North Atlantic margins. It is characterized by several phases of rifting, convergence and strike-slip motions (Srivastava et al, 1990., 1997; Maldonado et al.1997, Duarte et al 2010). Iberia has moved independently from the Eurasian plate and the African plate. this displacement allowed a tectonic sticking of Iberia and the African plate. Therefore the plate boundary between the Iberian Peninsula and Africa has become active again. Recently, scientific research provides several morpho-tectonic information on the study area, for instance, seismic reflection profiles helped to understand and locate the plate boundary Africa and Eurasia. Furthermore, bathymetric data reveal the existence of a series of subparallel WNW-ESE lineaments that extend from the Hirondelle Seamount to the Moroccan continental shelf, across the Horseshoe abyssal Plain and the Gulf of Cadiz accretionary wedge (Zitellini et al,. 2010). The present tectonics of the region is dominated by the reactivation of these faults lineaments as thrust or strike slip faults, which trend from the horseshoe Abyssal Plain to the Rharb Valey and are in places associated with fault scars and important mass wasting deposits (Gracia et al. 2003), (Zitellini et al. 2004). Gutscher et al (2008) show from bathymetric data and seismic reflection profiles, the location of the different active processes shaping the accretionary wedge. The boundary between the Iberian Peninsula, Eurasia and Africa is conditioned by the relative movement of these plates. Recetelly; data indicate the existence of an intense mechanical coupling between Iberia and Africa during the Tertiary, In the western part, initial displacement between these plates was divergent and progressively changed to strike-slip (Vicente et al,. 2008). In this region, scientists have successfully identified some traces of the lithospheric converging plates. In addition, bathymetric and tomography studies suggested the existence of a subduction zone west of the Gibraltar arc (Srivastava, et al 1990) and seem to indicate that the tectonic processes leading to the formation of an accretionary prism and the morphology 101 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ of the southern Gulf of Cadiz are influenced by processes associated with tectomorphic deformation of the accretionary prism of the Gulf of Cadiz (Maldonado, et al 1999) as well as a gravitational process (Gutscher, et al 2009). Based on an analysis of seismic data, it was suggested that the base of the accretionary wedge is dipping eastward and has a primarily tectonic origin (Gutscher, et al 2002). The majority of the accretionary wedge was constructed by offscraping of deep sea sediments during Miocene due to westward motion of the Gibraltar arc (Thiebot, et al 2006). Other geodynamic models suggest however, a delamination of continental lithosphere process (Platt,et al, 1989),(Calvert, et al, 2000). Recent detailed bathymetric mapping in the Gulf of Cadiz shows the existence of major inverse faults that trend NE-SW, Figure (2.2) mainly perpendicular to the principal stress direction, as well as sub-parallel WNW-ESE strike-slip trending lineaments (Stich, et al 2005),(Zitellini, et al., 2009); the SWIM Faults, that extend from the Hirondelle seamount to the Moroccan continental shelf. Based on this, it was suggested that the SWIM Faults zone (SFZ) constitute the plate boundary between Africa and Eurasia along a 600 km span between the Gloria Fault and the Rif-Tell plate boundary (Zitellini, et al., 2009). 102 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.2 Gulf of Cadiz region offshore SW Iberia, showing the bathymetry map and existing faults, SWIM is South West Iberian Margin faults lineament (Duarte, et al 2009). Zitellini, et al (2009) further suggest the existence of active thrust structures in the Gulf of Cadiz to explain the main clusters of seismicity. While some authors support that subduction is still active and poses significant seismic hazard to the region, others based on the low level of seismicity in the accretionary wedge and the undeformed package of deposited sediments, find that the subduction zone is not active at present time or is rather dying out and has largely ceased (Zitellini et al., 2009). Grevemeyer et al (2008) confirm the existence of an oblique collision between the Nubia and the Iberia plates. Some studied velocity model indicates that the Betic crustal root might be underlined by a low velocity anomaly in southeastern Iberian Peninsula, a variation in the uppermost mantle velocities that coincides with the structural complexity of the Eurasia and Nubian plate boundary in the Gulf of Cadiz. When a clear lowvelocity anomaly offshore from Cape San Vicente is shown, and high velocities distribution 103 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ are shown along the coast in the Gulf of Cadiz (Serrano et al 2005). Neves et al (2009) show that stresses are focused in the ocean-continent transition, between the base of the continental slope and the Horseshoe Abyssal Plain. Recently, based on focal mechanisms of seismic events occurred in the Gulf of Cadiz, it has been shown a compressional acting in the northern part of the Horseshoe fault (Geissler et al., 2010), While a strike-slip regime acts in its southern part. Trending parallel to the plate boundary, the seismic data reveal that the compressional deformation trend over a circle shape of about 100 km wide, delimited by the Pereira de Susa fault and the Tagus Abyssal Plainthrust, and 150 km length region between the Gorringe Bank and the Setúbal Peninsula (Cunha et al 2010). And a small relative motion between Iberia and the Maghrebian region is shown, proposing a model explain that Iberia is moving together with the Nubian plate (Cunha et al 2012). 104 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 4. Ray tracing and travel-times inversion Ray theory is an integral part of many seismological techniques, including body wave tomography, reflection data, and earthquake relocation, and has played a prominent role in the history of natural science, as a practical theory to explain the propagation of light. For both the rectilinear propagation of light and the law of reflection, throughout the development of geometric ray theory, it was understood that the theory was limited and that it could not explain a large number of phenomena observed in experiments with light (Kraaijpoel, 2003). However, finding correct geometry of a ray requires to trace rays following Snell’s law. This is comparatively easy in the case of layered or spherically symmetric media. On the other hand, if the seismic velocity is also a function of one or two horizontal coordinates, it may be very difficult. Fortunately, Fermat’s Principle allows us often to use background models with lateral homogeneity. Many approximations are used to predict wave propagation in smoothly varying media, for which length scale variations of Lamé coefficients are much larger than the seismic wavelength (the high frequency assumption). The application of the high frequency assumption to the wave equation immediately yields the eikonal equation as the basic equation to calculate travel-time and rays. In order to find the correct ray geometry between a given source and receiver location, we not only need an accurate solver for the differential equations, but also a way to determine which initial condition (ray orientation at the source) satisfies the end condition (ray arriving in the receiver), (Nolet,2008). In this chapter, we show how we can derive the eikonal equations for body waves propagation, defining rays as characteristics of this equation, called the system of ray equations. The eikonal equation is assessed for two waves which may propagate separately: P and S waves. The relevant travel times and rays of these waves are, however, again controlled by a similar eikonal equation with a different velocity (Serveny, 2000). More after much recent work has been done on computing travel times by solving the Eikonal equation. 105 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 4.1 The Eikonal equation 4.1.1 Eikonal equation for fluid mediums In fluid areas in the earth, the stress tensor, in the case of zero viscosity fluid, is given by where If denotes the Kronecker symbol, and P is the hydrostatic pressure. is the bulk modulus and is the density of the medium, we have, according to the Hook’s law Inserting By dividing by From in we get and differentiating according to , and We assume a harmonic solution of Where , we obtain , then becomes in the form is function of angular frequency 106 and position vector . BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Replacing in Where the spectrum of the source everything that follows we set , is modeled as the divergence of a stress tensor. For outside of the source. Let’s now consider Where is the amplitude which varies with location and the signal (Fourier transform of (2.5)) denoted by, is a constant and takes the shape of a delta function, with a delay , (Nolet,.2008). The amplitude only depends on the position so, It is known that As a consequence 107 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ We substitute in and keeping only terms up to order Ray theory is strictly valid for media with high frequency body waves assumption. At low frequencies, diffraction and scattering can be significant, and ray theory is not generally valid. The terms at zero order in yield the eikonal equation for the wavefront is known as the Eikonal equation. It describes the kinematic propagation (with velocity ) of high frequency waves in a zero viscosity fluid. It describes a nonlinear partial differential equation which solution requires numerical methods, basically, the Eikonal equation expresses how the local solution wave number is related to the local material properties. 4.1.2 Eikonal Equations in Isotropic Elastic Mediums In an isotropic elastic earth, the elasticity tensor takes into account only the Lamé coefficients and . For such a medium the stress tensor is given by with Referring to and inserting the expression of 108 , we get BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ In the frequency domain, we have Then This equation can also be expressed in term of vector equation For a constant and , when individual waves propagate independently in a smoothly varying structure Analogously to the displacement, solution of Let us now insert expression will take the form in the differential equation , as we are looking for high-frequency solutions, we can only consider the terms with the highest powers of obtain 109 . We BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Or in vector notation form This simple approach is used to derive the most important equations and related wave phenomena from the seismological point of view. It is shown how the elastic wave field is approximately separated into individual elementary waves (P,S), equation is true either by 1. Choosing Where to be parallel to give defines the velocity of compressional waves. The P-wave is linearly polarized, the particle motion has the same direction as , and the slowness vector can also be expressed as Where n is a unite vector parallel to the ray and perpendicular to the wavefront. 2. Or choosing Where perpendicular to which implies defines the velocity of shear waves. And the slowness vector of the S wave is given by the relation Likewise n is a unite vector parallel to the ray and perpendicular to wavefront. 