Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Solid Earth Discussions 20 km landward ∼ ort has been put into moni- ff 1002 1001 ¨ at Hannover, Callinstr. 30, 30167 Hannover, Germany ect the forearc region and the plate interface. The ff ect the seismic cycle of subduction thrusts. ff ¨ ur Geologie, Leibniz-Universit ect of glacial-interglacial sea-level ff This discussion paper is/has been under review for the journal Solid Earth (SE). Please refer to the corresponding final paper in SE if available. populated coastal regions.toring As the a seismicity beneath consequence, the much forearc e and the identification of parameters that may of 0.2–0.5 MPa and indicatedelayed during that sea-level rise. earthquakes Our are findingsglacial-interglacial promoted imply periods that during may eustatic sea-level sea-level have changes fallwere induced during large and displacements enough and to stress a changes that 1 Introduction Active faulting in subduction zones poses a serious seismic threat to the often densely during sea-level fall andfield, the landward sea-level changes during lead to sea-levelof variations up rise. in to the vertical 1.23 With MPa stressbeneath and and respect the the 0.4 shear coast, MPa, to stress respectively. i.e. theflexure. The in stress The shear the resulting stress area Coulomb variations where stress are the changes highest on sea-level the changes plate cause interface the are strongest of the order two-dimensional finite-element model of ainterglacial subduction sea-level zone changes to a investigatemodel how results glacial- show thatvertical a displacement, sea-level with fall thecoast. by maximum The 125 uplift uplift m signal occurring over induced by betweenof 100 the ka the the sea-level fall coastline. causes trench decreases to A up and zero which subsequent to the sea-level is 0.7 rise m again by of most 125changes m pronounced cause over in horizontal 20 ka the displacements causes of submarine subsidence, up part to of 0.12 m, the which forearc. are directed The seaward sea-level Combined seismological, space-geodetic andseismicity numerical at studies subduction have zones shown maytimescales that be of the modulated 1–100 a, by because tidesalter these and the changes glacier stress in fluctuations loads field on on in Earth’s the surface upper are able plate to and along the plate interface. Here we use a Abstract Received: 7 December 2011 – Accepted: 14Correspondence December to: 2011 T. – Li Published: ([email protected]) 21 DecemberPublished 2011 by Copernicus Publications on behalf of the European Geosciences Union. E changes on the displacement andfield stress in the forearc andinterface along of the subduction plate zones T. Li and A. Hampel Institut f Solid Earth Discuss., 3, 1001–1019,www.solid-earth-discuss.net/3/1001/2011/ 2011 doi:10.5194/sed-3-1001-2011 © Author(s) 2011. CC Attribution 3.0 License. 5 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | erent ff ect the stress ff ect on thrust and ff erent timescales. One ff 20 ka ago, the sea-level ∼ ect of these stress perturbations ff cient of 0.4. ffi ect the seismicity in subduction zones ff 1004 1003 -dipping plane, they calculated a change in the ◦ ect of eustatic sea-level changes on uplift and ff 125 m (Imbrie et al., 1984; Zachos et al., 2001; Peltier ects the vertically oriented maximum principal stress. ff ∼ ering from the background rate by a factor of 3 with the tidal ff 0.4 MPa, using a friction coe ∼ The results of the previous studies summarized above provide strong evidence that On the timescale of 10–100 ka, eustatic sea-level changes may a On the timescale of decades, the seismicity in subduction zones is influenced by fluc- subsidence of the forearc as wellresolved. as In on this the stress study, we alongzone the use geometry plate a to interface two-dimensional quantify remains numerical how un- level model the fall with forearc and and a the subduction- risethe plate model during interface respond setup a to anddisplacement glacial-interglacial the present and sea- period. the stress results fieldsseismogenic with In in part a the the of focus upper the following, on part platecycle we interface. the of of Finally, describe subduction induced the we thrusts. subduction changes discuss implications