Analog Experiments and Mechanical Analysis Applied to the Alaskan Accretionary Wedge Marc-André Gutscher, Nina Kukowski, Jacques Malavieille, Serge Lallemand

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Analog experiments and mechanical analysis applied to the Alaskan Accretionary Wedge Marc-André Gutscher, Nina Kukowski, Jacques Malavieille, Serge Lallemand

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Marc-André Gutscher, Nina Kukowski, Jacques Malavieille, Serge Lallemand. Analog experiments and mechanical analysis applied to the Alaskan Accretionary Wedge. Journal of Geophysical Research, American Geophysical Union, 1998, 103 (B5), pp.10161-10176. hal-01261538

HAL Id: hal-01261538 https://hal.archives-ouvertes.fr/hal-01261538 Submitted on 26 Jan 2016

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. B5, PAGES 10,161-10,176,MAY 10, 1998

Episodic imbricate thrusting and underthrusting' Analogexperiments and mechanicalanalysis applied to the Alaskan Accretionary Wedge

Marc-Andrd Gu•scher • and Nina Kukowski GEOMAR, Kiel, Germany

JacquesMalavieille and SergeLallemand Laboratoire de G•ophysique et Tectonique, Universit• de Montpellier II, Montpellier, France

Abstract. Seismic reflection profiles from the sediment rich Alaska subduction zone image short, frontally accreted, imbricate thrust slices and repeated se- quencesof long, underthrust sheets. Rapid landward increasesin wedgethickness, backthrusting,and uplift of the forearc are observed,suggesting underthrusting beneaththe wedge.These features and a widely varyingfrontal wedgemorphology are interpreted to be caused by different modes of accretion active concurrently along the trench at different locations. Episodicwedge growth is observedin high basal friction experiments using sand as an analog material. Two phasesof an accretionarycycle can be distinguished:frontal accretionof short imbricate thrust slices,alternating with underthrustingof long, undeformedsheets. The phase is shownexperimentally to dependupon the surfaceslope of the wedge. Mechanical analysis of the forces at work predicts these two modes of deformation due to the varying frictional forcesand yield strengthsfor a temporally varying wedge geometry.Maximum length of thrust slicesis calculatedfor experimentalconditions and confirmedby the observations.For a steepfrontal slope (at the upper limit of the Mohr-Coulombtaper stability field) the overburdenis too great to permit underthrusting,and failure occurs repeatedly at the wedgefront producing short imbricate slices. The wedgegrows forward, lowering the surfaceangle to the minimum critical taper. For a shallowfrontal slope the reducedoverburden along an active roof thrust permits sustainedunderthrusting, causingfrontal erosion and backthrusting,steepening the wedgeand thus completingthe cycle.

1. Introduction configurationat the Alaska convergentmargin showsa high degreeof lateral variation, and frontal slopesvary Seismicreflection profiling of convergentmargins has from less than 20 to over 150 within a few tens of kilo- recordeda high degreeof structural diversityin accre- meters. tionarywedges where deep sea sediments are imbricated An episodic variation in frontal configuration has against and subducted beneath the overriding plate been observedin a high basal friction analog experi- [Westbrooket al., 1988; Moore et al., 1990; Moore et mentsimulating accretionary wedge growth [Gutschef al., 1991;Shipley et al., 1992]. The causesfor structural et al., 1996]. Two distinct modesof deformation,as- diversityare not fully understoodbecause the most de- sociated with imbricate thrusting and underthrusting, formedportions of the wedgeare often poorly resolved. occurreddespite a constant thicknessof incomingsed- Furthermore, it is unclear whether wedge growth oc- iment and an unchangingbasal friction. Since direct curs by steady state processesor in episodicfashion, observationof the developmentof a submarine accre- alternatingwith periodsof erosion.The frontal wedge tionary wedgeover geologictimescales is not possible, analog modelingis a useful tool permitting observation Now at Laboratoire de Gdophysiqueet Tectonique,Uni- of the completeevolution of a model thrust wedgeunder versitd de Montpellier II, Montpellier, France. controlled boundary conditions. The objectivesof this study are threefold: (1) to Copyright 1998 by the American GeophysicalUnion. quantify the conditions controlling episodic accretion Paper number 97JB03541. in analogthrust wedges,(2) to providea mechanical 0148-0227/ 98 / 97J B- 03541 $09.00 explanation for the two distinct modes of deformation

10,161 10,162 GUTSCHERET AL.- EPISODICIMBRICATE THRUSTING in terms of the body and boundaryforces, and (3) to In the Eastern Aleutian Trench, 45 Ma old oceanic apply theseresults to the Alaska accretionarywedge. crust of the Pacific plate is subducting beneath the southernAlaskan margin at a rate of 5.7 cm/yr [DeMets 2. Tectonic Setting of the Alaska et al., 1990](Figure 1) ). The basal 500-600m sec- Convergent Margin tion of deep sea sediments,representing the Surveyor The Alaska convergentmargin offers a particularly Fan, is overlain by a 1400 m sequenceof alternating good study area since it has been investigatedby deep hemipelagicsediments and turbiditictrench fill [Kven- seadrilling [Kulmet al., 1973]and multichannel seismic voldenand yon Huene, 1985; yon Huene, 1989; Moore et reflectionprofiles [Kvenvolden and yon Huene, 1985; al., 1991].In lineEDGE-302, the frontal8 km of the ac- Moore et al., 1991], supplementedby depth-velocity cretionarywedge consist of three short imbricateslices controlfrom wide angleseismic data Iron Huene and (Figure2a), with a conjugateforethrust and backthrust Flueh, 1994; Ye et al., 1997]as well as high-resolution set defininga "pop-up"type of structure.The shallow swathmapping bathymetry [yon Huene and Flueh, 1994; 20 frontal slopeincreases to 5- 80 at the third major Friihn• 1995].The wedgeis markedby a largequantity thrust fault, locally reaching15 ø. At a distanceof 12- of incomingsediment (2--3 km) and is classedas a typ- 15 km from the deformationfront, the seismicsignature ical accretionarywedge [yon Huene and Scholl, 1991; losesits characterand the arcwarddipping and subhor- Lallemandet al., 1994]. izontal reflectorscan no longerbe assignedto any par-

,, o NORTH AMERICAN

PLATE

• .KSSD 2 \ \ \ \ \ \ \

ß KSSD 1 DSDP 182 PACIFIC

ß• / / / PLATE

•.g-• DSDP178 o

' ' 56* 208* 212'

Figure 1. Alaskalocation map, with multichannelseismic lines (solid lines are presentedin text, dashedlines are discussed,but not displayed),borehole locations (small, filled triangles)[Kulm et al., 1973;Kvenvolden and yonHuene, 1985]and bathymetry(depth in m) sources:TOPEX global2 arcminbathymetry [Smith and Sandwell,1994; 1997],high resolutionswath mapping bathymetryNE of line 71 Iron Hueneand Flueh, 1994]' GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING 10,163

a) NW EDGEline-302 SE

[km]

...... '" 40 [km] 20 0 b) NW line71 SE

. [km] __•5 .

' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I .... I ' ' ' ' I ' ' ' ' I .... I .... I ' ' ' '1'' • •1 •9 40 [km] 20 0 O) NW line 63 SE

fore arc basin [km]

½•:•:•:•:•k.::½•;-'•;-':.-'::• ...... -- • -5

•--•i-•::•:•:•-"•:::...... ••,• •_ ...•------•---• •---'-• -----•- • •---•" -•

40 [km] 20 0

Figure 2. Interpretativeline drawingof seismicreflection profiles (pre stack depth migration, VE - 1.5). Heavy lines indicatefaults or erosionalunconformities, dashed where uncertain, oceanicbasement, dark shadedregion, backstop, light shadedregion. (a) Line EDGE-302, one horizonwith a clearseismic signature is tracedas a shadedline, (b) Line 71, notethe longlayered sheetsbetween km 20 and 40, and (c) Line 63, note the longsheets and the 2 km deepfore arc basin at rear. ticular stratigraphic horizon Surface morphology and all accreted and those below are all transported farther dipping zonesof high reflectivity,however, suggest four arcward below the wedge. to seven more major thrust slices truncated at 6 km depth by a midlevel detachment. At a distance of 40- 60 km from the deformation front, a 0.5-1.5 km thick 3. Experimental Modeling sequenceof slope sedimentsis marked by strong land- The growth of accretionary wedges and fold-and- ward vergentfolding and shortening.At depth, a I km thrust belts has been the subject of numerous analog thick sectionof layered reflectorsis imaged above the modelingstudies [Davis et al., 1983; Malavieille, 1984; subductingoceanic crust and beneath the backstop. Mulugeta, 1988; Malavieille et al., 1991; Liu et al., 1992; Two parallel seismiclines to the SW, lines 71 and 63, Lallemand et al., 1992; Malavieille et al., 1993; Lalle- displaylong (10-20 km) repeatingsequences of reflectors mand et al., 1994; Kukowski et al., 1994; Larroque et al., (Figures2b and 2c) 30 km from the deformationfront. 1995; Wangand Davis, 1996]. Thesestudies have con- The overlyingridge in line 63 (at 35 km) shallowsto firmed the applicability of critical wedgetheory to mod- 2.5 km depth and bounds a 2 km deep forearc basin. eling deformationin the brittle, upper portions of sub- In both this basin and the I km deep basin along strike marine accretionarywedges [Davis et al., 1983; Dahlen at the rear of line 71 (at 35 km) folding,tilting, and et al., 1984, Dahlen, 1984]. The theory predictsthat uplift of the overlying slope sediment strata are visible the geometryof a growingwedge (as definedby the [Kunert,1995]. surfaceslope a and the basalslope fi) is a functionof In all three lines, the initial 2 km trench sectionis tec- the material strength and the basal friction according tonically thickenedto about 5 km within 30-35 km from to the deformation front. Volumetrically, this thickening amountsto a shorteningof 45-55km [Kunert,1995] as- (bb+ fi) (1) suming that the sedimentsabove the decollementare a+fi--(I+K) 10,164 GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING

where• isangle of basal friction, related to theco- efficient of basal friction by it0 = tanc)• and K is a a) FrontalAccretion dimensionlessparameter, usually of the order of 2. DE... o[• 8o rigid The experimentsreported here were designedto test •':•':i•i•::•,•'•:•:•i•i•:•:•,,,•,•,•...... :-...... -:::,•,•. -•;•'•.• ,eformable backstop wall the range of experimental conditions over which the _ ...... :::::'...... '"'"':':?::•::::•:?•':"•":•:•:::::•::::•:'•'•.•%•.• -...... (or arc) phenomenonof cyclicalaccretion occurs [Gutschef et Subductingplate• al., 1996]. Factorstested included the surfaceslope of .. the initial buttress,the length of the buttress,and the relative amount of subductedmaterial output. The experimental apparatus was the same in all cases,a 240 cm long and 30 cm wide glass-sidedbox. Sprinkled b) Underthrusting sand overliesa rigid basalplate, pulled beneatha rigid verticalwall [Malavieill½et al., 1991;Lallemand et al., I•l• ...... •/ ...... 1992;Kukowski et al., 1994; Gutschef½t al., 1996]. A deformablebuttress or "backstop"composed of packed sand is emplaced above the sprinkled sand layer and against the vertical, rigid, back wall. Figure 3. The two phasesof the accretionarycycle Eolian quartz sand (diameter 0.3-0.5 mm, internal (a) frontalimbricate thrusting and (b) underthrusting. friction tt = 0.6) is chosenas an analogmaterial, since The three observablequantities distinguishingthe two it exhibits a depth-dependentCoulomb rheology, ap- are (1) the lengthof thrustslices, (2) the surfaceslope, and (3) the advanceand retreat of the deformationfront propriate to studies of upper crustal rocks and marine DF. sediments. Scaling is such that 1 cm in the sandbox correspondsto 1 km in nature. Thus the cohesion of the accretingsand (Co • 20 Pa) and packedsand backstop (Co m 100 Pa) scaleto 2 and 10 MPa, respectively, reasonable values for unconsolidated marine sediments ments with the same high basal friction, same constant sedimentary input, and same constantoutput but with and lithifiedsedimentary rocks [Hoshino et al., 1972]. different initial surface slopesare first presentedin de- The 2 cm of sand (input) on the downgoingplate tail (Table 1, experiments1 and 12). For comparison, representsthe 2 km of deep sea sedimentson the sub- a typical low basal friction experiment,again with the ducting oceanic crust of the Pacific plate. The inter- sameinput and output, is introduced(Table 1, exper- face with the basal plate consistsof double-sidedadhe- iment 4). Finally, two high basalfriction experiments sive tape coveredwith sand and servesas a high fric- are briefly discussedwhere a very long initial buttress tion decollement(tt6 m 0.5). The deformablepacked wasincluded to test the maximumlength of underthrust sand buttress representsthe more competent portions of the Alaskan arc, composedof crystallinebasement or sheetsand the effectof zero subductedoutput (Table older, metamorphosed, accreted sediments. In the ex- 1, experiments33 and 34). perimentspresented here (with one exception)a 1 cm 4.1. Experimen• 1 (Shallow Initial Surface aperture at the baseof the wall (output) permitsma- Slope) terial to exit the system and representsthe substantial thickness of underthrust sediments known from seismic Experiment 1 begins with a shallow surfaceslope of reflectionprofiles from Alaska (Figure 2a) and other 10ø (Figure4a). After the first frontalthrust forms, the convergentmargins[Westbrook et al., 1982; Shipleyet roof thrust remains active, allowinga long sheet to be al., 1990]. underthrustbeneath the sandwedge, with very little in- A limitation of this experimentalapproach is that the ternaldeformation (Figure 4b). Note the soliddiamond "subaerial" sand has no fluids and thus no pore pres- markerbelow the tip of the advancingunit (Figures4a- sure. Thereforethe resultingangles of reposeand an- 4c). Once the roof thrust blocks,a major backthrust glesof taper are greater than thoseobserved in the sub- deformsthe overlyingbackstop wedge and a new basal marine environment. Additionally, the effects of com- thrust propagatesforward initiating frontal thrusting paction(e.g., porosityloss) are smallerthan in subma- (Figure4c). Sevenshort thrust slices form, are accreted, rine accretionarywedges. and build the wedge out forward, loweringthe frontal slope(Figure 4d). A secondlong sheet of" oceanic"sed- 4. Modeling Results iment and a small amount of previously accreted material is underthrust beneath the wedge. This removal In all experimentsperformed with high basalfriction of material at the toe steepensthe frontal slope to 2• ø, and input greater than output, cyclical behavior was despitethe occurrenceof slumping(Figure 4e). Frontal observedalternating betweenfrontal accretionof short thrusting resumes, building five more imbricate slices, imbricate thrust slicesand underthrustingof long, un- the rear most of which _areentrained into the subducfion deformedsheets (Figure 3). Two representativeexperi- channelalong a midleveldetachment (Figure 4f ). GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING 10,165

Table 1. Experimental Conditions When the surface slopesobserved in the experiments shownare plotted in the taper stability field for a high Expt. •ub •ui,t I, cm O, cm c• 13 $to,, cm basalfriction of 0.5 (Figure7a, shadedregion) wide fluc- tuations are seen. The wedgesuccessively moves from 1 0.5 0.6 2 1 10 ø 6 ø 140 an unstableregime at the upper boundary(the maxi- 12 0.5 0.6 2 1 22 ø 6 ø 160 mum or limiting taper), with failure alongtrenchward 4 0.35 0.6 2 1 6 ø 4 ø 150 33 0.5 0.6 2 I 15 ø 6 ø 120 dippingplanes causing slumps and slides,to a compres- 34 0.5 0.6 2 0 15 ø 6 ø 125 sionalregime at the lowerlimit (the mimimumor "critical taper") wherefailure occursrepeatedly along arcwarddipping planes generating short imbricateslices. Symbols: •ub,coefficient of basal friction; I•i,•t, coeffi- Plotting the frontal slope (c•) and the initiation of cient of internal friction; I, input; O, output; c•, initial sur- eachfrontal thrust as a functionof convergence(Figure face slope;fl, dip of subductingplate; $tot, total convergence during experiment. 7b), the truly cyclicalnature of theseunderthrusting and frontal accretion processesbecomes evident. The surfaceslope decreasesduring the imbricate thrusting phaseof the cycleas the wedgebuilds out forwardand increasesduring the underthrustingphase of the cycle 4.2. Experiment 12 (Steep Initial Surface as the front is oversteepenedby erosionalong the emerg- Slope) ing roofthrust (or "midleveldetachment"). The defor- A frontal thrust developsat the apex (Figure 5a), but due to the large overburden on the roof thrust, underthrusting is inhibited. Thus five frontal imbricate thrusts form at regular intervals and build the a) deformationct½'•Oø • 10 wedgeforward, reducing the frontalslope (Figure 5b). The tops of the slices are accreted, and the bases are ••.•.....,..... •:.:..._.•-••o•..•,• __ .••.[cm] shearedoff at a midlevel detachmentas they are pulled futurethrust, ...... '-•-•":":"-'""•'"•-""'.:'.':':.':.'• 0 along with the subductingplate. Once the surfaceslope has becomeshallower, a long unit is underthrust be- b) .....• "'-•'•-' • [cm]lO neath the overlying sand wedge. The underthrusting sheet causes frontal erosion which increases the sur- •'::..... :':•::'::•:'::":'"" 0 face slopeup to 280 (Figure5c). Anotherfrontal accretion phase follows, with five more imbricate slices c) _-...... ,• [cm]10 (Figure5d). Lastly,a secondunderthrusting phase oc-

curs, again steepeningthe wedgeto 280 through frontal o erosion(Figure 5e). In both experimentsi and 12, shearingof the lower d) lO portionsof the imbricateslices occurs along a midlevel "-" [cm] detachment(Figures 6a and 6b). Underplatingoccurs as the ramp thrust at the tip of the underthrusting o sheetuplifts the overlyingunits. If theseoverlying units consistof sheared,imbricate slices,then entrained, un- e) lO derplatedduplexes form (Figure6c) [Gutschefet al., [cm] 1996]. If theseconsist of longsheets, then layered,un- derplatedsheets form (Figures6d, 6e, and 6f). When o motion along the midleveldetachment ceases, a backthrust developsas material is underplatedbefore a new f) lO basaland frontalthrust propagates forward (Figures 6c [cm] and 6f). Underplatingwas only observedin highbasal friction experimentswith excessinput. The degreeof o underplatingas a functionof theseparameters is quan- 20 [cm] 0 tifiedelsewhere [Gutschef et al., 1998]. Figure 4. Tectonicsketches of experiment1 [Gutschef 4.3. Taper Stability Field, Cyclicity et al., 1996];(a) after0 cm;(b) 15cm; (c) 35 cm;(d) 70 and Phase Shift cm; (e) 120cm, and (f) 140cm of convergence.Heavy lines representfaults, heaviestwhen active, with sense Accordingto Mohr-Coulombwedge theory the inter- of motion. Hatchured area is rigid vertical rear wall. nal and basalfriction of a deformingwedge sliding over a Incipient thrust at the wedgeapex in the initial stage fault surfacedefine a taper stabilityfield [Dahlen,1984]. is shown dashed. 10,166 GUTSCHERET AL' EPISODICIMBRICATE THRUSTING