110 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 4.2 Ray geometry For waves propagating with velocity c, the Eikonal equation is given by where is called the slowness and the travel time function, , is called the phase factor. Shows that, the phase factor slowness. The function perpendicular to gradient of Equation has a gradient whose amplitude is equal to the local , defines surfaces called wavefronts. Lines or parallel to are termed rays. The ray direction is defined by the , (Shearer, 2009). allow us to define the unit normal vector Now let’s consider a ray, and is the tangent along this ray with length straightforward to see that we can define the slowness And it’s obvious that and So, Then 111 , thus it is BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 4.2.1 Ray solution in layered mediums Flat Earth Considering a wave which propagates in the x-z plan of flat earth, in which the velocity varies with depth z. Figure 2.3 Geometry of the ray segment along a path from a surface source to a surface receiver. The velocity of the medium varies only along the z direction, so there will be symmetry of down-going and up-going legs of the ray path. In this case , from and according to we find Where is the angle of incidence and it gives the inclination of a ray measured from the vertical (z direction) at any given depth Figure (2.3), The constant (not that, if lateral velocity gradients are present, then p will change along the ray path) is called the ray parameter, or horizontal slowness, represents the apparent slowness of the wavefront in a horizontal direction and varies from 0 (vertical travel path) to 1/c (horizontal travel path), 112 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ equation is also known as Snell's law, which can also be derived from Fermat's principle. Fermat's principle states that a ray- path is a path of stationary time. Thus travel time along a ray path is a minimum time, and is the familiar expression from optics called Snell's law after Willebrod Snell (1591-1626), the generalization of Snell's law is is also called the seismic parameter, is constant for the entire travel path of a ray. The consequence of a ray traversing material of changing velocity, c, is a change in inclination angle with respect to a reference plane. As a ray enters material of increasing velocity, the ray is deflected toward the horizontal. Conversely, as a ray enters material of decreasing velocity, it is deflected toward the vertical. If the ray is traveling vertically, then , and the ray will experience no deflection as velocity changes,), for the deepest point the ray parameter is given by at the maximum depth reached by the ray Figure (2.3), (Lay and Wallace 1995). Figure 2.4 Incidence angle of a ray 113 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ From the Figure (2.5), the ray parameter P can be determined directly from the travel time T(x), we see that , corresponding to the relation , and we have Using Figure (2.5), and integrating over the depth range, the distance travelled by the ray is given by Figure 2.5 Incidence angle of a ray When we specifies the integration over z varying between , Z is the maximum depth of penetration. The factor of 2 arises from the symmetry of the down-going and up-going portions of the ray path (see Figure (2.1)), and equation 114 is now given by BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ This is the where of ray equations; given the angle at which a ray leaves the source, we can calculate where it will arrive. The time it takes for the ray to arrive is obtained similarly Where is the travel time along the ray path to the distance .we note also that change in travel time with distance is equal to the ray parameter and is given by . Spherical Earth Let’s consider, in the equatorial plan a ray path in spherical earth Figure (2.6). If we denote by and the polar coordinates of a point on the ray and by coordinates of its vicinity on the ray. Figure 2.6 Polar coordinate system for a ray in equatorial plan 115 and the polar BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ If is the length between those two points, measured along the ray, we may write Taking in account spherically symmetric case, the velocity is radial dependence only , then If is parallel to the unit vector position and is the epicentral distance and T is the correspondent travel time, we have The formulas for travel time and epicentral distance note that an element of ray length is related to a change in radius by the incidence angle. By using we obtain 116 are easily obtained if we where is BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ And In the case when the source and receiver are located on the surface see Figure (2.5), we give the expression of the travel time radius and and epicentral distance , where is the smallest distance from the ray to the center of the earth. And Figure 2.7 Ray path in spherical earth model. 117 is the earth BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 4.2.2 Inversion of travel time Flat Earth When the travel time data are interpreted in terms of ray theory, velocities inside the earth can be inferred (Aki and Richards, 2002). Consider the equation And for a given ray By integrating over At the surface, the ray leaves the source with a velocity point from the source, the integration range between , and and , at the deepest . Equation is written in the standart form of Abel’s integral equation (Gorenflo and Vessella,.1991). The solution of inverse problem can be written as (Aki and Richards,. 2002) Where Integrating again over and using , we obtain: 118 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ By integrating and using the fact that, and , we finally get the expression of depth- velocity dependence: Spherical Earth Inversion of travel-time in the case of spherical Earth is obtained from : This expression is known as the Herglotz-Wiechert formulas, its gives the value of given value of which lead to the determination of one point velocity profile for a . The Herglotz-Wiechert formula is used for inverting a travel-time curve to find velocity as a function of depth. It was used extensively in the development of the earliest P-wave and Swave velocity models for the deep Earth structure. The procedure is stable as long as continuous, with is decreasing with . If a low-velocity zone is present at depth, the formula cannot be used directly, although it is possible to "strip off' layers above the lowvelocity zone and then use the contracted travel- time curve to construct smoothly increasing velocities at greater depth. Thus, one could build an Earth model for the mantle, and then strip this off before determining the velocity structure of the low-velocity core (Lay terry. Wallace,1995). Among the most common problems in seismology is the prediction of the path taken by the seismic rays from the source to reach the receiver. The presence of lateral velocity variations of the seismic waves makes it even more complicated task. Difficulties related to the precision of a path between two points resulting from non-linear relationship between velocity and path geometry. In a homogeneous medium, the path would be simple and not undergoing any deviation. Unfortunately it is not what we have in reality. The Methods that have been adopted are known as ray tracing methods (Julian and Gubbins, 1977; Cervený 1987; Virieux and Farra, 1991; Cervený, 2001), in which the trajectory of the path corresponding to the wavefront is calculated between two points. This approach is often very precise and efficient, and lends itself naturally to the prediction of various properties of 119 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ seismic waves. However, it may not always converge especially in highly heterogeneous medium. In this thesis, we describe two main techniques for ray tracing to solve the boundary value problem of locating rays between the source and receiver. The first method computes the shortest path and is known as a shooting method, the second method is a bending tracing method. The shortest path method is relatively simple, considered as an initial value problem which allows a ray path to be traced given an initial trajectory of the path (with appropriate application of Snell's law), taking into account its initial trajectory. The challenge is to find the initial direction of the ray source, the bending method is a technique in which we apply an iterative process in order to adjust the geometry of the path that connects the initial arbitrary source and receiver until it becomes a true ray path. The LOTOS-10 code (Koulakov,.2009) is a ray tracing algorithm, similar to the Um and Thurber (1987) algorithm, in which they attempt to minimize directly the travel-time as a function of the ray curve. For this purpose, they represent the ray by a number of points, connected by straight line segments Figure (2.9), based on the Fermat’s principle of travel time minimization. Because rays are the normals to the wavefront Figure (2.8), the rays will also change with time. Fermat's principle governs the geometry of ray paths. This usually means that the ray will follow a minimum-time path, the technique guarantees for the path to be the shortest one in term of timing, a very efficient algorithm to determine the shortest path in networks was proposed by (Dijkstra., 1959), used after to compute a tomographic model by (Nakanishi and Yamaguchi 1986), broadly modified in network ray tracing (Moser, 1991) trying to “bend” the ray , in order to obtain a more precise estimate of travel time (Moser et al, 1992), called bending ray tracing or just bending method. It’s used to solve boundary-value ray tracing problems. In our case, the bending method may be applied as a postprocessor, correcting the preliminary trajectories. This correction procedure is also known as bending the rays (Cerveny, 2000). 120 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.8 Ray and wavefront geometry. 4.2.3 Shortest travel-time path To compute the shortest travel-time path, Figure (2.9) we consider the rays to be composed on finite segments with a set of discrete angles, to get shortest travel time in general involves changing the segments coordinates of each node, in order to enhance the accuracy of travel time determined, this is in the method of shooting, rays are computed that leave point S in different directions by solving the ray tracing equations until one ray happens to arrive in R. Figure 2.9 An example of a shortest path followed by a seismic ray traveling from a source S to receiver R. 121 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ We discuss here the calculation of one selected ray, corresponding to specified positions of the source S and receiver R, we consider the ray traveling from S to R, and we are searching for the shortest path followed by the ray to reach the receiver R coming from a source S, Figure (2.9), we note by the length of segments or roads between the neighboring nodes, it’s obvious the travel time performed between S and R is a function of velocities fixed beforehand as initial velocity model ( note that each node can only be visited one time). Let’s now consider locations the average velocity between two nodes; the nodes satisfy a set of linear equations for a minimum travel time. The total travel time thus can be expressed as where N is the total number of segments of length , and for vertex and According to Fermat’s principle, say that the travel time of a ray between two given points in space must be stationary for small perturbations in the path followed by the ray, thus for varies between 2 and . where 122 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ and , Figure 2.10 Piece of the path shown in Figure (2.17). Finally this gives a system of equations of the form 4.3 Bending method Great advances were made in seismic tomography when bending ray tracing has been introduced for the first time by (Wesson,. 1971), there are two types of the bending method, the first one applied by (Julian and Gubbins, 1977), in which the ray tracing equations are approximated by discritezing the ray path into a number of points along the path, and the second one introduced by (Um and Thurber., 1987), when they attempts to minimize directly the travel time as a functional of the ray curve. One of the drawbacks of the Julian’s approach is that applying the algorithm makes lost precision by using the finite-difference approach; by contrast the second variant of the bending method makes the precision of the integration increasing with the number of segments. In the bending method, some initial guess of the ray is perturbed while source and receiver points are kept fixed until it satisfies the ray equations or minimizes the travel time (Nolet ,. 2008), so that, velocity discontinuities are easy to handle 123 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ with bending method algorithm, with a considerable precision, which can be considered necessary for many applications in seismic tomography, furthermore the method of ray bending is preferred over shooting method because it’s yields the travel time of the diffracted ray, even if the receiver is in the shadow zone where no "physical" rays arrive from the source (Moser et al., 1992). LOTOS code use a similar approach of bending tracing method with a slight modification, (Koulakov, 2009), the ray constructed in this way tends to travel through high-velocity anomalies and avoids low velocity patterns Figure (2.11), it can use any parameterization of the velocity distribution and can define uniquely one positive velocity values at any point of the study area. Figure 2.11 Process of bending algorithm used to determinate the shortest path. Hatched light grey patterns represent negative anomalies of -30%; dark grey patterns are positive anomalies of +30%. (Koulakov, 2009). 