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OC EANOLOG ICA ACTA , 1981, N' SP Eaf----- Con tine nt al margins G ulf of Aden Simple models of diffuse extension and the pre-seafloor spreading development of the continental margin of the Northeastern Gulf of Aden H eUI fl ow Rift leClonics Li thos phcric rif ling Marges con ti ne'lIales Go lfe d' Auen Flux de chaleur Tectonique des rift!; Rifling lithosphé rique J. R. Cochran Lamont-Doherl y GcoJogical Observatory of Columbia Universit y, Palisades. New York 10964. USA . ABSTRACT The pre-seafJoor spreadi ng developme nl of the continental margin of the Northeas tern Gulf of Aden is invcstigated us ing s im ple modcls for diffuse extension th ro ug h lîstric fa ulting and/o r dike intrusio n. Il is found Ihill provided dike inlrusion makes up a s ignificanl par t o f the extension mec hanism. the s imple model can adcquatcly cltplnin the obscrvcd heat fl ow and basement depths without violating eonstrain ts placed o n the tota l amoun t of exte ns ion by e rus tal th ic k nesses a nd pla te geome try , The infl uence of va rio us fa ctors o n the behavior of the models is inves tigated, and they are round to be qui te sensiti ve to the c hoice of initial cr ustal parame ters and to the dura tion and nat ure of the pre-seafloor s preading e x te nsion , T hus to adequa tely understand the rifting process a nd the de velo pment of continental margins, it is neçessary to obtain data from well s d rilled Înto the synrift and basement roc ks , and to stud y areas suc h as the Nor thern Red Sea, which arc presently in the pre-scafloor spreadi ng phase of the ir e volution, OcewlOl , At:/(J , 1981 , Proceedings 26,h Inte rna tio nal Geological CongreSs, Geology of conti nental margins symposium , Paris, Jul y 7-17 , 1980, 155- 165, RÉ SUMÉ Modèle s s impl es d 'exte nsion diffu se et développemen t pré-accrétion océa nique de 1<1 marge co ntine ntale du Go lfe d 'A den nord-orie nta l. Le dévelo ppement de la rn:lrge co ntinentrale du Go lfe d ' Aden no rd-orien tal pré cédant le s tage d 'accré tio n océanique est étudié à l' aide de modèles s imples d'extens ion diffuse par fa illes ou/et intrusion mag ma tique, S i l'o n ad met que l'intrusio n magma tique constitue une part s ign ificulive du mécanisme d'extensio n, on observe q ue le modèle s imple expliq ue c orrecteme nt les flux de c haleur et les profo nde urs de s ubstratum mesurés, sans violer les contraintes s ur l'cxte nsion tO lrale fo urnies par l'épa isseur de la çroûte ct la géométrie des plaques, L'influence de nombreux facle urs sur le comporteme nt des modè les est eX:lminée, e t o n montre quc ceux-ci sont sensibles a u c ho ix des paramètres c rus tau x initiaux, ains i qu 'à la durée ct la nra ture de l'ex tens ion pré-accré tioll , Ainsi pour comprend re correc te me nt le proçessus de d is tension et le dévelo ppement des m:uges co ntinen tales, il est nécessaire d 'obtenir des do nnées de pUi lS foré s da ns les roç hes s yn-dis tens io n et celles d u subs tratum . ct d'étudier les doma ines tels que la Mer Rouge se ptentrio nulc, qu i sont actuellement d;lOs la phase pré-accrétion océlinique de le ur évolution , Oela/wl. Acw, 1981. Actes 26" Congrès InternatÎoml1 de Géologie , co lloque Géologie des marges contÎnenta les, Pa ris . 7- 17 juil. 1980, 155-165, 155 J . A. COCHRAN INTRODUCTION been applied to several contine ntal margins (Royden. Kcen. 1980; Le Pichon. S îbuet. in press ; Steckler. Watts. 1980: Cochran. in press). The purpose of Ihis paper is to app!y thb. model 10 the young continen tal margin in the Gulf o f Aden a nd , in doing sa. to examine how vario us parame ters affec t the mode!. The conclusion is Ihat , al1bough the diffuse extension model can fit the observed behavior of th îs <lod other continental margins. there is enough uncertainty and extrapolation involved in its application. thal a de tailed understanding of the processes involved in continental rifting. and the initiation of seafloor spreadins depends on oblaining biostratigrap hi c dala from wells inlo the pre· and syn·rift sed iments. which has nOI yet been donc and on studying l-Irel-ls such as the Northern Red Sea. which appears to still be in the diffuse extension stage of ilS evolution. T hcrc has becn a grcal cmphasis during the past scveral yea rs on slUdying the s tructure and evolution of continental margins. Until recently, ve r y !iule was ac tually known of this region where ocean and continent meCI, and Drake and Burk (1974) were able \0 c haracterize continental margins as "a helt of ignorance extending sînuo us1y aç ross the Earlh's s urface··. Much of Ihis Jack of knowledge resuhed from Ihe difficulty of obtaining re1iable data, since