of the wedge.At shallowsurface slopes (experiment 1, 15 Figures4a and4b) underthrustingof long undeformed a) units is favored. At steepsurface slopes (experiment 10 future deformation 12,Figures 5a and5b) frontal imbricate thrusting is fa- thrust frontJ, •' [cm] vored. Thus the mechanicalforces controlling the phase of the accretionarycycle appear to dependon wedgegeometry.

15 5. Mechanical Analysis b) 10 The frictionaland gravitational forces acting on the [cm] variousfault surfaces,e.g., ramp thrust, basalthrust, '"'"'L'2'2'- and roof thrust can be calculated for a generalized wedgegeometry (Figure 8) andthus the instantaneous worknecessary to continueor initiatemotion along dif- 15 ferent surfacescan be quantifiedfor any set of wedge parameters(model or natural)[Schniirle, 1994]. This 10 allowspredictions to be madeconcerning the maxi- [cm] mumlength of thrustslices which can in turn be comparedto the averagelengths from experimental observations. A similar mechanicalanalysis [Platt, 1988] treatedonly lowerbasal frictions and constant,shallowsurface slopes (a < 5ø) andthus did not directly addressthe mechanicsof long underthrustsheets nor temporal variation in forces. The instantaneouswork (Fudx) requiredto underthrust a unit an incrementaldistance dx is equal to the frictionalresistance (f) alongthe roofthrust (A) and alongthe ramp thrust (B), plusthe force (w) required to upliftthe overlyingportion of the wedgealong the rampbase a verticaldistance dz (C).

F•,dx - f•tdx + f,.dr + w,.dz Equation(2) canbe comparedto the instantaneous work(Fidx) required to initiate a newbasal thrust, with accompanyingfrontal ramp thrust and an equivalent Figure5. Tectonicsketches ofexperiment 12; (a) after displacementdx whichis equalto the frictionalresis- 0 cm;(b) 25cm; (c) 75 cm; (d) 110cm, and (e) 160cm tance(f) alongthe basal thrust (D) andalong the toe of convergence(symbols same as in Figure4). rampthrust (E) plusthe force(w) requiredto uplift the toe alongthe rampa verticaldistance dz (F) (indices(R), roofthrust, (t), toe,(r), rampthrust, (u), marion front also alternatively advancesand retreats underthrusting,(i), initiation) (Figure3) [Gutschefet al.,1996]. In bothexperiments, Fidx - fBdx + ftdr + wtdz (3) twofull cyclesare observed.Experiment 1 startswith underthrustingand ends with frontalaccretion. Exper- in all casesf - pcos/3,where w -mg - p Vg. iment 12 is shiftedhalf a phaseand startswith frontal accretion and ends with underthrusting. In both cases,the energylost due to internaldefor- Forcomparison, a similar plot is shown(Figure 7c) mationwithin the sand(e.g., kink bands) is neglected. for a low basal friction experiment(experiment 4), Totalforces (F• andFi), frictionalforces (f), weights which otherwisehas almost the same initial configura- (w)and volumes (V) arecalculated for a crosssectional tionas experiment 1 (sameinput, same output, similar areaper perpendicular unit length. All areascan be ex- a' and/3. Continuous,frontal imbricate thrusting occurs pressedin termsof thelengths H, Ln, LB andLt and at fairly regularintervals of roughly6 cm, anda main- theangles a,/3 and0f. Lengthsin turn arerelated by tains a nearlyconstant value, barely increasing during LB = Ln + Lt, Lr = Lt, and Lt - HsinOf. 150 cm of convergencefrom 6o to 7ø. Substitutionand algebrayield unwieldybut uncom- Forhigh basal friction the modeof deformationis ob- plicatedexpressions (see the appendix for details) which servedexperimentally to dependon the configuration can be evaluatedfor any choiceof basalfriction and GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING 10,167

Underplating Duplexes UnderplatingSheets a)accreted"half slices"upper . mid-level "ent• '•detachmen ...... • .-.,••,-,; ..... ,[ •-X l•g sheet b) f f erosion•-<• ,' •"•,•• previouslyentrained :-,,' . _' '. .,'. .duplzs ,f" underthrustingsheet ' " • 2nd underthrusting sheet ""_=.,,• ' c) t t t frontal thrusbng] • underplated"entrained/•j frontalthrusting • .'• •<•.esumes•""%•1stsheet underplated 2nd underthrUsting sheethalt•

Figure 6. Evolutionary paths of two different underplated structures: duplexes and sheets. Underplatingof duplexes:(a) frontal accretionwith shearingof imbricateslices at a mid-level detachment,(b) underthrustingwith frontaluplift, and (c) underplatingof entrainedduplexes with backthrustingand uplift at rear of wedge(vertical arrowsindicate maximum uplift). Un- derplatingof sheets:(d) underthrustsheet following frontal accretion, (e) 2ndunderthrust sheet causingfrontal uplift, and (f) underplatingof first sheetthrough backthrusting and uplift at rear of wedge(vertical arrows indicate maximum uplift).

