REVIEWS OF GEOPHYSICS, VOL. 24, NO. 2, PAGES 217-284, MAY 1986

Relations Among Subduction Parameters

RICHARD D. JARRARD

Lamont-DohertyGeological Observatory, Palisades, New York

Clues to the dynamicsof the subductionprocess are found in the many measurableparameters of modern subductionzones. Based on a critical appraisal of the geophysicaland geologicalliterature, 26 parametersare estimatedfor each of 39 modern subductionzones. To isolate causalrelationships among theseparameters, multivariate analysis is appliedto this data set.This analysisyields empirical quantita- tive relationsthat predict strain regime and strike-slipfaulting in the overridingplate, maximum earth- quake magnitude,Benioff zone length, slab dip, arc-trenchgap, and maximum trench depth. Excellent correlation is found betweenlength of the Benioff zone and the product of convergencerate and age of the downgoingslab. This relationshipis consistentwith the conductiveheating model of Molnar et al. (1979), if the model is modified in one respect.The rate of heating of the slab is not constant; it is substantiallyslower during passageof the slab beneath the accretionaryprism and overriding plate. The structural style in the overriding plate is determined by its stressstate. Though the stressstate of overridingplates cannot be quantified, one can classifyeach individual subductionzone into one of seven semiquantitativestrain classesthat form a continuumfrom stronglyextensional (class 1, back-arc spread- ing) to strongly compressional(class 7, active folding and thrusting). This analysis indicates that strain classis probably determinedby a linear combinationof convergencerate, slab age, and shallow slab dip. Interplate coupling, controlled by convergencerate and slab age, is an important control on strain regime and the primary control on earthquake magnitude.Arc-parallel strike-slipfaulting is a common feature of convergentmargins, forming a forearc sliver betweenthe strike-slipfault and trench. Optimum conditionsfor the developmentof forearc sliversare oblique convergence,a compressionalenvironment, and a continental overriding plate. The primary factor controlling presenceof strike-slip faulting is coupling;strongly oblique convergenceis not required.The rate of strike-slipfaulting is affectedby both convergenceobliquity and convergencerate. Maximum trench depth is a responseto flexure of the underthrustingplate. The amount of flexural deflectionat the trench dependson the vertical component of slab pull force, which is very sensitiveto slab age and shallow slab dip. Shallow slab dip conformsto the cross-sectionalshape of the overriding plate, which is controlled by width of the accretionaryprism and duration of subduction.Deep slab dip is affected by the mantle trajectory establishedat shallow depth but may be modified by mantle flow. Much of the structuralcomplexity of convergentmargins is probably attributable to terrane juxtaposition associatedwith temporal changesin both forearc strike- slip faulting and strain regime. Empirical equationsrelating subductionparameters can provide both a focusfor future theoretical studiesand a conceptualand kinematic link betweenplate tectonicsand the geologyof subductionzones.

CONTENTS Product of convergencerate and slab age ...... 249 Intermediate dip and the product of slab age and convergence Introduction ...... 217 rate ...... 252 The data ...... 218 Earthquake magnitudemodel ...... 253 Choice of subduction zones ...... 218 Strain regime models...... 254 Arc curvature ...... 221 Convergence rate ...... 254 Benioff zone geometry ...... 222 Slab age ...... 255 Compression/extension...... 224 Absolute motion ...... 256 Convergencerates ...... 230 Absolute motion and slab age ...... 258 Absolute motions ...... 231 Convergencerate and slab age ...... 259 Slab age ...... 232 Slab dip ...... 262 Arc age...... 232 Convergence rate, intermediate dip, and either slab age or Trench depth ...... 235 absolute motion ...... 263 Strike-slip faulting ...... 235 Slab dip models ...... 266 Characteristics ...... 235 Radius of curvature ...... 267 Leading and trailing edges of forearc slivers ...... 238 Convergencerate ...... 267 Continental versus oceanic strike-slip faulting...... 238 Slab age ...... 267 Mechanism ...... 240 Convergencerate and slab age ...... 268 Effect of strike-slip faulting on slip vectors ...... 241 Convergencerate, slab age, and absolute motion ...... 268 Implications for Southeast Asian plate motions ...... 243 Mantle flow ...... 269 Forearc slivers and terrane motions ...... 245 Aseismic ridges ...... 270 Statisticalanalysis ...... 245 Accretion, arc age, and mantle flow ...... 270 Methods and limitations ...... 245 Crust of overriding plate ...... 273 Correlation between independentvariables ...... 248 Trench depth models...... 273 Models of slab length ...... 249 Conclusions ...... 276 Convergence rate ...... 249 Slab age ...... 249

INTRODUCTION The subductionprocess involves a complex interplay of Copyright1986 by the AmericanGeophysical Union. forcesthat affect plate motions and determinethe structural Paper number 5R0903. style behindtrenches. Clues to the dynamicsof the subduction 8755-1209/86/005R-0903515.00 processare found in the many measurableparameters that

217 218 JARRARD: RELATIONS AMONG $UBDUCTION PARAMETERS describe modern subduction zones. Traditionally, the major important step precedingapplication of the relationshipsto causalrelationships within subductionzones have beensought the prediction of past unknown parametersis the testing of through either theoreticalor qualitative analyses.Quantitative the models on the historiesof relatively well known regions physicalmodels have been unable to establishthese relation- (e.g.,western North America). shipswith confidence,due to uncertaintiesin essentialphysical The Pacific margins are now known to be largely a mosaic quantities(e.g., mantle viscosityand shearstress) and physical of displacedterranes, with complex geologichistories some- complexity of the subduction process.Many qualitative re- how related to changingrates and directionsof convergence. lationshipshave been proposed,usually based on a plausible Progressin describingthe kinematics of plate convergence, causal relationship and an apparent correlation between two both Pliocene-Pleistocene[Le Pichon, 1968; Minster et al., subduction parameters for modern subduction zones. Often 1974; Chase, 1978a; Minster and Jordan, 1978] and Tertiary theseproposed relationships are mutually exclusive. [Atwater and Molnar, 1973; Engebretson,1982], has not been The variety of structural environments and plate interac- accompanied by comparable progress in predicting terrane tions at convergentmargins is well illustrated by a brief com- motions [e.g., Stone et al., 1982; Alvarez et al., 1980]. In this parison of the Marianas and Peru-Chile plate boundaries.The paper I consider only one group of terrane motions: those Marianas is characterized by slowly converging,old oceanic occurringwithin the overriding plate. Two other types of ter- crust that is underthrustinga tensional overriding plate at an rane motion are beyond the scope of this paper: accretion almost vertical dip, accompaniedby relatively modest maxi- resultingfrom buoyant portions of the underridingplate col- mum earthquakes (M,• = 7.2). In contrast, the Peru-Chile liding with the trench [e.g., Nur, 1983] and the diffuse defor- plate boundary is characterized by rapidly converging, mation behind trenches that results from continent-continent younger oceaniccrust that is underthrustinga compressional collision [Dewey and Bird, 1970]. Instead, the emphasisis on overriding plate at a nearly horizontal dip, accompaniedby relationshipsduring "normal" subduction. very large (M,• = 8.6-9.5)earthquakes. Most other current The scope of this project is necessarilymore limited than convergentmargins can be describedas lying somewhereon a the entire range of relations among subduction parameters. continuum between the Marianas and Peru-Chile extremes Discussionof the tectonicsof the accretionaryprism is beyond [Uyeda and Kanamori, 1979]. the scope of this paper; some of the recent advancesin this This apparent continuum is as much a disadvantageas an subject are summarized by Davis et al. [1983], yon Huene advantagein the searchfor quantitative modelsthat will allow [1984], and l-lilde [1983]. Implications of subductionparame- the use of some characteristicsof convergentmargins to pre- ters for the driving force of plate motions [e.g., Forsyth and dict others. Some parameters(e.g., convergence rate, absolute Uyeda, 1975], mineralization [Uyeda and Nishiwaki, 1980], motion, age of the arc, and age of the underthrustingplate) uplift in the overridingplate [McGetchin et al., 1980; Parrish, can be thought of as independent variables, which will not 1983], sealevel changes[Malumitin and Ramos,1984], and arc necessarilyoccupy similar positionson a continuum of trench geochemistry[Green, 1980] are similarly beyond the scopeof styles.Other parameters(e.g., length and dip of the slab,com- this paper. pressionor tensionin the overriding plate, trench depth, and TIqE D^x^ maximum earthquake magnitude) are dependent variables which are probably controlled by the independentvariables The subductionzones considered in this analysisare shown but usually not in a manner predictable on theoretical in Figure 1. Table 1 indicatespreferred values for the key grounds. parametersfor thesesubduction zones; values shown in pa- The purposeof this paper is to evaluate and possiblyrevise renthesesare consideredto be too poorly known for inclusion models relating the dependent and independent parameters in statisticalanalyses. Some parameters are not listedbecause above. First, however, it is necessaryto compile our present theycan be simplyderived from a combinationof otherlisted best estimatesof these parametersfor as many modern sub- parameters.Table 2 lists all variablesconsidered and their duction zonesas possible.Often at least one parameteris not units. reliably known for a subduction zone, but relationships It must be emphasizedthat assignmentof a value for some among some of the other parametersfor that trench can still parametersis basedon a subjectiveevaluation of sometimes be utilized. Empirical equationsrelating independentand de- conflictingevidence; this is particularlytrue for strain classes. pendent variables are derived through multiple regression Consequently,one may anticipatethat someof the data of analysis.These empirical equations,in conjunctionwith theo- Table 1 will be subjectto substantialrevision. Because of the retical studies,may help us to isolate the primary cause-and- largenumber of subductionzones analyzed, such revisions are effect relationshipsbetween subduction parameters. Given the unlikely to have a major impact on the resultsof statistical coefficientsof this set of equations, one can also estimate analyses. valuesfor unknownor poorly known variablesfrom well- known variables for the same subduction zones. Choiceof $ubductionZones For timesprior to the Tertiary,empirical equations may Selection of the subduction zones in Table 1 is partially permitthe estimationof platetectonic variables (convergence influencedby the conceptof slab segmentation.For example, rate, crustalage, absolutemotion) from geologicvariables four trench segmentsare usedfor the Peru-ChileTrench, cor- (compression/extension,arccurvature, arc-trench gap) that are respondingto the segmentsseismically determined by lsacks decipherablefrom the rockrecord. An exampleis the history and Barazangi[1977]. Segmentationon the lateral scaleof 500 of the vanishedTethyan Ocean.The correlationcoefficients to 1500 km seems well established for South America and for the equationsprovide estimates of the reliabilitywith Central America [lsacks and Barazangi,1977; Burbachet al., whichmodern trench parameters can be predictedfrom other 1984]. The boundariesof these segmentsare zones of slab parameters.It doesnot necessarilyfollow that ancienttrench warping rather than tearing [Hasegawa and Sacks, 1980; parameterscan be predictedwith equalreliability. Thus an Grange et al., 1984; Bevis and lsacks, 1984]. Much smaller JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 219

z

z

=2 ztu N

z 220 JARRARD'RELATIONS AMONG SUBDUCTION PARAMETERS

TABLE 1.

Subduction Zone Upper Plate

Reference Azimuth Slab Trench Slab Extent Segment Position Perpendicular Strain Length Symbol Name Lat., Long. Trench Crust Class Dips DipI DipD M,•' Depth Ad Horizontal Depth Slab

AEG Aegean 36, 22 49 C 1 20+3 25+3 43 ...... 290 180 340 MAK Makran 24, 60 6 8 12 ...... 430 80 440 AND Andaman 9, 92 84 C 1 19 22 ...... 270 140 310 SUM Sumatra - 2, 98 53 C 5 16 19 50 + 5 7.9 5.9 0.7 370 170 380 JAV Java - 11, 112 8 T 5 16 21 63 7.1 7.45 2.15 570 630 870 SUL North Sulawesi 2, 122 185 O 2 18 26 68 ...... 290 300 460 SAN Sangihe 3, 126 280 ...... 56 ...... 620 + 20 670 920 PHL Philippine 8, 127 258 T -.. 43 41 ... ß.. 10.06 4.10 100 130 q- 20 170 RYK Ryukyu 25, 128 318 C 2 19 23 45 8.0 7.51 1.97 300 280 440 SJP SW Japan 33, 135 329 C 5 10 ...... 8.6 4.8 0.19 330 75 345 NZL New Zealand -40, 178 300 C 3 12 18 50 7.8 ...... 440 270 540 KER Kermadec - 34, - 178 289 O 1 23 30 71 8.1 10.05 4.49 330 500 640 TON Tonga -22, - 174 290 O 1 23 28 57 8.3 10.8 5.24 670 650 940 NHB New Hebrides - 17, 167 73 O 1 36 44 73 7.9 7.07 2.56 190 280 330 SOL Solomon -7, 155 40 O 4 35+5 42+5 84+4 ... 8.94 4.42 300 520 600 NBR New Britain -6, 150 338 O 1 30+5 35+5 58 -.' 8.24 3.73 250 290 390 PAL Palau 7, 135 315 O (4) ...... 8.05 3.55 ...... YAP Yap 8, 138 295 o (4) ...... 8.53 ...... MAR Marianas 17, 148 270 0 1 19 24 81 7.2 9.66 4.95 310 700 860 IZU Izu-Bonin 30, 143 262 0 2 22 28 65 + 9 7.2 9.70 3.54 580 600 860 NJP NE Japan 39, 144 282 c 6 15 19 27 8.35 8.0 1.95 1340 600 1480 KUR Kurile 45, 152 320 C (5) 22 28 50 8.8 9.78 4.27 650 _+_40 600 ___40 890 KAM Kamchatka 53, 162 301 C (5) 19 25 54 9.0 7.5 2.0 580 + 30 600 + 30 860 ALU Central Aleutians 50.5, 180 0 O 4 25 31 64 8.7 7.14 1.64 250 270 370 AKP Alaska Peninsula 60, - 152 285 C 4 9 13 51 ...... 470 155 530 ALA Alaska 62, - 149 328 C 6 7 10 .-. 9.1 ...... 620 160 650 CAS Cascades 45, - 125.5 87 C 4 9+4 ...... 97 34 103 WMX SW Mexico 17, - 103 23 C 6 19 25 ...... 5.29 1.79 210 90 230 SMX SE Mexico 15.5, -97 19 C 6 14 18 53 ... 5.12 1.62 400 210 480 NIC Middle America 12.5, -91 24 C 3 30 38 65 8.4 6.66 2.56 170 210 280 ANT LesserAntilles 16, - 59 250 O 4 16 22 51 7.5 7.0 1.8 320 200 410 COL Colombia 5, - 78 105 C 6 22 26 38 8.8 4.0 0.8 315 215 390 ECU Ecuador - 2, - 81 101 C 6 ... (31) (32) ...... 210 ... PER Peru - 10, - 80 55 C 6 14 13 (5) 8.6 6.3 1.6 710 190 730 NCH North Chile -21, -71 67 C 7 20 21 30 8.65 8.05 3.35 810 600 1040 CCH Central Chile - 30, - 72 100 C 7 16 14 (5) 8.65 6.4 2.2 720 180 730 SCH South Chile - 38, - 74 105 C 5 13 16 30 9.5 4.7 0.6 490 170 520 TDF Tierra del Fuego -49, -77 93 C (3) ...... SCO South Sandwich - 58, - 24 270 O 1 31 38 67 7.0 8.26 3.81 220 250 350

*C, Chase[1978a]. M, Minster and Jordan [1978]. scalesegmentation has also been proposed,often on the basis extent [Hamilton, 1979; Cardwell et al., 1980]. Both current of apparent offsetsin the volcanic arc, but is not assumedin and past activity of the nearby Cotabato Trench are un- this analysis.For example,proposed slab segmentation on the known, and no Benioff zone has been resolved [Hamilton, lateral scale of 100-300 km in Central America I-Stoiberand 1979; Cardwell et al., 1980]. Farther south, the Banda and Carr, 1973] and Makran I-Dykstra and Birnie, 1979] is not Seram subduction zones are excluded because of continental detectedseismically [Burbach et al., 1984;Jacob and Quittmey- collision,unknown slab age, and uncertainconvergence rates er, 1979]. and directions[Cardwell and lsacks,1978; Bowinet al., 1980]. Many subduction zones are not included in Table 1 or Farther east, the New Guinea, West Melanesian, and Tro- subsequentdiscussions, generally becausecurrent subduction briand trenchesare excludedbecause of uncertainpresent and is incipient,waning, or unknown. Most of theseexcluded sub- past activities [Fitch, 1972; Hamilton, 1979; Ripper, 1982; duction zones are in SoutheastAsia, a region of rapid Neo- Weisselet al., 1982]. The nearby Mussau Trench is excluded genetransitions in plate interactions[e.g., Hamilton, 1979]. In becausesubduction appears to have begun only about 1 mil- the Philippinesregion, the Manila, North Philippine,Halma- lion yearsago [Hegarty et al., 1982]. The region betweenthe hera, and Cotabato trenches are excluded. Subduction in the Solomon and New Hebrides subductionzones is potentially North Philippinesappears to be changingpolarity from east- usablebut has receivedlittle study, exceptin the South Solo- ward subduction at the Manila Trench to westward subduc- mon regionwhich is complicatedby ridge subductionand has tion at the northernPhilippine Trench. Differing opinionson only shallowseismicity [Weissel et al., 1982]. the timing of arc polarity changesin this region are summa- Several subduction zones outside Southeast Asia are also rized by Uyedaand McCabe [1983]. Justsouth of the Philip- excluded. The Benioff zone of southwest New Zealand exhibits pinesare the Halmahera and Cotabato subductionzones. The possiblebreakage and rotation, probably causedby the rapid Halmahera Trench is undergoingarc polarity reversal;its Be- changesin subductionhistory here [Smith and Davey, 1984]. nioff zone is very limited in both along-strike and vertical The "Bucarangasegment" of Venezuelahas a detectableBe- JARRARD' RELATIONSAMONG SUBDUCTION PARAMETERS 221

