JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. B5, PAGES 10,161-10,176,MAY 10, 1998
Episodic imbricate thrusting and underthrusting'
Analogexperimentsand mechanicalanalysisappliedto
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 slicesand repeated sequencesof long, underthrustsheets. Rapid landward increasesin wedgethickness,
backthrusting,and uplift of the forearc are observed,suggestingunderthrusting
beneaththe wedge.Thesefeaturesand a widely varyingfrontal wedgemorphology
are interpreted to be caused by different modes of accretion active concurrently
alongthe trench at different locations. Episodicwedgegrowth is observedin high
basal friction experiments using sand as an analog material. Two phasesof an
accretionarycyclecan be distinguished:frontal accretionof short imbricate thrust
slices,alternating with underthrustingof long, undeformedsheets. The phase is
shownexperimentallyto dependupon the surfaceslopeof the wedge. Mechanical
analysisof 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 stabilityfield) the overburdenis too great to permit
underthrusting,and failure occursrepeatedly at the wedgefront producingshort
imbricate slices. The wedgegrowsforward, loweringthe surfaceangle to the
minimum critical taper. For a shallowfrontal slope the reducedoverburdenalong
an active roof thrust permits sustainedunderthrusting, causingfrontal erosionand
backthrusting,steepeningthe wedgeand thus completingthe cycle.
1.
Introduction
Seismicreflectionprofilingof convergentmarginshas
recordeda high degreeof structural diversityin accretionarywedgeswheredeepseasedimentsare imbricated
against and subductedbeneath the overridingplate
[Westbrooket al., 1988; Moore et al., 1990; Moore et
al., 1991;Shipleyet al., 1992].The causesfor structural
diversityare not fully understoodbecausethe most deformedportionsof the wedgeare often poorly resolved.
Furthermore, it is unclear whether wedge growth occurs by steady state processes
or in episodicfashion,
alternatingwith periodsof erosion.The frontal wedge
Now at Laboratoire de Gdophysiqueet Tectonique,Universitd de Montpellier II, Montpellier, France.
Copyright 1998 by the American GeophysicalUnion.
configurationat the Alaskaconvergentmargin showsa
high degreeof lateral variation, and frontal slopesvary
from less than 20 to over 150 within
a few tens of kilo-
meters.
An episodic variation in frontal configuration has
been observedin a high basal friction analog experi-
mentsimulatingaccretionary
wedgegrowth[Gutschef
et al., 1996]. Two distinctmodesof deformation,associatedwith imbricate thrusting and underthrusting,
occurreddespitea constantthicknessof incomingsediment and an unchangingbasal friction. Since direct
observationof the developmentof a submarine accretionary wedgeover geologictimescalesis not possible,
analogmodelingis a useful tool permitting observation
of the completeevolutionof a model thrust wedgeunder
controlled boundary conditions.
The objectivesof this study are threefold: (1) to
quantify the conditions controlling episodic accretion
Paper number 97JB03541.
in analogthrust wedges,(2) to providea mechanical
0148-0227
/ 98/ 97JB-03541$09.00
explanation for the two distinct modes of deformation
10,161
10,162
GUTSCHERET AL.- EPISODICIMBRICATETHRUSTING
in terms of the body and boundaryforces,and (3) to
apply theseresultsto the Alaska accretionarywedge.
In the Eastern Aleutian Trench, 45 Ma old oceanic
crust of the Pacific plate is subductingbeneath the
southernAlaskanmarginat a rateof 5.7cm/yr [DeMets
et al., 1990](Figure 1) ). The basal500-600m sec-
2. Tectonic Setting of the Alaska
Convergent Margin
The Alaska convergentmargin offers a particularly
good study area sinceit has been investigatedby deep
tion of deep sea sediments,representingthe Surveyor
Fan, is overlain by a 1400 m sequenceof alternating
hemipelagic
sediments
andturbiditictrenchfill [Kven-
seadrilling[Kulmet al., 1973]andmultichannelseismic voldenand yon Huene, 1985; yon Huene, 1989; Moore et
reflectionprofiles[Kvenvoldenand yon Huene, 1985; al., 1991].In lineEDGE-302,thefrontal8 km of the acMoore et al., 1991], supplementedby depth-velocity cretionarywedgeconsistof three short imbricateslices
forethrust
andbackthrust
controlfrom wide angleseismicdata Iron Huene and (Figure2a), witha conjugate
set
defining
a
"pop-up"
type
of
structure.
The shallow
Flueh, 1994; Ye et al., 1997]as well as high-resolution
20
frontal
slope
increases
to
580
at
the
third major
swathmappingbathymetry[yonHueneandFlueh,1994;
thrust
fault,
locally
reaching
15
ø.
At
a
distance
of 12Friihn• 1995].The wedgeis markedby a largequantity
15
km
from
the
deformation
front,
the
seismic
signature
of incomingsediment(2--3km) and is classedas a typical accretionarywedge[yon Huene and Scholl, 1991; losesits characterand the arcwarddippingand subhorizontal reflectorscan no longerbe assignedto any parLallemandet al., 1994].
,,
o
NORTH
AMERICAN
PLATE
•
.KSSD 2
\
\
\
\
\
\
\
ß KSSD 1
DSDP 182
PACIFIC
ß
•
/
/
/
PLATE
•.g-•
DSDP
178 o
'
56*
208*
212'
Figure 1. Alaskalocationmap, with multichannelseismiclines(solidlinesare presentedin text,
dashedlinesare discussed,
but not displayed),boreholelocations(small,filled triangles)[Kulm
et al., 1973;Kvenvoldenand yonHuene,1985]and bathymetry(depthin m) sources:TOPEX
global2 arcminbathymetry[Smithand Sandwell,1994;1997],high resolutionswathmapping
bathymetryNE of line 71 Iron HueneandFlueh,1994]'
'
GUTSCHER
ET AL.: EPISODIC
a) NW
IMBRICATE
THRUSTING
10,163
EDGE
line-302
SE
[km]
..........