the sreat quantity of sediments (as muc h as 15 km ) on the much siudied margins of the Atlantic has prevented observai ion of the base ment s lructure by seismic methods, as weil as obviously preventing direci sam pli ng 10 determine the nature of the basement rocks. Scismic refraClion dala are a lso difficult 10 înterpret . giving a helerogeneous structure usually with a layer ha ving a ve10city of l-Iboul 7.4 km/sec. rather than normal mantle velocities as Ihe deepest refraclor (Drake, Nafe. 1968). Since the mid 1970·s, Ihere has been an inereased efforl 10 undersland the nature of continental margins. both because of Iheir reSOUTce potential and because man y of the more eas i1 y attacked problems related to the age and evolulion of the deep ocean bl-lsins have been solved. This increased interest. along with tec hnical advances s uc h as the de ve lopment of multichannel seismic methods and the increased number of deep explora tory wells o n continent<ll s hel ves, has 1ed 10 a beuer understanding of the behavior of continental margins. Bioslratigraphic data from exploratory wells showed that much of the sedime nt pile is made up of shal10w water sed iments (Jansa. Wade . 1975: G radstein et al., 1975). which would not he expcctcd mercly (rom the fill ing of a n exi~linl"l b:l~in . Steep (1971) correcle!! Ihe <;Llh~idence rale~ recorded in wells from the US coastl-ll plain for the effects of sediment loading , and found that the remaining subsidence was both s ubs lantial , and s howed an exponential decay in time with a time constant of about SU m.y. T his is the type of response expected from the cooling of a heated lithosphere (Sclater, Francheteau, 1970). and this observa· tion led 10 a Great emphasis o n the role of thermall y produced vertical motions at a continental margin. It was ve ry quickly realized Ihl-lt li mcchani sm is needed to cause the crust to subside below sea level since. if the litbosphere is simplY healed, it will expand and then COniTact back to its original position. Earl y models suggested that additiomtl s ubside nce could bc caused by crustal thinning through erosion of the therm<llly uplifted crust (Sleep, 1971 : Kinsman. 1975) or by densification of the lower erust through thermally induced phase changes (Falvey, 1974). These mode!s s uUer from the d iffi culties that al man y margins . the initial dom ing stage which the y requiTe d oes not appear to have occurred (for example. MontadeT! et al., 1979: Cochran, 1981). and that they cannot reasonably produce the required amount of subsidence (Steckler, Walls. 1978). This is pl-lrticularJ y truc of the crustal erosion model. which wo uld require 17 km of erosion to satisfy the observed tectonic subsidence in the ij·2 weil (5teçk1er. Walls, 1978). Tbese difficulties, along with the observation of bl-lsement fealures which have been interpreted as rolated fault blocks on MCS lines across some continental margins (de Charpel et al. , 1978), have led to another class of models which produce crustal and lithospheric thinning through diffuse extension. Variations of this mode!. fir st proposed by MeKenzie (978) to explain the behavior of areas of extension and subsidence within a continent. have recently MODELS FOR THE DE VELO PME NT OF A CONTI· NENTAL MA RGIN The s implest model which has been suggesled for d iffuse extension and the s ubseque nt evolution of the extended arel-l is tbe '·stretc hins· · or "atte nualion " model proposed by McKenzie (1978). This model s tarts with fi unit le ngth of lithos phere of th ic kness t with a crust of thîckness t. , over an isothermal asthenosphere with a temperl-lture of the order of 1 300' C-l 350"C. A simple linear tempe ra ture gradient is llssumed in the lithosphere (Fig. 1 a). At time T = 0, the lithos phere is instantaneously extended to a lenglh 13 in some unspec ified ma nner (Fig. 1 b). In arde r to conserve mass. the lithospheric thickness decre<lses to t Ip. and the crustal thickness to t;f, while Ihe ast henos phere pl-lssively rises in response to Ihe ]ithospberic Ihinning . The firS I result o f the litbosphe ric thinning is an isostalic adjustement, referred 10 liS the "f<lult bounded subsidence ,. by Sclater and C hris lie (1980). which is due 10 the fac i that the extension res ults in changing the mass in Il vertical column. T his adjus tme m can be determ ined by simply balancing m.. ss col umns ~tnd is given by S.= '1 )71,(, (P. - P. T" ) .T,p,]( ' -il') - 0 'V -~ P.