Subduction Parameters

Rate Perpendicularto Trench* Time Since Descent Arc Tip Subducted Angle Rollback Age Age Age Gap Slab Tip C M C M Arc a- t RC C M C M C M C M

...... 8.9 10.0 73 100 11 -I- 1 210 2 0.7 •.4 3.8 3.4 --1.1 --0.1 2.0 2.9 97 87 11.9 11.9 ...... 46 480 ß.. 3.7 3.7 3.7 3.7 --0.3 --0.4 --0.3 --0.4 72 -I- 5 51 -I- 7 9.7 11.9 ...... 100 -I- 40 270 7 2.1 1.4 3.2 2.6 --0.5 --0.1 0.6 1.1 55 __ 5 45 __ 7 6.1 6.8 50 48 27 +___3 300 22 6.2 5.6 6.2 5.6 0.0 -0.2 0.0 -0.2 138 -I- 10 107 -I- 10 10.6 10.7 68 61 27 -I- 3 300 39 8.2 8.1 8.2 8.1 0.7 -0.3 0.7 --0.3 38 9 -I- 6 15.3 15.3 ...... 7 -I- 4 150 6 3.0 3.0 3.0 3.0 ...... 13_____5 -" 7 ...... 0.6 0.0 ...... 3.7 2.1 ...... 6 _____4 250 18 4.6 8.0 4.6 8.0 0.3 0.1 0.3 0.1 49 37 __ 7 14.7 9.2 64 45 55 + 5 150 14 3.0 4.8 3.0 4.8 1.1 0.0 1.1 0.0 21 3 q- 3 26.5 17.2 ...... 175 -I- 5 300 4 1.3 2.0 1.3 2.0 1.2 0.0 1.2 0.0 98 97 q- 5 16.4 18.0 24 18 21 q- 3 280 50 3.3 3.0 3.3 3.0 -3.7 -5.3 -3.7 -5.3 113 114 10.4 11.3 87 79 30 -I- 2 165 50 5.1 4.7 10.5 10.1 -2.5 -4.0 2.9 1.4 120 q- 20 110 q- 30 9.6 10.0 74 67 24 q- 7 185 45 7.5 7.2 12.5 12.2 -1.2 -2.7 3.8 2.3 52 45 ...... 8 q- 3 140 30 (8.8) (8.4) (9.0) (8.6) (6.3) (6.7) (6.8) (6.9) 50 ___10 45 __ 16 5.0 5.1 98 96 8 ___3 100 12 12.0 11.8 12.0 11.8 3.0 2.5 3.0 2.5 50 + 10 47 + 14 2.7 2.6 76 70 8 + 3 125 6 4.3 4.5 14.7 14.9 -5.8 -7.1 4.6 3.3 31___3 ...... 45_+5 --- 3 0.6 0.6 0.6 0.6 -3.2 -7.1 -3.2 -7.1 33 ...... 45 q- 5 "- 4.5 1.2 1.2 1.2 1.2 -3.9 -8.1 -3.9 -8.1 155 134 9.4 17.1 87 66 45 _+ 5 225 8 6.0 3.4 10.3 7.7 -3.3 -6.5 1.0 -2.2 146 122 11.3 13.6 57 45 45 +__5 210 85 7.6 6.3 7.6 6.3 -1.2 -3.0 -1.2 -3.0 130 94 14.9 14.5 29 28 115 ___5 300 11 9.9 10.2 9.9 10.2 0.7 0.2 0.7 0.2 119 89 10.2 10.4 56 49 82 q-_16 190 15 8.7 8.6 8.7 8.6 1.1 -0.2 1.1 -0.2 90 q- 15 72 __ 18 9.8 10.0 60 54 153 q- 10 225 15 8.8 8.6 8.8 8.6 1.0 0.0 1.0 0.0 54 48 ___15 6.2 6.3 84 72 56 q- 6 190 14 6.0 5.9 6.0 5.9 2.1 0.9 2.1 0.9 46 50 q- 10 12.9 13.6 46 48 160 q- 10 400 14 4.1 3.9 4.1 3.9 -0.5 -0.3 -0.5 -0.3 46 48 q- 10 10.3 10.7 ...... 160 ___10 470 ß-- 6.3 6.1 6.3 6. t 1.2 0.8 1.2 0.8 8 9 3.0 3.0 ...... 175 q- 10 280 90 3.4 3.4 3.4 3.4 2.2 1.8 2•2 1.8 15 14 3.9 4.1 ...... 90 ___3 240 ß15 5.9 5.6 5.9 5.6 1.9 2.1 1.9 2.1 14 14 6.7 6.9 65 68 90 q- 3 380 15 7.2 7.0 7.2 7.0 1.6 1.9 1.6 1.9 23 q- 5 23 q- 5 4.3 4.4 59 63 100 q- 10 150 10 6.5 6.4 6.5 6.4 -0.8 -0.3 -0.8 -0.3 68 78 11.1 11.1 80 67 48 ___4 260 5.5 3.7 3.7 3.7 3.7 1.8 1.1 1.8 1.1 15+10 8+10 5.7 5.6 56 59 242+5 270 173 6.8 6.9 6.8 6.9 2.5 2.9 2.5 2.9 32 ...... 226 ___19 275 6 7.9 7.7 7.9 7.7 2.5 3.0 2.5 3.0 45 57 8.9 9.5 ...... 226 q- 19 ..- 19 8.2 7.7 8.2 7.7 1.5 2.7 1.5 2.7 82 112 10.4 11.7 35 43 226 ___19 300 140 10.0 8.9 10.0 8.9 1.6 2.9 1.6 2.9 48 68 7.4 8.6 ...... 226 ___19 '" 10 9.8 8.5 9.8 8.5 2.0 2.8 2.0 2.8 26 ___5 30 q- 6 5.4 6.3 36 42 226 ___19 300 55 9.7 8.2 9.7 8.2 1.7 2.5 1.7 2.5 20 ...... 150 q- 6 230 7 2.3 2.1 2.3 2.1 1.2 2.3 1.2 2.3 49 74 4.6 4.6 116 111 30 150 3 0.9 0.9 7.9 7.9 -0.4 -1.1 6.6 5.9

nioff zone, but it has a poorly known slab age, a complex Arc Curvature history of plate interactions,and possiblyanomalously thick crust in the slab [Pennington,1981]. A very short trench seg- Nearly all subductionzones are segmentedinto arc-shaped ment in the West Scotia region may have active back-arc portions in plan view. On the overriding plate a similar arcu- spreadingbut is otherwisepoorly known [Barker and Hill, ate band of active volcanoesis almost always present,usually 1981].The westernportion of the Aleutiansubduction zone is located above that portion of the down going slab that is 100 excludedbecause it is almost purely strike-slip [e.g., Chase, to 125 km deep. The geometry of most volcanic arcs and 1978a; Minster and Jordan, 1978]. The Wrangell segmentof trenchescan be closelyfit by a portion of a small circle on the Alaska is excluded because it is uncertain whether the short earth's surface [Frank, 1968], defining a radius of curvature Benioff zone is part of the Pacific plate or Yakutat block for the arc or trench.Radii of curvaturefor arcsare tabulated [Stephenset al., 1984]. All regionsof continent-continentcol- in Table 1; most have been determinedby Tovish and Schu- lisionare excluded (e.g., Burma, Hindu Kush, Roma•nia, and bert [1978] and are not remeasuredhere. Virtually all arc Spain). curvaturesare convexwith respectto the underthrustingplate. Several subduction zones are describedin the literature by Although the radius of curvature of either the arc or the various names. The South Sandwich zone is also called the trench could be utilized as a clue to subduction zone dynam- ScotiaArc. SouthwestJapan is also referredto as Shikoku or ics, arc curvatureis preferablefor two reasons.First, arc cur- as Nankai Trough. Java, Sumatra, and Andaman are col- vature is more readily estimatedfor ancientsubduction zones lectivelycalled the SundaArc. The Aegeanzone is alsocalled in the rock record than is trench curvature. Second, trench Hellenic Trench or Greece. The portion of the Middle location and curvature are easily modified by regional vari- America Trench consideredhere is Nicaragua.The portion of ations in forearc accretion [Karig et al., 1976]. In contrast, the West Indies (CaribbeanTrench) consideredhere is the continental and island arcs generallyclosely follow a Benioff Lesser Antilles. zone contour, usually about 100 to 125 km. Trench radii of 222 JARRARD":RELATIONS AMONG SUBDucTIoN PARAMETERS

ß

TABLE 2. SUbductionParameters Considered

Variable Symbol Units

Slab length of Benioff zone L s km horizontalextent of Benioffzone ß-- km maximum depth of Benloft zone ß-. km shallowdip (to 60-krndepth) Dips deg intermediatedip (to 100-kmdepth) DipI deg deepdip (150-400 km) DipD deg descentangl e of slabinto mantle DipU deg slab age at trench As m.y. ageof slab,tip At m.y. timeSince slab tip sUbdUcted Tst m.y. trenchdepth d km relative trench depth Ad km slab pull force F• N/m Upper plate durationof Subduction(arc age) A,, m.y. arc-trenchgap gap km arc radius of curvature RC deg strain regime strain class modern strike-slipdirection ......

Relative motion convergence rate Vc cm/yr (ratesperpendicular convergencerate including back-arc spreading Vct,• cm/yr to trench) rollback (absolute motion, forearc) V• cm/yr absolutemotion, overriding plate V• cm/yr absolute motion,underriding plate V• cm/yr obliquityof convergence 4• deg slip vector residual 0 deg maximum cumulativeearthquake moment

curvaturehave beentabulated by severalauthors [Aoki, 1974; it is sometimespossible to detect a double,planeBenioff zone DeFazio, 1974; Laravie,1975; Ness and Johnson,1976]. A [Hasegawa et al., 1978; House and Jacob, 1983], with an disadvantageof consideringarc curvaturerather than trench upper zone of earthquakesoriginating just below the upper curvature is that not all trenches have currently active arcs. surfaceof theslab and a lowerzone originating about 30 km The arcsof southwestJapan, Tierra del Fuego,Central Chile, below the upper surfaceof the slab. More often the hypocen- Peru,North Sulawesi,Yap, and Palau are currentlyinactive. ters appear to come from throughout the upper 30 km of the Their radii of curvatureare estimatedon the basisof Neogene slab, making estimationof the location of the top somewhat (first five) or mid-Tertiary(last two) volcanism.Subsequent subjective.Figure 2 showsthe cross-sectionalgeometry of the correlation of Tertiary radii of curvaturewith modern plate subductingslab fo r mostof the subductionzones of Table 1. parametersclearly requires caution. The locationof the top surfaceof the slabis basedon the Theradius of curvaturecan be precisely determined for arcs original author'sinterpretation for most subductionzones. if it is lessthan about 15ø to 20ø, but it is much lessprecise for For somesubduction zones the locationwas interpreted by arcs with large radii of curvature.Some determinations are this author from published cross-sectionalplots of hypocen- subjective;for example,the Kurile-Kamchatkaregion may be ters. Three subduction zones have Benioff zones too short to a singleare with a radiusof curvatureof 15ø, or it may be two bedetermined: Yap, Palau,and Tierra del Fuego. arcs with radii of curvature of 60 ø to 90 ø. Several of the sub- Most cross sectionsutilize hypocenterslocated with a duction zonesof Table 1 are tentativelyconsidered to be por- worldwidenetwork rather than local networks. Although local tions of larger continuousarcs with a singleradius of curva- networks are capable of locating earthquakesof smaller mag- ture: Kurile-Kamchatka, Java-Sumatra, and Kermadec-New nitude than thosedetected by a worldwidenetwork, they may Zealand. yield biased estimatesof slab dip. For example, the Benioff No estimate of radius of curvature is made for the Alaskan zones of Nicaragua and Costa Rica have been determined and Makran subduction zones, because the Neogene vol- both with local and globalnetworks; the resultis a steeper canism in both regionsis discontinuousalong strike and deepdip with the localnetworks [Burbach el al., 1984].The somewhatdiffuse [Jacob et al., 1977; Jacob and Quirtmeyer, deep dip of the New Zealand Benioff zone was originally 1979]. thoughtto be 67ø, based on a local network tAnselland Smith, 1975]. However, by using velocities that were about 11% BenloftZone Geometry faster for raypathswithin the slab than outsidethe slab, Most subduction zones have well-defined Benioff zones, Adamsand Ware [1977] found that station residualswere with earthquakehypoCenter distributions that indicatethe ge- reducedand that reiocatedhypocenters indicated a corrected ometryof the subductingplate. Except at shallowdepths, deepdip of only 50ø . focal mechanismsindicate that the hypocenters.originate Crosssections of manyBenioff zones were determined by withinthe top 30 km of thesubducting plate rather than at its lsacksand Barazangi[1977]. Other Benioffzones come from boundaries[lsacks and Molnar, 1971]. With exceptionally a variety of sources:Aegean [Richter and Strobach,1978], well locatedhypocenters (e.g., northeast Japan, East Aleutians) Alaska[Lahr, 1975],Andif/nan [Mukhopadhyay, 1984], Cen- / 200 400 600 200 400 600 ß iO0 • 100