'"
40
b)
[km]
NW
20
0
line71
SE
. [km]
__•5
.
'
'
'
'
I
'
'
'
'
I
40
O)
'
'
'
'
I
'
'
'
'
I
....
I
'
'
'
[km]
NW
'
I
'
'
'
'
I
....
I
....
I
'
'
20
'
'1''
•
•1
•9
0
line 63
SE
fore arc basin
[km]
½•:•:•:•:•k.::½•;-'•;-':.-'::•
........
-- •
•--•i-•::•:•:•-"•:::
..........
••,•
40
•_
[km]
...•------- •---•
20
•---'-•
-----•-
•
•---•"
-5
-•
0
Figure 2. Interpretativeline drawingof seismicreflectionprofiles(pre stack depth migration,
VE - 1.5). Heavy lines indicatefaults or erosionalunconformities,dashedwhere uncertain,
oceanicbasement,dark shadedregion,backstop,light shadedregion. (a) Line EDGE-302, one
horizonwith a clearseismicsignatureis tracedasa shadedline, (b) Line 71, notethe longlayered
sheetsbetweenkm 20 and 40, and (c) Line 63, note the longsheetsand the 2 km deepfore arc
basin at rear.
ticular stratigraphic horizon Surface morphology and
dipping zonesof high reflectivity,however,suggestfour
to seven more major thrust slices truncated at 6 km
depth by a midlevel detachment. At a distance of 4060 km from the deformation front, a 0.5-1.5 km thick
sequenceof slope sedimentsis marked by strong landward vergentfolding and shortening.At depth, a I km
thick sectionof layered reflectorsis imaged above the
subductingoceaniccrust and beneaththe backstop.
Two parallel seismiclines to the SW, lines 71 and 63,
all accreted and those below are all transported farther
arcward below the wedge.
3. Experimental Modeling
The growth of accretionary wedges and fold-andthrust belts has been the subject of numerous analog
modelingstudies[Davis et al., 1983; Malavieille, 1984;
Mulugeta, 1988; Malavieille et al., 1991; Liu et al., 1992;
Lallemand et al., 1992; Malavieille et al., 1993; Lalledisplaylong(10-20km) repeatingsequences
of reflectors mand et al., 1994; Kukowski et al., 1994; Larroque et al.,
(Figures2b and 2c) 30 km from the deformationfront.
The overlyingridge in line 63 (at 35 km) shallowsto
2.5 km depth and bounds a 2 km deep forearc basin.
In both this basin and the I km deep basin along strike
at the rear of line 71 (at 35 km) folding,tilting, and
uplift of the overlying slope sediment strata are visible
[Kunert,1995].
In all three lines, the initial 2 km trench sectionis tectonically thickenedto about 5 km within 30-35 km from
the deformation front. Volumetrically, this thickening
amountsto a shorteningof 45-55km [Kunert,1995]assumingthat the sedimentsabove the decollementare
1995; Wangand Davis, 1996]. Thesestudieshaveconfirmed the applicability of critical wedgetheory to modeling deformationin the brittle, upper portionsof sub-
marine accretionarywedges[Daviset al., 1983;Dahlen
et al., 1984, Dahlen, 1984]. The theory predictsthat
the geometryof a growingwedge(as definedby the
surfaceslopea and the basalslopefi) is a functionof
the material strength and the basal friction according
to
(bb
+fi)
a+fi--(I+K)
(1)
10,164
GUTSCHER
ET AL.: EPISODIC
where
• isangle
ofbasal
friction,
related
tothecoefficient of basal friction by it0 = tanc)• and K is a
dimensionlessparameter, usually of the order of 2.
The experimentsreported here were designedto test
the range of experimental conditions over which the
IMBRICATE
a)
Frontal
Accretion
8o
DE...
o[
•
rigid
•':•':i•i•::•,•'•:•:•i•i•:•:•,,,•,•,•
......................
...:.................
.-:::,•,•.
-•;•'•.•,eformable
backstop
wall
_ ............
:::::'
..........
'"'"':':?::•::::•:?•':"•":•:•:::::•::::•:'•'•.•%•.•
-.....................
(orarc)
Subducting
plate•
phenomenonof cyclicalaccretionoccurs[Gutschefet
al., 1996]. Factorstestedincludedthe surfaceslopeof
the initial buttress,the lengthof 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
sandoverliesa rigid basalplate, pulled beneatha rigid
THRUSTING
..
b)
Underthrusting
I•l•
verticalwall [Malavieill½et al., 1991;Lallemandet al.,
1992;Kukowskiet al., 1994; Gutschef½tal., 1996]. A
deformablebuttressor "backstop"composedof 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 (diameter0.3-0.5 mm, internal (a) frontalimbricatethrustingand (b) underthrusting.
friction tt = 0.6) is chosenas an analogmaterial,since The three observablequantities distinguishingthe two
it exhibits a depth-dependentCoulombrheology,ap- are (1) the lengthof thrustslices,(2) the surfaceslope,
front
propriate to studies of upper crustal rocks and marine and(3) the advanceandretreatof the deformation
DF.
sediments. Scaling is such that 1 cm in the sandbox
correspondsto 1 km in nature. Thus the cohesionof
the accretingsand(Co • 20 Pa) and packedsandbackstop (Co m 100Pa) scaleto 2 and 10 MPa, respectively,
reasonable
values for unconsolidated
marine sediments
and lithifiedsedimentaryrocks[Hoshinoet al., 1972].