(I nT ,) p~ where Po .. nd Pc are the densities of the mantle and crusi respectively, both at O~C. p ... is the density of sea water. « is tbe coefficient of thermal expansion ass umed to be the same in erusl and mantle. and T l is the asthenos pheric temperature . Once the extcnsion has occurred. the lithos phere will start to thicken , as heat is conducted to the surface. and with time will return 10 Îts equilibrium thickness (Fig. 1 cl. which is determined by a b::t lance of the heat being conducted to the surface and the heal supplied 10 the base of the lithosphere. Since the initial and final thermal s tates are known. the temperature distribution and th us the surface heat flow can be delermined as 11 fun ction of time. Knowledge of the thermal structure and thus of densities as a functio n of time also allow the s ubsidence history of the extended res ion to be calculatcd (Mc Kenzie. 1978: Ro y· den. Keen, 1980). A second model, which has been proposed by Royden el al. (1980). is bl-lsed on extension thro ugh dike injectio n. T hi s mechanism results in a d iffcrent temperature distribu tion than the stretching model (Fig. 1 a). with higher tempcralU' Tes near the surface. This heat is quickly lost resulting in 156 PRE-SEAFLOOR SPREADING DEVELOPMENT OF THE GULF OF ADEN INTRUSIQN MOOEL (Royden et 011 STRETCHING MODEl (McKenZII!.19781 A A B 1-0 B 1" 0 l. ,. • 1 ~ L------ 1' --.,-- C 1-00 Figure 1 !~~ Simple mode/l' for cruslal exlensioll, /11 voll, model.,. a a"il lell;:11I of lililospilere (A ) Is. af I;me T _ O. l'')'I/m/(meollsly exlellded la lell;:lh ~ (8) rnlll/l,,/: 1" Il c l,(Ullie ;11 I/le l emperalllre l'trl/(·IU'/'. [" Ille Si relchlll;: model, Ihe eXIi'IIsiO/I is " ccomplislled vy Ihilillin;:llle crllSI tllld Iilliospilue If} 11~ of 1/1I!;r o ri[.l;lIal Il!Îcknn~. fi, Ille ill/fl/slOIl /IIodel. il Is a ccli/llpli~I,ed by /III! ill/mslo" of dikes of /IImllle /II(l/eri,,/ fmm Ille uSlllenosphere. WilI, lime Ille Iitlws{)here Ih!ckells and Ihe Ilremwl ;:rIIdlelil relilms 10 ilS orl;:illol Slale ( e). Kll o"'/ed;:e (Jf Ille illililll will fillllllempefll!lIre /lm/lile densilies of cruslill (Uld maltl/e materil/I.r ullo",s Ille lIeul fla", and .wrfllce elel'{,/;ml 1,/ ve culeltl/ll ed /lS /1 fll ne/;on of lime. of extension is to cause a loss of heat and thus subsidence prioT to the initiation of seafloor s preadi ng thus res uhing in less subsidence and a slower subsidence rate during the post seaflOOf spreading period. Jarvis and Mc Ken zie (1980) in'lestigatcd the eHects of fin ile extension times a nd concl uded that ··for most basins the simple model Bives reasonably accuratc resulls provided the dura tio n of s preading is less than 20 m.y.· · Their results are used in Figure 2 to s how . as a function of 13. tbe maximum time over which extension can oecur for the McKenzie (1978) model 10 predict tbe post-stretching s ubsidence and heal fJow to witbin 10 %. In general , Ihe subs idence. wbicb is lhe mos t frequenlly used parame ter, will be predicted to within that amount if the extensional evenl is of Icss Ihan about 15 m.y . duration. higher hellt fl ow a nd subs idence rates during the time immediately following the exte nsional episode. Thus. during Ihis lime, a lower val ue of t3 would be required 10 match observed s ubsidence rates. depths or heal flow . After abo ut 10-1 5 m .y., however, it is probably not possible to d istinguish between tbe two models. Dike intrusion is a n important means of extension in Afar (Barberi el 141., 1975 ; Ch ristiansen et al., 1975). which may be a continental margin in formation. and intense dike s warms into the continental Cru SI ha ve been reported from areas as diverse as thc eastern margin of the Red Sea (Coleman et (lI. , 1975), the Atlantic margin of Greenland (Myers. 1980) and the margin of the proto-Athmtic ·· IapelUS" ocean in New Brunswick (Rast . 1979). In spiteof thesc observations. the dike injection model has not been used in su bsequent sl udies, probably in large measure beca usc of the Great impac t made by tbe discovery of fealUre s inte rpreled as rotated fault blot:ks and listric faults on the marg!n of the Ilay of Biscay (de C harpel et (II" 1978). FINITE EXTENSION TIMES The two model s dist:ussed above botb assume Înstantaneous extension. This ass umption makes the mathematical tTeatment much simpler by pro'liding simple and weil dcf incd initial conditions, but does not correspond 10 what is found in nature. The pre -seafloor spreading rifting his lory of continenta l margins appcars to last from about 10 m.y . (for example. Cochran . 1981 ) to perhaps as muc h as 50 m.y. for tbe southern marg!n of Australia (Konig. TalwanÎ, 1977). The final dep lh (corrected for sed iment loading) and the total amounl of excess heat re leased arc both independent of the time over which the extension occurred, since botb depend so lely o n the pammeter 1). The effec! of a finite time Figure 2 !