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Earthquakes Earth is a dynamic planet of a pretty dangerous sort Terremoto Haiti 2010. Duecentovetimila vittime Earthquakes occur along faults. A fault is a planar fracture or discontinuity in a volume of rock, across which there has been significant displacement. Large faults within the Earth's crust result from the action of tectonic forces. Energy release associated with rapid movement on active faults is the cause of most earthquakes. There are three main types of faults: A normal fault occurs when the crust is extended. The hanging wall moves downward relative to the footwall A thrust fault occurs when the crust is compressed. The hanging wall moves upward relative to the footwall The fault surface is usually near vertical and motion results from shearing forces. Doglioni et al., 2014 An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The elastic rebound theory is an explanation for how energy is spread during earthquakes. As rocks on opposite sides of a fault are subjected to force and shift, they accumulate stress energy and slowly deform (strain) until their internal strength is exceeded. At that time, a sudden movement occurs along the fault, releasing the accumulated energy, and the rocks snap back to their original undeformed shape. In geology, the elastic rebound theory was the first theory to satisfactorily explain earthquakes. Following the great 1906 San Francisco earthquake, Harry Fielding Reid examined the displacement of the ground surface around the San Andreas Fault. From his observations he concluded that the earthquake must have been the result of the elastic rebound of previously stored elastic stress energy in the rocks on either side of the fault. In an interseismic period, the Earth's plates move relative to each other except at most plate boundaries where they are locked. Suppose that rocks in the region of the locked fault have bilt up elastic stress energy in the form of elastic deformation (strain) over a time period of many years. When the accumulated strain is great enough to overcome the strength of the rocks, an earthquake occurs on the fault plane at Time 0. During the earthquake, the portions of the rock around the fault that were locked and had not moved 'spring' back, relieving the strain (accumulated over several years) in a few seconds. Like an elastic band, the more the rocks are strained the more elastic energy is stored and the greater potential for an event. The stored energy is released during the rupture partly as heat, partly in damaging the rock, and partly as elastic waves. Modern measurements using GPS largely support Reid’s theory as the basis of seismic movement, though actual events are often more complicated. An aftershock is an earthquake that occurs after a previous earthquake, the mainshock. An aftershock is in the same region of the main shock but always of a smaller magnitude. If an aftershock is larger than the main shock, the aftershock is redesignated as the main shock and the original main shock is redesignated as a foreshock. Aftershocks are formed as the crust around the displaced fault plane adjusts to the effects of the main shock. An earthquake's hypocenter is the position where the strain energy stored in the rock is first released, marking the point where the fault begins to rupture. This occurs at the focal depth below the epicenter. The epicenter is the point on the Earth's surface that is directly above the hypocenter, the point where an earthquake originates. There are two types of seismic waves, body wave and surface waves. Body waves originate in the hypocenter and propagate spherically through the interior of the Earth. They follow raypaths refracted by the varying density and modulus (stiffness) of the Earth's interior. The density and modulus, in turn, vary according to temperature, composition, and phase. There are two types of body waves: P-waves and S-waves. Surface waves are analogous to water waves and travel along the Earth's surface. They travel slower than body waves. Because of their low frequency, long duration, and large amplitude, they can be the most destructive type of seismic wave. There are two types of surface waves: Rayleigh waves and Love waves. The P-wave, where P stands for Primary wave or Pressure wave, can travel through gases, solids and liquids, including the Earth. It has