The 2 cm of sand (input) on the downgoingplate
representsthe 2 km of deep sea sedimentson the subducting oceanic crust of the Pacific plate. The interface with the basal plate consistsof double-sidedadhe-
mentswith the same high basal friction, sameconstant
sedimentaryinput, and same constantoutput but with
different initial surfaceslopesare first presentedin de-
tail (Table 1, experiments1 and 12). For comparison,
a typical low basal friction experiment,again with the
sameinput and output, is introduced(Table 1, experiment 4). Finally, two high basalfriction experiments
sive tape coveredwith sand and servesas a high fricare briefly discussedwhere a very long initial buttress
tion decollement(tt6 m 0.5). The deformablepacked
wasincludedto test the maximumlengthof underthrust
sand buttress representsthe more competent portions
sheets
and the effectof zerosubductedoutput (Table
of the Alaskan arc, composedof crystallinebasementor
1,
experiments
33 and 34).
older, metamorphosed, accreted sediments. In the ex-
perimentspresentedhere (with one exception)a 1 cm
apertureat the baseof the wall (output) permitsmaterial to exit the system and representsthe substantial
thickness of underthrust
sediments known from seismic
4.1. Experimen• 1 (Shallow Initial Surface
Slope)
Experiment 1 begins with a shallowsurfaceslope of
10ø (Figure4a). After the first frontalthrustforms,the
roof thrust remains active, allowinga long sheet to be
underthrustbeneaththe sandwedge,with very little inA limitation of this experimentalapproachis that the ternaldeformation(Figure4b). Note the soliddiamond
"subaerial" sand has no fluids and thus no pore pres- markerbelowthe tip of the advancingunit (Figures4asure. Thereforethe resultinganglesof reposeand an- 4c). Once the roof thrust blocks,a major backthrust
glesof taper are greater than thoseobservedin the sub- deformsthe overlyingbackstopwedgeand a new basal
marine environment. Additionally, the effects of com- thrust propagatesforward initiating frontal thrusting
paction(e.g.,porosityloss)are smallerthan in subma- (Figure4c). Sevenshortthrustslicesform,areaccreted,
and build the wedgeout forward, loweringthe frontal
rine accretionarywedges.
slope(Figure4d). A secondlongsheetof" oceanic"sedreflectionprofilesfrom Alaska (Figure 2a) and other
convergentmargins[Westbrook
et al., 1982; Shipleyet
al., 1990].
4. Modeling Results
In all experimentsperformedwith high basalfriction
and input greater than output, cyclical behavior was
observedalternating betweenfrontal accretionof short
imbricate thrust slicesand underthrustingof long, un-
iment and a small amount of previously accreted material is underthrust beneath the wedge. This removal
of material at the toe steepensthe frontal slope to 2• ø,
despitethe occurrence
of slumping(Figure4e). Frontal
thrusting resumes,building five more imbricate slices,
the rear most of which _areentrained into the subducfion
deformedsheets(Figure3). Two representative
experi- channelalonga midleveldetachment(Figure4f ).
GUTSCHER
ET AL.: EPISODIC
•ub
THRUSTING
10,165
When the surface slopesobservedin the experiments
shownare plotted in the taper stability field for a high
Table 1. Experimental Conditions
Expt.
IMBRICATE
•ui,t
I, cm
O, cm
c•
13
$to,, cm
0.6
0.6
0.6
0.6
0.6
2
2
2
2
2
1
1
1
I
0
10 ø
22 ø
6ø
15 ø
15 ø
6ø
6ø
4ø
6ø
6ø
140
160
150
120
125
basalfrictionof 0.5 (Figure7a, shadedregion)widefluctuations are seen. The wedgesuccessively
movesfrom
1
12
4
33
34
0.5
0.5
0.35
0.5
0.5
an unstableregimeat the upperboundary(the maximum or limiting taper), with failure alongtrenchward
dippingplanescausingslumpsand slides,to a compressionalregimeat the lowerlimit (the mimimumor "critical taper") wherefailureoccursrepeatedlyalongarcwarddippingplanesgeneratingshort imbricateslices.
Symbols: •ub,coefficientof basal friction; I•i,•t, coeffiPlotting the frontal slope(c•) and the initiation of
cient of internal friction; I, input; O, output; c•, initial sur- eachfrontalthrust as a functionof convergence
(Figure
faceslope;fl, dip of subductingplate; $tot, total convergence
7b), the truly cyclicalnatureof theseunderthrusting
during experiment.
4.2. Experiment 12 (Steep Initial Surface
Slope)
and frontal accretion processesbecomesevident. The
surfaceslope decreasesduring the imbricate thrusting
phaseof the cycleas the wedgebuildsout forwardand
increasesduring the underthrustingphaseof the cycle
as the front is oversteepened
by erosionalongthe emerg-
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
wedgeforward,reducingthe frontalslope(Figure5b).
The tops of the slicesare accreted, and the basesare
shearedoff at a midleveldetachmentas they are pulled
alongwith the subductingplate. Once the surfaceslope
has becomeshallower,a long unit is underthrust beneath the overlying sand wedge. The underthrusting
sheet causes frontal
erosion
which
increases
the sur-
faceslopeup to 280 (Figure5c). Anotherfrontal accretion phase follows, with five more imbricate slices
(Figure5d). Lastly,a secondunderthrusting
phaseoc-
a)
deformation
ct
½
'•Oø
•
••.•.....,.....
•:.:..._.•-•
•o•..
•,•
__
10
.••.[cm]
future
thrust, ........
'-•-•":":"-'""•'"•-""'.:'.':':.':.'•
0
b)
•'::
.....
•
lO
:':•
::'::
•:
'::":'""
0
.....•
"'-•'•-'
......,•
_-..
c)
curs, again steepeningthe wedgeto 280 through frontal
[cm]
10
[cm]
o
erosion(Figure5e).
In both experimentsi and 12, shearingof the lower
portionsof the imbricateslicesoccursalonga midlevel
detachment(Figures6a and 6b). Underplatingoccurs
as the ramp thrust at the tip of the underthrusting
sheetupliftsthe overlyingunits. If theseoverlyingunits
consistof sheared,imbricate slices,then entrained,un-
d)
lO
"-"
[cm]
o
e)
lO
derplatedduplexesform (Figure6c) [Gutschefet al.,
1996].If theseconsistof longsheets,then layered,underplatedsheetsform (Figures6d, 6e, and 6f). When
motion alongthe midleveldetachmentceases,a backthrust developsas material is underplatedbeforea new
basalandfrontalthrustpropagates
forward(Figures6c
[cm]
o
f)
lO
[cm]
and 6f). Underplatingwasonlyobserved
in highbasal
friction experimentswith excessinput. The degreeof
underplatingas a functionof theseparametersis quan-
tifiedelsewhere
[Gutschefet al., 1998].
