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Seamount Loading and Stress in the Ocean Lithosphere

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Seamount Loading and Stress in the Ocean Lithosphere JOURNAL OF GEOPHYSICAL RESEARCH,VOL. 85,NO. BI I, PAGES 6403-6418,NOVEMBER 1980 SeamountLoading and Stressin the OceanLithosphere KuRr Leunecr eNo S. M. N¡Kl¡oclu' Research School oJ Earth Sciences,Auslralian National University, Canberra 2600 Australia One of the principal arguments for large stress differences in the lithosphere comes from the modeling of the deflection of the ocean lithosphere under seamount loads. Most published models indicate maxi- mum stress differençes of 2-3 kba¡ per kilometer of deflection, and maximum values approach l0 kbar. Geophysical support for the elastic plate theory comes mainly from gravity, which requires a broad nega- tive anomaly on the flanks of theactual seamount, although these anomalies are not very sensitive to the density structure ofthe crust or to the density ofthe sediment fiIl-in or the extent ofthis fill-in. The stress in the plate, however, is sensitive to these parameters, and in consequence, gravity is not a reliable in- dicator of the stress stâte. The lithospheric flexure model has been examined in some detail to evaluate this stress dependence on crustal densities and rheology. The approximations inherent in the linear the- ory have also been investigated. The main conclusions are that the stress differences can be signiflcantly reãuced (l) by adopting a lower density for the sediment fill-i¡ than the usual 2.8 g cm-3, (2) by in- troducing a depth-dependent nonelastic rheology, and (3) by introducing large-deflection theory for the larger loads. For large loads, súch as Oahu Island discussed by Watts (1978), the maximum stress under the load can be reduced to about 2 kbar or less near the upper surface of the plate, and the maximum stressdiffe¡ences oû - ozzneed not exceed I kbar. The introduction of the nonelastic rheology results in a stress,temperature, and load duration dependence ofthe'apparent'flexu¡al rigidity; large loads, loads of long duration, or loads on a high-temperature lithosphere all result in a thinner apparent plate thickness than small loads, loads of short duration, or loads on a cool lithosphere, all.other factors being equal. INTRoDUCTIoN Evidence for a high finite strength of the lithosphere in a o The Hawaiian Archipelago and other seamoutt chaits geologicalsetting has come mainly from flexure calculations il,h¡vc,since the work by VeningMeinesz [1941], usually been of seamountloading and of the bending of the oceanplate at the ií.lntcrprete¿as being regionally rather than locally com- the trenches,but we will be concernedhere only with flexure model is usually tested f,pcnsatedfeatures, and thei¡ existencehas often been invoked former. The validity of the gravity Vening Meinesz, l94l; ¡,.l.rsevidence that the oceanlithosphere is capableof supporting agai¡st observationsof le.g., iìdeviatoricstresses that reach severalkilobars le.g., Walcott, Waus, 19781orgeoid height [e.g.,Cazenave et ø1.,1979, 1980¡' il1976l.The regional compensationis usually modeled as the Waus, 19791,but both observationsare poor indicators of de= it,elnsticsupport of the load by an elasticplate overlyi-nga fluid formation and evenpoorer i¡dicators of the stressstate of the f. mcdium[Gunn, 1943].These models typically indicate stress lithosphere. For example, the gravity anomaly over a sea- l:diflerencesof about 2 kbar per kilometerof deflection(e.g., mourt can be equally well explainedby a regional as by a lo- iì.llalcott [976]; seebelow), while the total deflectionmay at- cal compensationmodel ir which the depth of compensation ;1'Ininseveral kilometers. Watts et al. ll975l suggesta maximum exceedsthat of the regional model [e.g., Vening Meinesz, ;ii'dcflectionof about 2.5 km below the Great Meteor seamount, l94l], but the maximum stressdi-fferences in the two models i::whileWalcott U97Ol suggests deflections exceedi¡g 7 km be- will differ by as much as an order of magnitude. Only from i low the Hawaiian Archipelago.Hence stressdifferences of up other geophysicalobservations can a clear distinction be made I to l0 kbar are not uncommonin thesemodels and will occur betweenthese two models.There is usually little bathymetric at both the lower and upper surfacesof the elasticplate, which evidencefor the deflection,and this is attributed to any such lypicallyhave a thicknessof 20-30 km. If theseestimates, par- depressionbeing at least Partly filled in by volcanic material ticularly those at the lower boundary, where the plate is i-n and sediments.One exception to this is the flexure of the lension,are correct,they haveimportant implicationson both oceanlithosphere under the Hawaiian chain, where the posi- , the brittle and flow behaviorof the lithosphere.Laboratory tion of the outer