the highest velocity (5-8 km/s during an earthquake) and is therefore the first to be recorded, and it is formed from alternating compressions and rarefactions. In isotropic and homogeneous solids, the polarization of a P-wave is always longitudinal; thus, the particles in the solid have vibrations along (or parallel to) the travel direction of the wave energy. The velocity of P-waves in a homogeneous isotropic medium is given by where K is the modulus of compressibility (resistance to volume change), μ is the modulus of rigidity or shear (resistance to change in shape due to shear), ρ is the density of the material through which the wave propagates. The S-wave, where S stands for Secondary wave orShear wave, moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation: S-waves are like waves in a rope. S-waves can travel only through solids, as fluids (liquids and gases) do not support shear stresses. S-waves are slower than P waves, and speeds are typically around 60% of that of P waves in any given material. The velocity of S-waves in a homogeneous isotropic medium is given by where μ is the modulus of rigidity or shear, ρ is the density of the material through which the wave propagates. Nafe-Drake curve An important empirical relation exists between P and S waves velocity and density. P and S velocities increase with density of medium, i.e., in less dense sedimentary rocks, waves travel slower (black dots for S waves) than in denser igneous and metamorphic rocks (white dots for S waves). Seismic waves travel more quickly through denser materials and therefore generally travel more quickly with depth. P S However, as noted from the velocity equations, if density increases, P and S waves velocity decrease: Thus, the other properties, incompressibility K and rigidity or shear µ must increase with depth in the Earth at a greater rate than density increases. This explain the experimantal results illustrated in the Nafe-Drake curve. However, anomalously hot areas slow down seismic waves. Seismic waves move more slowly through a liquid than a solid. Molten areas within the Earth slow down P waves and stop S waves because in a liquid, rigidity or shear µ = 0; shearing motion cannot be transmitted through a liquid). Partially molten areas may slow down the P waves and attenuate or weaken S waves. Therefore, the actual velocity of P and S waves depends on the interplay between rock type, depth, and temperature. Velocità onde P (a) e onde S (b) Dipendono dalle caratteristiche del mezzo in cui viaggiano: K = modulo di incompressibilità del mezzo µ = modulo di rigidità o di taglio (shear) del mezzo r = densità del mezzo La velocità delle onde S è sempre minore della velocità delle Onde P in quanto manca il termine K. Le onde P vengono avvertite (arrivano) prima delle S. In un mezzo fluido (liquido o gas), K≠0, µ = 0 ovvero i fluidi sono comprimibili ma non ammettono taglio. Quindi: K b=0 Le onde P possono viaggiare nei solidi, liquidi e gas Le onde S possono viaggiare nei solidi, ma NON nei liquidi e gas La velocità delle onde P e S tende ad aumentare all’aumentare della densità r del mezzo (curva di Nafe-Drake) poichè all’aumentare della densità r di una roccia i moduli di incompressibilità K e rigidità o shear µ della roccia aumentono in proporzione maggiore. Ciò avviene ad esempio all’aumentare della profondità nella crosta: aumenta la pressione litostatica e l’incompressibilità K e rigidità µ delle rocce aumentano maggiormente dell’aumento di densità r …Ma la velocità delle onde P e S tende a diminuire all’aumentare della temperatura poichè aumentando la temperatura del mezzo i moduli di incompressibilità K e rigidità o shear µ del mezzo diminuiscono maggiormente rispetto alla densità r. Ciò avviene ad esempio all’aumentare della profondità nella crosta (gradiente geotermico). Dunque l’aumento di velocità in profondità legato all’aumento di pressione litostatica è contrastato dalla diminuzione di velocità causata dall’aumento di temperatura. LA VELOCITA’ DELLE ONDE E’ CONTROLLATA DALLE CONDIZIONI GEOLOGICHE ‘LOCALI’ Surface waves - Rayleigh and Love waves - are generated by the interaction of P- and Swaves at the surface of the earth, and travel with a velocity that is lower than the P-, S- wave velocities. They emanate outward from the epicenter (surface projection of hypocenter, where P- and Swaves are generated) of an earthquake. Rayleigh