zone in for including the the the seismic Coulomb stress of faults in thethe upper plate part interface of –timescales. are a susceptible So subduction to far, zone changes however, – in the including ice e the and seismogenic water loads part on of di sea-level rise and thetions resulting in flexural coastal loading regions caused worldwide.on considerable To estimate major stress the plate perturba- e boundarylated the faults, resolved which shear were andThe normal results not show stresses included that for in the selectedthe their post-LGM faults Coulomb sea-level of model, stress rise known by they should orientation. and up have calcu- North caused to an Anatolian 1.5 increase MPa faultszone, in on which (Luttrell they the approximated and vertically by Smith, a oriented 15 2010). San Andreas, For Alpine the Cascadia subduction state of the crustcycle at that the culminated borders infall of the and ocean subsequent Last rise basins. Glacialand was Maximum During Fairbanks, (LGM) 2006). the last Usinging glacial-interglacial a a viscoelastic semi-analytical half-space, approach Luttrell with and an Sandwell elastic (2010) plate showed overly- that the post-LGM promoted small earthquakes on thrust faults (Sauber and Ruppert, 2008). cal records, modern space-geodetic measurementsthat and glacier numerical modelling mass revealed fluctuationsduced over considerable the vertical displacements lastthe and 10-100 background seismicity stress years of changes in theSauber that south-central and subduction have Molina, Alaska zone 2004). modulated (Cohen, in- ForAlaska, 1993; example, a Sauber in large-scale et the redistribution al., eastern ofated 2000; Chugach glacier with Mountains, ice a southern between significant 19932000). increase and in This 1995 finding the was was number later associ- cal and confirmed and size by glaciological a of data comprehensive earthquakes for compilation southern (Sauber of Alaska, et seismologi- which al., showed that rapid ice fluctuations normal faults than on strike-slip faultsand because hence the latter less are susceptible oriented to mostly the subvertical variable ocean loading. tuations in the mass ofet glaciers al., situated 2000; in the Ivins upper and plate James, (e.g., 2004). Cohen, 1993; A Sauber combination of glaciological and seismologi- 1995; Kasahara, 2002; Cochran etdistributed al., high-magnitude seismic 2004). events, After Tsuruoka statisticallyfault et types analysing al. normal (1995) 988 faults concluded globally are thatthe most of susceptible all periodic to ocean tidally triggeredBased loading earthquakes on a because the analysis ofshowed earthquake that data from strong 1977–2000, ocean Cochranrate tides et of al. can (2004) earthquakes also later di triggerstress. shallow They thrust concluded earthquakes, that with the the tidal stress changes have more e of the first parameters thatwere was the recognized to ocean a tides.already The put hypothesis of forward ocean byin tides Nasu 1930. as et a al. Since triggercurrence (1931) then, of has after earthquakes a been was an positive documented correlation earthquake by between many that studies ocean hit (e.g., tides central Shlien, and Japan 1972; earthquake Tsuruoka oc- et al., modulate the frequency and magnitude of earthquakes on di 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 20 km landward of the coast. Dur- ∼ 1006 1005 ner, 2006). This model step is carried out using a vis- ff ected by the sea-level changes. In the control run without ff ect of sea-level changes on a subduction zone, we use a two- ff ect of the sea-level fall and rise on the upper part of the subduction Pa s for the lithospheric mantle. Afterwards, the continental plate is ff 23 10 × During the final model step, the falling and subsequently rising sea level during a respectively, are barely a sea-level changes, no vertical displacement occurs. zone rises by upregion to at 0.7 point m F. (Fig. Thedepth 2a), displacement and induced with landward by the whereing the uplift it the sea-level diminishes maximum fall subsequent to occurring decreases sea-level zero riseplate in both between with subside the 20 forearc by ka and uptemporal 0 to a, evolution 0.7 of the m forearc the owingthe and vertical to the points displacement oceanic the located at increase closestand points in to subsidence, P0–P4 the the whereas (Fig. ocean water points 2c) floor load P3 shows (P0–P2) (Fig. and that experience 2b). P4 the located The strongest at uplift a depth of 15 km and 20 km, figures. 