4.3. Taper Stability Field, Cyclicity
and
Phase
Shift
o
20
[cm]
0
Figure 4. Tectonicsketches
of experiment1 [Gutschef
et al., 1996];(a) after0 cm;(b) 15cm;(c) 35 cm;(d) 70
cm; (e) 120cm, and (f) 140cm of convergence.
Heavy
Accordingto Mohr-Coulombwedgetheory the internal and basalfriction of a deformingwedgeslidingovera
lines representfaults, heaviestwhen active, with sense
of motion. Hatchured area is rigid vertical rear wall.
Incipient thrust at the wedgeapex in the initial stage
fault surfacedefinea taperstabilityfield [Dahlen,1984].
is shown dashed.
10,166
GUTSCHER
ET AL' EPISODICIMBRICATETHRUSTING
of the wedge.At shallow
surface
slopes(experiment
1,
15
Figures
4a and4b)underthrusting
oflongundeformed
units is favored. At steepsurfaceslopes(experiment
a)
future
deformation
thrust front
J,•'
10
12,Figures
5aand5b)frontalimbricate
thrusting
isfa-
[cm]
vored. Thus the mechanicalforcescontrollingthe phase
ofthe accretionary
cycleappearto dependonwedgegeometry.
15
b)
10
[cm]
'"'"'L'2'2'-
5. Mechanical Analysis
The frictionalandgravitational
forcesactingon the
variousfault surfaces,
e.g., ramp thrust, basalthrust,
and roof thrust can be calculated for a generalized
wedgegeometry
(Figure8) andthusthe instantaneous
worknecessary
to continue
or initiatemotionalongdif15
10
[cm]
ferentsurfacescan be quantifiedfor any set of wedge
parameters
(modelor natural)[Schniirle,
1994].This
allowspredictions
to be madeconcerning
the maximumlengthof thrustslices
whichcanin turn becomparedto the average
lengths
fromexperimental
observations. A similar mechanicalanalysis[Platt, 1988]
treatedonly lowerbasalfrictionsand constant,shallowsurfaceslopes(a < 5ø) andthusdid not directly
addressthe mechanicsof long underthrustsheetsnor
temporal variation in forces.
The instantaneous
work (Fudx) requiredto underthrust a unit an incrementaldistancedx is equal to the
frictionalresistance
(f) alongthe roofthrust(A) and
alongtherampthrust(B), plustheforce(w) required
to upliftthe overlying
portionof the wedgealongthe
rampbasea verticaldistancedz (C).
F•,dx - f•tdx + f,.dr + w,.dz
Equation(2) canbe compared
to the instantaneous
work(Fidx)required
toinitiateanewbasal
thrust,with
accompanying
frontalrampthrustand an equivalent
displacement
dx
whichis equalto the frictionalresisFigure5. Tectonic
sketches
ofexperiment
12;(a)after
0 cm;(b) 25cm;(c)75cm;(d) 110cm,and(e)160cm tance(f) alongthebasalthrust(D) andalongthetoe
ofconvergence
(symbols
sameasin Figure4).
rampthrust(E) plusthe force(w) required
to uplift
the toe alongthe rampa verticaldistance
dz (F) (in-
dices(R), roofthrust,(t), toe,(r), rampthrust,(u),
marion front also alternatively advancesand retreats
underthrusting,
(i), initiation)
(Figure
3) [Gutschef
et al.,1996].In bothexperiments,
Fidx - fBdx + ftdr + wtdz
twofull cyclesareobserved.
Experiment
1 startswith
underthrusting
andendswith frontalaccretion.Exper- in all casesf - pcos/3,wherew -mg - pVg.
(3)
iment 12 is shiftedhalf a phaseand startswith frontal
accretion and ends with underthrusting.
In bothcases,the energylostdueto internaldefor-
Forcomparison,
a similarplotis shown(Figure7c) mationwithinthe sand(e.g.,kinkbands)is neglected.
forces(f), weights
for a low basalfriction experiment(experiment4), Totalforces(F• andFi), frictional
which otherwisehas almost the same initial configura- (w)andvolumes
(V) arecalculated
fora cross
sectional
unitlength.All areascanbeextionasexperiment
1 (sameinput,sameoutput,similar areaperperpendicular
in termsof thelengths
H, Ln, LB andLt and
a' and/3. Continuous,
frontalimbricatethrustingoccurs pressed
the
angles
a,/3
and
0f.
Lengths
in turnarerelatedby
at fairlyregularintervalsof roughly6 cm, anda maintains a nearlyconstantvalue,barelyincreasing
during LB = Ln + Lt, Lr = Lt, and Lt - HsinOf.
Substitutionand algebrayieldunwieldybut uncom150 cm of convergence
from 6o to 7ø.
plicated
expressions
(seetheappendix
fordetails)
which
Forhighbasalfrictionthemodeofdeformation
isobcan
be
evaluated
for
any
choice
of
basal
friction
and
servedexperimentally
to dependon the configuration
GUTSCHER
ET AL.: EPISODIC
IMBRICATE
"half
slices"
a)accreted
upper
. mid-level
• '•detachmen
,[
"ent
.... • .-
b)
•"•,••
10,167
UnderplatingSheets
Underplating Duplexes
..............
THRUSTING
.,••,-,;
.....
•-X
l•g sheet
f f
erosion•-<•
. _' '. .,'.
underthrusting
sheet'
c)
]•
frontal thrusbng
,'
previously
entrained :-,,'
.duplzs " ,f"
•
t t t
underplated
"entrained
/•j
2nd
underthrusting
sheet
""_=.,,•
'
frontal
thrusting
•
.'•
•<•.esumes
•""%•1st
sheet
underpla
2ndunderthrUsting
sheet
halt•
Figure 6. Evolutionary paths of two different underplated structures: duplexes and sheets.