Love Love waves are surface seismic waves that cause horizontal shifting of the earth during an earthquake. The particle motion of a Love wave forms a horizontal line perpendicular to the direction of propagation (i.e. are transverse waves). The amplitude, or maximum particle motion, often decreases rapidly with depth. Love waves travel with a slower velocity VL than S waves (b), but faster than Rayleigh waves (VR): VR < VL < b Rayleigh waves, also called ground roll, are surface waves that are confined to the Earth’s surface where they travel as ripples with motions that are similar to those of waves on the surface of water. The surface particles move in ellipses in planes normal to the surface and parallel to the direction of propagation. At the surface and at shallow depths this motion is retrograde (unlike water waves). Particles deeper in the material move in smaller ellipses with an eccentricity that changes with depth. The speed of Rayleigh waves (VR) on bulk solids, of the order is slightly less than the Love-waves velocity. VR<VL< b The amplitude of Surface waves decays as function of 1/sqrt(x) whereas the amplitude of Body waves decays as function of 1/x2, where x is the radial distance from the epicenter for S waves or from the hypocenter for Body waves. Surface waves therefore decay more slowly with distance than do body waves, which spread out in three dimensions from a point source (hypocenter). A Body waves A = f(x-2) x A Surface waves A = f(x-0.5) Surface waves therefore tend to be more destructive than body waves. x Surficial expression of waves P waves Love waves Rayleigh waves S waves Summary Waves Sismografi Wood-Anderson Un terremoto viene registrato attraverso un sismografo che consiste essenzialmente in un pendolo ed un apparato di registrazione. Il passaggio dell’onda sismica provoca il movimento del supporto del pendolo. Sequenza: P – S The difference of arrival time of P- and S-waves at a seismograph is function of distance of earthquake epicenter. A 11-minute difference equals to a distance of ~8600 km; a 8-minute difference equals to ~5600 km; a 3minute difference equals to ~1500 km, and so on. The arrival time difference of P- and S-waves measured at three seismographic stations reveals the location of the epicenter by smallcircles intersection. The difference in arrival time between P and S waves is used In Japan for the Early Warning System…it’s a matter of minutes...that can save your life... When two or more seismometers detect Pwaves (upper), the Japan Metereological Agency immediately analyzes the readings and distributes the warning information to advanced users such as; broadcasting stations and mobile phone companies, before the arrival of Swaves (lower). Local Magnitude (ML) or Richter scale. The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the variation in the distance between the various seismographs and the epicenter of the earthquake). The original formula is: Richter magnitude ML = log10A - log10A0(d) Where A is the maximum excursion of the seismograph; the empirical correction function A0 depends only on the epicentral distance of the station, δ. The Richter scale is obsolete and has been replaced by the MMS scale. The moment magnitude scale (abbreviated as MMS; denoted as Mw) was developed in the 1970s to succeed the 1930s-era Richter magnitude scale (ML). The MMS is now the scale used to estimate magnitudes for all modern large earthquakes. The magnitude is based on the seismic moment of the earthquake M0, which is equal to the rigidity of the Earth multiplied by the average amount of slip on the fault and the size of the area that slipped. µ = rigidity or shear modulus Seismic moment M0 = µAD A = LW = fault plane area in dyne centimeters (10−7 Nm) D = mean displacement along fault plane In order to create a moment magnitude scale (Mw) most consistent with older magnitude scales such as the Local Moment (or "Richter") scale the seismic moment (M0) is converted into a logarithmic scale using the following equation: Moment magnitude Mw = 2/3log10(M0) – 10.7 The Moment Magnitude Scale based on the Seismic moment M0 and calculated as Mw = 2/3log10(M0) – 10.7 extends from Mw = 0 to Mw = 10 Exercise 1 Exercise 2. Suppose you want to estimate the proportional difference fΔE in energy release between earthquakes of two different moment magnitudes Mw1 and Mw2, where Mw1 is larger than