3.1 Vertical displacement During the sea-level fall between 120 ka and 20 ka, the upper part of the subduction 3 Model results To analyse the e zone, we extracted the changes inthe the stress vertical field and horizontal from displacement the as model.of well these In as addition in parameters to through cross-sectionsF time of the will being model, also located the be evolution inthe shown the at plate submarine six interface selected part andFig. points, one of 1a). with point the point Note positioned forearc, that 360 four km the points seaward model (P1-P4) of time located is the shown on trench as (P0) time (see before present in all subsequent the plate interface is keptplates. locked, i.e. For no comparison, relative displacementlevel we occurs changes also occur. between calculated the two a reference model run, in which no sea- sea-level rise by the same amount over 20 ka (Fig. 1b). During these sea-level changes Fairbanks, 2006), we assume a sea-level fall by 125 m over 100 ka and a subsequent as well as the followingtion steps is are not computed as considered.sea-level a variations static occur As analysis, in the i.e. theto displacements viscous uppermost the deforma- and part thickness of stress of the the changesthe model plates, vertical resulting and the and are from two horizontal small the vertical directions compared to model facilitate sides the and calculation theglacial-interglacial of bottom cycle the is are model. simulated fixed by in changingter the pressure body. applied Based on top on of the(Imbrie the wa- global et sea-level al., curve 1984; derived Chappell from and the Shackleton, oxygen-isotope record 1986; Zachos et al., 2001; Peltier and added to the modelplate domain interface. with In the the contacttogether same between represent model the an step, ocean two a with plates a waterthe representing average body oceanic water the and depth plate of and a 5000 the pressure m,to continental are (Fig. 6580 added m. margin. 1a), on In At which top the the of third trench, model the step, water isostatic depth equilibrium increases is established. This model step tinental plate consisting of70 a km-thick 15 lithospheric km-thick mantle. upper Thestrain crust, model elements a domain with 15 km-thick is a lower meshedthe maximum model crust using edge are triangular and length given plane- a in ofin Fig. 1 1. Fig. km. 1a, To obtain The we the perform rheologicaldownflexed geometry to the of parameters take following a of into steps: subduction account zone First, theet as the bending depicted al., stresses initially in 2001; horizontal the oceanic Hampel subductingcosity plate plate and of is (cf. Pfi 1 Buiter To quantify thedimensional e finite-element model created withsion the commercial 6.11). software ABAQUS The (ver- modelinto consists a 8 of km-thick a crust 1500 and km-long a oceanic 72 km-thick plate, lithospheric which mantle, is and subdivided a 1000 km-long con- 2 Model setup 5 5 25 20 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | be- xz τ and the shear stress x σ 1008 1007 ect the style of deformation in the accretionary ff , the horizontal stress z σ ected is larger and located in the forearc beneath the ff is highest (0.4 MPa) beneath the coastline and in the vicinity of xz 12 m/ka (e.g., Peltier and Fairbanks, 2006), increases the rates of τ ∼ ect of the sea-level variations on the stress field, we extracted the ff ect the region seaward of the coastline (Fig. 4a, b). Changes in the horizontal ff 30 m/ka, as shown by U/Th dating of corals (Bard et al., 1990). An additional factor ∼ The displacements caused by unloading and subsequent loading of the oceanic plate and the forearc are associated with changes of the vertical and horizontal stresses plate is the transporttion of in sediments the from forearctransport the region and continent and deposition to the in the the trench.Slaymaker, 1989; oceans ocean Hebbeln have After and et increased glacial their al., considerably 2007; periods,sediments (e.g., deposi- Covault would Church the et