-~~--~c-~~~--~.,~-c~",--•., r ..... tm.y) M/lximum lime as II f llll C/ili li offi Q"t'r ",/lic/, e;rlen ûo n cali IICCllr for l 'imple Sl re/chlnl.( m odellO pretllel Il.e pm'I .rlre/dûnl.( .wfnicfe ll ce and /11'11/ fla ... 10 ... illlÎlI 1(} %. 157 J . A. COCHRAN CA LIBRATION OF THE MODEL Parsons a nd Scia ter (1977) used the observationaJJy determined val ue of 3.900 m fo r ClIO obtain es ti mlltes of 3. t 1 X 1Q- ' cC - 1 and 3.28 x to - l oc 1 for a. the coefficient of thermal expans ion . Ir th e revised Co rm is used, along with the val ues given in Table 1 for the o lher paramelers. a valuc o f 3.40 x 1Q- ' oC 1 is obtained. This fiu published value~ for olivine (Skinner . 1966) a s weil as does Parso ns and Sclater 's estima le. The subs idence a nd heat flow determined for o ur model mid-ocean ridge wi th the parameters given in Ta ble 1 is com pared with the empirical curves o f Parson~ and Sclmer (1977) in Figure 3. It is important not to pick the model pa ramcter~ cas ually. A s mall c hange in the c rustal parameters c an have a relatively large effec i on the ini lial "faull bounded " subsidence. a s can be seen on Figure 4. The range of crustal d ensi tj e~ c ho sen by various învestigators range (rom 2,78 glcm J (Le Pic ho n. Sibuet . in press) 10 2.9 glc m l ( Royden . Keen . 1980). This smaJJ d ifference c hanges the ctllcu lated "fa ult bound ed" su bs idence by 700 fi l fo r ~ = 2 and by over 1 km for ~ = 4. S imilarl y. various investigators have used crustal thiekness of 30 o r 35 km . causing estima tes o f the initinl subsidence to vary by 600 m (or ~ == 2 and 900 m for j3 == 4. The parameters used in th e modelling (Ta ble 1) we re chose n give an internally consistent. isostaticalJ y balanced system. Values of 2.8 g/cm l a nd 3.33 glc m J were chosen fo r the O' C densities of the CruS I and mantle respeçtively and a mid-ocean ridge crest. dcfined as a 5 km th ick cru st under 2.5 km of water, und e rlain by 1.333°C man tle. was c hosen as a rcference Îsostlllic se c tion. This implies that. for a 125 km thic k lithosphere and a linea r thermal gradi e nt , the pre-extension continental crust, ass umed 10 be al sea leve!. has a thickness of 31.2 km. 10 Table 1 Values of mudd puram~lt'r~ P.. rameter Symbol Value lithosphcric thickness continental crustal thicknes, crustal dcnsity (ifC) mantl ... densilY (O' C) walcr dcnsily çoeffiçicnl of thermal exp:lnsion aSlhenospheric temperalure thermal diffusivit y thermal condUcl ivity t l, p, Po p~. 125 km 31.2 km 2,8 Slcm' 3,33 t:lcm ' 1,03 g/cm' k 3.40 x tO "'c 1 33J"C (ide:l]) t 350' C(Sheba Ridge) .(IOS cml/,cc k .0075 cal/deg c m sec (l T! APPLICATI ON OF DIFFUSE EXTE NSION MO DE L TO TH E G ULF OF ADE N The Gulf of Ade n is a yo ung oceunie basin formed by the rifting of Arabia away (rom Africa ( Fig. 5). I I posse sse s a steep continental margin. small ab yssal basins and an a ctive mid·ocean ridge s pread ing cente r (S heba Ridge) c haraclerized by rough topography. a rift valley and fra ctur e zones. Riftin g beg:.n 20-25 m.y.b.p, in the late Oligocene or earlies t Miocene ( ~omal!land U il Explo ration Co .. 1'11:$4 : Azzaroli, Fo is, 1964 ; Beydoun , 1966) and Ihe o ldes t magnetic anomaly over Sheba Ridge is Anom:tly 5 (1 0 m.y.b.p,) (La ughton el al., 1970; Cochran. 1981 ). Of particular Înlcrcst 10 this st ud y i~ Ihat Iho::re b a n ar<!u !lpproximately 80 km wide belween Anomaly 5 and the coast , much of it deep wateT (Fig. 6). in wh ich the magnelic field is eilher fiat 1 h,we also sJîghtly modified the expression for Parsons a nd Sclfller's (1977) pflmmeter C l' whic h gi ves the total thermal expansion of the lithosphere at the mid-ocean r idge . The y assume th at th e asthcnospheric dens it y is iden lical 10 Po' the O"C density o f manlle malerio\f. In fact. fo r Po = 3.33 glcm j • the densi ty al l ,333'C will be 3. t8 gh:m l . which is signi fi cantly different. The revised form for C, is 2(p<>{l Po tu: T , a T ,) P.. )· " EliT FLOW Figure 3 Hi'ai f1"w ,,,,d d.".uûrm us li flUlctitm of li",e fo, • Il,,, n!vdd ",id·m'l'dll rid/{f uSI'd in l/lis slIIdy. rompu'cd ,,'ilh Iht l'tl/f};'icM rltr"t)· vf PI/n'VI!S il/Id Sr/ote, (1977). M odl'l rid/{e cr/!SI ('OIlSiSIS of ........ _ 5<10", '''1 /l" '" km a/ut (li! /I.Wht'JUllplle'e (1/ I.JJJ<C A li'!I?a, /I!rmwl /{'udit'III ü uuu", ,'d i" Il,,, rr/MI of Il,e ,id!:c cresl. _ 1/ .{ '. , , , ••0 Figutj: 4 1/!illal . "feulll" bmmded --- -------" , , ., ' , , • " , 158 ., ' , , • subsid~nre os i l fl mct;on of 13 fur "arjous '·l.Imf"S /lf rms· /allhidm~ss (A) ,md crus/al densily (B ). Shadtd /lre/l rep'esenl.i ran;:.'