length of thrust slice. (The length of a thrust sliceis typical steep frontal slope of c• : 25ø. The force re- measuredfrom the ramp cut off at the basal detachment quired to initiate a new frontal and basal thrust Fi is to the next basalramp cut off.) calculated for three different basal frictions, /•b = 0.5, 0.4, and 0.3, againfor both frontal slopes(in all cases for 1 m lateral trench width). It shouldbe noted that the frictionalong a faulted surfacein the sand (i.e., the activeroof thrust) has beenreported to be 10% lower (Pg){[(•) cøsj•(tanc•-l-tanfi) LR2] than the internalfriction of the sand [Liu et al., 1992] and that the correspondingvalues have been adopted +p) + p +p) for these calculations. The forces(F• and Fi) are plottedversus slice length '(•) (tan a+ tan "+tan Oy)(L• - Ls•) for a moderatefrontal slopeof 10ø (Figure9) and for a steepfrontal slope of 25o (Figure 10). The intersection (4) of the curvesF• and F/ predictsthe averagelength of -tan 0y(L• L• - L• •)} thrust slices. The maximum length of an underthrust unit (i.e., lengthof an activeroof thrust) variesaccord- ing to both the basal friction and the surface slope of the wedge.For low basalfrictions of 0.3-0.4 (50- 67% { cos(./--] LBcos/3 + (tan c•+2 tan/•) LB2) of the internalfriction),. less force is requiredto initiate a new basal and frontal thrust than to continue motion along an existingroof thrust. The predictedfault spac- +[(•)( cos 1 ) cos + +HLt• ing (for a 2 cm layer thicknessand shallow10 ø frontal slope)is 4-10 cm, whichcorresponds well to the 6 cm averagefault spacingobserved [Gutschef et al., 1998]. + + cos]} For a high basalfriction of 0.5 (83% of the internal For the experiments reported here, appropriate pa- friction) and 10ø surfaceslope, less force is requiredto rameters are; laint : /•r : /•t : 0.6, /•R : 0.54, sustain motion along the roof thrust because there is P = 170Ok#/m3,/7 : 9.8m/s2, H = 0.02m, then less total overburden than on the basal thrust. Thus, •: 31o (the angleof repose)and 0! = 28ø;fi = 6o . underthrustingis favored(experiment 1, Figuresla-lc) The underthrustingforce Fu is first calculatedfor a typ- and proceedsto the point where the overl:•ing wedge ical moderate frontal slope of c• - 10ø and then for a thickness increasessubstantially. The maximum slice 10,168 GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING

taper stability field high basal friction a) b) 35 underthrustingi__._,q.•_.•re • shallowinitial slope 3C =0.50 "angleofrepose" (slides)..-.• 3O 3 0-• Exp...•1

CLo •/d

• 20 2O m •15 ' 'd -_•

_• 10 1, = -•- '•.r •2-steep i•itialslope 10 10 5t,-...... thrusts _ 4m m m m m m m m m mm mm O '''•'''•'''•'''•'''•'''•'''•'''/ 0 20 40 60 80 100 120 140 160 convergence [cm]

0 0 -20 - 10 0 10 20 I• (plate dip)

low basal friction C) 35

3O Exp. #4 (final stage) Figure 7. (a) Stability fields for high basal friction 25- (0.5, shaded)and moderatebasal friction (0.4, dashed), '• • 20- showinginitial (opensymbols), intermediate and final 20 [cm] 0 (solidsymbols) surface slopes for highbasal friction ex- 15- periments i and 12 and low basal friction experiment 4. 10- (b) Surfaceslope fluctuation (open symbols with a cu- bic splinecurve fit) and thrustinitiation (solidsymbols) 5 •--:. - '- • thrusts•.• versusconvergence for high basal friction experiments1 o (squares)and 12 (circles),c: (sameas in Figure7b) for o" '2••;' '4••;' .....•'o •'o'•o'o'i•'o'i•'o'i•o• • low basal friction experiment 4, inset showinggeometry convergence [cm] of final stage after 150 cm of convergence.

a) dz Fu dx - fRdX+ frdr + wrdz

H Input ;'

b) Fi dx= fBdX+ ftdr + wtdz ••::••'•'"•......

toe

• ...... :.,...... -...... :.•...... :--...... -.:.:-..:•...:.r.::: -...... •,, ...... :-:.:::...... •u..___.•.•D.g•late u Da • L, • L.------'------r -••

F;gure 8. Gravitational(w) andfrictional (f) forces(a) actingon the roofand ramp thrusts of an underthrustingunit, and(b) actingon newlyinitiated basal and frontal ramp thrusts (indices R, roofthrust; r, rampthrust; B, basalthrust; t, toe thrust). GUTSCHER ET AL' EPISODIC IMBRICATE THRUSTING 10,169

a) (z- 10ø narrowly spacedin the length range 30-50+ cm. Thus, 400 a slight uncertainty(4-5%) in the basal friction or in the friction of the active roof thrust can result in 4-20 35O- ß F underthr. cm in the length of the sheets. This uncertainty does __o__ F init. 0.5 not, however, affect the overall trend. Underthrusting 300--'--F init-0'4 of long sheetscan only occur for a high basal friction 250..... [].... F init. 0.3 and for a shallow surface slope. 200- _../.'x -'...... --'[ Sincethe arcwardincrease in wedgethickness (and thusoverburden) is a functionof the surfaceslope (a),

00-• -' if this angle is large, then even with high basal friction, 1; Fig.9b .....•..•'...... a-" [ underthrustingis inhibited(Figures 10a and 10b). This is the casefor experiment 12, with an initial slopeof 22ø . The forcesrequired to underthrust below a steep surface 0 10 20 30 40 50 slope of 25o in all casesexceed the force necessaryto length of thrust slice [cm] initiate a new frontal thrust, for slice lengths > 6 cm (Figure 10b). Thus, repeatedfailure along basal and b) a- 10ø frontal thrust planes occurs and generatesshort slices 50 (experiment1; Figures4e and 4f and experiment12; Figures5a and 5b). 4O a) a - 25 ø 400 z 30 350 A F underthr. / ' o 20 300 --o--F init. 0.5 •,' / .,' --*--F init.0.4 /o" / •' 250 10 .....-.-, ,n,,. • 200 / .' (,3 /// ,.," o I • ' ' I ' ' ' I ' ' ' I ] ' ' I u_ 150 ,' / ...•' 0 2 4 6 8 10 length of thrust slice [cm] 100 •...," ." Fig lob •'o/.,•• -"- / "' 50 . Figure 9. Forcesrequired to underthrusta unit (F underthr.) and to initiate a new basaland frontal thrust 0 .... ,,,, , (F init.) versuslength of thrust slice for three basal 0 10 20 30 40 50 frictions, 0.5, 0.4, 0.3, for a moderate surface slope of length of thrust slice [cm] 10ø. (a) Slicelengths 0-50 cm, and (b) closeupnear origin for slicelengths of 0-10 cm (note "underthrusting" is consideredto begin at a slicelength of 4 cm, the b) a - 25 ø horizontallength of the thrust ramp). /