Underplatingof duplexes:(a) frontal accretionwith shearingof imbricateslicesat a mid-level
detachment,
(b) underthrusting
with frontaluplift, and (c) underplating
of entrainedduplexes
with backthrustingand uplift at rear of wedge(verticalarrowsindicatemaximumuplift). Underplatingof sheets:(d) underthrust
sheetfollowing
frontalaccretion,(e) 2ndunderthrust
sheet
causingfrontaluplift, and (f) underplating
of first sheetthroughbackthrusting
anduplift at rear
of wedge(verticalarrowsindicatemaximumuplift).
length of thrust slice. (The length of a thrust sliceis
measuredfrom the ramp cut off at the basal detachment
to the next basalramp cut off.)
typical steep frontal slope of c• : 25ø. The force required to initiate a new frontal and basal thrust Fi is
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 trenchwidth). It shouldbe noted that
the frictionalonga faultedsurfacein the sand(i.e., the
activeroofthrust) hasbeenreportedto be 10%lower
than the internalfrictionof the sand[Liu et al., 1992]
and that the correspondingvalues have been adopted
(Pg)
{[(•)cøsj•(tanc•-l-tanfi)
LR
2]
+p)+ p
+p)
'(•)(tan
a+tan
"+tan
Oy)
(L•- Ls
•)
-tan
0y
(L•
L•-L•
•)}
(4)
for these calculations.
The forces(F• and Fi) are plottedversusslicelength
for a moderatefrontalslopeof 10ø (Figure9) andfor a
steepfrontalslopeof 25o (Figure10). The intersection
of the curvesF• and F/ predictsthe averagelength of
thrust slices. The maximum length of an underthrust
unit (i.e., lengthof an activeroofthrust) variesaccording to both the basal friction and the surfaceslope of
LBcos/3
+(tan
2 tan/•)
{ cos(./--]
c•
+
LB2
)
the wedge.For low basalfrictionsof 0.3-0.4 (50- 67%
of the internalfriction),.lessforceis requiredto initiate
+[(•)(cos
1 ) cos+ +HLt•
a new basal and frontal thrust than to continue motion
alongan existingroof thrust. The predictedfault spacing (for a 2 cm layer thicknessand shallow10ø frontal
slope)is 4-10 cm, whichcorresponds
well to the 6 cm
averagefault spacingobserved[Gutschefet al., 1998].
For a high basalfriction of 0.5 (83% of the internal
For the experiments reported here, appropriate pa- friction) and 10ø surfaceslope,lessforceis requiredto
rameters are; laint : /•r : /•t : 0.6, /•R : 0.54, sustain motion along the roof thrust becausethere 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. underthrusting
is favored(experiment1, 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
+
+ cos]}
10,168
GUTSCHER ET AL.: EPISODIC IMBRICATE
taper
a)
stability
field
b) 35
underthrusting
i__._,q.•_.•
re
=0.50 "angle
of
repose"
(slides)..-.•
3C
3O
THRUSTING
high
basal
•
friction
shallow
initial
slope
30-•
Exp...•1
CL
•/d
o
• 20
_
1,
= -•- '•.r •2-steep
i•itial
slope
2O
m •15
•
10
'
'd
-_•
10
5t,-.........
10
_
4m
O
'''•'''•'''•'''•'''•'''•'''•'''/
0
20
40
60
m
m
m
m
m
m
m
80
m
100
mm
120
thrusts
mm
140
160
convergence [cm]
0
0
-20
- 10
0
10
20
I• (platedip)
low
C) 35
basal
friction
3O
Exp. #4 (final stage)
Figure 7. (a) Stability fieldsfor high basal friction
(0.5, shaded)andmoderatebasalfriction(0.4, dashed),
showinginitial (opensymbols),intermediateand final
(solidsymbols)surfaceslopesfor highbasalfrictionex-
25-
'• •
2020
[cm]
0
15-
periments i and 12 and low basal friction experiment 4.
(b) Surfaceslopefluctuation(opensymbolswith a cubicsplinecurvefit) andthrustinitiation(solidsymbols)
10-
5 •--:. - '- •
o
thrusts•.•
versusconvergence
for high basalfriction experiments1
• •
o" '2••;' '4••;' .....
•'o •'o'•o'o'i•'o'i•'o'i•o
low basalfriction experiment 4, inset showinggeometry
of final stage after 150 cm of convergence.
convergence [cm]
(squares)and 12 (circles),c: (sameasin Figure7b) for
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 roofandrampthrustsof
anunderthrusting
unit,and(b) actingonnewlyinitiatedbasalandfrontalrampthrusts(indices
R, roofthrust;r, rampthrust;B, basalthrust;t, toe thrust).
GUTSCHER ET AL' EPISODIC IMBRICATE
a)
a slight uncertainty(4-5%) in the basalfriction or in
400
the friction
ß F underthr.
__o__ F init. 0.5
300--'--F init0'4
250
..... []....Finit.
0.3
200_../.'x -'.......--'
[
00-•
-'
1; Fig.
9b .....•..•'......a-"
0
10
10,169
narrowly spacedin the length range 30-50+ cm. Thus,
(z- 10ø
35O-
THRUSTING
20
30
[
40
50
length of thrust slice [cm]
of the active roof thrust
can result
in 4-20
cm in the length of the sheets. This uncertainty does
not, however, affect the overall trend. Underthrusting
of long sheetscan only occur for a high basal friction
and for a shallow surface slope.
Sincethe arcwardincreasein wedgethickness(and
thusoverburden)
is a functionof the surfaceslope(a),
if this angleis large, then evenwith high basal friction,
underthrusting
is inhibited(Figures10aand 10b). This
is the casefor experiment 12, with an initial slopeof 22ø.
The forcesrequiredto underthrust below a steepsurface
slope of 25o in all casesexceed the force necessaryto
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
(experiment1; Figures4e and 4f and experiment12;
Figures5a and 5b).