200 ß 2130-1 \\ •r Yuk Yu si

6•

7

2• 4•

100

2• - • • /

100 4•

2• 5•

6•

4•

5•

I I 200 400 600 800 1000 1200I CLASS 6

Mexico • • Peru • Alaska Colombia SE • Mexico •

3OO

NE • Japan 400

5(00•...6 • • • 200 400 600 200 400 600 , ,CLASSlFiED j

100' 100 Phil

200 200

300 300

4O0- 400

500. 50O

6OO 6 Fig. 2. Cross-sectionalprofiles of the t. ops of seismically defined subducted slabs. Each profile starts (left) at thetrench andends (right) at thetip of theBenioff' zone. Slab position is interpolatedacross seismic gaps. Slab sc?:jz•ents that are interpretedasdisconnected from the main slab are not shown. Profiles are grouped according to strainclassification of Table 3. 224 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS tral Aleutians [Engdahl, 1977], Colombia [Pennington,1981], dip; in actuality it is usually5-10 km and variessubstantially East Alaska Peninsula [Lahr, 1975], Ecuador [Bevis and along the trench axis [e.g., Grellet and Dubois,1982; Hilde and lsacks, 1984], Java (K. R. Newcomb and W. R. McCann, Uyeda, 1983]. It should be noted that DipS, DipI, and DipD unpublishedmanuscript, 1986), LesserAntilles [McCann and do not correspondto the epicenterdepths normally referredto Sykes, 1984], Makran [Jacob and Quittmeyer,1979], Middle as shallow,intermediate, and deep. America [Burbachet al., 1984], New Britain [Pascal,1979], For brevity in this paper, the term "slab" is usedinstead of New Zealand [Adamsand Ware, 1977; Katz, 1982], northeast "seismicallyactive portion of the underthrust plate." This Japan [lchikawa,1966; Hasegawa et al., 1978; Yoshii,1979], usagedoes not imply that the underthrustplate ends at the Philippines[Cardwell et al., 1980], Ryukyu [Utsu, 1974;Kat- seismicallydetermined "slab tip." For example, seismicac- sumataand Sykes, 1969], Sangibe [Cardwell et al., 1980],Solo- tivity beneaththe Marianas extendsto 700-km depth, but a mon [Pascal, 1979], South Sandwich[Brett, 1977], South detectablevelocity anomaly to at least 1000-km depth indi- Mexico [Burbachet al., 1984], southwestJapan [Kanamori, cates the presenceof much deeper subductedplate [Creager 1972], and Sumatra (K. R. Newcomb and W. R. McCann, and Jordan, 1985]. unpublishedmanuscript, 1986). Also shown in Table 1 are the maximum horizontal extent Problems arise in the determination of Benioff zones for the of the slab, the maximum depth of slab earthquakes,and the Cascades,Ecuador, Philippines, and Sangihe.The Cascades length of the slab (measuredalong its upper surface).Maxi- Benloftzone, beneath Washington and Oregon,is poorlyde- mum slab depth and horizontal extent are includedonly for finedby seismicity[Smith and Knapp, 1980]; the combination completeness;they are not subsequentlyconsidered in this of seismicityand gravity modelingpermits its locationto be paper. Caution must be exercisedin comparingany of these estimateddown to only 20-km depth [Jachensand Griscom, three parametersbetween different subductionzones, as the 1983]. The EcuadorBenioff zone has poor shallowseismic deepesthypocentral depths detected for a Benioffzone depend control and a deep Benioff zone with an anomalousstrike somewhat on the duration of the available data and on wheth- approximatelyperpendicular to the trench[Pennington, 1981; er a worldwide or a local network was utilized. For example, Beyisand lsacks, 1984]. The southernPhilippines Benloft zone the maximum depth of hypocentersfrom the South Sandwich was once thought to extend to great depth. However, more Arc was extended from 170 km [Barker, 1972] to 250 km detailedwork showsthat the deepseismicity is actuallyrelat- [Brett, 1977] by a singleearthquake; slab length and horizon- ed to underthrustingof the nearby Molucca Sea beneaththe tal extent were similarly affected.Another extremeexample is SangiheTrench and that the Philippine Trench is a very northeastJapan, whose 1480-km slab length is the longestof •oungtrench With only a shallowBenioff zone [Cardwell et any current slab; this length is reduced by 560 km if the el., 1980]. Benioff zone of Yoshii [1979] is used,omitting two very deep Benioffzone geometryis parameterizedin Table 1 accord- epicentersof lchikawa [1966]. Farrat and Lowe [1978] de- ing to both lengthand dip. Dip is not constantwithin a slab; fined the tip of the slab not on the basisof the singledeepest characteristically,dip increasesgradually from the trenchto earthquake but on the basis of a percentageof total earth- about 80- to 150-km depth and remains almost constant quakes. This criterion partially ameliorates the problems belowthis depth.The "inflectionpoint," or greatestchange in above;it is not followedherein because one cannot accurately dip, usuallyoccurs between 60 and 100 km. Table 1 includes determine which shallow earthquakes are within the lower (wheneverpossible) the dip from the trenchto 60-km depth plate. ("shallowdip," or DipS),dip fromthe trench to 100-kmdepth Estimatesof slab length, depth, and horizontal extent may ("intermediatedip," or DipI), and the deepdip (DipD, usually also be biasedby seismicgaps, generally in the depth range of of part or all of the intervalfrom 100 to 400 km). The dip to about 300 to 500 km. In some cases(e.g., Java, North Chile, 60-km depth was selectedbecause the basalt/eclogitetransi- and Solomon)a deeperseismic zone appearsgeometrically to tion occursat about 60 km [Ahrensand Schubert,1975], sub- be a continuation of the shallower Benioff zone. For these stantiallyincreasing the densityof the slab and presumably subductionzones it is assumedthat the gap is causedby a alsoaffecting the dip inflectionpoint nearthis depth. The dip changein downdip stress[lsacks and Molnar, 1971] rather to 100-kmdepth was selected because arc volcanismgenerally than a break in the slab. In contrast, deep epicentersbeneath occursabove the portion of the slab at about 100- to 125-km the Peru, New Hebrides, and New Zealand subducted slabs depth; thus this dip may be estimablein ancientarc-trench and some of the deep epicentersbeneath the New Britain, systems.Thickness of the overridingplate, though generally Solomon, and Tonga slabs are not geometricallycontinuous unknown,is probablyabout 80-100 km for most subduction with the shallower slabs and are not included in estimates of zones; thus DipI is also an approximate measure of the Benioff zone parameters.Deep seismicitybeneath the Tonga averagedip of the contactzone between underriding and over- subduction zone has been attributed to collision of the riding plates.Estimates of DipI are usuallymuch more accu- modern slab with part of an older slab [Hanus and Vanek, rate than estimatesof DipS, becauseit is often difficult to 1978]. It is possiblethat the anomalousdeep seismicityof the distinguishintraplate from interplateearthquakes near 60-km Tonga, New Britain, New Hebrides, and Solomon Benioff depth. Becauseof this uncertaintyand the very high corre- zonesis a relict of the late Miocene arc polarity reversalsthat lation betweenDips and DipI, Dips is omitted from most have occurredin theseregions. subsequentstatistical analyses. Both the 60-km and 100-km measureddips are basedsimply on the horizontal distances Compression/Extension from the trenchto points above the 60-km and 100-km por- Of the variableslisted in Table 1, perhapsthe mostdifficult tions of the slab; thus they do not representdips at these to quantifyis the strainregime of the overridingplate. The depthsbut approximateaverage dips from the trenchto these stress(or strain)at any pointin a subductionzone is optimally depths.For simplicity,depth at the trenchis assumedto be describedas a stress(or strain)tensor. Because of data limi- zero in Figure2 and calculationsof shallowand intermediate tations,determination of the full stressor strain tensoris gen- JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS 225 erally not possible. Instead, a more limited description of TABLE 3. Strain Classification strain is used here, focussingon the azimuth of the maximum Class Description Subduction Zones horizontal componentof strain. Thus a "compressionalenvi- ronment" is usuallymanifested by thrusting or reversefaulting active back-arc spreading South Sandwich with maximum compressionapproximately perpendicular to New Britain the trench. However, the less common environment in which Marianas New Hebrides normal faults strike perpendicular to the trench is also con- Tonga sideredcompressional, because the maximum horizontal com- Kermadec pressionis perpendicularto the trench. Similarly, a strike-slip Andaman focal mechanismis consideredcompressional if the maximum Aegean horizontal compressionis perpendicularto the trench. "Exten- very slow back-arc spreading Ryukyu sional environments" are those with maximum horizontal ex- Izu-Bonin tension approximately perpendicular to the trench, usually North Sulawesi manifestedby normal faults striking parallel to the trench or 3 mildly tensional Middle America by back-arc spreading. New Zealand A variety of stress and strain indicators is used to (Tierra del Fuego?) characterizethe strain regime of the overriding plate, includ- 4a neutral Lesser Antilles ing focal mechanisms,Quaternary faults and folds, volcanic Solomon vent alignments,overcoring, and presenceof back-arc spread- Cascades ing. Theseindicators and their limitationshave beendescribed (Palau?) (Yap9,) by Richardson et al. [1979] and by Zoback and Zoback [1980]. This approach has two principal limitations. First, 4b gradient:mildly tensional Aleutians motion on a preexistingfault is not a reliable indicator of to mildly compressional Alaska Peninsula exact stressdirection. This limitation is probably not critical, 5 mildly compressional SW Japan as the focus here is on component of strain perpendicular to Java Sumatra the trench rather than precisestress direction, and data from South Chile many faults are usually used for a single subduction zone. (Kurile 9.) Second, data types vary from "instantaneous" (e.g., focal (Kamchatka 9.) mechanismsand overcoring) to Quaternary and sometimes moderately compressional Colombia slightly older in age (e.g.,faults, folds,and volcanic vent align- Ecuador ments). We must therefore assumethat the state of stresshas Peru not changedsubstantially over the past 2 m.y. Alaska Subduction zones can be ranked to some extent in terms of NE Japan SE Mexico their positions along a continuum from strongly extensional (SW Mexico 9.) to strongly compressional[Uyeda and Kanarnori, 1979]; how- ever, no quantitative estimation of either their stressstates or 7 very stronglycompressional North Chile Central Chile strain regimesis possible.Therefore the strain regimes of the overriding plates in modern subduction zones are considered semiquantitativelyby grouping them into sevenstrain classes (Table 3). Class 1 subduction zones are the most extensional, one class. For example, folds, reversefaults, and thrusts are with active back-arc spreading.Class 2 zones are those with often difficult to date precisely;a class7 subductionzone may very slow, incipient, or waning back-arc spreading. Class 3 have all three of these active but may be classifiedas class 6, zones are mildly extensional,with normal faulting but no sub- because no known Quaternary sediments are offset by the stantial crustal thinning. Class 4 zones include two different thrust(s). environmentsthat are difficult to rank relatively on an exten- Subduction zones with slow, incipient, or waning back-arc sion/compressioncontinuum: "neutral" zones, with little evi- spreading (class 2) are tentatively consideredto be lower in dence of either compressionor extension,and zones with a tensional stress than subduction zones with active, well- mildly compressionalarc and forearc and mildly extensional developed back-arc spreading (class 1), yet this assumption back-arc. Class 5 zones are mildly compressional,with gentle may not always be correct. All known examples of back-arc folding or with somewhatmore reversedthan normal faulting. spreading are short-lived, as shown by the compilations of Class 6 zones exhibit consistentfolding and/or reversefault- Weissel [1981] and of Taylor and Karner [1983]. It is not ing. Class 7 zones are the most compressional,with substan- known whether the early stage of a back-arc spreading epi- tial folding,faulting, and forelandthrusting. sode is lower tensionalstress than the active-spreadingstage; These sevenstrain classesare merely arbitrary points along we know only that it is lower extensional strain. The same the extension/compressioncontinuum. Although relative uncertainty applies to distinguishingclass 2 subductionzones ranking of the strain classesis straightforward,it is not possi- from class 3 zones, those with a tensional back-arc environ- ble to infer that the different classesconstitute equally spaced ment but no significantextension. points along either stressor strain continua.For instance,the Throughout the discussionsof compressional and exten- data may justify the separationof only five strain classes,with sional environmentsin this paper, the focusis on the back-arc, classes 2 and 3 combined and classes 6 and 7 combined. arc, and (to a lesserextent) forearc portions of the overriding Becauseof the assumptionsmade and the widely varying plate. The variations in strain regime of the underriding plate, quality and quantity of strain indicators for individual sub- accretionary prism, and plate interior are ignored. The in- duction zones,some zones have a classificationuncertainty of teriors of most plates are in a state of horizontal compression 226 JARRARD: RELATIONS AMONG $UBDUCTION PARAMETERS