further and rates al., increase 2011). of theby flexure The sediment studies induced additional by of loading the by the rising Cascadiainput sea and was level. Chilean As probably convergent shown high margins,prisms enough the (Bourgois to postglacial et a sediment al., 2000; Adam et al., 2004). and 5 ka at a ratesubsidence of and landward movement bytervals a in factor the of late two, Pleistocene, respectively.of the For rate short of time sea-level in- risethat even reached may maximum values further enhance the postglacial subsidence of the forearc and the oceanic and landward movements occur (Fig.est 5b). values (up The to vertical 0.7with displacements m) depth reach in the (Fig. the high- 2). upper0.12 10-15 m), Although km the the of region the horizontalcoastline two displacements that (Fig. plates are 3). is and relatively In a decrease smallof our rapidly the (up model, we sea to used leveldisplacements a over of simplified 20 0.035 ka, sea-level m/ka curve which and with 0.006 resultsical m/ka, a in evidence respectively. linear Taking indicating maximum into rise account that rates geolog- the of post-LGM vertical sea-level and rise horizontal occurred mainly between 15 Our model results indicate thatfect sea-level the changes displacement during and glacial-interglacialthe stress cycles upper field af- part in the ofand forearc, seaward the along movements downgoing the prevail oceanic plate (Fig. plate. interface, 5a), and whereas During in during a sea-level rise fall subsidence of the sea level, uplift 4 Discussion and conclusions point P3 (Fig. 4e,and f), subsequent i.e. bending in in the response area to that the experiences changing the water strongest load. flexural unbending value of 1.23 MPa, whichmarily is a equal to thestress magnitude of reach the a applied maximumrine water value load, part of and of 0.75 pri- the MPa forearcIn and and contrast are on to most the the pronounced platesea-level vertical interface in fall, and in the i.e. the horizontal when subma- vicinity stress, the ofregion the model landward point shear of region P2 the stress (Fig. seaward coastline increases of 4c, (Fig.shear during 2a), d). the stress and the change coastline decreases rises during the relative sea-level to rise. the The To illustrate the e changes in the vertical stress tween 120 and 20concert ka with (sea-level the fall) and changingfall and from water increases load, 20 during to the sea-level rise. vertical 0 ka stress The (sea-level vertical decreases rise) stress during (Fig. changes sea-level have 4). a maximum In directed seaward (Fig. 3a),rise whereas (Fig. landward 3b). movements occur Alongpoint the during P3 plate the interface, (Fig. sea-level the 3a,during highest the b). horizontal sea-level displacement fall, occurs This whereasdistance at it implies between increases that P3 during and the the sea-level P4the distance rise. increases sea-level between rise. In during contrast, P3 the the sea-level and fall P1 and decreases decreases3.3 during Stress changes The horizontal displacement (Fig. 3)imum induced by value the of sea-level changes 0.12 m.part reaches a of The max- the forearc, highest beneath horizontaloceanic the displacements lithospheric coastline occur in mantle. the in vicinity During the of the submarine the plate sea-level interface fall, and the in the horizontal displacement is 3.2 Horizontal displacement 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | τ ∆ , with n σ ∆ 0.1 MPa. µ 20 km. With re- 15 km (Fig. 6d). ∼ ∼ – ∼ the normal stress τ 0.3 and 0.4 MPa for n σ = ∆ µ = ∆ C ∆ cient of ffi cient and ffi ects the entire lithosphere. It diminishes ff 30 km landward of the trench and near point ∼ 1010 1009 the friction coe µ 0.1, respectively. In contrast, a sea-level rise reduces = cient we used values of 0.1, 0.2 and 0.3, respectively. ffi µ ect the deformation in the forearc and the state of stress ff We thank R. Hetzel for critical comments on an earlier version of the 0.3 and 0.22 MPa for = 0.1 Beneath the submarine forearc, the Coulomb stress is increased by 0.46 MPa µ In conclusion, our two-dimensional finite-element model shows that sea-level The part of the plate interface that experiences the most pronounced displacements = the plate interface may beFuture promoted, modelling