/! of .'nilles ustd b)' "UriOIlS in" I'Sligalvrs. Da)'''td /jllt ;n (b) r~prtsetJlS l'olue of 2,81irm l and 3/.2I1m lIud in lhis sllldy. - PRE-SEAF LOOR SPREADING DEVELOPMENT OF THE GULF OF ADEN Gu lf of Aden Bolhymelry in lallloms TopaIlraphy in leel (COII'O"" oJ,., l""91"011 " '" 0970 ) Figure 5 Loca/ion and ba/hyme/ry of the Gulf of Aden. Wide rulinR marks orea shol/ower rhon 1,000 lo/honts. Fine rulinR marks areos deeper rhan 1.OOOfa/homs. Borhymetry is alter LauRhton etai. (1970). S/udy art!u is Qu/lined. • ""...... ""• ~ _-_., _ . .... so,o ... so'........" ...... LIoo • .. ...- ... ~.-. a-oz...._, DS . D.~ f .. 50" '_Z.... + -, o Fillure 6 u Bathyme/ric und tec/ollic chart of the eos/em portion of th e srudy ureu. Bmh ymtlric C(Jr, /(mf.r ure ufler Laughton (unpublished). llIudilied by additiollol dlllo shawn us fine dou. FWCfUU lu ne ulld nWJ,:nelic anomaly idelll,jicmions are .. f/er Cac'lIron (1981). 159 J. A. CQCHRAN Soi ..... ~.".CI'" ..... .... '. ..',"..'.... ". FiGure 6 b Bul hymelric alld uctmrie clrart of Ih~ ..·ts/~rn portion of /ht sl udy artu. Bathymelrie COlltaurs art af/tr l.aughlOlI (u llpublishtd), modi{itd b)' addiliollal da/u sIIO"'n as {i1l~ do/s. Frac/urt =ont und rnu,llntric allomal)' idtnll{i~a/iQ/u art a/ur Cochrun (198 1). or consiSls of .. nom:llies whit'h cannot be correlated over d istances gre ater than about 20 km . The nature of this "magnetic quiet zone'· is obviously of greal importance, s ince it is situaled between the demonstrably oceanic crust of the Sheba Ridge a nd demonstrably contÎ nen tal crust on lohore and is separaled from both by disti nct boundaries. The landward boundary is an esearpmenl made up of a series of nor mal faults, and which extend from 2-3 km bclow sealevel to 1,500 m above sealevel. The.c;e esearpments whieh are round ail a long both sides of the Gulf of Aden are probably cquivalent to the ·· hÎnge zo ne ·' round at mature continental margin~ (J !In S!l, Wade. 1975). T he sea· ward boundary is an increase in depth of a fe w hundred meters 10 a lmost 1 km, which is found about 10 km land ward of Anomaly 5 (Cochran, 1981). The quiet zone is characlerized by moderately rough lopography al a Cairly constant depth withou t the topographie grad ient of a mid-ocean ridge fCochran. in press (Fig. 7)). It has a helerogeneous c rustal struc ture and, where Moho depths have been determined (Laughlon. Tramontini. 1969). the crus tallhickness is s lightly greale r than that of Sheba Ridge. l n previous studies which have utilized the "~Ire t c hing ·· mode!, the subsidence hilolOry as determined by da ta from exploratory wells has been used as the major const raint on Ihe modelling (for example . Sclater . Christie. 1980 : Steckler, Watts, 1980 : Royden, Keen. 1980). S inee the G ulf of Aden is a ··stltr ved " margin. s uc h s ubsidence data is not available and other conStraÎnts must he used. Total motion belYief!n Arabia IInd Alrica Cochran (1981) eSlimated th:.t 80 km more mOlion has occurred betwee n Arabia a nd Africa in the Easte r n Gulf of Aden {han can he aeco unted for by the seafloor ~ preading magnetic anomalies. This estima te is based on the 105 km of motion which has occ urred a long the Dead Sea Rift (Quennell. 1958 ; Freund n al .. 1970) and a n estimate o f 30 km of ope l'li ng in the Gulf of S uez. This estimale was d iloc ussed by Cochran (in press) who eoncluded {hal whi!e 80 km WII S probably Il good '·belot e~tÎmate'·. the non seafloor s preading opening could vary from 45 10115 km without contradicting any observations. allhough it is more likely 10 he near the center than the extremes of that range . lit ai floYi Seven heat flow s tations we re occupied in the Eastern Gulf of Aden during Vema crui.c;e 35 in 1978 along two lines from the magnetiç q uiet zone onto Sheba Rid ge (Table 2). The 160 PRE-SEAFLOOR SPR EAOING DEVELOPMENT OF THE GULF OF ADEN QUIET ZONE EASTERN GULF OF ADEN location of Ihe stations is s hown in Figure 6. The heat flow measure menlS in the quiet zone are generally high , and indicale a high temperature i radie nt and relative ly thin lithosphere. The measuremenlS are in the range of wh,lI would be expected fo r 15 1024 m.y. 011.1 seafloor. usi ng Parsons and Sclater's (1977) age-heat fl ow relationship. The measureme nts were oblained with a multipenetration appa· TalUS. so that severa! measuremenlS approximately 1 km apart were made at each station. The small scaller in the meas uremenlS at each statio n indicates Ihat Ihey are representati ve. The env iro nme ntal evaluatio n {Table 2) is based on the system of Sclaler et al . (1976). Il was ass umed in Ihe model calculatio ns Ihat the heat flow in Ihe undisturbcd continenlal crust is 58.5 m w/m 2 (1.4 h.f.u .) based on four val ues obtai ned from bottom hole temperatu res in wells in Northeastern Somalia (E va ns, Tammemagi, 1974). Il was also assumed Ihat Ihe heal flow from the as thenosphere is 33.4 m w/m1 (0. 