[Sykesand Sbar, 1973; Richardsonet al., 1979]; this environ- thrusting;however, only one of theseindicates pure thrusting, ment is generallynot difficult to distinguishfrom zonesof and assignmentto the upper plate is generally uncertain. In strain associated with modern subduction. Strain in the accre- spite of possibleminor thrusting,presence of back-arc spread- tionary prismmay be substantiallydifferent from strainin the ing causesthe Andaman subductionzone to be includedin the forearc.For example,normal faulting is commonin the inner l•ighly extensionalclass 1. trench slope of Alaska Peninsula[Fisher, 1979], Peru-Chile Back-arc spreadingbehind the New Hebrides and Tonga [Thornburg and Kulrn, 1981; Shepherdand Moberly, 1981], trenchesis apparentlycomplicated by proximity to a 90ø bend and northeastJapan Iron Huene et al., 1982], though com- in the Australia/Pacific plate boundary; both involve three- pressiondominates part or all of the more landwardportions plate back-arc systems.Spreading on the Fiji Plateau, behind of theseoverriding plates. Recent exciting work on the dynam- the New HebridesTrench, began about 10 m.y. ago [Malahoff ics of accretionaryprisms suggests that much of their varia- et al., 1982], rotating the New HebridesArc clockwisefrom its bility (includingerosion or activeaccretion, and thrustingor former position behind the Vitiaz Trench. Back-arc spreading normal faulting)may be explicableultimately in terms of a rates are best known for the southernridge of the three-plate "bulldozer" model in which one of the most important vari- system,where a 7.0-cm/yr full rate for the last 8 m.y. is ob- ablesis pore pressure[Davis et al., 1983]. Analysisof statesof served [Malahoff et al., 1982]. The present 500- to 700-km stressin the subductingplate, the accretionaryprism, and the separationof the spreadingaxis from the New Britain Trench plate interior is importantbut beyondthe scopeof this paper. is much wider than any other current back-arc spreading In the remainder of this section,evidence is compiledfor the region; concurrentincipient spreadingis also apparently oc- classification of modern subduction zones into the seven strain curringjust behind the arc, in the Coriolis Trough [Dubois et classes,from class 1 (active back-arc spreading)to class 7 al., 1978; Carney and Macfarlane, 1982]. Spreadingin the Lau (activethrusting). Two subductionzones are not classifiedbe- Basin, behind the Tonga Trench, began about 6 m.y. ago; the cause of insufficientevidence for their strain regime: Palau full rate for the last 2 m.y. is 7.6 cm/yr [Weissel, 1980b]. and Yap. Four subductionzones are tentativelyclassified but Magnetic anomalieshave not been identifiedin the portion of are not usedin subsequentstatistical analyses, because of lim- the Lau Basin correspondingto the referencelocation of ited data concerningtheir strain regime:Kamchatka, Kuriles, Table 1. Becausethis portion of the Lau Basin is only two- southwestMexico, and Tierra del Fuego. The Philippineand thirds the width of the region interpretedby Weissel[1980b], Sangihesubduction zones are excludedbecause arc-arc col- a full rate of only 5 cm/yr is assumedfor back-arc spreading lision may dominate the stresspattern [Silver and Moore, here. Just south of the Lau Basin, back-arc spreadingin the 1978]. Similarly,the Makran subductionzone is excludedbe- Havre Trough began about 2 m.y. ago, with a full rate of 5.4 causecontinent-continent collision in the flanking Zagros and cm/yr [Malahoff et al., 1982]. Hindu Kush regionsmay mask the normal stresspattern. For every active back-arc basin except the Andaman, the Subductionzones with a highly extensionalenvironment in spreading direction is approximately perpendicular to the the overridingplate (class1) exhibit back-arcspreading, the trench. Indeed, the oblique spreadingand major transform formation of oceaniccrust in a marginal basin behind the arc faultsof the Andaman Sea are often interpreted[Curray et al., [Karig, 1971; Packhamand Falvey, 1971]. Initial rifting may 1982; Weissel, 1981; Taylor and Karner, 1983] as evidence occuron either sideof the arc or may split the arc [Taylor and that it may not be appropriateto considerthe origin of this Karner, 1983]; subsequentarc volcanismis always between marginalbasin as typical back-arc spreading. the trenchand the growingmarginal basin. Taylor andKarner Activethinning of continentalcrust is occurringin a diffuse [1983] have listed all known Neogeneback-arc basinsand zone behind the Hellenic Trench in the Aegean Sea. Focal comparedtheir characteristicsto "normal"oceanic spreading. mechanisms[McKenzie, 1978], overcoring [Paquin et al., Older back-arc basins are often difficult to distinguishfrom 1984], and Quaternaryfaults [Mercier, 1981] indicatea domi- trapped portions of "normal" oceaniccrust [Weissel, 1981; nantly north-southextensional strain in the back-arcregion, Taylor and Karner, 1983]. Recognitionof ancient back-arc with both extension and compressionin the more hetero- spreadingis evenmore difficultif the basinwas collapsedby geneousforearc. This extensionis not simpleback-arc spread- subsequentcompression [e.g., Dalziel, 1981]. ing; high heat flow and crustalthickness variations indicate Activeback-arc spreading is currentlyoccurring behind the that extension occurs both in the forearc and behind the New Britain, South Sandwich,New Hebrides,Tonga, Kerma- Aegean Arc in a laterally heterogeneouspattern [McKenzie, dec, Mariana, and Andaman subductionzones. Bismarck Sea 1978;Le Pichonand Angelier,1981]. At presentit is not possi- spreading,behind the New BritainTrench, has been active for ble to unambiguouslyattribute this extensionto subduction the last 3.5 m.y. at a total openingrate of 13.2 cm/yr [Taylor, dynamics,as the back-arcregion is complicatedby collisionof 1979], the fastestmodern back-arc spreading. The mostrecent a Turkish plate with the Eurasian plate [McKenzie, 1978]. episodeof back-arcspreading in the East Scotia Sea,behind Subduction-relatedextension of about 4 cm/yr [Le Pichonand the South SandwichTrench, began about 8 m.y. ago with a Angelier,1981] is tentativelyassumed herein. full rate of 5 cm/yr, acceleratingto the current 7 cm/yr rate Three subductionzones exhibit incipientor very slow back- about 4 m.y. ago [Barker, 1972; Barker and Hill, 1981]. Back- arc spreading(class 2): Ryukyu,Izu-Bonin, and North Sula- arc spreadingin the Mariana Trough beganabout 6 to 7 m.y. wesi.The Okinawa Trough, behind the Ryukyu Trench,has a ago, with a full rate of 4.3 cm/yr [Hussongand Uyeda,1982; singlenormal fault focal mechanism[Fitch, 1972], shallow Bibee et al., 1980]. Back-arc spreadingin the Andaman Sea focusearthquakes, high heat flow, thinned continentalcrust, has averaged3.7 cm/yr for the last 13 m.y.; prior spreadingis and a thick sedimentfill with growth-faultedgrabens indica- poorly known becauseof very subduedmagnetic anomalies tive of currently slow extension[Herman et al., 1979; Lee et [Curray et al., 1982; Lawyer and Curray, 1981]. A few focal al., 1980; Letouzey and Kimura, 1985]. Spreadinghere may mechanismsfrom behind the Andaman-Nicobar Ridge are in- have been more rapid in the Pliocene, based on apparent terpreted by Mukhopadhyay[1984] as indicating forearc patternsin the lower portion of the sedimentfill [Herman et JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS 227 al., 1979]. Extension may have begun about 6-9 m.y. ago Young strike-slip faults and thrusting have been observedin [Letouzey and Kimura, 1985]. seismiclines near the east Nicaragua shelf,but the most recent Incipient or very slow back-arc spreadingis evident in the deformation is clearly extensional[Bowland, 1984]. This ex- Bonin Arc, where fresh, glassytholeiites have been dredged tensional graben formation may be part of a transtensional from 40-km-wide grabens [Taylor et al., 1984]. Total exten- plate boundary[Christofferson, 1983] rather than a part of the sion appears to decreasenorthward from near the actively subduction-relatedextensional environment of Nicaragua. spreadingMariana Trough to near the north end of the arc at South of Nicaragua, collision of Panama with South America the Nankai Trough [Karig and Moore, 1975]. The northern creates a complex pattern of deformation of the Caribbean end of the Bonin Arc has been broken by north-south com- plate [Pennington,1981]. Whether this collision affects the pressionapproximately parallel to the arc [Karig and Moore, Nicaraguanstress pattern is not known. Burbachet al. [1984] 1975; Bandy and Hilde, 1983]. This compression,tentatively present 10 publishedand new focal mechanismsfrom Nicara- dated as Miocene [Bandy and Hilde, 1983], is probably unre- gua; of these,nine indicateshallow thrusting near the contact lated to the modern stress pattern, though strike-slip and betweenthe two platesor compressionin the downgoingslab. reverse-faulting focal mechanisms are common [lchikawa, The only mechanismsthat are clearly within the overriding 1980]. plate are one strike-slipmechanism of Burbachet al. [1984] Slow or waning spreadingmay be occurring in the Goron- and the strike-slipmechanism of the 1972 Managua earth- talo Basin and Gulf of Tomini, behind the North Sulawesi quake [Deweyand Algermissen,1974]. Trench. Hamilton [1979] infers a Neogene opening of this Class4 subductionzones include two types:those with little region, following late Miocene or Pliocene arc polarity re- evidenceof either compressionor extension and those that versal [Hamilton, 1979; Silver et al., 1983a]. Four shallow exhibit back-arc extensional strain but arc and forearc com- focal mechanisms from within the Gorontalo Basin indicate pression. Examples of the former are the Cascades,Lesser normal faulting [Cardwell et al., 1980], suggestingthat the Antilles, and Solomons;examples of the latter are Central region may still be extensional. Aleutiansand Alaska Peninsula.Recognition of strain gradi- The Middle America and North New Zealand subduction entsacross subduction zones led Nakamuraand Uyeda [1980] zones representclass 3, with a tensional environment but no to concludethat the continuumin subductionstrain regime significantextension. It is plausibleto assumethat the Middle hypothesizedby Uyeda and Kanamori [1979] is overly sim- America and possibly New Zealand subduction zones have plistic. While recognizingthat this is true and that the two had a relatively constant subduction environment long typesof class4 subductionzones may be fundamentallydiffer- enoughto proceedto the spreadingstage, unless they are truly ent, both are neverthelesstentatively considered to represent lower in tensional stressthan the slow-spreadingarcs. How- an intermediatepoint on a continuumfrom totally extensional ever, this assumption is not testable. Indeed, the Tonga- to totally compressionaloverriding plates. Kermadec-New Zealand trench systemmay be experiencinga The strain regime of the Aleutians is better documentedin southward propagation of back-arc spreading, beginning the eastern Aleutians than in the Central Aleutian zone chosen about 5 or 6 m.y. ago in the Lau Basin [Weissel, 1980b], as a reference location. Focal mechanisms and volcanic vent about 2 m.y. ago in the Havre Trough [Malahoff et al., 1982], alignmentsin the easternAleutians and Alaska Peninsula in- and lessthan 2 m.y. ago in the Taupo Zone of New Zealand dicate horizontal compressionroughly perpendicularto the [Ballance, 1976]. The Taupo Zone of volcanism and minor trench in the forearcand arc, possiblychanging to extension extension is laterally continuous with the Kermadec Arc behindthe arc [Nakamuraet al., 1980]. The paucity of data rather than the actively spreading Lau Basin; consequently, from the back-arc regionsof the Aleutiansand Alaska Penin- Ballance [1976] concludedthat the Taupo Zone is not a zone sula make the inferredtransition from compressionto exten- of incipient back-arc spreading.However, back-arc spreading sionhighly tentativefor theseregions [Nakamura et al., 1980]. does not always begin behind the arc [Taylor and Karner, In general, reverse faults are dominant in the forearc of the 1983]. Active back-arc spreadingin the Taupo Zone was in- Alaska Peninsula, with normal faults dominant in the back- ferred by Stern [1985], on the basis of tensional tectonics, arc [Nakamura et al., 1980]. However, the transition from geodeticevidence of slow historic extension,anomalously thin compressionto extensionis probably at least 250 km behind crust, and very high heat flow. The future evolution of the the arc of the Alaska Peninsula,as thrustingand reversefault- Taupo zone is uncertain, but the current environment is ap- ing accompanystrike-slip motion on the Holitna and Togiak- parently one of tension but minor extension.Tension is not Tikchik faults, both thought to be still active [Lathram et al., confinedto the Taupo Zone; the East Coast fold belt of North 1974]. Plioceneto Recentfolding occursin the forearc,attenu- New Zealand is also currentlyextensional [Katz, 1982]. How- ating to minor foldingin the arc and only tilting beyondthe ever, this zone should probably be consideredas accretionary Holitna and Togiak-Tikchik faults [Lathram et al., 1974]. In prism and therefore may not be relevant to the strain regime the Aleutian Arc the most recentfolding appearsto be early of the overriding plate. The North New Zealand extensional Mioceneto late Pliocene,with Quaternaryfaulting and uplift environment changesrapidly to strike-slip and oblique com- but no folding [Lathram, 1974]. pressionfarther south [Carter and Norris, 1976], beyond the The Cascades,Lesser Antilles, and Solomonsrepresent the region consideredhere. "neutral" group of class 4 strain environments.The Pacific The Middle America (Nicaragua) subductionzone is similar Northwest (includingthe CascadesArc) has north-southcom- to North New Zealand, with arc volcanism occurring within pressionapproximately parallel to the trench, resulting in an activelysubsiding region, the Nicaragua depression[McBir- strike-slipand thrust focal mechanisms[Zoback and Zoback, ney and Williams, 1965]. North striking tensional fractures 1980] and active north-south trending normal faults [Ham- associatedwith Recent volcanoessuggest mild east-westex- mond,1979]. This environment,in which the least principal tensional strain in the vicinity of the arc [McBirney and Wil- strain is perpendicularto the trench, includesboth the forearc liams, 1965; Dewey and Algermissen,1974; Nakamura, 1977]. (Olympic Peninsula)and the back-arc (Columbia Plateau). 228 JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS

Classificationof the Cascadesas "neutral" is thereforeclearly ilton [1979] found no evidenceof major strike-slipfaults on an oversimplification.The Cascadesmay be more appropri- Landsat images.Back-arc thrustingeast of Java is probably ately considered as mildly extensional [Cross and Pilger, causedby continental collision of Australia with the Banda 1982], or the subduction-relatedstrain pattern may be domi- subductionzone and is not relevant to the strain regime of nated by the more pervasivestrike-slip environmentof the Java [Silver et al., 1983b]. westernmost United States and Canada. The adjacentsegments of South Chile and Tierra del Fuego The Lesser Antilles experiencedforearc folding until the are consideredmildly compressional(class 5), though seismici- Pliocene but apparently no Quaternary deformation [Tom- ty and other relevant data are sparsefor Tierra del Fuego. blin, 1974], exceptin the accretionaryprism. Faulting in the The boundary betweenthese two segmentsis chosenas the Solomonsis dominatedby late Plioceneto Quaternarystrike- intersection of the Chile Rise with the Chile Trench. The slip roughly parallel to the arc, with Pliocene-Pleistocene forearc in South Chile appearsto be mildly extensional,with normal faulting common and reversefaulting occasionalnear both uplift and subsidence.The only focal mechanismavail- the arc [Coleman and Hackman, 1974]. Back-arc folding of able from South Chile is from the arc and indicatescompres- Miocene to Recent age is observed only on the islands of sion [Jordan et al., 1983]. Andean volcanoesin a portion of Santa Ysabel and Malaita [Colemanand Hackman, 1974], east the South Chile segment (37.5ø-41.5øS)exhibit flank crater of the segmentstudied and behind a portion of the Solomon distributions suggestinga maximum horizontal compression Trench currently experiencingridge-crest subduction [Weissel direction of N65øE + 10ø [Nakamura, 1977], relatively close et al., 1982]. to the presentconvergence direction of N79øE. Active gentle SouthwestJapan, Sumatra, and possiblyJava, South Chile, folding is observedin the foreland of South Chile between33 ø and Tierra del Fuego representthe class5 subductionzones, and 34.5øS, while farther south extensive Pliocene-Pleistocene which are consideredto be mildly compressional.Ichikawa foreland volcanismoccurs with only minor faulting and fold- [1980], synthesizingthe resultsof over 1500 focal mechanism ing [Jordan et al., 1983]. Foreland volcanismcontinues south solutionsfrom the Japaneseregion, found generallylow seis- through the Tierra del Fuego segment.Episodes of extensive micity in SouthwestJapan, with a slight dominanceof normal plateau basalt volcanismaway from the main arc, suchas the faulting over reversefaulting in the forearc and with reverse Pliocene-Pleistoceneepisode in South Chile and Tierra del faulting dominant farther from the trench, in the Japan Sea. Fuego, are interpreted by Malumitin and Ramos [1984] as Late Quaternary thrustingwith a right-lateral componenthas indicative of an extensionalregime, consistentwith the gener- occurred on the Median Tectonic Line, and some mid- alization of Christiansenand Lipman [1972] and of Lipmanet Pleistocenethrusting occurson faults north (landward)of the al. [1972] concerningstress environments of basaltic and an- Median Tectonic Line [Matsumoto and Kimura, 1974]. Syn- desitic magmas. Indeed, fissuresin the PleistocenePalei-Aike thesizingthe results of active faults, focal mechanisms,and volcanic field have east-west and northwest-southeast orienta- late Quaternary dikes, Nakamura and Uyeda [1980] find that tions [Skewesand Stern, 1979], suggestingextension approxi- the direction of principal horizontal strain is roughly parallel mately perpendicular to the trench. The strain regime of to the direction of plate convergence,except near the Ryukyu Tierra del Fuego is consideredto be too poorly known for Arc where a gradual changeto the class2 extensionalenviron- inclusion in subsequentstatistical analyses,but the available ment of the Ryukyusoccurs. Analysis of older faultsand dikes data suggestthe possibilityof a gradual southwarddecrease in suggeststhat southwestJapan was also compressionalfrom 11 compressionthrough both South Chile and Tierra del Fuego. to 2 m.y. ago, though with a somewhatdifferent azimuth of Class 6 subduction zones, characterizedby active folding maximumcompression. Southwest Japan had a compressional and reverse faulting with no significant extension, include forearc and extensionalback-arc (class4) from about 21 to 11 northeast Japan, Alaska, the three adjacent segmentsCol- m.y. ago [Nakamura and Uyeda, 1980]. ombia, Ecuador, and Peru, and possiblysoutheast Mexico, the The back-arc region of eastern Sumatra exhibits moderate Kuriles and Kamchatka. Thrusting, if present,appears to be but pervasivePliocene-Pleistocene folding and some Quater- confinedto preexistingfault zones. nary thrusting,both with compressionapproximately parallel The strain regime of northeast Japan is well known' the to the plate convergencedirection [Katili, 1974]. Similarly, maximum compressiondirection is approximately parallel to compressionalong the northwest coast is indicated by two convergencedirection throughout northeast Japan, based on focal mechanisms[Fitch, 1972]. Except for thesetwo back-arc vent distributionsof numerouspolygenetic volcanoes [Naka- regions, little or no evidenceof compressionor tension is mura and Uyeda, 1980] and on severalhundred focal mecha- found in Sumatra [Katili, 1974]. nisms [Ichikawa, 1980; Maki, 1983]. Most epicenterswithin The Java segment,adjacent to Sumatra,also appearsto be the overriding plate occur in the forearc, between the coast mildly compressional.A singlefocal mechanism,from beneath and the trench, with reversedfocal mechanismsabout twice as the arc near the eastern end of Java, indicates intraplate common as normal [Ichikawa, 1980]. Rare inland focal mech- thrusting [Fitch, 1972]. Deformation is active in the foreland anisms are almost all reversed[Ichikawa, 1980]. Quaternary basin of North Java and the nearby offshorearea, with mild folding is observed[Matsuda and Kitamura, 1974], and a lev- open folds in north central Java and the South Madura Basin eling net demonstratesthat both folding and reversefaulting in the Quaternary, and Miocene to Quaternary northward are occurringin the inner zone of northeast Japan, near the directed folds and thrusts in the West Java Basin [Hamilton, Japan Sea [Mizoue et al., 1982]. The current strain regimeof 1979]. However, much of this deformation may be attribu- the Japan Sea is poorly known; a single focal mechanism table to magmatism rather than subduction-relatedcompres- indicatescompression [Hager, 1983]. A tensionalenvironment sion, as the folds arc around large volcanicedifices [Hamilton, for both Japan and the nearby Kuriles has been inferredby 1979]. Chotin et al. [1985] concludethat south central Java is some authors [e.g., Molnar and Atwater, 1978; Englandand experiencingnorth-south to northeast-southwestcompression, Wortel, 1980], basedon Cenozoicback-arc spreadingin the mostlyaccommodated on many strike-slipfaults, though Ham- Japan Sea and Kurile Basin. However, neither basin is cur- JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 229 rently active,and Neogenechange from extensionto compres- by Cross and Pilger [1982], based on subtle northeast- sion in northeastJapan is now well documented[Nakamura southwestregional alignmentsof volcanoes,but relevant data and Uyeda, 1980]. were not shown. Thrusting and east-west compressionare The strain regimes of the nearby Kurile and Kamchatka clearly presenton seismiclines offshoreeastern Mexico, in- segmentsare largely unknown. These subduction zones are volving beds as young as Pleistocene and possibly Recent tentatively consideredto be similar to northeast Japan, based [Buffler et al., 1979]. This thrusting could result either from on dominantly reversedfocal mechanismsin the forearc of the deep crustal stress or massive gravity sliding [Buffler et al., South Kuriles [lchikawa, 1980] and late Pliocene folding 1979]. Some thrustscan be followed updip into normal faults; roughly parallel to the Kamchatka Arc, adjacent to Kam- thus gravity sliding appearsto be the more likely origin of at chatka in the Sea of Okhotsk [Gnibidenko and Khvedchuk, least some of this thrusting [Tharp, 1985]. A possiblegradient 1982]. Udias and Stauder [1964] report 34 focal mechanisms in stress exists between the southeast Mexico and southwest from the Kurile-Kamchatka region; all may be interplate Mexico subduction zones' the westernmost portion of the thrusts, but depth control is poor. Stauder and Mualchin Mexican Arc occupies grabens that are probably currently [1976] determined 120 focal mechanismsfrom this region. Ot extensional. This extension may be caused by an incipient these, one reversed faulting mechanism from the back-arc ridge jump rather than subduction-relatedextension [Luhr et regionof the SouthKuriles is certainlywithin the upperplate; al., 1985], but the latter may be a necessaryprerequisite for two other reversedfocal mechanismsfrom the forearc region the former [Vink et al., 1984]. Although the southwestportion may be within the upper plate. Becauseof the limited strain of the Mexican subduction zone is tentatively considered as data for the Kuriles and Kamchatka, the strain classes for more tensional than the class 6 southeastportion, it is not theseregions are not usedin subsequentstatistical analyses. known well enough for use in subsequentstatistical analyses. Alaska is similar to the class4 regionsof Alaska Peninsula Of 13 focal mechanismsfor southernMexico, none appearsto and Central Aleutians in one respect:all three regionsshow a bewithin the overridingplate [Burbach et al., 1984]. strain gradient, with decreasingcompression away from the The adjacent Central Chile and North Chile subduction trench [Nakamura et al., 1980]. However, unlike the latter zones appear to be the most compressional(class 7) of all two, the maximum compressionalaxis remainshorizontal and modern subduction zones. The discussion that follows is based roughly parallel to convergencedirection for a much greater' primarily on the detailed analysisof Jordan et al. [1983]. In distance from the trench, about 500 km. The few volcanic both regions,modern deformationis concentratedin the fore- alignments and fault offsets farther inland suggestthat the land. In North Chile, 30 to 80 km of shorteningsince the end maximum compressionalaxis changesto vertical but that the of the Miocene has been accommodatedon east verging folds maximum horizontal compressionalaxis does not undergo and west dipping, thin-skinned thrusts. Continuing major substantial change [Nakamura et al., 1980]. The many strike- compressionin North Chile is indicated by focal mechanisms slip faults in Alaska, with ages of initiation ranging from Ju- [Chinn, 1982] and Holocene folds and thrusts [Lobmann, rassicto Pleistocene,show Quaternary dextral slip, commonly 1970]. Foreland compressionin Central Chile is different in with either reverse or thrusting components [Lathram et al., style, with uplift of crystalline basement on reverse faults in 1974]. Quaternaryfolding appearsto be largely confinedto the Pliocene-Pleistocene,as well as late Pliocene to Quater- the arc and forearc regions[Lathram et al., 1974]. nary imbricate thrusting. Upper plate seismicity in Central The class 6 segmentsColombia, Ecuador, and Peru are Chile occupiesa broaderzone, with larger magnitudes,than in adjacent. In all three regions, intracontinental seismicityis North Chile. The forearc region of Central Chile exhibits concentrated along the easternmost(foreland) flank of the Quaternarystability, while uplift and subsidencein the North Andean'Cordillera, generally with strike-slipor high-angle Chilean forearc suggestsome extension. thrust focal mechanisms [Stauder, 1975; Pennington, 1981; Mercier [1981] has emphasized alternation of compres- Sudrezet al., 1983]. Much of the east-westcompression ap- sional and extensionalperiods in the Andes of North Chile, pears to be accommodatedthrough a combination of under- suggestingthat active normal faulting extends from the West- thrusting of the Brazilian shieldbeneath the easternmargin of ern Cordillera to the Eastern Cordillera, with only the sub- the Andes [Dalmayrac and Molnar, 1981; Sudrezet al., 1983] Andean zone (foreland) currently experiencingcompression. and strike-slip motion of the Ecuadorian and Colombian Pleistoceneto Recent normal faults in the Altiplano, striking forearc as a relatively rigid block [Pennington,1981]. In Ecua- east-west,have also been noted by other authors [e.g., James, dor and Colombia the main Andean orogeny appears to have 1971;Sebrier et al., 1982]and detectedthrough focal mecha- peakedin the late Miocene or Pliocene,with major thrusting nisms[Grange et al., 1984]. These observationsled England and moderate folding in the easternAndes [Campbell, 1974a, and Wortel [1980] to classifyNorth Chile as extensional.As b]. Similarly,moderate Neogene folding and northeastverging in the normal faulting of the Peruvian AltiPlano, body forces reverse faulting have been mapped in the eastern Andes of associatedwith uplift may be responsible[Jordan et al., 1983]. Peru [Jordan et al., 1983]. In the Altiplano (Or high plateau) Unlike the PeruvianAltiplano, the maximumhorizontal co m- of Peru, seismicityis low and normal faulting is OCcurringon pressionaxis in the North Chilean Altiplano is approximately planes approximatelyparallel to the trench. This extensionis perpendicularto the trench [Grange et al., 1984]. The low probably a local effect of body forces associatedwith the seismicityof the Altiplanocontrasts markedly with the high higher elevation of the uplifting Altiplano compared with seismicityof the actively deformingforeland. In both North flanking regions; the overall strain regime of the Peruvian Chile and Central Chile, compressionappears to have been segment is clearly compressional[Dalmayrac and Molnar, even greaterin the Mioceneand Pliocene[James, 1971; Rut- 1981; Sudrez et al., 1983] but probably less compressional land, 1974; Mercier, 1981]. than Central Chile [Jordan et al., 1983]. Becausecompression is accommodatedin a generallydiffer- SoutheastMexico is tentatively included in class6, basedon ent style in Peru and Central Chile than in North Chile and limited data. Compressionin the back-arc region was inferred South Chile [Jordan et al., 1983], relative strain rankings for 230 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS thesefour regions are tentative. For example, it is not known pacific/Philippinemotion determination• ofKarig [1975]. As whetherthe amountof uplift in North Chile is indicativeof discussed-in the subsequentsection on strike-slipfaulting, the moreor lesscompression than the.more diffuse faulting of existenceof a SoutheastAsia plate suggeststhat actualcon- Central Chile. Although the differencesin styleare often inter- vergencerates may be about 1-2 cm/yr larger than those preted as differencesin stress,they probably are more• closely givenin Table 1 for the philippine,Sangihe, Ryukyu, and related to differences in crustal composition and palc- southwestJapan arcs, and the perpendicularcomponent of ogeography[Jordan et al., 1983; Allmendingeret al., 1983]. convergencemay be substantiallysmaller than is givenfor the Andaman and Sumatran arcs. ConvergenceRates The least known convergencerates among SoutheastAsian Present convergencedirections at subductionzones are in, subductionzones are those for the Philippine,$angihe, and dicated by slip vectors of shallow interplate thrust earth- North Sulawesi trenches. Subduction of the small Molucca quakes.Convergence rates cannot be directly measured.Accu- plate on both the east and west sidesis causingarc-arc col- rate convergencerates betweenthe major plates can be deter- lision in southern Mindinao and incipient collision in the mined from world wide motion models [Chase, 1978a; Min- MoluccaSea [Hamilton, 1979; Cardwell et al.,1980]. The rela- ster and Jordan, 1978], based on inversion of Pliocene- tive motion betweenthe SoutheastAsia and Philippineplates Pleistocenespreading rates, transform fault azimuths, and just south of the southernPhilippines is thereforepartitioned focal mechanisms.Table 1 includes convergencerates from between the waning East Sangihe and Halmahera trenches both inversions. Confidence limits for convergencerates are and the recentlyformed Philippine Trench [Hamilton,1979; not includedin Table 1, becausethey can be readily estimated Ca/dwellet al., 1980].The North SulawesiTrench is the lead- fromthese authors' 95% confidence limits for angularrotation ing edgeof a small plate that appearsto be driven northward rates about relevant poles of rotation. Becausethe pole of by collisionof the Sula platform.Fault offsetsand volumetric rotation is also subjectto some uncertainty,such confidence analysisof the accretionaryprism suggesta possibleconver- limitsslightly underestimate the total uncertaintyin conver- gencerate of 5 cm/yr at the westernend of the trench,but this gence rate. rate is highly dependenton the assumedduration of subduc- With two exceptions,convergence rates listed in Table 1 are tion [Silver et al., 1983a]. for the componentof convergenceperpendicular to the trench. Convergencerates for the Yap and Palau subductionzones For the Alaska and Alaska Peninsula subduction zones, the reflectrelative motions between the Caroline and Philippine very wide accretionaryprism makesthe presenttrench axis of plates[Weissel and Anderson,1978]. The Caroline/Philippine limited physicalsignificance' downdip azimuth of the Benioff relative motion pole is near the southern end of the Palau zone is used instead. Rates are given for both the relative Trench, at the transitionfrom a subductingto a spreading motion betweenthe underthrustingplate and the major over- plateboundary [Weissel and Anderson, 1978]. Rotation rate riding plate (l/c) and relative motion betweenthe underriding uncertainties,compounded by proximityof the Yap and Palau plate and the forearc (Vcba).Unless specificallystated other- trenchesto the Caroline/Philippinepole, lead to very large wise,subsequent references to convergencerate refer to l/c,not uncertaintiesin Yap and Palau convergencerates. Vcbaß Th9 global motion modelsof both Chase[1978a] and Min- The arc and forearc may have substantialmotion relative to ster and Jordan [1978] assume that India and Australia are the major overriding plate, manifested as strike-slip faults part of a single plate. However, significantrelative motion [Fitch, 1972] or back-arc spreading. Slip vectors used in between the two can be resolved [Minster and Jordan, 1978; worldwide motion models reflect motion between forearc and Stein and Gordon,1984], indicatingcompression of about 1.4 underthrustingplate. Consequently,both Chase[1978a] and cm/yr in the vicinity of the Ninetyeast Ridge. Model A of Minster and Jordan [1978] largely avoided using slip vectors Minster and Jordan [1978], which describes this relative from regionswith back-arcspreading. However, most slip vec- motion, is usedas an approximateadjustment to both global tors usedby Minster and Jordan [1978] from the India/Pacific models.The effectof thiscorrection is to decreaseconvergence plate boundarywere from the KermadecTrench, with current rates by 0-1.5 cm/yr for the following subductionzones' An- back-arcspreading in the Havre Trough of 5.4 cm/yr full rate daman, Sumatra, Java, New Britain, Solomon,New Hebrides, [Malahoffet al., 1982]. Similarly,estimates of Philippine/Paci- Tonga, Kermadec, and New Zealand. fic relative motion by Seno [1977] and Chase[1978a] use slip Convergence rates for both the New Britain and Solomon vectorsfrom the Mariana Trench, though back-arc spreading subduction zones combine Australia/Pacific relative motions of 4.3 cm/yr full rate occursin the Mariana Trough [Hussong [Chase, 1978a' Minster and Jordan, 1978] with Aus- and U yeda, 1982]. Resultingerrors in India/Pacific and Philip- tralia/Solomon relative motions determined from magnetic pine/Pacific relative motions may be small, becausein both anomaly correlationsin the Woodlark Basin [Weissel et al., regions the back-arc spreading direction is approximately 1982]. However, the overriding plate for the New Britain parallelto the convergencedirection of the majorplates. Trench is not known with certainty. If the nearly aseismic Convergence rates for many of the trenches in Southeast West MelanesianTrench is currently inactive,the overriding Asia are poorly known for two reasons'(1) uncertaint•yin rate plate is probably the Caroline plate. If the West Melanesian of Philippineplate rotation relative to Eurasiaand Pacific Trenchis currentlya plate boundary,then the overridingplate plates and (2) largely unknown motion of the SoutheastAsia is either the Pacificplate or possiblya North Bismarckplate plate. Becausethe Philippine plate is boundedon all sidesby [Hamilton, 1979]. Assuming Caroline/Solomon relative trenches,its convergencerates are uncertain by about a factor motion for the New Britai•nsubduction zone, insteadof Pacif- of 2 [e.g., Chase,1978a]. Minster and Jordan [1978] did not ic/Solomonrelative motion, reduces the total convergencerate model Philippine plate motion; the ratesshown in the Minster of Table 1 by 2.4 cm/yr but changesthe convergencerate and Jordan (M) column of Table 1 for Philippine plate bound- perpendicular to the trench and component of absolute ariescombine their Pacific/Eurasiarelative motions with the motion perpendicularto the trench by less than 0.3 cm/yr. JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS 231