50
4O
z
30
o
20
a)
a -
25 ø
400
350
A
10
•'
250
•(,3
200
F underthr.
--o--F
300
2
•
'
'
I
4
'
'
'
I
'
6
'
'
I
8
]
'
'
u_
I
.....-.-, ,n,,.
/
.,'
.'
///
,.,"
,•• / ."
"'
.... ,,,, ,
•...,"
100
Fig. lob
50
Figure 9. Forcesrequiredto underthrusta unit (F underthr.) and to initiate a new basaland frontal thrust
(F init.) versuslength of thrust slicefor three basal
/o" /
'
/
,' / ...•'
150
10
length of thrust slice [cm]
•,'
--*--F init.0.4
o
I
0
/
init. 0.5
•'o/.
0
0
10
-"-
20
30
40
50
length of thrust slice [cm]
frictions, 0.5, 0.4, 0.3, for a moderate surface slope of
10ø. (a) Slicelengths0-50 cm, and (b) closeupnear
origin for slicelengthsof 0-10 cm (note "underthrust-
b)
ing" is consideredto begin at a slicelength of 4 cm, the
a -
25 ø
horizontallengthof 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
intersectionof the two curvesto be • 50 cm (Figure
3O
2O
Two high basal friction experimentswith very long
initial buttresses(• 70 cm length)wereperformedto
testthe maximumlengthof the underthrustsheets(Figure 11). Experiment33 hadthe same1 cm outputasthe
10
'
'
'
I
'
'
'
I
'
'
'
I
'
'
'
I
'
'
'
other experimentsreported here, while experiment 34
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 experimentshad the same 2 cm input Figure 10. Forcesrequiredto underthrusta unit (F
as the other experiments reported and both produced underthr.) andto initiate a newbasalandfrontalthrust
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 25ø.
between the theoretically predicted and the observed
(a) Slicelengths0-50 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 newthrustfault (Fi in Figure9a are very
9.
10,170
GUTSCHER
ET AL.' EPISODIC
Experiment 33
IMBRICATE
THRUSTING
(120 cm)
25
20
a)
15
lO
[cm]
20
[cm]
0
Experiment 34
(125 cm)
b)
25
20
15
lO
[cm]
Figure 11. Tectonicsketches
of (a) experiment33, input of 2 cm, outputof 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
for natural thrust wedgeswith a basal friction exceeding 80% of the internal friction and with excesssediment input, cyclicalaccretionis expected,varying from
the frontal accretionmodeto the underthrustingmode.
Accordingly,wide variations in the frontal wedgemorphologyare alsoexpected,so that a singlemargin may
havefrontal slopesvaryingfrom a few degreesup to the
angle of reposefor the accretingsediments. We favor
this interpretation for explaining the structural diversity in the Alaska accretionarywedge.
6. Application to Alaskan Accretionary
Wedge
basal friction experiment correlate well with structures
and surface morphology observedin reflection seismic
lines from the Alaskan convergentmargin and offer a
viable
mechanism
for their formation.
Lines 71 and 63
(Figures2b and 2c) provideclearevidencethat several
long (15-20km), relativelyundeformedsheetsof 1-1.5
km thicknesshave been emplaced beneath the wedge
throughrepeatedunderthrusting(Figures6d-6f). The
folding, tilting and uplift of the slope sedimentsin the
forearc
basins at the rear
of all three
lines attest
to
backthrustingfrom material addition below and imply
recent underplating.
Line 71 is marked by an extremely steep frontal slope
of 170 (Figure 2 b) and appearsto representa wedge
late in the underthrustingphaseof 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 extremelysteepfrontalslopeof 160[Friihn,1995]
10 timeslayerthickness[Collettaet al., 1991;Mulugeta and may also representa wedge currently in the unand Koyi, 1992]. The largeconvergence
(140-160cm) derthrustingphase. Line 63 on the other hand (Figexperimentspresentedhere have a shorteningequal to ure 2c) has a relativelyconstantsurfaceslopeof 4- 60
frontalthrusts,
70-80 times layer thickness. At the scaling factor of over35 km [Kunert,1995]andnumerous
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).
Line EDGE-302 appears to represent a wedge havof 6 cm/yr, for the Alaskanmargin.
The accretionarycyclesand widely varying range of ing recently entered the imbricate thrusting phase of
frontal slopesobservedduring the courseof a singlehigh the cycle (Figure 6c). The frontal portion displaysa
GUTSCHER
ET AL.: EPISODIC
gentle 2o surfaceslope and consistsof short sliceswith
backthrustsanda "pop-up"structure(Figure2a). At a
IMBRICATE
THRUSTING
10,171
7. Variations in Wedge Taper
distance of 11 km from the deformation front, the mean
A wide range of frontal slopes and thus wedge taslopeincreases
to 60 overthe next 19 km (locallyreachmargin(Figing 15ø). This slopebreakmay representthe endof the persare observedat the Alaskaconvergent
last underthrustingepisode. The tops of several imbri- ure 12 and Table 2). For comparison,wedgetapers
cate sliceshave been accreted, while the lower portions
appear to have been shearedbelow a mid-level detach-
have been compiled for the Nankai, Oregon-Cascadia
and Barbados accretionary wedgeswhere multichannel
seismicrecordsand deep sea drilling data are also avail-
ment (Figures6a-6c). The overallgeometryis similar
to experimenti after 120 cm convergence
(Figure 5e), able [Mooreet 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 wedgeshaverelativelylargequanfront formed during the underthrusting phase. The five tities (1-34-km) of sedimentat the trench,threeof them
appear to belongto a similar class;thesehave moderate
or six sheared and stretched slices correlate well with
the zoneof dipping reflectorsin the EDGE line and the
uplifted point at the top of these units matches closely
with the shallow(< 3 km depth) ridge27 km from the
deformationfront (Figure2a).