124 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 4.3.1 Pseudo bending method If represents the position vector of a point on a wavefront, and the path length of the curve traced out by this point as the wavefront evolves, then The travel time can be expressed as Where represents the path, the rate of change of travel time along the path is simply the slowness, so and by taking the gradient of both sides , we can derive the following expression From differential geometry, the tangential and normal unit vectors position Q indicated by the vector q Fig (2.20) are given as The normal vector to the ray is given by 125 and of a ray at the BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.12 Tangential, normal and anti-normal unit vectors along the ray path (Kazuki et al,. 1997) Knowing and If we now let , we derive the relation that express in terms of and , so represent the anti-normal unit vector to the ray path at point , and substitute velocity for slowness , then Vector defines the direction of path curvature. To update points along a path, we need three points along this path Fig (2.20), , , 126 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.13 Three point perturbation scheme used in pseudo bending method, Um & Thurber (1987). The aim is to replace the initial guess point with an improved estimate improved estimate is obtained by considering a perturbation to the point the midpoint between and . The , which lies at . The vector can then be simply approximated by and the anti-normal unit vector , which specifies the bending direction, is computed from , The next step is to find the distance in the direction which results in an improved estimate of the path. An approximate analytic expression for the travel time and between can be obtained using the trapezoidal rule (Rawlinson et al,. 2008) The appropriate value for R can be obtained by appealing directly to Fermat’s principle of stationary time, which in this case equates to setting 127 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Where 128 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 5. Seismicity of the Gulf of Cadiz The Gulf of Cadiz, located at the southwestern Iberian margin and NW of the Moroccan margin Atlantic, is characterized by widespread seismicity, compressional and strike-slip fault plane solutions (Gràcia et al 2003),(Geissler et al 2010), Instrumental seismicity in the Gulf of Cadiz, can be considered of moderate magnitudes and shallow to intermediate depth, mostly above 60 Km. Most events occurring between W and W are located at shallow depths between 5 and 25 Km, and can sometimes reach 90 Km in the oceanic domain (Grandin., et al,. 2007), Since the 1969 earthquake, no other event has exceeded magnitude 6 in the region. Seismic catalogues report seismicity down to 100 km depth. According to structural models for the region, this includes earthquakes that occur in the uppermost continental mantle (Stich, et al 2005). Seismicity in the west is located around the Horseshoe Abyssal Plain in offshore lithosphere; it’s restricted to a relative narrow zone of 100 Km and the Moho depth of about 15 km (Tortella et al., 1997; Rovere et al., 2004). The Seismicity is concentrated along the Azores–Gibraltar Fracture Zone, in the Azores and Gloria Fault, it becomes disperse in the Gulf of Cadiz and Gibraltar Arc, indicating the more diffuse nature of the contact in this area (Maldonado et al ,.1997) and a complex behavior of seismicity was shown in the Gulf of Cadiz, where shallow events (h < 30 km) occur (Buforn et al ,. 2004). 5.1 Nearest (integrated observations from near shore sources of tsunamis: towards an early warning system) Nearest (integrated observations from near shore sources of tsunamis: towards an early warning system) is a scientific project that was sponsored by the european conncil (EC) and which aimed to study the Gulf of Cadiz region, which very complex area in the Atlantic Ocean in this project which 24 ocean-bottom seismometer’s (OBS) were deployed, for a period of one year in 2007-2008, the NEAREST consortiums consisted of the partnership of several institutions: 1) Centre National pour la Recherche Scientifique et Technique, Morocco. 2) Consiglio Nazionale delle Ricerche, Istituto Scienze Marine, Dipartimento di Bologna, Italy. 3) Fundação da Faculdade de Ciências da Universidade de Lisboa - Centro de Geofísica da 129 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Universidade de Lisboa, Portugal. 4) Consejo Superior de Investigaciones Cientificas – Unitat de Tecnologia Marina - Centre Mediterrani d’Investigacions Marines i Ambientals, Barcelona, Spain. 5) Alfred-Wegener-Institute fur Polar-und Meeresforschung, Geophysics section, Germany. 6) Université de Bretagne Occidentale, UMR 6358 Domaines Océaniques, France. 7) Istituto Nazionale Geofisica e Vulcanologia, Roma 2 section, Roma, Italy. 8) Technische Fachhochschule Berlin - FB VIII - Maschinenbau, Verfahrens- und Umwelttechnik AG Tiefseesysteme, Germany. 9) Instituto Andaluz de Geofísica - Universidad De Granada, Spain. 10) Instituto de Meteorologia, Divisão de Sismologia, Lisbon, Portugal. 11) XISTOS Développement S.A, Paris, France. The scientific OBS deployment whiting the nearest project was performed between 16th August and 4th September 2007 offshore Cap Sao Vicente and in the Gulf of Cadiz, in the Portuguese and international waters. The main goals of the cruise were the deployment of a multiparameter seafloor observatory (GEOSTAR), its communication buoy and an array of the bottom seismeters. In addition, subbottom profiles, multibeam data and seafloor sampling were collected. These data will improve both the geological and the geophysical knowledge of the tectonic architecture of this area, presumed to be the source of the 1755 Lisbon Earthquake. 130 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.14 Seismicity of the Gulf of Cadiz as recorded between august 2007 and July 2008 as shown by the red dots;, GB : Gorringe Bank , CP: Coral Pach, , SVC: Sâo vicente Canyon, RV : Rharb Valley , PB: Portimâo Bank, AB: Algarve Bassin, AJB: Alentijo Bassin , Ocean Bottom Seismometers (OBS) blue triangles and Portugal Land stations green triangles. The cruise was split in two legs cause of the large volume of instruments to be deployed: the first leg was from 16th of August until the 27th of August and the second one from 28th of August until 4th of September 2007. Tectonic structures in the transition from the Azores fracture zone to the postulated subduction zone in the area of the Strait of Gibraltar will be localized and characterized. The 131 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ structure have the potential to cause Tsunamis. For this purposes, we deployed 22 broadband ocean bottom seismometers (OBS) Figure (2.15) from the German DEPAS instrument pool coordinated by the Alfred Wegener Institute for Polar and Marine Research, Bremerhaven and the GeoForschungsZentrum, Potsdam. Seismicity studies and passive seismic imaging techniques will be performed after 12 months recording, when the OBS have been recovered. During the transfer among the OBSs Chirp and Multibeam data were collected. Despite the project to build an array of 24 OBSs, cause technical problems during the second leg, it was possible to deploy only 22 instead of 25 planned initially. Figure 2.15 Ocean Bottom Seismometer’s on board, (Zitellini N., Carrara G. & NEAREST Team. - ISMAR Bologna Technical Report, June 2009). 132 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Thus, within the NEAREST project, 24 Ocean Bottom Seismometers (OBS) were deployed in the Gulf of Cadiz to collect seismic data during this project experiment for a period of one year from August 2007 to July 2008. Figure (2.16) shows the location of the seismometers. They were equipped each with a Güralp CMG-40T broadband seismometer incorporated in titanium pressure housing, a hydrophone, and a GEOLON MCS (Marine Compact Seismocorder). The electric power supply for the recorder and the seismometer is driven by 132 lithium power cells. Each sensor channel is sampled with 100 Hz, preamplifier gain of the hydrophone channel is 4 and 1 for the three seismometer components (Geissler et al, 2010). Figure 2.16 Location of the broad band stations used in this study, ocean Bottom Seismometers (OBS) blue triangles and Portugal Land stations green triangles. 133 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 5.2 Data format The most and basic challenge to solve in seismology is to locate the recorded seismic events. For that purpose geophysicists need at least 3 stations. We therefore precise an OBS’s network as being a group of stations working together to listen to what that is happen under the ground. The OBS’s recorded seismic data are collected in SEED format (Standard for Exchange of Earthquake Data). SEED is the most common International used waveform format. There are thus many ways of representing the response information, SEED is the most complete and best defined but also the most complex. However, the most standard open format currently available is the MiniSEED format used by Quanterra recorders and a few others. It is also an agreed upon international format; MiniSEED is similar to SEED format of data only with heathers; the present the propensity is that newer recorders use MiniSEED, and can accommodate a huge mass memory capacity. In this project (NEAREST) all events recorded by the OBS’s and eight Portugal land-stations were extracted for processing and analysis, in order to determine their hypocenters and local magnitudes. The first work we have to do is to choose the program for processing our data. 5.3 Seisan analysis software The early improvement in seismic sensors and experiment provided very large quantity of data. the source locations and origin time becomes very useful for several studies to cover different area. The data used in this study come from Ocean Bottom Seismometers digital record. after that we have to choose a program to use to analyze all recorded events, The earliest, formal earthquake locations use arrival time information from seismic phases applied in direct-search procedures such as graphical methods (Milne 1886) or simple grid-searches (Reid, 1910). Presently, earthquakes location can be adequately computed using modern location techniques and there are numerous advanced location programs in use and most are free standing. However, in some cases they are also tightly integrated with general processing software like HYPOCENTER in SEISAN. and most programs are made for local events. HYPO71, was first released in 1971, and was program designed to determine hypocenter, magnitude, and first motion pattern of local earthquakes. HYPO71 is still a quite used 134 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ program. (Lee and Lahr, 1975). HYPOINVERSE, is among location programs used to determine earthquake locations and magnitudes from seismic network data like first-arrival P and S arrival times, amplitudes and coda durations. HYPOCENTER can use nearly all seismic phases and azimuths of arrivals and calculates most magnitudes. It is the main program used in SEISAN for earthquake location and magnitude determination (Lienert and Havskov,.1995). There are also many programs that are currently used like HYPOELLIPSE, HYPOSAT, PITSA, SAC and SHM analysis software (Lars, 2009). We have seen all these common processing software listed above; we choose to analyze our data using the SEISAN program. As well known, the exact location of a source, radiating seismic energy, is one of the most important tasks in practical seismology and most seismologists have been from time to time involved in this task. For this purpose and to avoid the errors in the arrival time picks, we have consecrated a rigorous attention when we are picking P and S phases. The SEISAN seismic analysis system is a complete set of programs and a simple database for analyzing earthquakes from analog and digital data. Then we have chosen the SEISAN processing Program for these reasons. Furthermore, SEISAN has several advantages. It is mostly designed for local events, and also there are several options integrated in the program, such as the VELEST routine that can be used via SEISAN. With SEISAN it is possible for local and global earthquakes to enter phase readings manually or directly pick them with a cursor on seismograms, events can located, edited, determine spectral parameters, seismic moment, determining the azimuth of arrival from 3-component stations and plot epicenters. The system consists of a set of programs tied to the same database. Using the search programs it is possible to use different criteria to search the database for particular events and work with this subset without extracting the events (Havskov et al 2010). One of the reasons why we have chosen SEISAN is that most programs are made for local events, which is the case our study, we are not interesting in analyzing of teleseismic events. 