Mw2 Starting from the equation of Moment magnitude Mw = 2/3log10(M0) – 10.7 and solving for M0 we obtain: log10(M0) = 3/2(Mw + 10.7) and M01 = 103/2(Mw1 + 10.7) M02 = 103/2(Mw2 + 10.7) fDE = M01 / M02 = (103/2(Mw1 + 10.7)) / (103/2(Mw2 + 10.7)) = 103/2(Mw1-Mw2) The difference fΔE in energy release between earthquakes of two different moment magnitudes Mw1 > Mw2 is: fDE = 103/2(Mw1-Mw2) An increase of 1 on the moment magnitude Mw logarithmic scale corresponds to a 101.5 ≈ 32 times increase in the amount of energy released, an increase of 2 corresponds to a 103 = 1000 times increase in energy, an increase of 3 corresponds to a 104.5 = 31622 times increase in energy etc. Japan earthquake of Friday, March 11, 2011; Mw1 = 9.0; Depth 32 km L’Aquila earthquake of Monday, April 06, 2009; Mw2 = 6.3; Depth 8.8 km Mw1-Mw2 = 2.7 fDE = 103/2(2.7) = 11.220 The Japan quake was eleven thousands times more energetic than the L’Aquila earthquake Each earthquake has only one magnitude, but the effects of any one earthquake can vary greatly from place to place. The Modified Mercalli Intensity scale generally deal with the manner in which the earthquake is felt by people. The higher numbers of the scale are based on observed structural damage. Peak ground acceleration (PGA) measured in g is equal to the maximum ground acceleration that occurred during earthquake shaking at a location. Unlike the moment magnitude scale, it is not a measure of the total energy (magnitude, or size) of an earthquake, but rather of how hard the earth shakes at a given geographic point. Correlation with the Mercalli scale 1. Focal mechanisms. Orientation of fault plane can be represented by beach balls 1.Reconsider Elastic Rebound 2. Focal mechanisms No offset Earthquake break No offset 3. Focal mechanisms Volume decrease (compression) Volume increase (dilation) Volume increase (dilation) Volume decrease (compression) 4. Focal mechanisms Direction of P-wave first motion 5. Focal mechanisms Direction of P-wave first motion BEACH BALL 6. Focal mechanisms La Rete Sismica Nazionale (INGV) registra più di 2000 terremoti l'anno in Italia. Il catalogo sismico strumentale riporta circa 35.000 terremoti verificatisi in Italia a partire dal 1975. La sismicità crostale rappresenta la maggior parte dell'attività sismica registrata (Fig. 1). Terremoti intermedi e profondi (Fig.2) avvengono nella zona del Tirreno meridionale verso i 300 km di profondità, dove i terremoti possono raggiungere anche M = 7. Questi terremoti suggeriscono un processo di subduzione attiva (Fig. 3). Fig. 1 Fig. 2 Fig. 3 Peak ground acceleration (PGA) is a measure of earthquake acceleration on the ground. It is not a measure of a quake magnitude (Richter or MMS scales) but rather a measure of how hard the earth shakes in a given geographic area. The PGA scale is measured by accelerographs and it generally correlates well with the Mercalli scale. La pericolosità sismica, intesa in senso probabilistico, è lo scuotimento del suolo atteso in un dato sito con una certa probabilità di eccedenza in un dato intervallo di tempo, ovvero la probabilità che un certo valore di scuotimento si verifichi in un dato intervallo di tempo. Mappa a destra: PGA con 10% probabilità di essere superata in 50 Anni; periodo di ritorno T=475 Anni (INGV) Il rischio sismico, determinato dalla combinazione della pericolosità, della vulnerabilità e dell’esposizione, è la misura dei danni attesi in un dato intervallo di tempo, in base al tipo di sismicità, di resistenza delle costruzioni e di antropizzazione (natura, qualità e quantità dei beni esposti). Mappa Intensità su scala MCS da grado V a grado XI su dati da 1DC a 1992-> utile per rischio sismico Rischio = Pericolosità x Vulnerabilità x Esposizione Per ridurre il rischio possiamo agire sulla vulnerabilità Prior to the introduction of modern seismic codes in the late 1960s for developed countries (US, Japan) many structures were designed without adequate detailing and reinforcement for seismic protection. Example: Casa dello Studente, L’Aquila …non sono necessari controlli periodici su palazzi costruiti negli anni 60 (prima dell’entrata in vigore delle normative in materia di edilizia anti-sismica) in una zona a classe di massima pericolosità sismica. Professore dica qualcosa…Seismic retrofitting is the modification of existing structures to make them more resistant to seismic activity, ground