8 h.f.u.) (Parsons, Sclaler. 1977; Lachenbruch, 5as5,1978), with 25.1 m w /m 1 (0.6 hJ.u .) contributed by rad ioacti ve elements in the conti· nental crusl , and that the mdioactive elements are uniforml y dis tri buted through the crust. 50 that the ir cont rÎbutio n 10 the heal flow is inve rsely proportionallo crustal thickness. V3!H8 V ~ I~ • 1 1 ,,,.. VJ~·09 • • ! ... ", • Present basemenl depth Alt hough the lack of sediments prevents determ inatio n of the subsidence his tory of the Easlern Gulf of Ade n. one point of the s ubsidence curve, the present basement depth . can be dete rmined. Sediment thickness and seismic velocÎlY information fro m Cochran (in press) were used to obtain base ment depths in the Eastern G ulf of Aden. The sediment was then removed , and the basement allowed to respo nd isostalically resulling in the basemenl depth shown in Figure 8. ln preparing Figure 8, basement depths were Figu re 7 Seismic rtf/retion profilrs from Iht Ea.llun Gulf of Aden. Hea~y ~rrtlcal UntS ma rk Iht bounda ry btl"'un Iht Shtba Ridgt f/ank ond Ih r magntlic q uitl tont. Shtba Ridgt rifl "allly con bt sUn in prof/lu VJ! -OB. V35-09 and V35-1O. Profi/ts tnd 10 mi/ts (37 km) from shon. Table 2 Vtm/l J5 Iif/ii SUl/ion V353· 1 /10'" JWlio 'l s flil 1 2 ) V3.S 4-2 1 2 , ) V35 6·4 1 2 ) V357·5 1 2 ) Vl5 &-6 1 2 ) V3.'l9-7 1 2 ) V35 10-8 1 2 ill the Gillf Luliludt 14°32.9' 14"30.8' 14"29.7' 14"21.9' 14"22.2' 14"22.5' 14"22.3' 13· 54.4' 11"54.6' 13°56.2' 11"26.4' 13"25 .6 ' 13"25.4' 1)°08.9' 13"08.2' 13°07.8 ' 12"58.6 ' 12"58 .0 ' 12' 57.4 ' 12°42.1 ' 12°4) .4' 0/ Ai/tn LOIIJ.:Ï1udt SO"30.H' 50"31.7 ' SO"32.6' 50"26.9' 50"27.) ' 50"27.6 ' 50"27.7' 50"14. 1' 5<M).O' 50"13.0' 47"51.9' 47"50. 1' 47"411.11 ' 47"37.8' 47"36.6 ' 47"35.7' 47"27. 4' 47"26.6 ' 47"211 .11 ' 47"29.1 ' 47"29.11' Dtplh (ml l .n6 1.874 1.914 2.001 1.992 1.984 1.998 2.460 2.457 2.455 1.912 1.932 1,930 2.0·12 1.971 2.011 1.880 1.856 1,1154 2.193 2.202 Sedimtnl thickntss stc.lm 1.5 1.700 1.6 1.1165 .6 ''''' 1.0 1.080 A' '10 .S> 520 ., '" 16 1 N .T. ,, ,, ,, ,,, ,, ,, ,,, ,,, ,, Enl'iron . tvo/. A A A A A A A B " B A A A A A A B 0 B D 0 Gr/lditnl . 102 .11 9 Cflllducti.'ily .Im'C .938 .112 .126 . 116 .1111 .125 .155 .163 .143 .123 . 123 .12 1 . 128 . 119 . 1)2 .1,. . 146 . 147 .178 . 182 .938 .938 .934 .,.. .934 .934 Q m ..·/"r 95.7 111 .6 105.t 11 8.2 l08.M 110.7 117 .3 145.4 152.9 134. 1 114.9 114.9 112.1 119.6 111.1 123.3 127.0 136.4 137.) 166.3 170.0 J . R. COCHRAN Figure 8 tI SmIHJl h~d . btll·tm~nl dtpllrs in Ih/,' l'Qstem ponÎon of rhl' sfUdy arl'U (uluT C /KhTtln . in IIf~U). C/J nWIlTS liTt În ml'rt'TS. i"." ~·~"~=="""""",,~"F=.................. avcraged over a hour of ships trac k (about HI km) to smooth o ut the locli i rOllghne~~ and make the General !evcl more e videnl. Va riatio ns ln r idge crest d epth ." T ." ; LJ - T hcre is anothc r d ifficulty with mode! calculations in the G ulf of Ad en, and perhaps also Ilt o t her margins such as those in the North Atlantic, where the adjacent mid·ocean ridge has significant varia tions in ridge crest d epth. Specifi. ca11y, the model was cal ibrated using a mid-ocean ridgc c rest depth of 2.500 m, which is the worldwide standard (Parsons. Sclaler , 1977). w hile the ridge crest depth on Sheba ridge is about 1,800 m in the eastern portion of the study area and about 1,300 m in the wes tern portion (Fig. 6). The shallow ridge c rest depths are the rcsult of a generlll s hallowing o f the Gulf of Aden loward the Afar hot spot. The ridge crest dep t h decreases from about 2.500 m tO sealevel in Afar. The gravit y fie ld does not reflecl this shalJowing (Talwani . Kahle . 1975 : Cochran, in press) and both heat flow values on the ridge flank and s ubsidence away from the ridge crest are close to the values predicted by the empirical curves o f Parsons and Sclater (1977). The average unloaded basement depth in the magnetiç quiet zone al liO vary from East 10 Wes t (Fig. 8) with depths of about 3.200 m round eas t of Fracture Zone C and 2,5002.600 m round west of FraclUre Zone F. Thus the depth of the quiet zone below the ridge crest remains constant a s the rid ge crest shaJlows. Cothran (in press) considered severa! methods of modelling the shallow depths . and concluded that the most satisfactory is to slightly inc rease the thermal gradient in the mantle down to d epths of several hundred kilometers. This model whjçh was suggested by Zielinski (1977 ; 1979) to explain ." ~ Figure Il h SmlHJ/lted un/utldl,'d ba stml'n/ deplhs in Ihl' ..