135 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 5.4 Seismicity The OBS Network allowed the detection of a large number of local events that could not otherwise be detected with the Morocco, Spain or Portugal land stations. These are Local earthquakes with magnitude . After collecting the data, we have proceed to location of the events recorded using both the OBS and Portuguese land stations. It is clear that the seismic rays travel through a part of the continental crust to reach the land stations. The influence of the continental crust is taken into account when we are picking the phases of the first arrivals, to which we have assigned a different weight to promote the localization by OBS’s for the offshore events. The initial hypocentral locations were performed using the SEISAN software package (Havskov, J. et al.,1999), The OBS network revealed that the seismicity in the study area is characterized by a nearlycontinuous activity of low magnitude events. The that occurred on January 1st, 2008 earthquake is the largest event recorded by the OBS network and the Portugal seismic stations used in this observation period. The large number of earthquakes recorded in this one-year time period shows that the Gulf of Cadiz is a quite active area and testifies of the great sensitivity of the deployed OBS network, This activity is largely due to the convergence between the plates and is distributed over a wide area of deformation. In southern of Iberia, numerous active thrust faults were identified (Zitellini et al., 2001; Gracia et al., 2003, Zitellini et al., 2004) and associated with instrumental seismicity, including the Horseshoe fault, the Marquês de Pombal fault and Sâo Vicente fault, while the Tagus and the Seine Abyssal Plains are remaind aseismic in this period (Lbadaoui et al 2012). In general seismicity in the Gulf of Cadiz and south Iberia peninsula, is accommodated by structures located north of the SWIM Fault Zone. Figure (2.17) shows that the seismic activity concentrates in three main blocs; namely clusters around the south of the Gorringe Ridge, the eastern part of the Horseshoe Abyssal Plain; and, north and NW of the Horseshoe fault, near and along the Marques de Pombal plateau and the Sâo Vicente Fault. Few earthquakes occurred in the accretionary wedge zone while dispersed seismicity is found south of the Algarve Bassin and Portimâo Bank Figure (2.17). The determined local magnitudes showed that approximately 61 % of the events have local magnitudes less than 2, and 22 % have magnitudes between 2 and 3. The depth distribution of the hypocenters varies 136 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ from shallow to intermediate and show that the majority of the located events are between 20 and 80 Km depth Figure (2.19), Figure (2.20) , with very few events with depths shallower than 20 km. Figure 2.17 Seismicity of the Gulf of Cadiz as recorded between august 2007 and July 2008 as shown by the black circles; AB: Algarve Bassin, AJB: Alentijo Bassin the inclined blue line represents the SWIM faults zone (SFZ), and red lines are the possible faults.CP: Coral Pach, GB : Gorringe Bank , GF : Gorringe fault , HsF : horseshoe fault ,MPF : Marques de Pombal fault , PB: Portimâo Bank, PSF: Pereira de Sousa fault, RV : Rharb Valley , SVC: Sâo vicente Canyon, SVF: Sâo vicente fault, 137 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Also, a NW-SE trend of seismicity that crosses the horseshoe fault can be observed to the south of our study area Figure (2.19) and seismic profile 2 on Figure (2.20). This seismic alignment seems to occur rather in segments of seismicity, with depths that vary between 35 and 80 km. This trend of seismicity is nearly along and parallel to the SFZ and may thus, be correlated to the SWIM faults, which were mapped on the surface, mainly based on bathymetric scanning. These profiles further reveal the thrusting geometries in this area, evidenced by active faulting and associated processes. Figure 2.18 Seismic profiles shown in the map Figure (2.9), showing events that occurred within 40 km distance from the profile. This profile indicates a more continuous pattern of seismicity. HsF: Horseshoe fault, GB: Gorring Bank. 138 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ The first seismicity cross section Figure (2.19) shows three main blocs of earthquakes along the Gorringe bank, Sâo Vicente fault and the accretionary wedge, while the second profile shows that seismicity concentrates in two areas, in the Gorringe bank and horseshoe fault. On profile 2, we can identify a pattern that seems to indicate a thrusting shape of the horseshoe fault, with a slope of about 50 km in length. GB SVF AW Figure 2.19 Seismic profiles shown in the map Figure (2.26), showing events that occurred within 40 km distance from the profile, this shows three separate clusters of seismicity. AW: Accretionary wedge, GB: Gorring Bank , SVF: Sao Vicente fault. GB HsF Figure 2.20 Seismic profiles shown in the map Figure (2.26), showing events that occurred within 40 km distance from the profile, this shows three separate clusters of seismicity. AW: Accretionary wedge, GB: Gorring Bank , HsF: horsechoe Fault. 139 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 5.5 Inversion method and procedure A tomographic algorithm, LOTOS-10 (Local Tomography system of program) is designed for simultaneous inversion for P and S velocity structures and source coordinates. The LOTOS10 algorithm can be directly applied to very different data sets without complicated tuning of parameters. It has a quite wide range of possibilities for performing different test and is quite easy to operate. Figure 2.21 Chart showing the General structure of the LOTOS code working process. 140 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ LOTOS code is easy to use, it consists of many of folders and files well organized, the main folder contains eight folders and four files: COMMON folder: contains subfolder for the control of the display. DATA folder contains: Model_01 folder contains two files, this folder contains : 1) MAJOR_PARAM : contain the parameters for source location and inversion. 2) ref_start : contain the starting velocity model using for inversion. MAJOR_PARAM is a file containing most of the settings parameters (e.g. sources location and conversion settings), the file control all subroutines written in FORTRAN language, through specified the keys introduced in the file. In this file we can specify the study area (geographical coordinates) in AREA_CENTER rows, it allow to set the choice of the inversion of P and S waves or , and if is it synthetic or the actual data. In this file we can set all the parameters needed for optimization of the initial model. To set the parameter of damping and noise effect, you have to perform a several series of synthetic test, in this work a selective settings of the data have been made, we don’t have a huge quantity of data, but we have an excellent coverage area Figure (2.22), Figure (2.23), our results comes from a set in which the residue should not exceed 1, and the maximum number of outliers must not exceed 30%, if it is not the case the event is rejected. For the 3D setting parameter, we have chosen the parameterization with nodes rather sells grid construction , and performing the process of inversion in multi-orientation direction, this orientation deals with our seismicity trend, we set the minimum spacing between nodes at 5 km, the nodes are Imbricates on vertical lines distributed regularly in the study area previously chosen; the nodes are installed according to the density of the ray existing and first computed using the bending ray tracing theory (see bending tracing).the velocity distribution is approximated linearly between two adjacent nodes. The file ref_start is a file with extension .dat, below the reference model used in this inversion process. 1.79 0.000 5.500 10.000 Ratio 3.10 5.58 6.75 vp/vs 1.73 3.11 3.77 141 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 24.000 31.000 90.000 500.000 7.50 8.13 8.38 10.00 4.19 4.54 4.68 5.58 This file consists of three columns, the first one contain de values of the chosen depth , and the second one contain the velocities in km/s and the third one contain the ratio . Figure 2.22 Ray paths in the map view at depth of 20, 40, 60 and 80 Km showing the coverage paths, purple point are the stations. Figure 2.23 Ray paths in the map view in a vertical cross section shown by grey dots. Blue triangles are the stations. 142 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Inidata folder when we have to put the two files ray.dat and stat-ft.dat in appropriate file format. EXAMPLE OF LOTOS INPUT FILE FORMAT ( ray.dat ) -10.84300 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 -9.699000 1 2 1 1 2 1 2 1 1 1 1 2 35.88600 26 26 21 21 45 45 51 51 41 41 31 31 18 18 22 22 15 15 40 40 16 12 12 47 47 23 11 11 13 13 19 43 43 36.68900 14 14 18 13 13 15 15 22 23 21 17 17 42.10000 5.988281 11.06836 7.439453 14.17969 7.410156 14.16992 9.208984 15.97852 9.660156 16.83008 11.95898 20.46875 12.59961 22.70898 12.81836 23.11914 14.92969 26.10937 17.86914 30.69922 30.56836 18.59961 31.86914 19.83984 35.70898 36.09961 20.41016 36.54883 21.13867 36.54883 51.69922 29.39844 50.66016 15.00000 7.101562 12.64062 10.75000 10.67969 19.74219 12.40234 22.23047 12.55078 12.94922 15.97266 16.49219 29.26953 143 33 26 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 1 2 1 2 1 1 1 2 1 2 1 2 1 2 28 28 27 27 29 26 30 20 11 11 31 31 32 32 17.19922 31.30078 17.76953 31.69922 19.08984 21.69141 21.57031 38.62109 22.50000 39.92969 22.06250 39.74219 24.83203 45.50000 The second file in the folder inidata is stat_ft.dat, this file contains the geographical coordinates of the stations. EXAMPLE OF LOTOS INPUT FILE FORMAT ( stat_ft.dat ) -07.03900 -07.93117 -07.86633 -11.44995 -10.73435 -10.22993 -9.700130 -8.800130 -8.249570 -10.93892 -10.34030 -9.750400 -9.100180 -8.599950 -10.40025 -9.285130 -9.282530 -9.573120 38.17450 37.24300 38.02633 37.05038 37.02558 37.10048 36.94997 35.99980 35.94983 35.77972 35.70988 35.62993 35.59978 35.64973 35.35015 35.11682 36.53183 36.36078 -0.20500 -0.47100 -0.27000 4.800000 2.269000 3.935000 1.980000 3.360000 2.061000 4.764000 4.605000 4.394000 3.442000 2.575000 4.101000 4.745000 1.234000 1.234000 PBAR PBDV PBEJ n0701 n0702 n0703 n0704 NRT15 NRT16 NRT17 NRT18 NRT19 NRT20 NRT21 NRT22 NRT23 NRT24 NRT25 Here above we show an example of an input file, each event is composed of one line (head) and three columns, the line contains the coordinates of the epicenters, earthquake depth and number of phases used (33 for the first event and 26 for the second), the first column contains two possible index (1) for the phase and (2) for , the second column contains the number of stations used in locating the events, and finally the third column contains the travel time, the second is the file containing the station coordinates (Latitudes , Longitudes and 144 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Elevations). It is necessary to generate this file in this exact format to be accepted and red by the LOTOS code, in our case, and for those who use SEISAN (Havskov and Ottemöller, 1999) for locating seismic events, input file ray.dat is automatically generated by SEISANLOTOS format conversion given in appendix. Map folder : contains two files : Coastal_line file to allow determination of coastal limits in maps. Polit_bound file to allow determination of politic boundaries between different countries. FIG_files folder : with subfolders contains GRD, BLN and DAT file which represent the intermediary and final results. They can be used directly in SURFER for visualization. PICS folder : with subfolders contains PNG bitmap files with previewing the results PROG_1D_MODEL folder : folder with programs for preliminary location of sources and 1D velocity model optimization. PROGRAMS folder : contains all the source code Fortran. Subr folder: folder which contains all the subroutines. It is necessary only if re-compiling of the programs will be performed. Tmp folder: contains temporary files which are used only for current calculations. all_areas file : file which defines areas and models to be processed for inversion. model file : file with information about currently processed model. preview_key file : with a key for previewing should be also defined. START file: command to start. 