whereas will it be may neededand be to stress delayed assess by the changes a order inducedtional rising of by magnitude loading sea sea-level of level. by variations the enhanced displacement ifinterseismic late-glacial deformation viscoelastic sediment of deposition deformation, the as addi- upper well plate are as takenAcknowledgements. coseismic into and account. manuscript. Fundingframework was of provided an Emmy-Noether by fellowship the granted to German A. Hampel Research (grant Foundation HA 3473/2-1). (DFG) within the the Coulomb stress (Fig.This 6f), implies that with the the occurrence of minimum earthquakes values is occurring delayed duringchanges beneath a may the rising be coast. sea able level. along to the a seismogenic part of the plate interface. During sea-level fall, seismic slip of being the shear stresschange. change, For theThe friction results coe show that sea-level fallbetween increases points the P1 Coulomb and stress P4 onfalling (Fig. the sea 6e), plate level. which interface The implies highest thatwhere increase earthquakes it in are reaches Coulomb promoted a stress by value occurs a ofµ beneath 0.55 the MPa coastline, for a frictionfor coe on inter-plate faults haveand been Anderson, inferred 1975; to Hanks, 1977; belevel Scholz, of variations 2002), may the the ultimately stress order changes bezones. of induced able To 0.01–10 by evaluate to MPa sea- the promote (Kanamori impact ordetail, of delay the we earthquakes sea-level variations in calculated on subduction the the plate change interface in in more the Coulomb stress 30–50 km depth (Hyndman and Wang, 1995; Stern, 2002). As coseismic stress drops seismogenic plate interface, which typically extends from a depth of a few kilometers to P3 (Fig. 6b). During thedecreases sea-level by fall, up the to resolved 1.2 normal MPalow stress beneath part on the of the submarine the plate part plateSimilar interface of to interface, the the whereas forearc, vertical it i.e. displacement, in increases theP4. changes the during The in shal- the change normal in sea-level stress rise the diminishthe resolved toward (Fig. point shear coastline, 6c). stress where on the itBeneath plate most reaches interface of has a the a submarine peak value beneath forearc, of the 0.32 change MPa in at shearand stress a stress is depth changes of in the model coincides, in nature, with the upper portion of the between the trench, i.e. pointspect P1, to and the point vertical P4 displacement,uplift located the or at profile subsidence a shows of depth thatvertical 0.58 of the m displacement sea-level in decreases changes to the cause almostdisplacement shallow reaches zero part the at highest of point values the P4. plate In interface contrast, (Fig. the 6a). horizontal The the region below thestress coast is experiences consistent the with the strongestSandwell, results variations 2010), from of which semi-analytical showed flexural vertical that modelling andvariations the (Luttrell are shear flexural and stresses highest induced near by the(2010), eustatic coast. who sea-level In approximated contrast the to Cascadiaour the subduction model study thrust setup by by Luttrell allows aalong and the plane to Sandwell convex of analyse contact constant between theThe dip, the spatial bended results oceanic variations of plate in this and displacement analysis the continental are and plate. shown stress in Fig. 6 for a profile along the plate interface lent to the changein in a the narrow water transitiontion load of zone and the underneath vertical a stress thestrongest indicates flexure, that coast which the (Fig. area is beneath 4a,that also the is reflected b). coastline focussed in experiences in the the The a spatial bell-shaped spatial distribution area distribu- of beneath the the shear coast stress (Fig. 4e, f). Our finding that (Fig. 4). In the region seaward of the coastline, the vertical stress change is equiva- 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , S), J. Geophys. ◦ , 2010. , 2011. doi:10.1029/2001RG000108 ¨ om, G., Geophys. Monograph , 2004. doi:10.1130/G31801.1 ects on stress at near shore plate boundary fault ¨ uh, E.: Upward delamination of Cascadia Basin ff doi:10.1029/2009JB006541 1011 1012 doi:10.1029/2002TC001475 , 2004. ner, A.: Relative