Assuming North Bismarck/Solomonrelative motion has a, forearc region. The sign conventionis that positive absolute similar effect. motions are toward the underthrustingplate. As with conver- Complexitiesin the spreadingpattern behind the New He'- gencerates, minimum uncertainties can be readily calculated bridesTrench precludedetermination of accurateconvergence from 95% confidencelimits in rate of rotation given by Chase rates, both with and without back-arc spreading. Aus- [1978a] and Minster and Jordan [1978]. tralia/Pacific relative motion is assumedfor Vc' this choice The absolutemotion model of Minster and Jordan [1978] is appearsto be reliable only for the northern half of the New based on their RM2 world relative motion model, azimuths of HebridesTrench. The overridingplate for the southernhalf of nine hot-spot traces, and volcanic propagation rates of five the trench may be a small subplate,separated from the Aus- Pacifichot-spot traces. Eight of the nine hot-spotazimuths are tralian plate by a small amount of strike-slip motion on the from the Pacific Ocean. The similar analysisof Chase [1978a] Hunter fracture zone. Back-arc spreadingof 7 cm/yr full rate is based on his P071 world relative motion model and 18 is well documented [Malahoff et al., 1982] between this hy- worldwide azimuths of hot-spot traces from Minster et al. pothesizedmicroplate and the New Hebrides forearc. Strike- [!974]. Neitherthe hot-spotrates nor azimuthsare truly in- slip motion of about 2 cm/yr on the Hunter fracture zone can stantaneous;those of Minster and Jordan [1978] representan reconcilethe rates for the northern and southern portions of averageof up to 10 m.y., and severalof those of Minster et al. the New Hebridean forearc, implying very little back-arc [1974] are substantiallyolder. Absolute motion of the Pacific spreadingbetween the Pacificplate and northwestNew He- plate appearsto have changedsignificantly about 5 m.y. ago, brides.The ratesshown in Table 1 are substantiallyless than but reference frames based on hot spots [Cox and œn- the 12 cm/yr inferred by Dubois et al. [1977] on the basis of gebretson, 1984] and torque balance [Davis and Solomon, uplift rates on the outer rise of the New Hebrides Trench. In 1981] do not agree on the direction of this change. This view of the uncertainties,convergence rates for New Hebrides changeis not fully reflectedin the uncertaintiesassigned to are not usedin subsequentstatistical analyses. absolute motions by Chase [1978a] and Minster and Jordan Convergencerates for the South Sandwich Arc assumethe [1978], and the two absolutemotion modelsmust thereforebe existenceof a Scotia plate I-Forsyth, 1975; Barker and Hill, considered tentative. !981] betweenSouth America and Antarctica.The transform Slight motion between hot spots is likely. Relative motion faults bounding the Scotia plate on the north and south must of about 1 cm/yr was suggestedby early studies [Morgan, together accommodatethe 1.8 cm/yr relative motion between 1972; Molnar and Atwater, 1973; Burke et al., 1973; Molnar South America and Antarctica. Since both exhibit weak seis- and Francheteau,1975], but more recent studiessuggest sub- mic activity [Forsyth, 1975], equal offset rates are tentatively stantially less motion [Morgan, 1980; Duncan, 1981]. Much assumed. larger relative motions among Pacific hot spots have been Convergencerates for the Cascadescombine Pacific/North inferred by Chaseand Sprowl[1984]. However, the likelihood America relative motion [Chase, 1978a; Minster and Jordan, of a changein Pacific/hot-spotmotion at 5 m.y.B.P. and the 1978] with Paci.fic/Juan de Fuca relative motion [Engebretson, tendency of hot-spot volcanism to be affected by zones of 1982; Wilson et al., 1984]. crustal weakness cast doubt on this conclusion. Slow relative Motion of the Caribbean plate is based on the analysisof motion of hot spotsis also implied by mantle/lithospheremass Sykeset al. [1982]; their resultssuggest about 2 cm/yr more balance models [e.g., Hager and O'Connell, 1978], unlessthe eastward component of motion than previous analyses[e.g., mantle source of hot spots is deeper than mantle flow. The Minster and Jordan, 1978]. hot-spot azimuth misfitsfor both the Chase[1978a] and Min- Seafloor spreadingin the Bismarck Sea [Taylor, 1979] and ster and Jordan [1978] models are generallyless than 10¸, crustal thinning behind the AegeanArc [McKenzie, 1978] are suggestingthat the hot-spot referenceframe is viable, in spite tentatively consideredas back-arc spreadingand not included of its uncertaintiesand slow relativemotions among hot spots. in convergence rates. However, as previously mentioned, Minster and Jordan [1978] have compared their absolute Aegean crustal thinning may reflect collision-drivenmotion of motion model with models based on different assumptions. an Aegean plate rather than subduction-driven extension Models based on no net rotation of the lithosphere or on a [McKenzie, 1978]. • fixed African plate are broadly similar to the hot-spot model; however, they appear to be significantlydifferent at the 95% Absolute Motions confidencelevel. A modelbased on the assumptionof a fixed The searchfor an "absolute,"or deepmantle, reference Caribbean plate is not significantlydifferent from the hot-spot frame has led to numerous absolute motion models based on model.This conclusionwould probably not be changedby different assumptions'(1) fixed hot spots[Morgan, 1972; Min- usingthe revisedCaribbean/North America relative motions ster et al., 1974; Minster and Jordan, 1978; Chase, 1978a; of Sykeset al. [1982], which would have the effect of increas- Morgan, 1980], (2) no net motion of the lithosphereas a whole ing predictedvolcanic propagation rates by about 2 cm/yr, to [Lliboutry, 1974; Minster et al., 1974; Solomonand Sleep, valuesmore in agreementwith thoseobserved. 1974; Minster and Jordan, 1978], (3) no motion of the African As With convergencerates, the largestuncertainties in abso- plate [Burke and Wilson, 1972], (4) no motion of the Carib- lute motion are associated with the Southeast Asian and Phil- bean plate [Jordan, 1975], and (5) minimum horizontal ippine plates. motionof plateboundaries [Kaula, 1975]. Modification of the Chase [1978a] and Minster and Jordan Table 1 liststhe componentof absolutemotion perpendicu- [1978] absolute motion models was required for some sub- lar to the trench for the overriding plate at each subduction duction zones, resulti.ngfrom the relative motion revisions zone, based on the worldwide motion models of Chase discussedin the preceding section. Tonga, Kermadec, and [1978a] and of Minster and Jordan[1978] and the fixed-hot- New Zealand were considered part of an Australian plate spot hypothesis.As with convergencerates, the overriding rather than a combinedIndia-Australia plate. Caribbean plate plate is defined as the major plate behind the arc, not the motion was modifiedß as suggestedby Sykeset al. [1982]. Exis- 232 JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS tence of a Scotia plate was assumed.Because Minster and wide magnetic anomaly compilation (S.C. Cande, unpub- Jordan [1978] did not determine Philippine plate motion, ab- lished manuscript, 1986) used by Larson et al. [1985]. Other solute motion of the Philippine plate combinestheir Pacific sourceswere used for Colombia [Pennington, 1981], Ecuador absolutemotion with the Pacific/Philippinerelative motion of [Pennington, 1981], Mexico [Klitgord and Marnrnerickx, Karig [1975]. 1982], Middle America [von Huene et al., 1980], North Sula- wesi [Weissel, 1980a], Palau [Weissel and Anderson, 1978], Slab Age South Sandwich (J. L. LaBrecque, personal communication, Two measuresof the age of the downgoing slab are tabu- 1985), and Yap [Weissel and Anderson,1978]. Slab ages used lated in Table 1: the average age of crust now entering the for the Makran, Ryukyus, New Britain, and Solomon zones trench and the averageage of the tip of the slab. The latter is require some explanation. not the presentage of the slab tip, but the age at the time that The estimateof slab age for the Makran is basedon exten- the current slab tip first enteredthe subductionzone, basedon sive field work in the nearby Samail ophiolite of Oman. No the relationship magneticanomalies are identifiedin the remnant of Tethyan oceaniccrust in the Gulf of Oman, probably becauseof crustal A t = As + L s x (dA/dL- 1/V•b,,) formation during the CretaceousQuiet Zone. The Samall where At is effectiveage of the slab tip, As is the age of crust ophiolite includesa paleo-spreadingridge [-Pallister,1981] now enteringthe subductionzone, L s is the downdiplength of formed 95 m.y. ago, basedon uranium-leaddating [-Tilton et the slab, dA/dL is the age gradient of the slab perpendicularto al., 1981]. Becauseof probablehigh spreadingrates [Tilton et the trench (m.y./km, positive for age increasingdowndip), and al., 1981], the Makran slab age most likely can be estimated Vc0ais the perpendicular component of convergencerate relativelyaccurately, in spiteof the tectoniccomplexities sum- (km/m.y.), including back-arc spreading.As discussedsubse- marized by Coleman[1981]. quently, this effectiveage is relevant to models of the thermal The Ryukyus segmentused is southwestof the probably history of the slab [Farrat and Lowe, 1978; Sykeset al., 1982], CretaceousDaito Ridge.The northwestsubbasin of the West in which the oceaniccrust is assumedto cool until it begins PhilippineBasin probably originated as part of the main basin subducting,and thereafterto heat. but acquired a NNE trendingfabric during later deformation Calculated time since subductionof the slab tip (Tst)and [Mrozowski et al., 1982]. If so, its age may be similar to that effectiveage of the slab tip are compiled in Table 1. Separate at Deep Sea Drilling Project (DSDP) sites294 and 295 to the estimatesof At are not shown for Chase[1978a] and Minster east,where •øAr/39Ar dating yieldsan age of 48.8 +_2 m.y. and Jordan [1978] rates,as other sourcesof variancegenerally [Ozima et al., 1977]. An alternative interpretation, not fol- dominate the uncertaintiesshown for A t. Convergencerates lowed here, is that anomaly 9 and possibly8 can be identified usedto calculateT•t and At differ from thosegiven in Table 1 near the Ryukyusas part of an anomaly pattern decreasingin for Tonga, Kermadec, Marianas, and South Sandwich. In age to the north [Shih, 1980]. If the latter is correct,the age of thesefour regionsthe presentback-arc spreadingrate has not the slab is much youngerthan assumedin Table 1. persistedsince subduction of the slab tip. Therefore a time- No magneticanomalies have beenidentified in the Solomon varying convergencerate was usedto determine Tst.The effect Sea, the basin being consumedat the New Britain and Solo- of this correctionis to reduceA t by 1.0-3.5%, comparedwith mon trenches.Davies et al. [1984] estimate an age of 40 to 60 assumingpresent Vc0a since the slab tip was subducted.The m.y. for this basin basedon heat flow, depth, paleomagnetism history of crustal extensionin the Aegean is not known with of New Britain, flexure, and slab length. Age gradients are confidence;Le Pichonand Angelier [1981] suggestthat crustal unknown, both within the basin and within the slabs. extension began at about the same time as subduction.Be- No age estimatesare includedin Table 1 for crust subduct- causeof uncertaintyin both timing and rate of early extension ing at the Aegean,Sangihe, and Philippinezones. The portion in the Aegean,the estimateof Tstmay be a minimum value. of Tethys now subductingin the Aegeanis undated but may Determination of At is often much more uncertain than be Cretaceousor Jurassic(W. B. F. Ryan, personalcommuni- determinationof As , primarily becauseof uncertaintyin age cation, 1985).Only a thin, undated sliver of the Molucca plate gradient. Age gradientsused in Table 1 are based usually on remains seaward of the Sangihe Trench [Silver and Moore, age gradientsnear the trench, but changesin spreadingrates 1978]. The southern subbasinof the West Philippine Basin, and ridge jumps within the subductedlithosphere are often adjacent to the Philippine Trench, does not appear to be a unknown. Three extreme examples of this problem are the continuation of the spreadingpattern in the rest of the West Central Aleutians, Sumatra-Andaman, and Peru-North Chile. Philippine Basin [Mrozowski et al., 1982]. The Kula/Pacific ridge may have ceasedin the late Paleocene [Byrne, 1979], implying increasingslab age downdip in the Arc Age CentralAleutians, or about43 m.y.ago [Engebretson, 1982], Initiation of subductionis usually followed in less than 5 implying decreasingage downdip. In the Sumatra and Anda- m.y. by initiation of arc volcanism[Gill, 1981]. Thereforethe man segments, ages increase northward, but because of oldest arc-relatedrocks in a subductionzone provide an esti- oblique convergenceand closely spaced fracture zones, age mate of duration of subduction. probably decreasesdiscontinuously downdip. In the Peru and Arc ages in Table 1 indicate for each arc the oldest arc- North Chile segments,extrapolation of age gradients from related rocks that are associated with the current trench. In unsubductedto subductedcrust can be substantiallyin error somecases (e.g., Sumatra and Java), older granites have been becauseof changesin spreadingrate. For thesetwo segments dated but appear to be associatedwith an arc-trenchsystem only, At is basedon a reconstructionof the subductedportion having a substantiallydifferent trend than the presentone. In of the Nazca plate [Cande, 1983]. Ideally, all estimatesof A t other cases(e.g., New Britain, Solomons,New Hebrides, and should be based on such reconstructions. Philippines)an older arc has a trend similar to the present Almost all estimatesof As and At are basedon the world- one, but a reversalof subductionpolarity has occurred.If an JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 233 apparentpause in subductionhas occurred,the older age is and volcanogenicrocks also outcrop on the Bonin Islands still used.When suchpauses are prolonged,they can perhaps [Karig, 1971]. affect current tectonic style and probably should be used to Suggestionsof both youngerand older agesfor the trenches correct somehowthe arc age. However, often the apparent from Izu-Bonin to Palau also exist, however. The oldest dated pausesare an artifact of incompleteexposures and dating; rocks from Yap are brecciaswith middle(?) Miocene shallow thus no attempt to correct for pausesis made herein. Error water Foraminifera [Cole et al., 1960]. DSDP site 448 on the limits shownfor agesin Table 1 representage uncertaintiesin Palau-KyushuRidge bottomedin middle Oligocenevolcanics dating of the oldestdated arc-relatedrocks. These error limits I-Kroenkeand Scott, 1978]. In neither caseis an older arc age do not indicateuncertainties in the age of the arc, as in most excluded. Dredges on the inner wall of the Mariana Trench casesthe possibilityremains that the earliestarc-related rocks recovered(in addition to the late Eocenearc complex)isolated are not exposedor dated. assemblagesof alkalic basalts,chert, and Late Cretaceoussed- Dickinson[1973] has compiledestimates of arc ages for iments interpretedas accretedseamount fragments [Bloomer, mostof the subductionzones of Table 1. In general,ages given 1983]. ReworkedLate Cretaceousforaminifera have also been hereinare similar to his in spiteof accessto newerage data. identified at DSDP site 290 I-Karig et al., 1975], located on the However,field work and datingin the last decadesuggest that Palau-Kyushuapron on oceaniccrust thought to be Eocene the agesof severalarcs require substantialrevision (e.g., Su- in age [Watts et al., 1977; Shih, 1980]. This age impliesthat at matra, Java,Philippines, and New Britain). leastpart of the Palau-KyushuRidge existedin the Late Cre- The Tonga-Kermadec-NewZealand convergentmargin is taceous, though possibly not as an arc. Uyeda and Ben- approximatelymiddle Tertiary in age. The oldestK-Ar age Avraharn[1972] suggestedthat the Palau-KyushuRidge was from andesiticvolcanism in New Zealand is 18 m.y., but the a fracturezone until a major changein Pacificplate motion 43 presenceof underlyingvolcaniclastic sediments suggests that m.y. ago I-Clagueand Jarrard, 1973; Dalryrnpleet al., 1980] subduction here began about 18-24 m.y.B.P. I-Ballance, causedinitiation of subductionalong this ridge. Although de- 1976]. For the Kermadec zone the Colville Ridge yields tails of this model have been revisedowing to newer data on middle Oligoceneages at both DSDP site 205 and in the Lau the location of the Philippine/Eurasia/Pacifictriple junction Islands [Hochsteinet al., 1974]. Subductionin Tonga is well and age of the PhilippineBasin, the estimatedtiming of sub- representedfor late Oligocene-early Miocene to present duction initiation has not changed[Ben-Avraham and Uyeda, [Hochsteinet al., 1974]. Rare middle Eoceneophiolitic rocks 1983]. This 43 m.y. estimatedage correspondswell with the may indicate an earlier inception of subduction, but their majority of age estimatesfor the Palau-Kyushu Arc system. provenanceis uncertain!-Ewart and Bryan, 1972]. However, the curvature of the Palau-Kyushu Ridge and the The presentsubduction patterns in the New Hebrides,New azimuth of anomaliesin the West Philippine Basin are diffi- Britain, and Solomonzones began with arc polarity reversal. cult to reconcile with this model [Mrozowski et al., 1982]. In the New Hebrides, arc polarity reversal occurred in the Theseuncertainties in the early history of the West Philippine middle Miocene; a new arc formed in the late Miocene, coeval Basin and Palau-KyushuRidge do not weakenthe firm age of with rifting in the North Fiji Basin [Carney and Macfarlane, 45 +_3 m.y. for inceptionof subduction. • 1982]. In New Britain, Eocene andesitesand volcaniclastics Inception of the modern subductionpattern in Andaman- and late Oligocene-Miocene plutons show increasing Sumatra-Java is controversial. In Sumatra, scattered Cre- K20/SiO 2 to the southeast,indicating a subductionpolarity taceousand PaleogeneK-Ar agesare found for granitic rocks, oppositeto the present[Page and Ryburn,1977]. Modern arc but the orientation of thesebelts is not reliably known. Katili polarity began in the upper Miocene [Page and Ryburn, [1973] interpreted the Cretaceous arc as parallel to the 1977], substantiallyyounger than the Eocene age used by modernone, while Hamilton [1979] suggested that the belt Dickinson[1973]. Solomon polarity reversalis less reliably may be strongly oblique to the modern trench and truncated timed but may be similar: upper Eoceneand Oligoceneba- at the trench.Similarly, Hamilton [1979] interpretedLate Cre- saltic and andesiticrocks preceded polarity reversaland were taceousand Paleogenemelanges and igneousrocks in Java as followed by depositionof widespreadlower-middle Miocene forming an arc trending from westernJava through Borneo. shallowwater limestones[Karig andMamrnerickx, 1972]. In both Java and Sumatra, late Oligocenecalc-alkaline rocks The presentarcs of Izu-Bonin, Marianas, Yap, and Palau are the oldest arc-related rocks that are clearly part of the all appearto have initiated as part of the Palau-KyushuArc presentsubduction geometry [Hamilton, 1979]. The interpre- about 45 ___3 m.y. ago. DSDP site 296, near the Palau- tation of Hamilton is tentativelyfollowed here, though a much KyushuRidge, bottomed in tuffsyielding an ½øAr/39Arage of older age may be appropriate.The poorly dated Andaman about 48 m.y. [Ozima et al., 1977], and DSDP site 290 in the region is at least as old as the late Oligocenestart of conti- West PhilippineBasin penetrated a middle Eoceneconglom- nental thinning, and probably Cretaceous [Curray et al., erate in an apron derived from the Palau-Kyushu Ridge 1982]. [Karig et al., 1975]. Upper Eocenefossils have beenidentified Middle Miocene K-Ar ages in North Sulawesiprobably on Palau [Hamilton, 1979], near the southern end 'of the predate polarity change [Hamilton, 1979]. The current po- Palau-KyushuRidge. Back-arc spreadingin the Parece Vela larity may have been establishedas recently as 5 m.y.B.P., Basin [Mrozowskiand Hayes, 1979], ShikokuBasin [Kobay- based on amount of accretionand slab length [Silver et al., ashi and Isezaki, 1976; Watts et al., 1977], and Mariana 1983a]. Progressivepolarity reversalalong this arc has not yet Trough [Bibeeet al., 1980] have subsequentlysplit the ances- reached the Sangihe Arc; Sangihe may therefore be middle tral Palau-KyushuArc and led to the isolationof the present Miocene, but it has not yet been directly dated [Hamilton, Izu-Bonin, Marianas, and probably Yap arcs. A late Eocene 1979]. Just north of Sangihe, Miocene and older andesitic arc complexhas been dredgedon the landward slope of the rocks are found in Mindinao [Martin, 1976]. These rocks are Mariana Trench [Bloomer,1983], consistentwith outcropsof not associatedwith the very recent breakthrough of the Phil- Eocenevolcanogenics on Guam and Saipan.Eocene volcanic ippine Trench but with an older arc of uncertain polarity that 234 JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS precededarc-arc collision and developmentof the Philippine throughout the arc [Tomblin, 1974]. Late Cretaceous to Trench [Hamilton, 1979]. Eocenearcmagrnatism is common in the nearby Greater An- Andesitic volcanogenicsin the Ryukyus indicate that this tilles [Malfait and Dinkelman, 1972; Mattson, 1976], but no subduction zone is at least as old as the beginning of the subsequentarc magmatismis observedthere [Mattson, 1979]. Miocene [Matsumoto and Kimura, 1974]. Karig [1973] sug- Thus the age data from both arcs are most consistentwith a gestedthat the Ryukyu Arc may have been active throughout hypothesizedEocene change from subduction beneath the the Tertiary; a 55 __+5 m.y. K-Ar age [Nozawa, 1968] is con- Greater Antilles and a transform boundary in the LesserAn- sistentwith this interpretation. tilles to subductionbeneath the LesserAntilles [Sykes et al., Southwest Japan, adjacent to Ryukyu, has probably the 1982]. most uncertainduration of modern subductionof any subduc- Most of the Pacificmargin of South America has beena site tion zone. Granitic rocks as old as 420-430 m.y. form a belt of subductionsince at least the early Paleozoic [e.g., Allmend- striking obliquely to the present trench [Maruyama et al., inger et al., 1983], but the presentmagmatic trends date only 1984]. Intermittent arc volcanismfrom that time to the pres- from the Triassic [James,1971; Campbell,1974a, b]. In Tierra ent is detected,punctuated by more pronounced volcanismin del Fuego, the southernmostpart of South-America,arc vol- Cretaceous and early Tertiary but also including weak to canism began in the Jurassic[Skewes and Stern, 1979], prob- moderate volcanism through most of the Neogene [Matsu- ably in the uppermostJurassic [Malumicin and Ramos,1984]. moto and Kimura, 1974]. Plutons 170-180 m.y. in age may In the South Sandwich region, the present subductionge- represent the oldest belt parallel to present tectonic trends ometry has persistedfor at least 7-8 m.y., the duration of the [Dickinson,1973]. Choi [1984] consideredevidence of possible current back-arc spreading pattern [Barker and Griffiths, microplate accretion and rifting in Japan and concludedthat 1972]. Back-arc spreadingfrom 21 m.y. to about 8 m.y. was large landmassesrifted away from both northeastand south- associatedwith more northerly subductionthan the present west Japan during the Permian. A post-Permianage therefore pattern but probably included some subduction along the seemsappropriate for modern subductiongeometry, but the modern trench [Barker and Hill, 1981]. In contrast, 21-30 175 m.y. age assignedin Table 1 is extremelytentative. Dura- m.y. spreadingin the West Scotia Sea was approximately tion of the present pattern is apparently better known for parallel to the present direction of back-arc spreading but northeastJapan, with 110-120 m.y. plutons the oldest that are cannot be unambiguouslyattributed to back-arc spreading related to the modern trend I-Kawanoand Ueda, 1967]. [Barker and Hill, 1981]. Middle Late Cretaceousthrough Cenozoic volcanism is In the Aegean,initiation of the modern trench and back-arc well documented for the nearby Kuriles [Markhinin, 1968]. extension probably began only shortly before intrusion of Older K-Ar ages of about 150 m.y. and 219 _+5 m.y. are also granodioritesdated as 10-12 m.y. [Le Pichon and Angelier, found for dredged granites of this continental region [Gnibi- 1981]. denkoand Khvedchuk,1982], but their subductiongeometry is The duration of subduction and arc volcanism for the unknown. A middle Late Cretaceousage is tentatively used Makran subductionzone may vary substantiallyalong strike. here, while recognizingthat the 150 m.y. agesare more consis- The overridingEurasian plate hereis composedof two conti- tent with the Late Jurassic[Avdeiko, 1971] beginningof arc nental blocks,the Lut and Afghan,which collidedand sutured volcanismin adjacentKamchatka. at about the end of the Paleogene[Arthurton et al., 1979]. The The Aleutian Arc is at least as old as Eocene, based on presentBenioff zone may be segmentedinto two segments dating of volcaniclastic rocks [Scholl et al., 1975], and [Jacob and Quirtmeyer,1979], with the boundaryoccurring younger than the M sequenceoceanic crust trapped behind near the Lut/Afghansuture. Only the western(Lut) segmentis the arc. An age of about 56 m.y. (D. Scholl, personal com- consideredin Table 1, becausesparse seismicity in the eastern munication to D.C. Engebretson, 1982) is tentatively as- zone precludesidentification of a Benioffzone. Prior to col- sumed.Initial plutonism in nearby Alaska and Alaska Penin- lision, widespreadSenonian (Late Cretaceous)arc volcanism sula is well dated as 150-175 m.y., with subsequentextensive occurredaround the southernboundary of the Afghan block volcanismfrom Late Cretaceousto middle Tertiary [Reed and [Auden, 1974; Arthurtonet al., 1979], roughly parallel to the Lanphere, 1969]. However, estimation of duration of the modern trench. Scattered sills, dikes, and stocks, some of late modern subduction pattern is complicated by contradictory Paleogeneage, also occurin this region.Northward subduc- evidenceof possiblepolarity reversal, middle Cretaceoussu- tion beneath the Lut block probably began in the Eocene, turing [Csejtey et al., 1982], and possiblyeven later terrane based on the ages of calc-alkalinevolcanics in this region emplacement[e.g., Stoneet al., 1982]. A substantiallyyounger [Jun• et al., 1976]. Extensiveforearc fiysch sedimentation of age than the 160 __+10 m.y. assumedhere may be appropriate. Eocene through Miocene age [Auden, 1974], accompanied Arc volcanismbegan in the Cascadesin the Middle Jurassic and followedby rapid developmentof a very wide accretion- [Coney, 1972; Dickinson,1972] and in Mexico in the Turonian ary prism [White, 1979], occurssouth of both blocks.The [Coney, 1972]. In both regions,subsequent disruption of sub- modestvolcanism of the modern arc probably beganin about duction patterns by terrane motions is possible.In Middle the late Plioceneor early Quaternary [Arthurton et al., 1979]. America the oldest arc-related rocks are middle Cretaceous, Thus subduction beneath the Lut block appears to have with Late Cretaceousvolcanics common [Dengo and Bohnen- begunin the Eocene,much later than the Senonianinception berger,1969]. of subductionbeneath the Afghan block. The oldest arc-related rocks from the Lesser Antilles are Durations of subductionshould always be greaterthan time spillites and keratophyres at least 142 _+10 m.y. old, found sincesubduction of the slab tip (T•,).Comparison of thesetwo only on the island of Desirade I-Tomblin, 1974]. The relation columnsin Table 1 showsonly one exception'North Sulawesi of these rocks to former subduction patterns is unknown. has an estimatedarc age of 7 + 4 m.y. and T•, of 15.3 m.y. More likely, arc volcanismbegan in about the middle Eocene, When the large uncertaintyassigned to convergencerate is as Eocene and younger calc-alkaline volcanics are found considered(3 + 2 cm/yr), the resultingrange of T• is 9.2-46 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS 235