·tSIUn p ortio n 01 thl Sil/if)' arf a (aIrer CochrQn . in prl'S5). Coltlour~ are in m~I~n. '62 PAE-SEAFLOOA SPREAOING DEVELOPMENT OF THE GULF OF ADEN A shalJow depths in the Nor wegian-G reenland Sea, res ults ln shalJow depths wÎtho ut significanlly altering the ridge s ubsidence rate or heat flow. Thus it is assumed that as the Afar hot spot is approached, the thermal gradie nt in the mantle becomes progressively steeper. In the Eastern Gulf of Aden. it is o nl y neceiisary to inc rease Ihe temperalUre at 125 km by 20"C. PRE-RifT MODEL CALCULATrO NS ·i~~4 Profile V35 -10(Fig. 7) was c hosen as a typical profile across the magnetic quiet zone for modelling purpoiies. This c hoice was based on the faci that it is nearly paralleJ 10 the fl ow lines weil away from fractu re zones, has a clear magnetie pattern and is less Ihan 15 km from the heat flow stations on profile V35-11 , so that Ihey can easily be projected onto il (no usable magnetic or seiiimic renection data are available from profile V35-t l ). The bathymetric profile was continued onto shore us ing Ihe Saudi Arabian Ministry of Petroleum and Mineral Resources topograp hie map of the Arabian Peninsula (US Geo[ogica[ S urvey, 1972). • ,. The three model constraints discussed in the previous seClion should be adequate 10 tes t the crus lal extension model and, if it proves satisfactory , to define t he behavior of the lithos phere dur ing Ihe pre-seafJoor s preading s lage of ils de velopment. The basement depths are dete rmined by a combination of s ubsidence due to c ruslal thinning and uplift due to thermal ell:pansion caused by heatins due 10 lilhospherie Ihinning: Ihe heal fl ow is primarily determined by the lithospheric Ihinning : and we have limits on reasonable amounts of cruSlal extension. Thus the a mo unt of crus lal extension and lithospheric thinning can be varied 10 matc h the observed unloaded basement deplhs, and the heat flow and c rustal ell:lension constraints used to determine whether the val ues oblained are reasonable. ,. ·I~ ~ • " l " ., " ~I ~ u' _ _ 1 1 - L...!!....!" .., Figure 9 10 .,. Model for Ih e developmen/ of Ihe cunline" ",1 margin in Ille Gulf of Aden /Ising sire/('hing model. A 725 km liliek Iilhosphere Wilh a 31.2 km Ihiek eruSI (A)is t:lunded as .d'l'''''' in Ihe Jowerpart o[(B). Fine lines show "boxes" uud in modet ealelllOlions. Numbers show ~ values for crusl und li/hosphere. Upper diagram of (8) sho,.,! morph%gy o[ Ihe rifl ~alley 01 Ille en d of the ex/tl/sion plJllse. A mid-ocean ridge is assumed 10 de"e/op ill Ille eenlerof IIII! rifl .'ulley (dashed /ine). DISCUSS ION The res ults of the model calculations are s hown in Figu res 9 a nd 10. Figure 9 s hows the amounl of pre-seafloor s preading extension and Iithosphe ric thinning across the G ul f of Ade n rift at the lime of initiation of seafloor spreading. Figure 10 shows the situation 10 m.y. later, and compares the caJcuJated res ults with those observed in the Eastern Gulf of Ade n. It can be seen in Figure 10 that the "stretChing" model is capable of explaining the observed deplhs and hea t fl o w. However, a great deal of ell:tension is required , primarily within Ihe deep portio n of the magnetic quiet zone. The lotal amount of ell:lensio n ac ross the 280 km wide rifl in Figure 9 is 115 km. 95 km of which occurs in Ihe deep central 120 km of the rift. The amount of exte nsion req uired in this region implies cruSla[ thicknesses of 5.2 10 7.8 km , wh ich is only slightly grealer than the thickness of oceanic crust in the model , a nd s lighlly less than the observed c rus tal thickness of 7.2 to 9.7 km (Laughto n. Tramontini. 1969). The observed crustal thickness ca n he used to pUI a n upper bound on the amount of ell:tensiOn t ha t has occurred in the quiet zone. If an average crustal thickness of 9 km is assumed, then fi value o f 3.5 is implied for the parame ter 13. a nd the tolal amo unt of extensio n occurring wilhin Ihe deep, central 120 km of the rift valley in Figure 9 is 85 km o r 10 km less than deduced above . It should also he remembered t hat Ihis represents a ma ximum estima te as the average crustal Ihickness is liable to he greater than that deduced from the Ihree stations whieh recorded mantle arrivais (Talwani et al., 1979). The s imple "strelching" model appears to require slightl y more extension t hlln can he reaso nably accounted for from geological and geometricaJ arg ue ments. There are, however, several factors not acco un ted for in the model which would result in a n overeslimate of the a mo unt of extension. One factor. whic h was mentioned above. is the fact that the model assumes tha! the extension occurred insta nlaneous ly , while in reality it occurred over a period of 10-15 m.y. in t he Gulf of Ade n. The efrect of a finite time of extension is to tmnsfer pa rt of the subsidence from the post-rift