importance of trenchward upper plate motion and friction ff ¨ ¨ uller, J. T., Haeussler, P. J., Wesson, R. L., and Ekstr aschen, D., Kukowski, N., and Fl glacial fluctuations in the eastern Chugach8077, Mountains, 2000. Alaska, J. Geophys. Res., 105, 8055– New York, 496 pp., 2002. motions, Pure Appl. Geophys., 115, 441–458, 1977. climate variability on erosion of the southern Andes, Geology, 35, 2, 131–134, 2007. systems, J. Geophys. Res., 115, B08411, Occurrence in Southern Alaska?, in:by: Active Tectonics Freym and Seismic Potential ofSeries, Alaska, edited 179, 369–384, 2008. along the plate interfaceNumerical for Modelling the of topographic Crustal-Scale evolutionG., Processes, of Geol. Soc. edited mountain London by: belts, Spec. in: Publ., Buiter, 253, S. Analogue 105–115, J. and 2006. H. and Schreurs, doi:10.1029/2004GL021500 Bull. Seismol. Soc. Am., 65, 1073–1095, 1975. tion from an extended Barbados sea level record, Quat.active Sci. Southern Rev., 25, Alaska, 3322–3337, Global 2006. Planet. Change., 42, 279–293, 2004. deep-sea sink sediment budgets atSouthern high California, and Geology, low 39, sea 619–622, levels: Insights from tectonically active Prell, W. L., and Shackleton,a revised N. chronology J.: of The theing marine orbital the ?18 theory O Response of record, to Pleistocene in:Workshop, climate Palisades, Astronomical Milankovitch New : and Forcing, York, USA, Climate: Proceedings support 30 Understand- A. of from November L., – the Imbrie, 4 NATO J., December Advanced Hays, 1982, J., Research edited Kukla, by: G., Berger, and Saltzman,day B., D. Reidel glaciation Publishing, 269-305, 1984. in southernmost South America, Geophys. Res. Lett., 31, L-24613, I), Bull. Earthquake Res. Inst., Tokyo Imperial Univ., 9, 22–35, 1931. quakes, Science, 306, 1164–1166, 2004. glaciated, tectonically active regions? Geophys. Res. Lett., 20, 2123–2126, 1993. deformation and the thermal regime, J. Geophys. Res., 100, B11, 22133–22154, 1995. ments at convergent plate margins, Geophys. J. Int., 147, 415–427,1986. 2001. Columbia, Nature, 337, 452–454, 1989. in corals from Barbados:1990. sea level during the past 130,000interglacial years, trench Nature, supply 346, variation,the 456–458, spreading-ridge Andean subduction, marginRes., and development 105, at feedback 8355–8386, controls the 2000. on Chile triple junction area (45–48 sediment infill with landward frontalflux, Tectonics, accretion 23, thrusting TC3009, caused by rapid glacial age material Stern, R. J.: Subduction zones, Rev. Geophysics, 40, 1012, Shlien, S.: Earthquake-tide correlation, Geophys. J. R. Astr. Soc., 28, 27–34, 1972. Scholz, C. H.: The mechanics of earthquakes and faulting, Cambridge University Press, 2 Edn., Hebbeln, D., Lamy, F., Mohtadi, M., and Echtler, H.: Tracing the impact of glacial-interglacial Sauber, J., Plafker, G., Molnia, B. F., and Bryant, M. A.: Crustal deformation associated with Hanks, T. C.: Earthquake stress drops, ambient tectonic stresses and stresses that drive plate Kasahara, J.: Tides, earthquakes andLuttrell, volcanoes, K. Science, and 297, Sandwell, D.: 348–349, Ocean 2004. loading e Sauber, J. and Ruppert, N. A.: Rapid Ice Mass Loss: Does it have an influence on Earthquake Hampel, A. and Pfi Kanamori, H. and Anderson, D. L.: Theoretical basis of some empirical relations in seismology, Sauber, J. and Molnia, B. F.: Glacier ice mass fluctuations and fault instability in tectonically Peltier, W. R. and Fairbanks, R. G.: Global glacial ice volume and Last Glacial Maximum dura- Ivins, E. R. and James, T. S.: Bedrock response to Llanquihue Holocene and present- Nasu, N., Kishinouye, F., and Kodaira, T.: Recent seismic activities in the Idu Peninsula (Part Covault, J. A., Romans, B. W., Graham, S. A., Fildani, A., and Hilley, G. E.: Terrestrial source to Imbrie, J., Hays, J. D., Martinson, D. G., Mcintyre, A., Mix, A. C., Morley, J. J., Pisias, N. G., Cohen, S. C.: Does rapid change in ice loading modulate strain accumulation and release in Cochran, E. S., Vidale, J. E., and Tanaka, S.: Earth tides can trigger shallow thrust fault earth- Hyndman, R. D. and Wang, K.: The rupture zone of Cascadia great earthquakes from current Church, M. and Slaymaker, O.: Disequilibrium of Holocene sediment yield in glaciated British Buiter, S. J. H., Govers, R., and