m.y. Thus this comparisonmay indicate that convergencerate STRIKE-SLIP FAULTING is faster than assumed. However, neither value has been modi- Characteristics fied in Table 1, becauseone cannot confidentlyidentify which variable is erroneous. Most considerationsof convergencerate in this paper focus on the componentof convergenceperpendicular to the trench Trench Depth rather than total convergencerate, as the former is probably more relevant to such subductionzone parametersas overall Two measuresof trench depth are included in Table 1: the stressstate. Indeed, because of the control of downdip slab maximum trench depth within the segmentand relative depth, pull on motion of the subducting plate, most convergence the difference between maximum trench depth and abyssal directions are within 25ø of perpendicular to the trench plain depth. Most values are from the compilation of Hilde (Figure 3). Nevertheless,oblique convergencehas an impor- and Uyeda [1983], who cite the original sources.Maximum tant impact on the overriding plate, through its control of trench depth for Java and abyssalplain depth for Palau are strike-slipfaulting. from Grellet and Dubois [1982]. For the following subduction Strike-slip faults often develop parallel to the trench and zonesnot analyzedby either of the above,depths are from the 100 to 300 km inland from it, usually near or within the arc. GEBCO maps [IHO/IOC/CHS, 1984]: Sumatra, Kurile, These faults accommodatepart of the trench-parallelcompo- Kamchatka, Central Aleutians, Lesser Antilles, and Colombia. nent of oblique convergence.Reliable estimation of current Some abyssalplain depths are also from the GEBCO maps: rates of strike-slipmotion from field relations is seldompossi- Java, southwest Mexico, southeast Mexico, Peru, North Chile, ble, so the proportions of trench-parallel component accom- Central Chile, and South Chile. Maximum trench depths for modated by strike-slipmotion and oblique convergenceare southwest Mexico and southeast Mexico are from the Times not known. Atlas [Times, 1975]. Most of the depths based on GEBCO These strike-slipfaults separatingthe forearc from the re- maps are consideredless reliable than other depths,because of mainder of the overriding plate are probably transform faults, the 100- to 500-m contour interval employed.All abyssalplain with the forearc acting as a narrow or sliver plate [Fitch, depthsare determinedfrom regionsseaward of the outer rise, 1972; Dickinson, 1972; Kari•l and Marnrnerickx, 1972]. The therebyavoiding any subductioneffects on depth. variety of relative movements possible for such sliver plates, Trench depths can be affectedby three variablesthat are potentially including transform faulting and/or back-arc not specificallytreated in this study: thicknessof sedimentary spreading,is consideredin detail by Dewey [1980]. In the trench fill, thickness of sediments on the oceanic crust before discussionsthat follow, the term "strike-slip fault" is used enteringthe trench, and presenceof aseismicridges. Thickness rather than "transform fault," because near-arc strike-slip of trenchfill is usuallydifficult to estimatefor trencheslacking faults may form a more diffuse zone than typical oceanic migrated multichannel seismicdata. This effect, as well as the transformfaults and becausethe subsurfacenature of the plate effectof subductingaseismic ridges, is reducedby considering boundaryis not known. maximum trench depth rather than averagetrench depth. Pel- In most modern subduction zones only a narrow zone of agic sedimentthickness on the abyssalplain is generallysimi- anastomozingor en echelonfaults is present,usually occurring lar to that on the portion of plate at the trench;thus this effect along the arc. The most notable and longest recognizedof can be largely avoided by focusingon relative trench depth these "simple" strike-slip faults are the Semangko (or Su- rather than maximum trench depth. Sedimenteffects are fur- matran) Fault of Sumatra, the Philippine Fault, the Median ther reduced by excludingdepth estimatesfrom Table 1 for Tectonic Line of southwestJapan, the Atacama Fault of Chile, subductionzones with very thick trenchfill or very thick sedi- and the Alpine Fault of New Zealand. Similar strike-slipfaults mentsin the nearby abyssalplain. are the Dolores-Guayaquilof Colombia and Ecuador and the Trench depth estimatesin Table 1 differ from all other pa- Liquina-Ofqui of South Chile. Of these, the clearestassoci- -rametersin Table 1 in an important respect: they do not ation between fault location and the location of the modern necessarilycome from near the referenceposition at which arc is found in the Semangko, Dolores-Guayaquil, and other parametersare determined.This differenceis a conse- Liquine-Ofqui faults. In many subductionzones, strike-slip quenceof the focuson maximumtrench depth within a seg- faultingis not confinedto the modernarc. The Atacama Fault ment. The most extremeexample of this is the Marianas, with of North Chile and Central Chile is located seaward of the a maximum depth of 11 km, the deepestof all trenches.This presentarc, along an older magmatic belt (Figure 4). Strike- maximum depth occursin the southernmost• Marianas, which slip faulting in Alaska has involved several widely spaced is characterizedby highly obliqueconvergence and a poorly major faults,with an overall seawardmigration of activity: the definedBenioff zone. Maximum trenchdepth in the vicinityof Jurassicor Early Cretaceousinitiation of motion on the Tin- the Marianas referencelocation is 1.3 km shallower, and this tina Fault, Late Cretaceous or Paleocene initiation of the depth is used in Table 1. Another notable example is the Denali Fault, and Pleistocene initiation of the Fairweather South Sandwichsubduction zone, which has a major change Fault [Lathram et al., 1974]. Although current motion here is in trenchdepth acrossa fracturezone separating crust of very predominantly on the Fairweather Fault, all three show some differentages. In subsequentanalyses of trench depth, an age Holocenemotion [Lathram et al., 1974]. Strike-slipfaulting in of 65 m.y. is assumedfor the subductingslab in this region, Colombia and Ecuador is somewhat analogous to that in rather than the 49 m.y. averagefor the entire subductionzone. Alaska, occurring not only along the modern arc but also Although65 m.y. is a more appropriateage than 49 m.y. for farther inland, along older magmatic belts [Pennington,1981]. the slab at the maximumtrench depth, both agesare highly In contrast, in both Sumatra and Andaman subduction zones, uncertain. For all other subductionzones, differencesbetween major dextral faults occur both within the arc and forearc trench depth location and referencelocation probably have a [Kari•] et al., 1980; Mukhopadhyay,1984]. In the South Kuri- relatively minor effect. les and northeast Japan, diffuse strike-slipfaulting occursbe- 236 JARRARD'RELATIONS AMONG $UBDUCTIONPARAMETERS

STRIKE-SLIP NCH I NJP FAULTING CCH I KAM -•o NOSlNISTRALFAULT SCHKu•:cu NIC I JAVSMX PER ß NOSL!P COL I ALA <- DEXTRALSUM AEG TDFi WMXMAK

NZLCAS SJP I PHL

i

TON KER •C• NBR

O RYKANTS[JL ! NHB MARIZU •=• ALU ? • PAL • YAP

Fig. 3. Convergencerate and azimuth with respect to the trench for each modern subduction zone of Table 1. Symbols at the head of each convergencevector indicate geological evidence of Pleistocene strike-slip faulting and associatedoffset direction. Note that nearly all offsetdirections are consistentwith the directionsof oblique convergence.

tween the coast and the trench [Ichikawa, 1980]. In southwest faults of Peru [Philip and Megard, 1977]. In contrast,nearly Japan, no active arc is found; the Median Tectonic Line lies perpendicularconvergence in northeastJapan causescurrent mostly along an older arc. Modern strike-slip faulting is not activity on the North Japan Line to be almost pure dip-slip only along the Median Tectonic Line but also along numer- [Okayarea,1961], though this fault may have begunas strike- ous faults, with various azimuths, north of the Median Tec- slip [Kaizuka, 1975] and focal mechanismsindicate a diffuse tonic Line [Matsumoto and Kimura, 1974]. zone of current strike-slip motion in the forearc [Ichikawa, Once a strike-slipfault has been establisheddue to oblique 1980]. The Coriolis Trough of the New Hebrides may be an- convergence,subsequent stress is accommodatedalong this other example;Dubois et al. [1978] suggesta strike-sliporigin, zone of weakness,though not necessarilyas pure strike-slip but the trough is now entirely extensional.Substantial dip-slip motion. For example,the northern portion of the Alpine Fault also accompaniesmodern strike-slipmotion on the Semangko of New Zealand is undergoinga transition from pure dextral Fault of Sumatra [Katili, 1974; Page et al., 1979], the slip prior to 10 m.y.B.P. to transpressionsince 10 m.y.B.P.; Liquina-Ofqui Fault of South Chile [Hervd et al., 1979], and uplift and mountain building now dominate strike-slipmotion the Atacama Fault of North Chile and Central Chile [St. along the fault [Carter and Norris, 1976]. This changeis ap- Areandand Allen, 1960]. parentlya responseto southwardmigration of the India/Paci- Transpressionsometimes forms en echelon ridges, usually fic pole of relative motion [Norris and Carter, 1982] and ac- just behind the strike-slipfault but sometimeswithin the for- companyingchange to lessoblique convergence.The Tintina, earc [Kaizuka, 1975]. The senseof en echelonarrangement in Denali, and Fairweather faults of Alaska currently include theseridges dependson the direction of oblique convergence. both dextral slip and reversefaulting [Lathram et al., 1974]. En echelonridges, such as those of Sumatra and the Kuriles, Similarly, both reverse and strike-slip components are analogous to the smaller-scaledrag folds that often ac- characterize faulting along the Median Tectonic Line of company strike-slip faults. More rarely, strike-slip motion is southwestJapan [Matsumoto and Kimura, 1974] and the accommodatedthrough a complex pattern of fault-bounded JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS 237

-t- 8@UTH

AMERICA

0 km I000 \ k I0 cm/yr +

ß

ß /• / :. ßß ALASKA I .1" i ß

km ß ß $00 ß

ß

ß ß ../. •,-/' 20 ø

/5'0o

,_+ ,,,- //

.,,,•-= convergence direction ß = octive volcono • = strike-slipfoult •= crustolthickness.kin ('-•= 2000m elevotion 80 ø