6.5.1 Using the LOTOS code To use the code, you must first have the seismic data. input files for our calculations include a list of the stations with coordinates and elevations, and a catalog of the arrival times from local earthquakes, in our case, the work was done by exploiting a huge database of seismic data recorded by OBS’s in the Gulf of Cadiz, the data are collected in the SEED format, then converted to SEISAN format for processing (Havskov, J. et al.,1999). After that all events occurring in the period between 2007 and 2008 in Gulf of Cadiz are extracted and grouped using SEISEI from different seismic networks (Ocean bottom seismometers and Portuguese land stations). SEISAN is the software that provides a complete set of programs written 145 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ mainly in Fortran and a simple database to analyze digital data. The program allows a perfect management of the database of seismic events, and accurate analysis especially if the data are of good quality. All seismic data recorded by 24 stations OBS has been analyzed by manual picking arrival times of and phases. More than 600 events was analyzed, we used the VELEST program for data inversion (Kissling, 1994) to derive velocity models in one dimension as the starting velocity model, as well known, achieving good results depends on carefully choosing the initial model and we have defined all free parameters such as amplitude, damping and smoothing, by checking a series of synthetic tests (see appendix). Then calculations begin with preliminary earthquake locations in a 1-D velocity model. We used a starting 1-D velocity model obtained when the database was relocated using the VELEST inversion algorithm (Kissling et al,. 1994) we further tested several other initial velocity models (cf. to section V below). At this stage, the source coordinates and origin times are determined using a grid search method (Koulakov et al., 2006). Several causes can produce errors when trying to locate sources, for example the outliers in the initial data set, incorrect identification of phases, or an excessive residuals related to wrong picking of phases, for the purpose of good source location performing and avoiding these problems, the method allows the optimization of a Goal Function (Koulakov and Sobolev, 2006) that reflects the probability of the source location in the 3-Dimensional space. Model travel-times are computed using tabulated values calculated in the 1-D velocity model at a preliminary stage, and matrix inversion for P and S velocities and source parameters are performed using a least-squares method (Paige, C et al,.1982),( Van der Sluis, A et al,. 1987). 5.5.2 One dimensional velocity optimization and preliminary source location algorithm The inversion of seismic data requires a credible reference model, data are selected for optimization. From the entire events, only data distributed as uniformly with depth are selected. This is done by selecting for each depth interval the events with the maximum number of recorded phases. Then a travel time table in a current 1D model is calculated. the model is defined manually according to priori previous research study. Travel times between 146 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ sources at different depths to the receivers at different epicentral distances are computed in a 1D model using this analytical formula Where is the ray parameter (Nolet, 1981). The algorithm allows the incidence angles of the rays to be defined in order to achieve similar distances between rays at the surface. When the travel times are defined they are corrected for elevations of stations and then the sources are located based on calculating a goal function (Koulakov, Sobolev, 2006). This location algorithm is very stable. For example, it can find the correct source coordinates even if it is located at a distance of 400-500 km from the initial searching point. After that, the calculation of the first derivative matrix along the rays is performed. Each element of the matrix the is equal to the time deviation along the ray caused by a unit velocity variation at depth level. The depth levels are defined uniformly and the velocity between the levels is approximated as linear. Matrix inversion is performed simultaneously for the P and S data using the matrix previously computed. In addition to the velocity parameters, the matrix contains the elements to correct the source parameters ( ). The data vector contains the residuals. Regularization is performed by adding a special smoothing block. Each line of this block contains two equal non-zero elements with opposite signs that correspond to neighboring depth levels. The data vector in this block is zero; increasing the weight of this block smoothes the solution. If there is a-priori information about existence of interfaces (e.g. Moho), it can be included in the inversion. In this case, the link between the pair of nodes just above and below the interface would be skipped. Optimum values for free parameters (Smoothing coefficients and weights for the source parameters) are evaluated on the basis of synthetic modeling. The inversion of this sparse matrix is performed using the LSQR method (Page, Saunders, 1982, Van der Sluis, Van der Vorst, 1987). A sum of the obtained velocity variations and the current reference model is used as a reference model for the next iteration. 147 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 5.6 Starting velocity model In general case; nonlinear parameter estimation problems can often be solved by choosing a starting model and then iteratively improving it until a good solution is obtained. In this work we start with the model proposed in the 2008 NEAREST-cruise and was improved subsequently (Matias,, et al., 2009). Afterwards, all recorded events are localized with the resulting appropriate initial velocity model obtained using the VELEST inversion algorithm (Kissling, et al., 1994). The data set thus collected, consists of more than 600 local events Figure (2.24). The quality of the initial earthquake locations is rather high, with an RMS travel time residual less than 0.8 s. These events allowed us to obtain a total of 9194 arrival times, consisting of 2968 P-wave and 6226-S wave arrival times. Figure 2.24 Earthquakes location of more than 600 events recorded during NEAREST cruise survey. 148 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ One dimensional initial velocity model optimization The inversion process requires an initial 1-D velocity model; we used different starting velocity models in order to select one which gives optimal locations. Thus, we tested seven initial velocity models, including the one yielded by the VELEST algorithm Figure (2.25, a). (Kissling et al., 1994), in addition to several variants of these initial models GULF OF CADIZ VELOCITY MODELS 10 0 -10 -20 -30 -40 DEPTH (km) -50 -60 -70 -80 -90 -100 -110 Legend Title -120 OBS model -130 OBS + Portugal mod -140 Portugal Model -150 5.50 6.0 6.50 7.0 7.50 8.0 8.50 9.0 P-wave velocity (km/sec) Figure 2.25.a Velocity model obtained by the VELEST algorithm , the black line plot represent the model given by OBS location , the red line represent the model given using both OBS’s and Portugal land station and the blue model is given using only the Portugal land stations. 149 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.25.b Different starting P-velocity models used for optimization of the initial velocity model; model 1 is the velocity model proposed in the NEAREST-2008 cruise report, model 3 is the model derived using VELEST, while models 2,4,5,6 and 7 are initial-velocity models with slight modifications of the previous ones. Based on the analysis of the resulting velocity distributions and the RMS of residuals, we find that the 1-D velocity model which gives the least RMS residuals in the Gulf of Cadiz region corresponds to model 3 presented in Table (2.1) and Figure (2.25.b), which is the model found using the VELEST inversion algorithm (Kissling et al 1994),. This model consists of a crust with three layers with an interface at ~6 km depth, and the Moho at 30 km depth. Using the LOTOS software, Model 3 was then optimized and yielded the model given in Table (2.1). 150 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ TAB 2.1 P and S velocities in the reference 1-d model after Optimization by the lotos software. Vp (Km/s) Vs (Km/s) 0 2.713239 0.919177 10 6.093362 3.755473 20 6.839791 3.845567 30 7.766315 4.629175 40 8.243161 4.554774 50 7.922880 4.675756 60 7.808963 4.645917 70 7.722842 4.563402 80 7.685386 4.518101 90 7.939282 4.506800 100 8.103004 4.549830 Depth (Km) 151 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 6. Synthetic tests A rather common way of assessing the reliability of tomographic models consists of so-called synthetic tests, where the ability to image a known input model often a regular pattern of alternating positive velocity variations is tested, such test mainly addressed the resolution of the inversion scheme. It is a reliable technique that helps examine the resolution of the used data, before inversion, we performed several series of synthetic tests in order to get the optimum parameterization parameters, the average amplitude of noise was defined at 0.1 s and 0.1 s for P and S waves, respectively. Figure (2.26) and Figure (2.27) show the result of our synthetic test and checkerboard test respectively , in map view at depths between 25 and 50 km and in two vertical sections AA’ and BB’, it can be seen that in the upper section the periodic anomalies are reconstructed in most parts of the study area, the Figures bellow show the results for this tests, the resolution is much higher in area bounded by, the Gorringe ridge in the west, Saô Vicente Cap in the north, Portimaô Bank in the East and the Coral patch ridge in the south, especially for S velocity model, We lost reliability of model S-W of the horseshoe abyssal plain and in the S-E of Coral patch ridge, however, the largest part of the adequately sampled inversion volume exhibits good resolution of this structure. (Koulakov, 2009) has used a specific technique to estimate the capacity in terms of contribution of the noise present in the real data used in the conversion process, this technique consist in performing the inversion separating the data into two categories, those with odd index in the list of data, and those with an even index, and perform the process of inversion for each list separately. In addition to checkerboard test, it is very useful to perform this test to give more credibility to the tomographic results previously found. The test can give a subtle interpretation of the results; it also allows you to check the lucidity of obtained anomalies. The checkerboard test is often sufficient to check the robustness of the tomographic results, however, the odd-even test events test can provide much additional important information that can often help to estimate the effect of the use of half of the data, and to compare it with the results obtained using all data, Figure (2.30, 2.31) show the result obtained using odd and even events inversion process for P and S waves, the parameterization and grid reconstruction used in this test is the same used for the real data. 152 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.26 Checkerboard test performed for P and S waves in horizontals sections. 153 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 8 Figure 2.27 Synthetic test performed for P and S waves in horizontals sections at 35 Km depth. 154 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.28 Checkerboard test performed for P waves in vertical sections, AA’ and BB’ shown in Figure below. Figure 2.29 Checkerboard test performed for S waves in vertical sections, AA’ and BB’ shown in Figure below. 155 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.30 Anomalies of P velocities distribution, test with inversion of two independent data subsets (with odd/even numbers of events). 