arch is usedas a measureof the flexural pa- measurements,employing large strai-nrates and short loading rameter / deûnedbelow fWalcott, 19701.Another exceptionis . cycles,indicate that brittle fractureor signiflcantflow will not the observationof uplift of islands on or near the outer arch ' occur in the lithosphereuntil stressdi-fferences reach several and Menard, 1978].In both thesecases the deduced ' [McNuu kilobars,but the dìfficultiesof extrapolatiogfrom laboratory quantity is /, but the quantity of interestis the flexural rigidity ' to geologicalconditions are geûerally well understood [e.g., D, which is proportional to /4, and neither measurementswill Paterson,1976, lgigl. In particular, any deformation mecha- give a partiCuhily precisedetermination of D unlessthe den- nlsmoperative in the laboratory at a given temperaturewill sity structureof the load and crust is well defined.Seismic ob- lr probably become impofant at much lower temperaturesin servationsof the i¡creasing depth of the Moho le.g-,Furumoto ' gcologicalsituations: and anv additional mechanisms.not evi- et al.,19681or ofthe increasingthickness ofthe oceanlayer 2 dcnt under the laboratory ctnditions but which becomesig- fWootlard, 19701under the Hawaiian load have also been nificant in geologicalsituations, will only reducethe strength used as evidencefor regional compensation,although Suyen- , ot the material. aga ll979l has interpreted theseresults as indicating a com- t:.ç- ' is partly local and partly regional. On leave pensatiot model that : from University of Queensland, Department of Survey- its tng, St. Lucia 4067. Australia. In this paper we explore further the plate theory and geologicalapplication rather than add to an expandinglitera- Copyright @ 1980 by the American Geophysical Union. ture on flexural rigidity estimates'The elastic plate theory " Paper g0B0549. 6403 . number o¡ 48-0227/80/o8oB_0549$o r.oo fr fi:. 6404 LAMBECK AND NAKIBOGLU: STRESSES TN THE OCEAN LTTHOSPHERE goesback at least as far as the work of Hertz in 1884lHertz, the point of loading, the deformation w(r) can be readily ex- 18951,and early applicationswere by VeningMeinesz |9411 pressedin terms of zero-orderKelvi¡-Bessel functions as and by Gunn ll943l. The theory is well developedin the engi- neering mechanicsliterature le.g., Reisner, 1944,1946; Fred- -#"^lî) erick, 1956; Timoshenkoand Woinowsky-Krieger, 1959; Fung, ,(i): Qa) 19651and in the recentgeophysical literature by Brotchieand Silvester[969] and Brotchie[971]. Most geophysicalappli- where /o : D/p"g, / is the'radius of relative sti,ffness,'or the 'flexural cationshave usedthe thi¡ plate, small-deflectiontheory, even parameter.'The solution (2a) is equivalent to that though the computed deflectionsreach a signi,ûcantfraction given by Hertz ll895l. At the origin r : 0, of the elastic plate thickness.In the subsequentsections we (2) will addressourselves to (l) the thin plate theory, the w(A): -ql2/8D (2b) large-deflectiontheory, (3) the geophysicalapplications of this (4) the stress theory, the consequencesof seamountloadilg on The solution (2a) behavesas a damped sinusoidwith the sign in light statein the oceancrust, and (5) somepublished results of w changingabout every 4/ but with a rapid decreasei¡ the of the above analysis. maximum amplitudesbetween successive zeros. With the typ- ical parametersgiven in Table I the maximum negative w THIN PLATETHeony value, occurring at about 5/, is only abottt l.5Voof w(0), and The basicequation expressingthe deformationw(x, y) of an the next maximum, occurring at about 9.5/, is only O.4Voof elasticplate of flexural rigidity D, loadedat its upper surfacez u(0). Thus for a l-km downward deflectionat z : 0 the maxi- : -H/2 by q(x, y) is mum upward deflectionwill be only of the order of 15 m and will occur at about 5/ from the point of loading. In evaluating DYYw + p"gw: q (l) the Kelvi¡ functions for point or axisymmetricloads (seebe- where low) somecare needs to be taket in evaluatingthem when the argumentsare large, and we have found it convenientto use ü (t- when r,// exceedsabout 7. V: -* the asymptoticapproximations dx- dY Solutionsfor (l) take a particularly simple form for simple (see, Brotchieand Silvester The vertical coordi¡ate z is measureddownward from the axisymmetricalloads for example, density p, height å, and middle plane of the undeformedinûnite plate whosesurfaces [1969]).For a uniform disc load of < is are given by z : +H/2. Thus positive w indicatesa depres- radiusl the deflectionat r I sion, and negativew an upfft of the plate. Parameterp" is the the underlying fluidlike and g is gravity. density of medium, ,: * ., t* + c,B"t (3a) This equation expressesthe force balancebetween the surface nú[, (i (;)] load q, the elasticresponse ofthe plate, and the reaction p¿w of the substratumor the base of the plate, assumi¡g that
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