Though long underthrust units are not clearly imaged
as in lines 71 and 63, underthrusting is interpreted to
be responsiblefor the rapid thickening of the initial 2
km section at the trench to 5 km, 30 km arcward. The
presenceof two distinct detachments, mass balance calculations and section balancing, all require a substan-
tial underthrustsectionequal to 0• 2/3 of the entire
sedimentaryinput Iron Huene et al., 1998]. The poor
quality of the seismicimage at this depth, however,cannot clearly resolve the question of whether the underthrust section consists of sheets or entrained, sheared
duplexes. Additionally, the prominent backthrusting at
the back of the section,with 0• 1 km offsetson numerous
backthrustsin the overlyingslopesediments,document
strong deformation of the backstop, suggestingunder-
thrustingandprobableunderplatingat depth lye et al.,
1997].
convergentrates (4-6 cm/yr) and their physicalproperties(e.g.,internalfriction,porepressure)
are believed
to be fairly similar [Lallemandet al., 1994].
At each margin except Barbados, wide variations in
surface slope occur arcward along individual lines as
well as laterally,alongtrenchstrike (Figure 12), with
maximum surfaceslopesof 17ø, 140 and 10ø for Alaska,
Cascadia, and Nankai, respectively. Cyclical accretion
(as observedin the experiments)offersa plausibleexplanation, as a thrust wedge successivelyreachesthe
upper and lower limits of the taper stability field during the underthrustingand the frontal accretionphases.
Invoking lateral and arcward variations in material
parameters to explain the structural diversity in a single
wedgedoesnot appearsatisfactory.Physicalproperties
(e.g., porosity,fluid pressure)are knownto changeas
high porosity trench turbidites are compressedand de-
watered during the early stagesof deformation[Bray
and Karig, 1985; Byrne and Fisher, 1990]. This generally leads to an overall increasein sedimentstrength,
but also locally to a decreasein strength where pore-
pressures
are high [$hi and Wang,1988;Byeflee,1990].
GhostRocksFormationson Kodiak Island (an exposed The decollementregionis typically marked by high pore
late Cretaceous
to earlyTertiary 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 lowerboundaryof the stabilityfield) [Daviset al., 1983;
structuresfound include a seriesof SE vergent thrust Lallemandet al., 1994] and thus cannotexplain steep
Finally, field geologicalstudies of the Kodiak and
slices,rotated over ramp faults, and duplexesbounded
frontal slopesapproachingthe angle of repose. Further-
belowby a low-angledetachment(basaldecollement) more, dewatering and compactionwould be expectedto
and aboveby a roofthrust (midleveldetachment).The produceprimarily arcward changes,not lateral changes.
rotated series of thrust slices are interpreted to sole
into a common detachment and thus represent an im-
A "strong decollement" leading to accretionary cyclescan result from either moderatepore-pressurealong
bricate fan. The duplexesare interpreted as having the basal detachment or relatively high pore-pressures
been formed when thick sections of undeformed sedithroughout the entire deforming wedge. The resultment werethrust beneaththe toe of the overlyingwedge ing two-phaseepisodicprocessobservedexperimentally
to be underplatedfarther arcward[Sampleand Fisher, provides an explanation for these wide variations along
1986;Fisher and Byrne, 1987]. The tectonicprocesses a single trench where material properties and deformawhich producedthe imbricate fan and underthrust units tional historiesare likely to be similar. Variation along
match well with the dynamicsobservedin high basal strike could be the result of time transgressivefault
friction sandbox experiments and suggestthat simi- propagation causingdifferent segmentsalong the defrolar 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
tapers..
••
maximum
critical
.,•
:.-..::.-.<::..::::::::::-•c.:•...•_
......"..•...::•:::.......::.`.•``.`.•.•.•;.•..%...:::``.`..`.•::•`;::•4•::•:•::•:•:•:•:•::•::::::::::;•4•`•*:•::•:::::•::::::•`.•..?•::::•:•::•:::::•
.:: .: . .:::•::.
............. •..... .:. : .;..•::-... . .. .......
•.::::
mum
critical
taper
-4
0
4
8
12
16
(in degrees)
Figure 12. Wedgetapers from Alaska and for, comparison,two other marginswith wide taper
variationsand onewith little variation(meansurfaceslope,solidsymbols;and maximumslope,
opensymbols).Dashedline is a possiblestabilityfield for the Alaskahighbasalfrictionwedge.
8.
Conclusions
Appendix: Calculation of Work and
Cyclical behavior, alternating from imbricate thrusting to underthrustingof long sheetsis observedin high
basal friction sandbox experiments simulating accretionary wedge growth. The dynamics observedin the
models closelyreproducestructures observedin seismic
reflectionimagesfrom the Alaskan accretionarywedge.
Long layeredsheetsare observedas well as short frontal
thrust slices. Some imbricate
dlevel detachment.
Similar
slices are sheared at a mi-
structures
are also observed
in an exposed Cretaceousaccretionary complex on Kodiak Island, Alaska.
The different phasesof the cyclecan be explained mechanicallyin terms of the temporally varying, geometrydependentforcesrequired to maintain an existing roof
thrust
versus
the
forces
to initiate
a new
basal
and
Frictional
Forces
The instantaneous
work (Fudx) requiredto underthrust a unit is the sumof the frictionalresistance(f)
alongthe roof thrust in direction• (A) and alongthe
ramp thrust in directionr (B), plus the forcerequired
to uplift the overlying portion of the wedge along the
ramp basea verticaldistancedz (C)
(A)
(B)
(C)
F,,dz - fl•dz + f•dr + w•dz
(A1)
The instantaneous
work (Fidx) requiredto initiate a
new basal thrust is equal to the frictional resistance
alongthe basalthrustin directionx (D) and alongthe
toe ramp thrust in directionr (E) plus the force re-
frontal thrust. During one complete cycle, the up- quired to uplift the toe alongthe 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 surfaceslope. At shallowtapers, a longunit is underthrust,
Fidx = fBdx + ftdr + wtdz
(A2)
causing erosion at the oversteepenedfront and uplift
in all casesf- ttw cos/3,and w- mg- pVg, thus
and shorteningin the wedgethrough backthrusting.