156 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.31 Anomalies of P velocities distribution, test with inversion of two independent data subsets (with odd/even numbers of events). From the two last Figures, we can see that this additional test exhibit a good correlation results in most working area. 157 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 7. Results and discussion Using the relocated hypocenters in the optimized initial model, the inversion scheme described before allowed us to invert for the three-dimensional structures beneath the Gulf of Cadiz, high-quality events were used for the inversion of local earthquake data. Thus, Figure (2.32-36) show the obtained P-velocity tomograms at selected depths; namely at 10 km, 15 km, 25 km, 35 km and 50 km depths, while Figure (2.37-41) show the S-velocity tomograms at the same depths. These depths were selected for their importance in terms of velocity distribution and also because the tomograms have higher resolution at these depths. For shallower depths and for depths greater than 50 km, the synthetic tests show that the results are rather not reliable (Appendix). The main general observation from the tomograms of Figure (2.32-36) and Figure (2.37-41), is that the limits reveled between the different high and low velocity anomalies in this study area, strike either in a NE-SW or in NW-SE directions. We further notice that the tomograms of P and S show more or less similar velocity distributions and features. In addition, we observe that the S-waves tomograms show a better resolution as indicated by the synthetic tests (see Appendix). This can be explained by the fact that there are about twice as many Sarrivals than P-arrivals in our earthquake hypocentral phases. At depths 35 km and shallower, P and S velocity distrubutions show a large negative anomaly trending SE of the study area, approximately delimited into latitudes 35.1°N and 37°N and between 8°W and 10°W longitudes, this anomaly coincides with the inverted part of the accretionary wedge and extends all the way to the Portugal continental margin, at shallow depths, this anomaly can be attributed to the existence of an area with a large concentration of sediments (the accretionary wedge), while at greater depths, this anomaly could be interpreted as reflecting, that this part of the Gulf of Cadiz is rather made out of continental crust and thus, its northern part delineates more or less the limit between continental and oceanic crust. However, the many alternances between high and low velocity anomalies in these tomographic images do not seem to clearly delineate a continent-ocean boundary such as previously reported by Stich, et al,. (2005). 158 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.32 P-velocity distribution at 10 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). Figure 2.33 P-velocity distribution at 15 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). 159 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.34 P-velocity distribution at 25 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). Figure 2.35 P-velocity distribution at 35 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). 160 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.36 P-velocity distribution at 50 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). Figure 2.37 S-velocity distribution anomalies at 10 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). 161 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.38 S-velocity distribution anomalies at 15 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). Figure 2.39 S-velocity distribution anomalies at 25 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). 162 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.40 S-velocity distribution anomalies at 35 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). Figure 2.41 S-velocity distribution anomalies at 50 km. Solid lines show the existing faults and dotted lines show possible strike-slip faults, and black dots show the Epicenters location given by tomography program and inclined gray line represent the SWIM fault zone (SFZ). 163 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.42 Horizontal sections of P-velocity anomalies at 15,25,35,50 km depth. (perspective view) Figure 2.43 Horizontal sections of P-velocity anomalies at 15,25,35,50 km depth. (perspective view) 164 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 7.1 Swim lineaments (SFZ) Throughout the south of the study area, the tomographic images show a NW-SE belt of high velocity anomaly distribution extending from the Gorringe Bank to the Accretionary wedge crossing the horseshoe abyssal plain Figure (2.44). This anomaly approximately follows and coincides with the SWIM lineaments (SFZ), which consist of a set of strike-slip faults and proposed to be a zone plate boundary between Eurasia and Nubia plates (Zitellini et al., 2009). The SWIM lineament (SFZ) is trending WNW-ESE and occurs from the western part of the Gorring Bank, cutting across the Horseshoe Abyssal Plain, and accretionary wedge towards the Morocco margin Figure (2.44), extends over a discontinuous length of about 600 km (Terrinha et al. 2009). This SWIM lineament was suggested by several authors to be the boundary between the Nubia and the Eurasia plates, as taken from GPS measurements (Nocquet and Calais, 2004). Recently several studies of high-resolution bathymetry of Gulf of Cadiz area was made, helped to improve the identification of this strike-slip faults lineament (Zitellini et al., 2009). In this part of the study region along the SFZ, we find a high velocity anomaly belt (mostly for S phase) from the surface layers towards to about 35 km depth. This belt of high velocity anomalies shows a transition zone that exhibited a clear separation of two structures, they can be interpreted as the result of an oblique compressive deformation of Iberia with respect to the Nubia plate. Our results thus, seem to support the (Zitellini et al, 2009) suggestion that this zone constitutes the boundary of these two plates (Eurasia and Africa) within the Gulf of Cadiz. Although they not extend far enough to the south to definitely confirm this observation, due to lack of data in this part of the study area. 165 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.44 NW-SE belt of high velocity anomaly (SWIM lineament). 166 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 7.2 Sâo Vicente Canyon The Marques de Pombal fault Figure (2.45) is a NNE-SSW trending, fault which was first recognized by (Zitellini et al., 1999), it was interpreted to be the surface expression of a thrust fault ( Gracia et al, 2003), and as a part of an active fault system located about 100 Km westward of Sâo Vicente Cap, with a rather high shear stresses acting on it ( Grevemayer et al 2003). Considered the most likely source for the 1755 earthquake, in spite of the estimated Mw 8.7, it have been suggested an active lithosphere folding, with the inherent topographic expression, related with the Marques de Pombal-Horseshoe Fault System (MarquesFigueiredo et al, 2010); our model show a wide positive anomaly extending over 50 Km depth westward of the Sâo Vicente Cap. This anomaly is rather clear and the S wave velocity anomaly distribution has almost similar features to the P waves velocities Figure (2.45), Thus, the Marques de Pombal Plateau is likely to be associated to an anomaly related to deep mantle uplift as well. Figure 2.45 Horizontal P-velocity distribution at 25, 35 and 50 km, showing high velocity anomaly southwest Portuguese Margin. 167 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ To the north, the Sâo Vicente Canyon, is an area where our synthetic tests provide higher accuracy velocity estimates. This area located roughly at 37°00N, is characterized by rough, irregular physiography; dominated by massive ridges, large seamounts, and extensive abyssal plains, where active faults, such as the NE–SW trending Marques de Pombal, and the Sâo Vicente faults (Zitellini et al., 2001), representing a major morphological feature separating Alentejo and Algarve margins. It follows a simple NE-SW orientation forming a wide submarine channel terminating on the Horseshoe Abyssal Plain, where the homogeneous parallel reflectors are interpreted as comprising shelf-derived sediments deposited at the base of the slope. In its southern part a pronounced hummocky character is seen, (Alves et al, 2000). The seamounts may represent either horsts formed during the Early Cretaceous rifting episode or uplifted Eocene structures. The Sâo Vicente Canyon appear to be controlled by the late Hercynian fracture pattern (Sibuet,et al 1987). All these deductions reveal that this part is also characterized by a complex geological structure. To help understand the structure beneath the Sâo Vicente Canyon; we have made vertical cross-sections along the profiles shown on Figure (2.46). These vertical cross sections show tomographic on profiles Figure (2.47-48-4950) and represent the true-velocity seismic vertical section, rather than velocity perturbations. Thus, vertical sections 1 and 2 are oriented in a NW-SE direction. Vertical cross-section 1 crosses the seismic cluster along the Gorringe Bank, while vertical section 2 crosses the seismicity cluster along the Sâo Vicente fault (SVF). The tomographic vertical cross-section 2 Figure (2.49, 2.50) show a mantle uplift at the level of the Sâo Vicente fault coinciding with the Marques de Pombal Plateau (see Figure 5 of Terrinha, et al,. 2009), where both of these cross-sections (1 & 2) show that the Moho underneath the Gulf of Cadiz is rather deep, with an average depth of about 26 km below sea surface. This part of the study area was interpreted as a rectangular shaped monocline structure limited to the east by the São Vicente Canyon and has been suggested as potential sources of large magnitude earthquakes and tsunamis (Vizcaino et al, 2006). 168 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.46 Positions of the vertical cross-sections velocity profiles 1 and 2 169 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ GB HsF Figure 2.47 P velocity distribution in vertical cross-sections 1, the position of vertical section is shown in the Figure (2.39)., GB: Gorringe Bank. HsF: Horseshoe Fault GB HsF Figure 2.48 S velocity distribution in vertical cross-sections 1, the position of vertical section is shown in the Figure (2.39)., GB: Gorringe Bank. HsF: Horseshoe Fault. 170 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ SVF AW Figure 2.49 P velocity distribution in vertical cross-sections 2, the position of vertical section is shown in the Figure (2.39), SVF : Sao Vicente Fault, AW : Accretionary wedge. SVF AW Figure 2.50 S velocity distribution in vertical cross-sections 2, the position of vertical section is shown in the Figure (2.39), SVF : Sao Vicente Fault, AW : Accretionary wedge. 171 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 7.3 Gorringe Bank To the NW of the study area, a distinct high velocity anomaly extends indeed from 10 km to 35 km depth and approximately coincides with the uplifted Gorringe Bank Figure (2.51). Below these depths, this high velocity anomaly continues with depth, but appears rather attenuated. Figure (2.52) shows the density and temperature depth profiles in the Gorringe bank and its surroundings, it clearly exhibits three pieces density variations, increasing until 14 km with a rapid increase in density and continues increasing slowly up to 40 km, where no compositional density contrast exists with the surrounding lithospheric mantle (Jiménez, Munt et al 2010). Below this depth the density decreases, which explains the appearance of the lowvelocity anomaly beneath the Gorring Bank. Figure 2.51 Horizontal P-velocity distribution at 25, 35 and 50 km, showing the attenuation of anomaly A between the Gorringe bank and horsechoe abyssal plain. 172 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.52 Density and temperature depth profiles at four positions identified in Fig (2.26): Tagus Abyssal Plain (profile a), Gorringe Bank (profile b), and Horseshoe Abyssal Plain (profiles c and d), (Jiménez, Munt et al 2010). The tomographic vertical cross-sections 1 Figure (2.53) clearly shows that the Gorringe bank is an anomaly that involves mantle uplift and that this topographic feature comes from deep within the mantle, this feature clearly stands out from horizontals P and S velocity distribution at depths of 10 km, 15 km and 25 km. Some authors explained that the Gorringe Bank structure is resulting from about 50 km of thrusting of African oceanic crust upon the Eurasian plate, (Jiménez Munt et al 2010), Profile 1 Figure (2.54) indicates this possible movement related to a NW-directed thrust carrying upper mantle rocks, explain as well the existence of that several seamounts in this region, as the Gorringe Bank, and the Coral Patch seamounts and Ridge, bordered by the abyssal plains, they are incontestably formed by the NW–SE compression movement during the Iberia– Nubia rapprochement. 173 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.53 Model results showing the lithosphere structure. The map above show the position of the profile. White dots are earthquake hypocenters, (Jiménez, Munt et al 2010). Figure 2.54 P- velocity distribution in vertical cross-sections 1, shows the layers going to 50 km depth , precising the direction in which the African oceanic lithosphere thrust Eurasian plate. 