motion, or soil failure due to earthquakes. With better understanding of seismic demand on structures and with our recent experiences with large earthquakes near urban centers, the need of seismic retrofitting is well acknowledged. Example from San Francisco: Community Action Plan for Seismic Safety (CAPSS) The CAPSS project will make policy recommendations to the Department of Building Inspection (DBI) regarding the earthquake performance of most privately-owned, existing buildings in the city. When enacted, these policy recommendations would reduce future earthquake damage and facilitate the repair of buildings damaged by earthquakes. Professore dica qualcosa … 6 Aprile 2009 - L’Aquila 31 Ottobre 2001 - San Giuliano di Puglia - crollo scuola: 27 bambini morti…"quella sopraelevazione - ha ricordato il procuratore generale della Cassazione, Francesco Iacoviello - è stata costruita senza rispettare le norme antisismiche necessarie in una zona, come quella di San Giuliano, ad elevato rischio sismico e il sindaco non avrebbe dovuto consentire l'apertura di quella scuola senza nemmeno un certificato di collaudo". Tsunami can be generated when the sea floor abruptly deforms and vertically displaces the overlying water. When earthquakes occur beneath the sea, the water above the deformed area is displaced from its equilibrium position. More specifically, a tsunami can be generated when thrust faults associated with convergent or destructive plate boundaries move abruptly, resulting in water displacement, owing to the vertical component of movement involved. Movement on normal faults will also cause displacement of the seabed, but the size of the largest of such events is normally too small to give rise to a significant tsunami. Tsunamis in pills: While everyday wind waves have a wavelength (from crest to crest) of about 100 metres and a height of roughly 2 metres, a tsunami in the deep ocean has a wavelength of about 200 kilometres. Such a wave travels at well over 800 kilometres per hour over deep water. As the tsunami approaches the coast and the waters become shallow, wave shoaling compresses the wave and its velocity slows below 80 kilometres per hour. Its wavelength diminishes to less than 20 kilometres and its amplitude grows enormously. Since the wave still has the same very long period (time from crest to crest), the tsunami may take minutes to reach full height. Except for the very largest tsunamis, the approaching wave does not break, but rather appears like a fast-moving tidal bore. Small amplitude theory for wave celerity Wave celerity (speed): where g is acceleration of gravity 980 cm/sec2 Wave Period, which is the length of time it takes for a wave to pass a fixed point (crest to crest), is: T=L/C T=L/C In the open ocean, a Tsunami typical wave lenght L is 200 km. Therefore, the term d/L is very small, on the order of 0.03; The equation of celerity C becomes: C = sqrt(gL/2pi)= sqrt(980 X 2000000/2pi) = 636 km/h (for a 200 km L wave) And the Period T of such a wave is: T = L / C = 200km / 636km/h = 19 min Whereas a typical amplitude of a Tsunami is of only about 1 metre. Long periods and small amplitudes make tsunamis difficult to detect over deep water. Ships rarely notice their passage. As the tsunami approaches the coast and the waters become shallow, wave shoaling compresses the wave and its velocity slows below 80 kilometres per hour: C= = sqrt(980 X 5000) = 80 km/h (for a 50 m-deep ocean) Its wavelength L diminishes to less than 20 kilometres and its amplitude A grows enormously, A ~ 1/d1/4 whereas he Period T remains the same: T = L / C = 20 / 80 = 15 min Since the wave still has the same very long period, the tsunami may take minutes to reach full height. The approaching wave does not usually break, but rather appears like a fast-moving tidal bore. Since the wave still has the same very long period, the approaching wave appears like a fast-moving tidal bore. The whole ocean is coming upon land! e.g The 2011 Japan tsunami Note the enormous wavelenght (~200 km) of Tsunami waves Ancient Mediterranean Tsunami May Strike Again A map depicts the Mediterranean Sea (green) and the degree of sea-level displacement caused by a tsunami after the Crete earthqake (magnitude ~8) that wracked the Mediterranean region in A.D. 365. Such tsunamis are relatively frequent in the region, striking perhaps as often as every 800 years.