4O length for a basal friction of 0.5 (for a shallowslope of 10ø and 2 cm layer thickness)is predictedby the 3O intersectionof the two curvesto be • 50 cm (Figure

2O Two high basal friction experimentswith very long initial buttresses(• 70 cm length) wereperformed to 10 testthe maximumlength of the underthrustsheets (Fig- ure 11). Experiment33 hadthe same1 cm output asthe other experiments reported here, while experiment 34 ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' 0 2 4 6 8 10 had zerooutput to demonstratethat the underthrusting length of thrust slice [cm] phenomenonis not an artifact of the open subduction window. Both experiments had the same 2 cm input Figure 10. Forcesrequired to underthrusta unit (F as the other experiments reported and both produced underthr.) and to initiate a newbasal and frontal thrust sheetsof 40-50 cm length (Figure 11). The agreement (F init.) versuslength of thrust slicefor three basal frictions, 0.5, 0.4, 0.3, for a steep surface slope of 25 ø. between the theoretically predicted and the observed (a) Slicelengths 0-50 cm, and (b) closeupnear origin length of the sheetsis within the margin of error be- for slice lengths of 0-10 cm. Note all forces are higher causethe two curvesfor underthrusting(F•) and for than for the same frictions and slice lengths in Figure initiationof a new thrust fault (Fi in Figure9a are very 9. 10,170 GUTSCHER ET AL.' EPISODIC IMBRICATE THRUSTING

Experiment 33 (120 cm) 25

a) 15

lO [cm]

20 [cm] 0

Experiment 34 (125 cm)

b) 25

lO [cm]

Figure 11. Tectonicsketches of (a) experiment33, input of 2 cm, output of I cm, after 120cm of convergence,and (b) experiment34, input of 2 cm, output of 0 cm, after 125 cm of convergence.

The implication of this mechanical analysis is that basal friction experiment correlate well with structures for natural thrust wedgeswith a basal friction exceed- and surface morphology observedin reflection seismic ing 80% of the internal friction and with excesssedi- lines from the Alaskan convergent margin and offer a ment input, cyclicalaccretion is expected,varying from viable mechanism for their formation. Lines 71 and 63 the frontal accretionmode to the underthrustingmode. (Figures2b and 2c) provideclear evidencethat several Accordingly,wide variations in the frontal wedgemor- long (15-20 km), relativelyundeformed sheets of 1-1.5 phologyare alsoexpected, so that a singlemargin may km thicknesshave been emplaced beneath the wedge have frontal slopesvarying from a few degreesup to the throughrepeated underthrusting (Figures 6d-6f). The angle of reposefor the accreting sediments. We favor folding, tilting and uplift of the slope sedimentsin the this interpretation for explaining the structural diver- forearc basins at the rear of all three lines attest to sity in the Alaska accretionarywedge. backthrustingfrom material addition below and imply recent underplating. Line 71 is marked by an extremely steep frontal slope 6. Application to Alaskan Accretionary of 170 (Figure 2 b) and appearsto representa wedge Wedge late in the underthrustingphase of the accretionarycy- Studies of convergentmargin evolution require ex- cle (e.g., Figures4c and 4e). There are indicationsthat periments with large convergenceallowing observation a new frontal thrust is just beginning to form, thereby of any deviation from the initial, "stable wedge," con- initiating a new phaseof imbricate thrusting (Figure figuration. Previous analog studies of thrust initiation 60. Farther to the NE, line HINCH-88 is alsomarked and wedgegrowth often featured convergenceof only 5- by an extremelysteep frontal slope of 160 [Friihn,1995] 10 timeslayer thickness [Colletta et al., 1991;Mulugeta and may also representa wedge currently in the un- and Koyi, 1992]. The large convergence(140-160 cm) derthrustingphase. Line 63 on the other hand (Fig- experimentspresented here have a shortening equal to ure 2c) has a relativelyconstant surface slope of 4- 60 70-80 times layer thickness. At the scaling factor of over35 km [Kunert,1995] and numerous frontal thrusts, 10-5 usedhere, this represents• 150km or 2.5 Myr of suggestinga wedgecurrently in the imbricate thrusting margin evolution at the current plate convergencerate mode (Figure6a). of 6 cm/yr, for the Alaskanmargin. Line EDGE-302 appears to represent a wedge hav- The accretionarycycles and widely varying range of ing recently entered the imbricate thrusting phase of frontal slopesobserved during the courseof a singlehigh the cycle (Figure 6c). The frontal portion displaysa GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING 10,171 gentle 2o surfaceslope and consistsof short sliceswith 7. Variations in Wedge Taper backthrustsand a "pop-up"structure (Figure 2a). At a distance of 11 km from the deformation front, the mean slopeincreases to 60 overthe next 19 km (locallyreach- A wide range of frontal slopes and thus wedge ta- ing 15ø). This slopebreak may representthe end of the persare observedat the Alaskaconvergent margin (Fig- last underthrusting episode. The tops of several imbri- ure 12 and Table 2). For comparison,wedge tapers cate sliceshave been accreted, while the lower portions have been compiled for the Nankai, Oregon-Cascadia appear to have been shearedbelow a mid-level detach- and Barbados accretionary wedgeswhere multichannel ment (Figures6a-6c). The overallgeometry is similar seismicrecords and deep sea drilling data are also avail- to experimenti after 120 cm convergence(Figure 5e), able [Moore et al., 1990; Taira et al., 1992; Shayelyet where the resumption of frontal thrusting has produced al., 1986; Davis and Hyndman, 1989; Westbrooket al., a very shallow surface slope beneath the oversteepened 1988]. While all four wedgeshave relatively large quan- front formed during the underthrusting phase. The five tities (1-34-km) of sedimentat the trench,three of them or six sheared and stretched slices correlate well with appear to belongto a similar class;these have moderate the zone of dipping reflectorsin the EDGE line and the convergentrates (4-6 cm/yr) and their physicalprop- uplifted point at the top of these units matches closely erties (e.g., internalfriction, porepressure) are believed with the shallow(< 3 km depth) ridge27 km from the to be fairly similar [Lallemandet al., 1994]. deformationfront (Figure2a). At each margin except Barbados, wide variations in Though long underthrust units are not clearly imaged surface slope occur arcward along individual lines as as in lines 71 and 63, underthrusting is interpreted to well as laterally, alongtrench strike (Figure 12), with be responsiblefor the rapid thickening of the initial 2 maximum surface slopesof 17ø, 140 and 10ø for Alaska, km section at the trench to 5 km, 30 km arcward. The Cascadia, and Nankai, respectively. Cyclical accretion presenceof two distinct detachments, mass balance cal- (as observedin the experiments)offers a plausibleex- culations and section balancing, all require a substan- planation, as a thrust wedge successivelyreaches the tial underthrust sectionequal to 0• 2/3 of the entire upper and lower limits of the taper stability field dur- sedimentaryinput Iron Huene et al., 1998]. The poor ing the underthrustingand the frontal accretionphases. quality of the seismicimage at this depth, however,can- Invoking lateral and arcward variations in material not clearly resolve the question of whether the under- parameters to explain the structural diversity in a single thrust section consists of sheets or entrained, sheared wedgedoes not appear satisfactory.Physical properties duplexes. Additionally, the prominent backthrusting at (e.g., porosity,fluid pressure)are knownto changeas the back of the section, with 0• 1 km offsetson numerous high porosity trench turbidites are compressedand de- backthrustsin the overlyingslope sediments, document watered during the early stagesof deformation[Bray strong deformation of the backstop, suggestingunder- and Karig, 1985; Byrne and Fisher, 1990]. This gen- thrustingand probableunderplating at depth lye et al., erally leads to an overall increasein sedimentstrength, 1997]. but also locally to a decreasein strength where pore- Finally, field geological studies of the Kodiak and pressuresare high [$hi and Wang,1988; Byeflee, 1990]. GhostRocks Formations on Kodiak Island (an exposed The decollementregion is typically marked by high pore late Cretaceousto early Tertiary accretionarycomplex) pressureand commonlyhas very low strength[Hubbert indicate they formed at a convergentmargin with a and Rubey, 1959; Byrne and Fisher, 1990; Moore et thick sedimentary section, comparable to the present al., 1995]. However,a strongermaterial or a weaker day situation at the Eastern Aleutian Trench [Sam- decollementboth reducethe angleof critical taper (the ple and Fisher, 1986; Fisher and Byrne, 1987]. The lowerboundary of the stabilityfield) [Daviset al., 1983; structuresfound include a seriesof SE vergent thrust Lallemand et al., 1994] and thus cannot explain steep slices, rotated over ramp faults, and duplexesbounded frontal slopesapproaching the angle of repose. Further- belowby a low-angledetachment (basal decollement) more, dewatering and compactionwould be expected to and aboveby a roof thrust (midleveldetachment). The produce primarily arcward changes,not lateral changes. rotated series of thrust slices are interpreted to sole A "strong decollement" leading to accretionary cy- into a common detachment and thus represent an im- clescan result from either moderate pore-pressurealong bricate fan. The duplexesare interpreted as having the basal detachment or relatively high pore-pressures been formed when thick sections of undeformed sedi- throughout the entire deforming wedge. The result- ment werethrust beneaththe toe of the overlyingwedge ing two-phaseepisodic process observed experimentally to be underplatedfarther arcward[Sample and Fisher, provides an explanation for these wide variations along 1986;Fisher and Byrne, 1987]. The tectonicprocesses a single trench where material properties and deforma- which produced the imbricate fan and underthrust units tional histories are likely to be similar. Variation along match well with the dynamics observedin high basal strike could be the result of time transgressivefault friction sandbox experiments and suggestthat simi- propagation causingdifferent segmentsalong the defro- lar processesmay be active in the current accretionary mation front to be in different phasesof the accretionary prism. cycle. 10,172 GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING

16- 0 Alaska [] Nankai /• Cascadia 0 BarbadosRidge

[] [] A

-- ¸ 0 • - ' - ' ... .,• maximumcriticaltapers..•• - :.-..::.-.<::..::::::::::-•c.:•...•_...... "..•...::•:::...... ::.`.•``.`.•.•.•;.•..%...:::``.`..`.•::•`;::•4•::•:•::•:•:•:•:•::•::::::::::;•4•`•*:•::•:::::•::::::•`.•..?•::::•:•::•:::::• .:: .: . .:::•::...... •...... :. : .;..•::-...... •.::::

mumcritical taper

-4 0 4 8 12 16 (in degrees) Figure 12. Wedgetapers from Alaska and for, comparison,two other margins with wide taper variationsand onewith little variation (meansurface slope, solid symbols; and maximumslope, opensymbols). Dashed line is a possiblestability field for the Alaskahigh basalfriction wedge.

8. Conclusions Appendix: Calculation of Work and Frictional Forces Cyclical behavior, alternating from imbricate thrusting to underthrusting of long sheetsis observedin high The instantaneouswork (Fudx) requiredto under- basal friction sandbox experiments simulating accre- thrust a unit is the sum of the frictionalresistance (f) tionary wedge growth. The dynamics observedin the alongthe roof thrust in direction• (A) and alongthe models closely reproducestructures observedin seismic ramp thrust in directionr (B), plus the forcerequired reflectionimages from the Alaskan accretionarywedge. to uplift the overlying portion of the wedge along the Long layeredsheets are observedas well as short frontal ramp basea verticaldistance dz (C) thrust slices. Some imbricate slices are sheared at a midlevel detachment. Similar structures are also observed (A) (B) (C) in an exposed Cretaceousaccretionary complex on Ko- diak Island, Alaska. F,,dz - fl•dz + f•dr + w•dz (A1) The different phasesof the cycle can be explained me- The instantaneouswork (Fidx) requiredto initiate a chanicallyin terms of the temporally varying, geometry- new basal thrust is equal to the frictional resistance dependentforces required to maintain an existing roof alongthe basalthrust in directionx (D) and alongthe thrust versus the forces to initiate a new basal and toe ramp thrust in directionr (E) plus the force re- frontal thrust. During one complete cycle, the up- quired to uplift the toe along the frontal ramp a vertical per and lower limits of the taper stability field are distancedz (F). successivelyreached. A steep wedge builds forward (D) (E) (F) through repeated imbricate thrusting, reducingthe surface slope. At shallowtapers, a long unit is underthrust, Fidx = fBdx + ftdr + wtdz (A2) causing erosion at the oversteepenedfront and uplift and shortening in the wedgethrough backthrusting. in all casesf- ttw cos/3,and w- mg- pVg, thus Cyclical accretion provides one possibleexplanation for wide variationsin frontal slopealong a singletrench, fn - wn(cosfi)lUl• - pVl•g(cosfi)lUl• (A3) where sediment and material properties are presumably f• - w• cos(Of+ fi)lU,•- pV•gcos(Of + fi)•u• (A4) GUTSCHER ET AL.- EPISODIC IMBRICATE THRUSTING 10,173