174 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 7.4 Portimao-Bank The convergence of Iberia–Nubia plates is probably due to other geodynamic processes, at the moment of slab rupture when the subduction stops (Billi et al, 2011), while the trending direction of these seamounts is probably due to the oblique convergence, can then justify the W-E trending of the Portimao-Bank. where a clear high velocity anomaly is shown in Portimao-Bank Figure (2.55), source of the largest event of January 1st, 2008 ( recorded by NEAREST network, explain the evidence of (Pliocene-Quaternary) associated with seismic recent activity (Cunha et al, 2012). It is not presumptuous to say, or to highlight the existence of an active subduction zone beneath the Gulf of Cadiz, GPS data overall system (Global Positioning System) showed no differential movement through the Strait of Gibraltar (Stich et al, 2006; Serpelloni et al, 2007), actually, bellow 50Km depth, our velocity profiles do not show any indication of subduction zone to the SE of our study area. Figure 2.55 Horizontal P-velocity distribution at 25, 35 and 50 km, showing high velocity anomaly in the Porimaô Bank. 175 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 7.5 Horseshoe Abyssal Plain The part of the horseshoe Abyssal plain we are studying is bounded in its northern side by the Gorringe Bank and in its southern side by the Coral Patch, characterized by a topographic pattern that reflects a complex geological structural trend, this is due to the fact that the Horseshoe Abyssal plain is close to the African plate Eurasia boundary, this area strongly also influenced by a compression movements, interpreted by some authors as giant submarine debris flows sourced from the Gulf of Cadiz accretionary wedge, ( Iribarren et al, 2007), Other authors have suggested the existence of a plate boundary Nubia-Eurasia WNW-ESE trend; starts from the Gloria fault and finish in Rharb basin; reveal that these deep-sea basins preserve a record of episodic deposition of turbidites (Gràcia et al 2010), transported towards the west and coming from the Imbricate accretionary wedge in Gulf of Cadiz that covers the entire Iberian and Morocco margins, the tomographic images in the northern part of the horseshoe abyssal plain show a low velocity anomaly separating two blocs of a positive anomalies along the SWIM lineament Figure (2.56), where earthquake activity is minor, Undoubtedly this anomaly can be interpreted as the contact zone between Horseshoe Fault and SWIM lineament Fault Zone, such contact, in addition to the oblique compression movement that governs this area, can clearly create a tension zone. 176 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Figure 2.56 Horizontal P-velocity distribution at 25, 35 and 50 km, showing low velocity anomaly in the N-W of the horseshoe Abyssal Plain. 177 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 8. Conclusion The recorded OBS seismicity data set used in this study has revealed a wealth of new information. Thus, these data reveal that most of the seismicity in the Gulf of Cadiz occurs at depths that vary between 20 and 80 km. Very few events occurred at depths shallower than 20 km. Prominent clusters of seismicity are found to be associated with the Gorringe bank, at the SW branch of the horseshoe fault and along the Marques de Pombal Plateau and the Sâo Vicente fault. Diffuse seismicity is observed offshore to the south of Portugal and very little seismicity along the accretionary wedge. A NW-SE band of seismicity is further observed to the SW of our study area. The hypocenters along this band have depths that vary mostly from 35 to 80 km. The tomographic inversion of the recorded seismic data yielded results that indicate that patterns of velocity anomalies within the study area are generally oriented along NE-SW and NW-SE directions. Both the P- and S-velocity distributions show that a low velocity zone is found at the SE of our study area. At shallow depths, this LVZ is interpreted as corresponding to thick sediments associated with the accretionary wedge. The velocity tomograms indicate that the Moho underneath the Gulf of Cadiz has an average depth of 30 km. On the other hand, higher velocity anomalies are found to the NW and to the north of our study area. The NW anomaly coincides with the Gorringe bank, and its prolongation in depth clearly shows that this bank is not a surficial feature, but is rather connected to a deep mantle uprising. The tomographic images in the northern part of the horseshoe abyssal plain show a low velocity anomaly separating two blocs of a positive anomalies along the SWIM lineament, where earthquake activity is minor, Undoubtedly this anomaly can be interpreted as the contact zone between Horseshoe Fault and SWIM lineament Fault zone, such contact, in addition to the oblique compression movement that governs this area, can clearly create a tension zone. Some authors support the existence of an active subduction zone beneath the Gulf of Cadiz, GPS data overall system showed no differential movement through the Strait of Gibraltar (Stich et al, 2006; Serpelloni et al, 2007), actually, bellow 50Km depth, our velocity profiles do not show any indication of subduction zone to the SE of our study area. 178 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Similarly, our inversion results show that the Marques de Pombal Plateau is related to a deep mantle anomaly. Both the Gorringe ridge and the Marques de Pombal Plateau anomalies are associated with high levels of seismicity, thus, indicating that the mantle process behind their uplift is likely to be still ongoing. All these results obtained by inversion travel-time of seismic waves are very important, however, there is still 10 km area that should be studied. In general we use surface waves tomography technique to investigate the shallow depth rather than technique used this thesis, this is the technique in terms of the theory, because it deal with another types of waves, called surface waves (Appedix for more details) . In our next work, we will proceed to investigate the shallow depth using this technique, in order to image all structure in the Gulf of Cadiz. 179 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ 9. References Adam M. Dziewonski, Don L. Anderson, Preliminary reference Earth model, Physics of the Earth and Planetary Interiors, Volume 25, Issue 4, June 1981, Pages 297–356. 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Matias , Neogene Through Quaternary Tectonic Reactivation of SW Iberian Passive Margin, Geodynamics of Azores-Tunisia, Pageoph Topical Volumes, pp 565-587. (2004). Zitellini Nevio et al, Source of 1755 Lisbon Earthquake And Tsunami Investigated, Eos, Transactions American Geophysical Union, Volume 82, Issue 26, pages 285–291, 26 June (2001). 188 BODY WAVES TOMOGRAPHY OF THE GULF OF CADIZ Appendix CHAPTER OUTLINE 1. Least squares method 2. Snell’s law 3. Plane wave 4. Conversion of format Seisan to Lotos 5. Surface waves Tomography 189 APPENDIX 1. Least squares method Measurement addresses fundamental responses that arise in many scientific studies (and everyday activities), Answering several question and making lows for natural behaviors, involving either direct or indirect measurements, it can be seen also as an integral aspect of the scientific method, namely testing or proving some hypothesis always requires collecting data, unfortunately, Even if measuring devices were perfectly accurate, it would not be humanly possible to read them with perfect precision. In brief, even direct measurement involves some degree or margin of error, despite that, the scientific method does not guarantee exact results and definitive proof of a hypothesis, scientists continue to seek ways to minimize these measurement errors by deferent ways, to construct an increasingly accurate and thorough understanding of our world. Nowadays, instruments can generate large amounts of data; yields in the most case over determined systems of equations that arise in geophysics, to solve these systems, several algorithms were used to fit the seismological observed data, the most stable and used one is the least squares method, which is a standard approach to the approximate solution of over determined systems, and can be used for any real data, there will be some misfit to the spectrum, which can be measured as error. If the data vector is in the column space, it will makes linear combination of a column and it will have the form of linear system is in the column space , , the data solve exactly the problem. However, be in the column space, but unknown, the system , if has to is probably not, given probability more equations than may have no solution and its really problem. In seismology and in its most cases, thus we have to use a large quantity of data, because we have no reason to say that this measurement are good or are useless, our purpose is to use all data available to get the maximum information, for this we often solve when is not in the column space (when there is no solution). So we try to solve for the closest vector in the column space , where is the projection on to the column space, we take instead of mistakes in measurement and it’s the errors . Now consider the system 188 making a , in that case APPENDIX is square invertible matrix, multiplying two sides in the equation lead to again instead of , because , don’t have the solution. We can see that geometrically in Figure (3.7.a) below, the tow pieces of were the projection and the other part is the error, so and Where is the projection of vector d on to the perpendicular space. error vector can be expressed as . The error vector is the is perpendicular to the projection plane so we get where Not that is the identity matrix when has an inverse, but it’s not the case we are looking for. Figure 3.1.a projection in subspace, p is the projection in column space, d is the data vector and e is the error vector. b) Illustrate the projection of the data vector in terms of components, showing the error quantities and is an outlier. 189 APPENDIX The particular application method of determining the parameter vector is known as the method of least squares, consisting of adjustment the parameters of a model function to best fit a data set let as take the simplest way to illustrate an approximation of a solution to over determined systems by least squares is to consider the case of tree data points of any measure, and try to find the best straight line that fit these data points. We have to be careful about least squares, when at least one of the data point is way of, this measurement change completely the shape of the best fit, this can be called an outlier and its represented by the fourth data measurement Figure (3.7.b). The best fit can then be written in this form or This is the system representing the equation that can be written in matrix form as Where and We certainly make tree errors for that example, one error for each equation, the way to find best fit is to square and to sum all these errors and find the smallest possible sum, If has independent columns then where , by some function is invertible for a set of experimental data that contains then take the deviations (or residuals) 190 parameters , we APPENDIX We can also form the weighted sum of squares of the deviations or residuals where the weights express our confidence in the accuracy of the experimental data. If the points are equally weighted, the that can all be set to 1, we can determine these parameters so is a minimum , ……… , , The set of those equations is called the normal equations and serves to determine the unknown as in . Until now we treat the problem as a linear appearance, in the case of a non-linear least squares problem. Numerical algorithms are used to find the value of model parameters which minimize the misfit to data. The most algorithms used are the LSQR method (Page, Saunders, 1982, Van Der Luis, Van Der Vorst, 1987). Choosing initial values for the parameters as initial model, then, the parameters are refined iteratively, that is the values are obtained by successive approximation. 