Wortel, M. J.Chappell, R.: A J. modelling and study of Shackleton, vertical N. surface displace- J.: Oxygen isotopes and sea level, Nature, 324, 137–140, Bourgois, J., Guivel, C., Lagabrielle, Y., Calmus, T., Boulegue, J., and Daux, V.: Glacial- Bard, E., Hamelin, B., Fairbanks, R. G., and Zindler, A.: U-Th ages from mass spectrometry Adam, J., Kl References 5 5 30 30 15 25 25 20 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Temporal evolution (b) Poisson’s ratio. Gravity ν Young’s modulus, and E density, ρ 1014 1013 ect, Geophys. J. Int., 122, 183–194, 1995. ff acceleration of gravity). An ocean on top of the oceanic plate and the continental margin g equivalent to 125 m of water (blue arrows). This pressure is decreased and subsequently increased oc P Setup of the finite-element model with an oceanic and a continental plate that are in contact along a locked (a) tions in Global Climate 65 Ma to Present, Science, 292, 686–693, 2001. 2002. contribution of the ocean tide loading e of the sea level inand the Fairbanks, 2006). model, For reflecting comparison, a a fall control and run subsequent was rise performed by with 125 a m constant over sea 120 ka level (dashed (cf. line). Imbrie et al. 1984; Peltier to simulate the fallingfor the and temporal subsequently evolution rising oflithostatic the sea pressure pressure). and level elastic At during foundation thein at a the beginning the glacial-interglacial bottom of horizontal of the cycle, and the modelat vertical model. respectively run, which directions Afterwards, (see displacements isostatic the (see Fig. and model equilibrium text sides stresses 1b ispart for and were established details). of bottom extracted by are the from Red a fixed the model triangles model for mark (Figs. which the 2–4, the locations 6). displacement of Box and points with vertical F dashed stress outline and fields marks P0–P4, are the shown in Figs. 2–4. is included as a bodywith force a ( average water depthand of a 5000 m pressure is implemented as a combination of a water body (average water depth: 4875 m) plate interface (solid red line). Rheological parameters are Fig. 1. Zachos, J., Pagani, M., Sloan, L., Thomas, E., and Billups, K.: Trends, Rhythms, and Aberra- Tsuruoka, H., Ohtake, M., and Sato, H.: Statistical test of the tidal triggering of earthquakes: 5 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | a rising sea level (20–0 ka). a rising sea level (20–0 ka). (b) (b) 1016 1015 a falling sea level (120–20 ka) and a falling sea level (120–20 ka) and (a) (a) Vertical displacement induced by Horizontal displacement induced by Temporal evolution of the horizontal displacements at point F in the forearc and at points P0–P4 located on the Temporal evolution of the vertical displacements at point F in the forearc and at points P0–P4 located on the plate Fig. 3. (c) plate interface (Figs. 1a, 3a). For reference, the result from the control run (constant sea level) is shown for point P1. (c) interface (Figs. 1a, 2a). For reference, the result from the control run (constant sea level) is shown for point P1. Fig. 2. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | a falling (a) horizontal stress during sea-level fall (d) , xz z τ σ shear stress (c) the vertical stress and (b) x σ 1018 1017 horizontal stress . during sea-level rise (20–0 ka). (b) , xz z τ σ a rising sea level (not to scale). (b) shear stress Stress variations caused by the sea-level changes. Left column shows the change in (f) Sketch summarizing the vertical and horizontal displacements resulting from the vertical stress and x Fig. 5. sea level and σ Fig. 4. (a) (120–20 ka). Right column shows the change in Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Vertical (a) during sea- (e) erent values (0.1, 0.2 and 0.3) ff resolved normal stress on plate interface and 1019 (c) cient µ. For location of points P1–P4 see Fig. 1a. horizontal displacement, ffi during sea-level rise were calculated using di (b) (f) Profiles along the plate interface showing displacement and stress changes induced by resolved shear stress on plate interface. Changes in the Coulomb stress displacement, level fall and for the friction coe sea-level fall (red curves and scales) and sea-level rise (blue curves and scales). Fig. 6. (d)