Table 2. Accretionary Parameters

Experiments flint lib I, cm O, cm a,,•,•x a,,•,. /3 H x L, cm v, cm/min

1 0.6 0.5 2.1 1.1 27 ø 6 ø 6 ø 14x40 10 12 0.6 0.5 2.0 1.0 28 ø 12 ø 6 ø 12x30 10

Region Line •,nt t• I, km O, km a,,•,•x a,,•e,• /3 H x L, km v, cm/yr

Alaska HINCH88 3.7 1.57 16 ø 2.6 ø 1.4 ø 6.5x40 5.7 EDGE302 2.0 1.27 15 ø 2.8 ø 2.4 ø 5.8x40 5.7 71 2.0 1.27 17 ø 3.30 2.5 ø 5.5x35 5.7 63 2.0 1.27 6 ø 4.1 ø 2.0 ø 5.5x35 5.7 Alb-111 0.45 -i- 0.1 0.3 4- 0.1 3.0 ?? 5 ø 3.6 ø 3.5 ø 5.5x35 5.7

Nankai NT62-8 0.50 4- 0.1 0.2 4- 0.1 1.1 0.4? 9 ø 2.3 ø 2.7 ø 3.2x26 4 4- 1.5 NK5 0.75 0.4? 3.5 0.6? 10 ø 5.0 ø 5.0 ø 8.0x20 4 4- 1.5

Oregon/ Or76-4 0.62 4- 0.1 0.23 4- 0.1 4.0 ?? 14ø 3.3ø 2.3ø 9x50 2.0 Or76-5 4.0 ?? 13 ø 3.3 ø 4.6 ø 11x50 2.0 Cascadia Ca85-01 2.4 ?? 9 ø 4.0 ø 5.0 ø 14x50 2.0

Barbados (N) 465 0.6 ?? 3ø 1.0ø 3.0ø 7x100 2.0 Ridge (N) A1-D 0.7 ?? 6ø 3.0ø 1.5ø 10xl10 2.0 (S) 105 6.0 ?? 9ø 1.4ø 0.6ø 15x300 2.0

Symbols: I.lint, coefficient of internal friction; t•b, coefficient of basal friction; I, input; O, output; a .... maximum surface slope; a,m,•, minimum surface slope; a,,•a•, mean surface slope; •, dip of subducting plate; H x L, height and width of recent accretionarywedge imaged on multichannelseismic reflection profiles; v, convergencerate of the subducting plate. Sources:for/•i,•t and t•; Alb-111, Davis and yon Huene [1987];NT62-8 and Or76-4, Lallemandet al. [1994];for Pacific Plate convergencerate at Alaskan margin, DeMets et al. [1990]; for Philippine Sea Plate convergencerate in Nankai Trench, Taira et al. [1992]and Senoet al. [1993]for Nankai seismicprofiles NT62-8, Moore et al. [1990]and NKS, LePichonet al. [1992];for Oregonseismic profiles, Shayely et al. [1986];for Cascadiaseismic profiles and convergencerate Davis and Hyndman[1989]; and for BarbadosRidge seismicprofiles and convergencerate, Ladd et al. [1990],Moore et al. [1988], Westbrooket al. [1988],and Mascleet al. [1990].

- - pva(os (A5) Sincedr- (1/cos07)dx, substituting(A8) into (A4) - w, os(0 + - p¬a os(0 + (A6) yields term B

Total forces(F. and Fi), frictionalforces (f), weights frdr (w), andvolumes (V) arecalculated for a cross-sectional cos(0+ areaper perpendicularunit length(l). All areas(A) can cos0 7 be expressedin terms of the lengthsH, LR, LB, and Lt and the anglesa, fi, and 07. For example, ' • -- - tanO•(LsLa - La•)]dx (A12) AR -- (•)L/•2(tana+tan/•)(A7) Similarly,substituting (A9) into (A5) yieldsterm D Ar - (•)(tana+tan/•+tanOT)(LB2-Lt•2) - tan07(LBLa - La2) (AS) fBdx =(I •B Pg) cos/•[ H LB cos/• AB - HLscos•+ • (1)(tan a+ tan fi)L. 2(A9) +(•) (tana +tan/•) LB2]dx (A13)

(10) Sincedr - (1/cos07)dx, substituting(A10) into Substituting(A7) into (A3) yieldsterm A (A6) yieldsterm E

f-• Id x _- (I-t-• 2Pg ) cos/•(tan aq- tan/•)Ln2dx (All) ftdrI = (ytpg)2 cos107 cos(07+/•)HLtdx (A14) 10,174 GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING

To uplift wedge or toe, an incrementalvertical dis- Dirk Kl'eischen,JSrg Kunert, Jfirgen Frfihn, Bernard Sanche, tance dz, the horizontal component of dx, cos/•dx is and Stephane Dominguez for fruitful discussions,access to valuable seismic reflection data, and technical assistance in multipliedby the componentalong the ramp, tan(Of+ the laboratory. We also thank the reviewers Dan Davis, Eli /7), givingdz = cos/?tan(Of +/?)dx, and term F then Silver, and Associate Editor Mike Ellis for constructive and becomes critical comments which helped improve the manuscript.

wtdz :(•#)cos/•tan(Of+/•)(HLtcos/•)dx(A15)References

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M.-A. Gutscher,S. Lallemand,and J. MalavieilleLabo- (ReceivedNovember 15, 1996; revisedNovember 27, 1997; ratoire de G•ophysiqueet Tectonique,Universitd de Mont- acceptedDecember 3, 1997.)