191 APPENDIX 2. Snell’s law The Snell’s law describe the behavior of light at the interface of two media with the rectilinear propagation of light in homogeneous and isotropic medium, these laws are the basis of geometrical optics, and can also be interpreted by different models: wave model Huygens (Huygens' principle), model of least action Fermat (Fermat's principle) or model of the electromagnetic wave of Maxwell. To derive Snell’s law, we consider a plane wave, propagating in homogenous medium of uniform velocity c, the wave fronts at time time are separated by a distance along the ray path. The ray angle from the vertical, termed the incidence angle. Figure 3.2 A plane wave incident on a horizontal surface, incidence angle, denote the length of the ray. We can see from the Figure above Since , we have 192 is the and is APPENDIX Finally we get , where U is the slowness , P is the ray parameter, P can be measured when the arrival’s of the wavefront are known at two different stations. Consider now a down going plane wave with horizontal interface between two homogeneous layers of different velocity and the resulting transmitted plane wave Figure (3.3). If we draw wave fronts at evenly spaced times along the ray, they will be separated by different distances in the different layers, and we see that the ray angle at the interface must change to preserve the timing of the wave fronts across the interface. In the case illustrated the top layer has a slower velocity and a correspondingly larger slowness . The ray parameter may be expressed in terms of the slowness and ray angle from the vertical within each layer Figure 3.3 A plane wave crossing a horizontal interface between two homogeneous half-spaces. This is basic seismic version of Snell’s law in geometrical optics. Equation (3.9) may also be obtained from Fermat’s principle, which states that the travel time between two points must be stationary (usually, but not always, the minimum time) with respect to small variations in the ray path. For more details see also, (Aki and Richards,2002), (John.A. scales, 1997), (Seth Stein and Michael Wysession,2003), (Serveny,2000). 193 APPENDIX 3. Plane wave A plane wave is one of particular waves in which the disturbance is constant over all points of a plane drawn perpendicular to the direction of propagation. Such a plane is often called a wavefront, and this wavefront moves perpendicular to itself with the velocity of propagation c, Figure (3.4). Figure 3.4 Propagation of plane wave. Harmonic plane waves can be expressed as From the Figure above we see that , hence Can also be expressed in this form 194 APPENDIX where this plane wave represent a simple solutions of wave equations, from the same Figure we consider the same wave propagating along the x-axis with an apparent velocity , and along the ray with , the wavefront reach point P and R at same time , from the Figure again , we get Lead to the formula that gives the relation between the body wave velocity wave velocity This formula; can be generated for a homogeneous isotropic Where the quantity is the ray parameter. 195 layers. and surface APPENDIX 4. Conversion of format Seisan to Lotos Before reorganization of file, we have to convert our data (Source location and station coordinates) from the SEISAN format to LOTOS format, the output format obtained is used as input format for LOTOS processing, and in the following we give the routine used to convert the files. Code Fortran for conversion character*8 re character*1 pol character*2 ps character*5 stac,stacod(200),stbad(200) real fstat(200),tstat(200) real tobkr(200),tobkr1(200) integer istkr(200),ipskr(200) integer istkr1(200),ipskr1(200) open(1,file='set.dat') read(1,'(a8)') re close(1) open(1,file='data_in/stations.dat') open(11,file='data_out/stat_ft.dat') nst=0 1 continue read(1,*,end=2)stac,tet,fi,met !write(*,*)pol,stac,it1,at2,if1,af2,met if(stac.eq.' ') goto 2 nst=nst+1 stacod(nst)=stac fstat(nst)=fi tstat(nst)=tet z=-met/1000. write(11,*)fi,tet,z,stac !write(*,*)stac,fi,tet,z goto 1 2 close(1) close(11) write(*,*)' nst=',nst open(1,file='data_in/seisan.out') 196 APPENDIX open(11,file='data_out/rays.dat') 3 read(1,12,end=4)iyr,imt,idy,ihr,imn,sec,tzt,fzt,zzt 12 format(1x,i4,i3,i2,i3,i2,f5.1,4x,f6.3,f8.3,f5.1) tmzt=ihr*3600.+imn*60.+sec ! write(*,*)' fzt=',fzt,' tzt=',tzt,' zzt=',zzt,' t=',tmzt ! write(*,*)iyr,imt,idy,ihr,imn 34 read(1,'(1x,a4)',end=4)stac if(stac.ne.'STAT') goto 34 ikr=0 5 read(1,14,err=5) stac,ps,ihr2,imn2,sec2 14 format(1x,a5,3x,a2,7x,2i2,f6.3) if(ps.eq.' A') goto 5 ! write(*,*) stac,pol,ps,ihr2,imn2,sec2 !****************** if(stac.eq.' ') then if(ikr.eq.0) goto 3 ikr1=ikr ipskr1=ipskr istkr1=istkr tobkr1=tobkr ikr=0 do i=1,ikr1 ips=ipskr1(i) ist=istkr1(i) if(ips.eq.0) cycle tmin=999999 do i1=1,ikr1 if(istkr1(i1).ne.ist) cycle if(ipskr1(i1).ne.ips) cycle if(tobkr1(i1).gt.tmin) cycle imin=i1 tmin=tobkr1(i1) end do do i1=1,ikr1 if(istkr1(i1).ne.ist) cycle if(ipskr1(i1).ne.ips) cycle ipskr1(i1)=0 istkr1(i1)=0 end do ikr=ikr+1 ipskr(ikr)=ips 197 APPENDIX istkr(ikr)=ist tobkr(ikr)=tmin !write(*,*)ikr,ipskr(ikr),istkr(ikr),tobkr(ikr) end do if(abs(fzt).lt.0.1) then !write(*,*)' nzt=',nzt !write(*,*)fzt,tzt,zzt,ikr tmin=999999 do i=1,ikr if(tobkr(i).gt.tmin) cycle imin=i tmin=tobkr(i) end do fzt=fstat(imin)+0.03 tzt=tstat(imin)+0.03 zzt=5. !write(*,*)fzt,tzt,zzt,ikr !pause end if write(11,*)fzt,tzt,zzt,ikr nzt=nzt+1 !if(mod(nzt,50).eq.0) write(*,*)iyr,imt,idy,ihr,imn nray=nray+ikr do i=1,ikr write(11,*)ipskr(i),istkr(i),tobkr(i) !write(*,*)ipskr(i),istkr(i),tobkr(i) end do goto 3 end if !************************************** tmst=ihr2*3600.+imn2*60.+sec2 time=tmst-tmzt ips=0 if(ps.eq.' P') ips=1 if(ps.eq.'EP') ips=1 if(ps.eq.'IP') ips=1 if(ps.eq.' S') ips=2 if(ps.eq.'ES') ips=2 if(ps.eq.'IS') ips=2 if(ps.eq.' A') ips=3 if(ips.eq.0) then 198 APPENDIX write(*,*)' Cannot find phase ps=',ps !pause goto 5 end if do ist=1,nst if(stac.eq.stacod(ist)) goto 15 end do !write(*,*)' cannot find station:',stac if(nbad.ne.0) then do ibad=1,nbad if(stac.eq.stbad(ibad)) goto 5 end do end if nbad=nbad+1 stbad(nbad)=stac !write(*,*)nbad,stac goto 5 15 continue if(ips.ne.1.and.ips.ne.2) goto 5 ikr=ikr+1 ipskr(ikr)=ips istkr(ikr)=ist tobkr(ikr)=time goto 5 4 close(1) write(*,*)' n_events=',nzt,' n_rays=',nray write(*,*)' unknown stations:' open(11,file='data_out/unknown_sta.dat') do i=1,nbad write(*,*)i,stbad(i) write(11,*)stbad(i) end do close(11) stop end 199 APPENDIX 5. Surface waves Tomography When an earthquake is happed, the seismograms are dominated by a large longer period waves arriving after body waves, this waves are the surface waves, Two types of surface waves, known as love and Rayleigh waves, shows a large surface wave train arriving on a seismometer’s, transverse component shows the arrival of Love waves, followed by Rayleigh waves on a vertical and radial component. Notice that the love waves resulting from SH waves and Rayleigh are the result of P and SV interactions, it’s bright and straightforward to show the surface waves on seismograms. It’s necessary to indicate also that, at large distance from the sources the surface waves are prominent on seismograms, and the radial component of Rayleigh wave is different from the vertical one. When the displacement of the vertical component is zero, the radial displacement is maximum and vice-versa, After a large earthquake, contrary to the body waves whose energy spreads three dimensionally, the surface waves can circle the globe many times, and their energy spreads tow dimensionally and it’s concentrated near the earth surface. Dispersion: The dispersion phenomenon, known as geometrical dispersion, occurs in the earth when the velocity along the surface varied with the frequency, The fact that the surface velocities vary depending on the depth range sampled by each period makes surface wave dispersion valuable for studying earth structure, Use the observed Rayleigh waves dispersion allow us to examine the possible correlation between The lateral change in Rayleigh waves dispersion and geology structure. The dispersion further can be explored easily if we consider the sum of tow harmonic waves with slightly different frequencies and wave numbers. The dispersive waves of different frequencies propagate with different velocities. This can express these waves according to frequency, using the Fourier transform. 200 APPENDIX is a complex function can be written as : The inverse transform of allows us to express the displacement field. With initial phase generated by seismic source), A first order linearization of the wave ( number in about than: So, we can write the displacement field in the form: iwdw iwdw With: 201 APPENDIX we see that G varies with where is a velocity of traveling wave expressed by G function, G varies much more slowly than . We can say that G is the envelope function of the wave packet. v represents the velocity of the envelope of the wave packet, or of the wave group. We then define the group velocity as: U(w) can be infered from the dispersion relation: For an infinitesimal variation of w and k, the dispersion relation can be written as: If are also a solution of the dispersion equation, then the group velocity is given by: On seismogram, we remark that the wave with long period arrive or appear first on seismogram. Therefore, those waves are faster. The group velocity is found by dividing the distance between the sources and receivers by the travel time of the wave group, so for each period we seek the group velocity and plot group velocity – period curve. This technique is applied using the Fourier transform of a recorded signal, knowing that a signal which is periodic and exists for all time has a discrete frequency spectrum, therefore the Fourier transform is used to isolate the wave group of different periods. 202 APPENDIX Objectives: Determination of S-velocity models for shallow structure, using the Rayleigh waveforms which depend strongly on the shallow velocity structure of the medium. Method: Group the seismic events in source zones to get an average dispersion curve for each sourcestation path. Nb: it’s important to group the seismic events (short path : same elastic properties of the medium). The coordinate differences for a group of events must be less than or equal to 0.2 degrees in latitude and longitude to consider them grouped in the same source zone. To avoid the time lag, we have to take the instrument response into account. The figure below shows the path coverage for the study area. Apply the digital filtering with a combination of Multiple Filter Technique (MFT) (Badal et al) .The Multiple Filter Technique (MFT) is a filtering technique (Dziewonski et al., 1969), which is used to obtain the group-velocity dispersion curve from a pre-processed trace (instrument corrected). It’s used to study variations of amplitude (or energy) of a signa1 as a function of velocity (time) and period (frequency), the relative energy contour maps obtained by multiple filtering of the sample wave trains permit determination of the respective dispersion curves, as the group velocity of the fundamental mode is that associated with the observed maximum spectral amplitudes. A simple computer routine is used to locate all these spectral amplitudes whereby the corresponding group times that give us the observed group velocity dispersion (Y. Chen et al.2009) The time in which the envelope of the filtering seismic signal given by where is the Gaussian filter 203 APPENDIX Reaches the maximum, is the group time for the frequency selected as center of the Gaussian filter. The group velocity is obtained dividing the epicentral distance by the group time. Group-velocity dispersion curve can be computed by means of the procedure shown in the flow chart presented below: Figure 3.5 Chart of processing method. When the MFT has been applied for an interval of centre periods Tn, we get the contour map of relative energy normalized to 99 decibels, as a function of period and group time. The white curve denotes the group time inferred from the energy map. And the group-time curve can be inferred from the energy map. After, the group-velocity curve is calculated from the group times and the epicentral distance, dividing the epicentral distance by the group time for each period. Apply Time Variable Filtering signal (TVF). The Time Variable Filtering (TVF) is a filtering technique that does not give a dispersion curve but a smooth signal (a signal time-variable filtered), in which all effects of noise, higher 204 APPENDIX modes and other undesirable perturbations can be removed (Cara, 1973). Nb: combination of MFT and TVF works better than the application of the MFT alone, because the signal/noise ratio is highly increased. Apply an inversion theory to get S-wave velocity models. Initial model requirement. Regionalization: Sometimes we have to proceed to the regionalization as is known as a process to obtain dispersion curves in sub-regions from ray-path velocities crossing two or more different structures. Reliability: 1) We have to take just the traces which present a well developed Rayleigh wave train and discard the others. 2) We than match the: Theoretical dispersion (Calculated). Observed dispersion. The reliability is checked by the comparison between the observed group velocity (considered as observed data) and the theoretical group velocity (calculated from the actual model by forward modelling and considered as theoretical data). Resolution: Calculate the resolving kernels at various reference depths. This resolution is obtained when the absolute maxima fall over the reference depths. 205 APPENDIX Figure 3.5 Resolution Kernel (Badal et al 2003). The solution for the inversion problem is more reliable when the maxima of these resolving kernels are narrower. 206