Cyclical accretion provides one possibleexplanation
fn - wn(cosfi)lUl•- pVl•g(cos
fi)lUl•
(A3)
for wide variationsin frontal slopealong a singletrench,
where sedimentand 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
Region
Alaska
Nankai
Oregon/
Cascadia
Barbados
Ridge
Experiments
flint
lib
I, cm
O, cm
a,,•,•x
a,,•,.
/3
H x L, cm
v, cm/min
1
12
0.6
0.6
0.5
0.5
2.1
2.0
1.1
1.0
27 ø
28 ø
6ø
12 ø
6ø
6ø
14x40
12x30
10
10
Line
•,nt
t•
I, km
O, km
/3
H x L, km
v, cm/yr
1.57
1.27
1.27
1.27
??
16 ø
15 ø
17 ø
6ø
5ø
2.6 ø
2.8 ø
3.30
4.1 ø
3.6 ø
1.4 ø
2.4 ø
2.5 ø
2.0 ø
3.5 ø
6.5x40
5.8x40
5.5x35
5.5x35
5.5x35
5.7
5.7
5.7
5.7
5.7
0.4?
0.6?
9ø
10 ø
2.3 ø
5.0 ø
2.7 ø
5.0 ø
3.2x26
8.0x20
4 4- 1.5
4 4- 1.5
HINCH88
EDGE302
71
63
Alb-111
0.45 -i- 0.1
0.3 4- 0.1
3.7
2.0
2.0
2.0
3.0
NT62-8
NK5
0.50 4- 0.1
0.75
0.2 4- 0.1
0.4?
1.1
3.5
Or76-4
0.624- 0.1
0.234- 0.1
a,,•,•x a,,•e,•
4.0
??
14ø
3.3ø
2.3ø
9x50
Or76-5
4.0
??
13 ø
3.3 ø
4.6 ø
11x50
2.0
Ca85-01
2.4
??
9ø
4.0 ø
5.0 ø
14x50
2.0
(N) 465
(N) A1-D
(S) 105
0.6
0.7
6.0
??
??
??
3ø
6ø
9ø
1.0ø
3.0ø
1.4ø
3.0ø
1.5ø
0.6ø
7x100
10xl10
15x300
2.0
2.0
2.0
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 surfaceslope; a,,•a•, mean surface slope; •, dip of subducting plate; H x L, height and
width of recent accretionarywedgeimagedon multichannelseismicreflectionprofiles;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 convergence
rate at Alaskan margin, DeMets et al. [1990]; for Philippine Sea Plate convergence
rate in
Nankai Trench, Taira et al. [1992]and Senoet al. [1993]for Nankai seismicprofilesNT62-8, Moore et al. [1990]and NKS,
LePichonet al. [1992];for Oregonseismicprofiles,Shayelyet al. [1986];for Cascadiaseismicprofilesand convergence
rate
Davis and Hyndman[1989];and for BarbadosRidgeseismicprofilesand convergence
rate, Ladd et al. [1990],Moore et al.
[1988], Westbrook
et al. [1988],and Mascleet al. [1990].
- w, os(0 +
- pva(os
- p¬a os(0 +
(A5)
(A6)
Sincedr- (1/cos07)dx, substituting(A8) into (A4)
yields term B
Totalforces(F. and Fi), frictionalforces(f), weights frdr
(w), andvolumes(V) arecalculatedfor a cross-sectional
areaper perpendicular
unit length(l). All areas(A) can
cos(0
+
cos07
be expressedin terms of the lengthsH, LR, LB, and Lt
'
and the anglesa, fi, and 07. For example,
AR
Ar
•
- tan
O•(LsLa
- La•)]
dx
--
(A12)
-- (•)L/•2(tana+tan/•)
(A7)Similarly,substituting(A9) into (A5) yieldstermD
- (•)(tana+tan/•+tanOT)(LB2-Lt•
2)
- tan07(LBLa- La2)
(AS)
=(I•BPg)
cos/•
[HLBcos/•
- HLscos•+(1)
• (tan
a+tan
fi)L.
2(A9)
+(•)(tana
+tan/•)
LB2]
dx(A13)
(10) Sincedr - (1/cos07)dx, substituting(A10) into
fBdx
AB
Substituting(A7) into (A3) yieldsterm A
f-•Idx_
g) cos/•(tan
- (I-t-•
2P
aq-tan/•)Ln2dx
(All)
(A6) yieldsterm E
ftdr
107 cos(07
+/•)HLtdx
(A14)
I =(ytpg)
2 cos
10,174
GUTSCHER ET AL.: EPISODIC IMBRICATE THRUSTING
To uplift wedgeor toe, an incrementalvertical distance dz, the horizontal component of dx, cos/•dx is
multipliedby the componentalongthe ramp,tan(Of+
/7), givingdz = cos/?tan(Of +/?)dx, and term F then
becomes
wtdz
Dirk Kl'eischen,JSrg Kunert, Jfirgen Frfihn, Bernard Sanche,
and Stephane Dominguez for fruitful discussions,accessto
valuable seismic reflection data, and technical assistance in
the laboratory. We also thank the reviewers Dan Davis, Eli
Silver, and Associate Editor Mike Ellis for constructive and
critical comments which helped improve the manuscript.
:(•#)cos/•tan(Of+/•)(HLtcos/•)dx
(A15)
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pellier II, UMR 5573, CNRS, Place E. Bataillon, F-34095
M.-A. Gutscher,S. Lallemand,and J. MalavieilleLaboratoire de G•ophysiqueet Tectonique,Universitdde Mont-
(ReceivedNovember15, 1996; revisedNovember27, 1997;
acceptedDecember3, 1997.)
MontpellierCedex, France. (e-mail: gutscher@dstu.univmontp2.fr)
N. Kukowski, GEOMAR, Wischhofstr.
1-3, D-24148,
Kiel, Germany.(e-mail:nkukowski@geomar.de)