to the syn-rift stage of development whic h, for times Ilot too long aft er rifting, will result in grealer basement dept hs than predic ted by the instantaneous mode!. The effecl of a finile ell:tens ion time on the basement depths can be invesligated us ing ;In error funclion formulatio n and constanl ell:lension rates (Haxby. in prep.) with the result Ihal if the ell:lension is assu med ro occur over a period of 12 m.y., the ins tantaneous model predicts depths that are about 250 m too shal low al 10 m. y. alter Ihe extens ion ceases for values o f t3 grealer than abou t 2. Thus. in Ihe dee p part of t he quiet zone, less extensio n is necessary to produce the observed basement deplhs a nd the 13 val ues of 4, 5, and 6deduced for the centra l Ihree "boxes" (Fig. 9) can be reduced to 3.4, 4 a nd 4.8 respec tively . T his reduces Ihe average 13 in the deep quiet zone from 5 (400 % exte ns ion) 10 aboul4 (300 % ell:tension). 163 J . R. COCHRAN HEAT FLOW :.~. ., , œ , , •• "• 1 1 1 OOSERVED DEPTH 1 UNLOAOED OEPTH 1 Figure 10 !~~---=:~.~ '~I ~&. -rl.-·----)(--: ! ~ oct:ANIC CRUS! 1 1 ' QUIET ZONE" - l '~'"· Comp(lrisou of model reStllls or 10 m. y. (Ifter initimion of uaflaor l prtading ... Itlr obse"'ed ,'alues fram tire Ea stem Gulf o{ Aden. Pre-uaflaar spreading exrensian is assumed as il! Figure 9. Solid heul {Io", Clm.·e givts model caJcul(l/i01l s and apen circlel oblU\'ed hem flo .... Solid circ/es f[il'tr hear fla ... corrected for Ihemtal blankeling. Ali meaSU ffm ents ar i'ach .</(/Iion are ...itlriu rhe circli'. Obsen'cd b(lume," deprhs m l profile Vj5-IO ...ere co rrected for si'dim enr laading la Rit·€" u"loadi'd depths. -~ However , another observatio n that can he drawn Crom this study is that in the gulf o f Aden. where scafloor spreading has been occurr ing for 10 m.y., wc are rcachi ng the maximum time at which information can be obtained concerning t he nature of the pre-seafloor spreading development of the margin , as transient effects related to the exact mechanism of rifting hlwc nearl y dissipaled. Ii is precisely the nalu re and du ra tion of this pre-seafJoor spread ing development of t he margin which is important in determ ining the mechanism and causes of rifting and the development of the oceancontinent transition. Il is th u5 imporrant to obtain data from the syn-rifl sediments when st ud yi ng the su bsidence history of the margin. These sed iments are, unfortunately. se ldom drilled. lt will nlso be im portant to s tud y the struct ure and tectonic processes at work in the few areas, 5uch as the No rlhern Red Sen, which presently appeaT to he in the pre-seafloor spread ing stage of their development. Anothe r fac tor which will result in an ovcreslimate of the amoun t of extension is that it is quite likely that part of the extension occurred t hrough diffuse di ke injection rather than ro ta lional fauhing. Volcanic ac ti vity within the quiet zone is indicated by the recovery of a 13 m.y . old basait at DS DP s ile 231 in the Southern Gulf o f Aden (Shipboard Scie ntific Pa rty , 1974). Extension Ih rough dike injection results in a diffcrent temperature dis trib utio n tha n the s tretc hing model (Fig. 1). with highcr temperatures found near the s urface. This heat is quic kly lost resulting in higher subs idence ra tes immedialely a fter the stretching episode (Royden et al .. 1980) , 50 that during thÎs time a lower i3 value is needed to produce a given depth. T hus, if the extension occurred entirely through d iffuse dike injec tion , at 10 rn.y . pos t extens ion, approximately the same depths and heat flow are obtained wilh a i3 of 3 as wil h a i3 of 4 us ing the "stretc hi ng" model. It is difficult to estimale the relative cOntribut Îo ns of dike injec tio n and rO lational fauhing to the fo rmation of the magnetic quiet zone. but if dike injection is a major component, the amo unt of extension requ ired 10 produce the obseTved depths, and heat flow is within the bounds set by geographic constraims and observed crustal thicknesses. We are thus able to state Ihat the diffuse extension model can explain the observed geological and geophysÎCal features o f t he magnetic quiet zone in the G ulf of Aden . Acknowledgements This work was supported by Natio nal Science Foundation grants OCE-77-20098 a nd OCE-79-19241. The ma nuscript was reviewed by A. B. Watts and M. S. Steckler. LamontDoherty Geological Obse r vatory Contribution Numher 3110. RE FERE NCES Chrl, lillnstn T. B.. Sch~eftr II.-U., Schünleld M. , 1975. Geology of Sout hern ilnd Central Afar. Eth iopia. in: Afar f:Hpre ssiolt of Ethiapia , ediled by A. Pilger and A. RosIer. Schweizerban. StutIgart. 259-277. 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