Fig. 4. Modernplate tectonic setting and locations of activestrike-slip faults in westernSouth America and southern Alaska. 238 JAggAgD' RELATIONSAMONG SUBDUCTION PAgAMETERS blocks which may experiencedifferential rotation and uplift, by shorteningthan by extrusiveand intrusive activity; Isacks such as in New Zealand [Norris and Carter, 1982]. Local [1985] showsthat thisassumption is probablyvalid. forearc block rotation may be more commonthan is geologi- The bight of Alaska may be analogousto that of Peru-Chile callyrecognized; paleomagnetic evidence of suchrotations is (Figure 4). At present,oblique convergence in Alaska suggests not unusual[e.g., Jarrard and Sasajima,1980; Stoneet al., collisionof a dextrally slippingeastern and slightlysinistrally 1982; Beck, 1980]. slippingwestern portion of thesliver plate(s) of southcentral Alaska. During the early Tertiary and all of the Cretaceous, Leadingand Trailing Edgesof Forearc Slivers the convergencedirection was closerto due north, implying major strike-slipmotion on both segmentsand consequent The relative motion of forearcslivers has important impli- compressionin this bight. The substantialconvexity of this cationsfor the tectonicsof regionsat the leadingand trailing region is more appropriatelyseen in the faults than in the edgesof slivers:compression is often predictedat the leading presenttrench, because of the very wide accretionaryprism. It edge, and tensionis predictedat the trailing edge of each may not be coincidentalthat the tallest mountain in North sliver. The Sumatra sliver plate, bounded by the Semangko America,Mount Denali (formerlyMcKinley), is at the apex of Fault and Sunda Trench, is perhaps the best example of a this bight and adjacent to the major Tertiary strike-slipfault forearc plate, with a trailing edge in the Sunda Strait. The of Alaska, the Denali Fault (Figure 4). The Cenozoichistory fault apparentlydoes not extendall the way to the trenchas a of strike-slipmotion on the faults of Alaska is enigmatic,with simplestrike-slip fault; instead a diffusezone of crustalexten- major dextral slip east of Mount Denali [Forbeset el., 1974] sion in the southern Sunda Strait accommodates the motion but little evidence of substantial offset near Mount Denali [Huchon and Le Pichon, 1984]. Similarly, the Liquine-Ofqui [Reed and Lanphere,1974; Csejteyet el., 1982]. Perhapssome Fault of South Chile has a trailing edge which curvesaway of the motion of the sliver plates has been accommodatedas from the arc and into the Golfo de Penas-Taitao Basin,where crustalthickening, due to the changein senseof obliquecon- extension is probable [Forsythe and Nelson, 1985]. Alter- vergencenear the bight. An additional probablesource of the natively, the location of this trailing edge adjacent to the apparentlyconflicting evidence is the assumptionof constant SouthAmerica/Nazca/Antarctica triple junction makes it pos- strike-sliprates sincethe time of formation of the offsetrocks; sible that the fault morphologyand offsetare a spreading- Tertiary changesin convergenceobliquity imply substantial center indenter effect [Forsythe and Nelson, 1985]. The changesin strike-slip rates and even senseof offset in the Dolores-GuayaquilFault of Colombia and Ecuador appears vicinityof Mount Denali. to be similar to the Semangkoand Liquine-Ofquifaults in Compressionat the head of a sliverhas also beensuggested that its trailing edgeswings offshore and is lost in a gulf, the as a cause of mountain building in Japan [Kaizuka, 1975]. Gulf of Guayaquil [Campbell,1974b]. It is not known whether The changein azimuth from obliqueconvergence in the Kuri- the fault continuesto the trenchor causescrustal thinning in les to perpendicularconvergence in northeastJapan occursin the Gulf of Guayaquil. the vicinity of the Hidaka Mountains of Hokkaido, one of the The leading edgesof most forearc sliversare characterized areas of strongestNeogene folding in Japan [Matsuda et al., by compression,but the structuralstyle depends on curvature 1966]. Shallow focal mechanismsfrom this region indicate of the edgeof the overridingplate. For example,the strongly reversefaulting with maximum compressionalaxes approxi- convex (as seen from the upper plate) western end of the mately parallel to the trench; similar focal mechanismsare Sunda Trench causesSumatran strike-slip motion to be ac- found in the underlyingslab, possibly indicating tearing of the commodatedwestward as back-arcspreading in the Andaman slab [Stauder and Mualchin, 1976]. However, the structural Basin(Figure 7). In contrast,both Alaska and Peru-Chile have style in this region may be complicatedby proximity to the concaveplate boundariesand thereforecompression. poorly located Pacific/North America/Eurasiatriple junction. Presentmotion of the Nazca platecauses sinistral strike-slip Farther south, sinistral slip of the Izu-Bonin sliver may be in Peru and dextral slip in Chile, implyingcompression be- responsiblefor the strong Neogene folding in the adjacent tween collidingslivers in the bight of northernmostChile and portionof Japan[Kaizuka, 1975]. Again, however, proximity southeasternPeru (Figure4). Northwest-southeastshortening to a triple junction (Pacific/Philippine/Eurasia)may compli- in the WesternCordillera of SouthPeru is indicatedby focal cate the structural style. Furthermore, the presenceof ac•tive mechanisms[Grange et al., 1984]; collisionmay be the cause strike-slipfaulting parallel to the Izu-Bonin Arc has not been of this otherwiseinexplicable compression direction. Cande clearly demonstrated. [1983] has shownthat the presentconvergence direction has Continental Versus Oceanic remained relatively constant since about 26 m.y.B.P.; earlier Tertiary convergencewas consistentlyto the northeast. Thus Strike-SlipFaulting compressionin the Peru-Chile bight is expectedthroughout A remarkable correlation exists between the presenceof the Tertiary, with a changefrom Early Tertiary dominanceof strike-slipfaults and th e typeof crustin theoverriding plate. motion on the Chilean faults to late Tertiary dominanceof the Two thirds of the modern subduction zones with continental Peruvian faults. One may speculatethat the substantially crust as the overriding plate have active strike-slipmotion greater crustal thicknessin the bight [James,1971] and much near the arc, while only one fifth of oceanicoverriding plates greater present relief and width of the Altiplano compared have similar faulting (Table 4). In part, this observationcould with other portions of the Andesare consequencesof the con- be an artifact of the less completeoutcrops within oceanic tinuous strike-slip-drivencollision (Figure 4). If so, the wide overridingplates, but the scarcityof strike-slipfocal mecha- zone of crustal thickening is not a simple collision of "sliver nismsand tendencyof strike-slipfaults to lie within the arc plates"; it is the cumulative effect of transpressionon many largelyobviate this qualification. Because continental arcs are faults. This speculationis dependenton the assumptionthat generallyolder than oceanicarcs, the paucity of strike-slip presentAltiplano relief and crustalthickness are affectedmore faults in oceanicoverriding plates could be due to the shorter JARRARD.'RELATIONS AMONG SUBDUCTION PARAMETERS 239

TABLE 4. Arc-Parallel Strike-SlipFaulting

Type Crust Subduction Zone Major Fault Offset* Reference

Continental New Zealand Alpine D Wellman [1964], Carter and Norris [1976], Norris and Carter [1982] Aegean Mercier [1981] Makran Kazmi [1979], Quittmeyeret al. [1979] Andaman D Mukhopadhyay[1984] Sumatra Semangko D Fitch [1972], Katili [1974], (Barisan) Huchon cindLe Pichon [1984] Ryukyu ... SW Japan Median Tectonic D Okada [1971], Matsumotoand Line Kimura [1974], lchikawa [1980] NE Japan North Japan D Okayarea [1961], Matsuda and Line, etc. Kitamura [1974] Kurile D Kaizuka [1975], Ichikawa [1980] Kamchatka ... Alaska Peninsula Farewell, Holitna, D Lathram et al. [1974] Togiak-Tikchik Alaska Fairweather, etc D Lathram et al. [1974] Cascades St. Helens D Weaverand Smith [ 1981] SW Mexico ... SE Mexico ... Middle America .,. Colombia Dolores D Campbell[1974a], Pennington[1981] Ecuador Guayaquil D Campbell[1974b], Pennington[1981] Cotopaxi-Ban6s S Peru S $tauder [ 1975], Philip and Megard [1977], Sudrez et al. [1983] North Chile Atacama D St. Amandand Allen [1960], Arabasz[1971] Central Chile Atacama D St. Amandand Allen [1960], Arabasz[1971] South Chile Liquifie-Ofqui D Herv• et al. [1979] Tierra del Fuego ... Transitional Java s Tjia [1968], Katili [1970], Chotin et al. [1985] Philippines Philippine S Allen [1962], Fitch [1972], Hamilton [1979]

Oceanic Kermadec ... Tonga New Hebrides ?Coriolis(inactive) ... Dubois et al. [1978] Solomon D? Colemanand Hackman [1974] New Britain ... Palau ... Yap ,., Marianas ... Izu-Bonin ?Nishi-Schichito S ? Kaizuka [1975], Karig and Bonin Ridge S ? Moore [1975], lchikawa [1980] (inactive) North Sulawesi Sangihe Central Aleutians Cormier [1975] Lesser Antilles South Sandwich

*D, dextral' S, sinistral; three dots, none. opportunity for oblique convergenceto occur and initiate sodatedwith the Eurasia/India plate boundary [Kazmi, 1979; strike-slipmotion. However,in neithercontinental nor ocean- Quittmeyer et al., 1979]. Strike-slip faults are common in ic overridingplates is there a correlationbetween subduction southern Mexico only east of the Isthmus of Tehuantapec. duration and occurrenceof strike-slipfaults. The Salina Cruz fault, a major sinistralstrike-slip fault which Of the 23 subduction zones with continental overriding may be currently active, trends approximatelyperpendicular platesof Table 4, arc-parallelstrike-slip faults appear to be to the Mexican trench and separatesthe zone of numerous absent only in the Aegean, Makran, Mexico, Kamchatka, Paleogenesinistral faults from the subductionsegments con- Middle America, Ryukyu, and Tierra del Fuego. Discrete sideredhere [Viniegra, 1971]. Strike-slipfocal mechanismsare strike-slip faults are apparently unnecessaryin the Aegean, reported from the Cascades region [Zoback and Zoback, becauseof diffuse and variable crustal thinning. Scattered 1980], but slip planes may differ substantiallyfrom the arc strike-slipfaults in the far northern Aegean [Mercier, 1981] trend [Crossonand Lin, 1975], and only one significantstrike- are probablyrelated to collisionof the Turkish and Eurasian slip fault parallel to the arc is reported [Weaver and Smith, plates[McKenzie, 1978]. The Makran forearcis heavilyfaul- 1981]. In Middle America, three dominant structural trends ted,but thesefaults are mainlythrust faults; all major strike- are probably currently active, with northwest-southeast, slip faults are approximatelyperpendicular to the trench,as- north-south,and northeast-southwestazimuths, but strike-slip 240 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS focal mechanismssuch as that of the Managua earthquake vergencewithout strike-slipmotion distributesfrictional shear indicate slip planes perpendicularto the trench [Ward et al., over a long path at the boundary betweenoverthrusting and 1974]. underthrustingplates. In contrast, a vertical surfacecan con- Java and the Philippinesmight more appropriatelybe con- centrateshear more effectivelyand minimize the total effective sidered transitional crust than continental. True continental length of plate boundary accommodatingthe shear. By this crust in Java is confined to the northwest portion, though rationale, a strike-slipfault would develop wheneverconver- crustal thicknessestypical of continental crust are present genceis oblique by more than about 45ø [Fitch, 1972]. Strike- throughoutJava [Hamilton,1979]. Nearly perpendicularcon- slip faulting is currently active even in somesubduction zones vergencein Java is not accommodatedby any significant with near-perpendicularconvergence (e.g., Chile), though it is trench-parallelstrike-slip faults [Hamilton, 1979], though a more common when subductionis oblique (Figure 3). Fitch's short sinistral fault has been inferred in continental western- 45ø estimateassumes equal friction per unit area for the thrust most Java [Tjia, 1968; Katili, 1970] and many minor strike- boundarybetween plates and the strike-slipfault. Instead,the slip faultswith a wide varietyof azimuthshave beenmapped strike-slipfault must be much weaker, as evidencedby ab- throughoutJava [Chotin et al., 1985]. A long historyof arc senceof major earthquakesand occurrenceof strike-slipin magmatismand collisionin the Philippineshas resultedin subductionzones with low obliquityof convergence.Figure 3 near-continentalcrustal thicknesses,and current oblique con- and Table 4 yield information on the conditionsrequired for vergencein the Philippinesmakes the PhilippineFault one of presentactivity on a preexistingstrike-slip fault; they cannot the most obvious of modern strike-slip faults [Fitch, 1972]. place useful empirical limits on the amount of convergence However, this fault may be more complex in origin than obliquity requiredfor initiation of strike-slipmotion. simpleoblique convergence, as it extendsfrom behind the Beck [1980] revised the criterion of Fitch [1972] for in- eastwarddipping Manila Trench of the northern Philippines itiation of strike-slip faulting, by assuming oblique shear to behind the westward dipping Philippine Trench of the rather than horizontal shear and allowing the resistanceto southernPhilippines. slip per unit area on the strike-slipfault (rt) to differ from that The Andaman subduction zone is included in subduction on the contact betweenmajor plates (rs). Beck [1980] con- zones with continental overriding plates, though the present cludedthat strike-slipfaulting is expectedwhenever distribution of continental crust within the arc and forearc is t't discontinuous[Curray et al., 1982]. Strike-slipfaulting within tan•b >_ sin D s rs the Andamanregion is mostlyassociated with transformfaults that offset the back-arc spreadingsegments, but focal mecha- where q• is the obliquity of convergenceand Ds is the dip nisms[Mukhopadhyay, 1984] and seismicprofiling [Curray et along the interfacebetween subducting and overridingplates. al., 1982] indicate the presenceof other strike-slip faults Using modern valuesof q• and Ds, this inequalityallows one within and parallel to the forearc. to estimate an average ratio of rt to rs required for active In contrastto the ubiquityof strike-slipfaulting within con- strike-slipfaulting. Eighty-six percent of the modern subduc- tinental overriding plates,only 2 or 3 of the 14 oceanicover- tion zones with active strike-slip faulting have a ratio tan riding platespossess known arc-parallelstrike-slip faults. The q•/sinDs of greaterthan 0.8; in contrast,80% of modern sub- best exampleof the latter is the WesternAleutians, omitted ductionzones lacking active strike-slip faulting have a ratio of from Tables 1 and 4 because"convergence" is almost pure less than 0.8. Before attaching physical significanceto this strike-slip.Nevertheless, an underthrustslab is present,and cutoff ratio of about 0.8, however,two important assumptions focal mechanismsindicate the presenceof a major dextral made by Beck [1980] must be verified.First, the inequalityis fault along the north ("landward") margin of the Aleutian basedon the assumptionthat partitioningof the arc-parallel Ridge,extending from the Near Islandsto Kamchatka [Cor- componentof oblique convergenceinto strike-slipis either ruler, 1975]. Whether this faulting extendsas far east as the completeor completelyabsent. Second, presence or absenceof Central Aleutian transectof Table 1 is not yet known. In the strike-slipfaulting is assumedto be independentof the com- Izu-Bonin region, Oligocene sinistral displacementof the pressionalor extensionalregime of the overridingplate. As we Bonin Ridge has beenhypothesized [Karig and Moore, 1975]. will seesubsequently, neither assumption appears to be valid. A diffuse zone of sinistral motion near the eastern ("land- The senseof strike-slipmotion is nearly always consistent ward") margin of the northern Bonin Ridge, the Nishi- with the direction of oblique convergence(Figure 3). Only Shichito zone, may be currently active [Kaizuka, 1975]. Solomon, Alaska, and Alaska Peninsula are apparent excep- Strike-slipfocal mechanismsare commonfrom the Izu-Bonin tions. All three regions appear to have dextral slip though region [lchikawa, 1980], but slip planes are generally not sinistralmotion is predicted.Solomon motion is possiblydex- parallel to the arc. Thus the existenceof modernarc-parallel tral but not known with confidence[Coleman and Hackman, strike-slipfaulting in Izu-Boninis uncertain.In the Solomons, 1974]. Furthermore,the convergenceobliquity is smallerthan late Pliocene and Quaternary strike-slip fractures are combined uncertainties in Pacific/Australia and Aus- common, along trends approximately parallel to the arc. tralia/Solomonrelative motions.The discrepancyfor Alaska These possiblydextral faults are also found within the arc, and Alaska Peninsulais more important, though it is much althoughnormal faultingpredominates [Coleman and Hack- lessthan implied by Figure 3 when azimuth perpendicularto man, 1974]. the currentlyactive faults is consideredrather than azimuth perpendicularto the presentarcs (Figure 4). One possibleex- planation is that the major dextral motion known and ex- Mechanism pectedfarther east along the Denali Fault may be more im- The mechanismof strike-slipdecoupling of the forearcfrom portant for overall motion of the "sliver plate" than local the remainder of the overriding plate was first explored by slightly sinistralforces. More study of Pleistocenefault mo- Fitch [1972], basedon considerationof the Semangko,Philip- tions in Alaska is required to resolvethe possibleinconsist- pine, Median TectonicLine, and Alpinefaults. Oblique con- enciesin this region. JARRARD: RELATIONS AMONG SUBDUCTION PAgAMETEgS 241

The much more common occurrenceof strike-slipfaulting and Ryukyu subductionzones. Even back-arcspreading per- in continental lithosphere than in oceanic lithosphere is a pendicularto the trench reducesthe probabilityof strike-slip consequenceof the greater strength of oceanic lithosphere. faultingparallel to the trench,because the additionalcompo- Vink et al. [1984] have consideredthe analogouscase of pref- nent of convergencereduces the convergenceobliquity. An erential rifting of continental lithosphere. Little differenceis extreme example is New Britain, where back-arc spreading found in the strengthsof continentaland oceanicupper crust. reducesobliquity from 57o-67ø to lessthan 8ø. Becauseolivine has a greatertensile strength than quartz, the It is possiblethat the good correlationof lithospherictype compositional difference between continental and oceanic with presenceor absenceof strike-slipfaulting is an indirect lithospherebelow 13 km resultsin much weaker continental rather than causal relationship.The excellentcorrelation of lithosphere.When lithospherictensile strength is integrated strain regime with strike-slipmay lead to an indirect corre- over depth, the total strength of continental lithosphere is lation of lithospherictype with strike-slip,because continental found to be about a factor of 3 lessthan oceaniclithosphere overridingplates tend to be more compressionalthan oceanic [Vink et al., 1984]. Thus not only rifting [Vink et al., 1984] ones.As discussedin subsequentsections on dip and strain but also major strike-slip faulting should be much more regime models, the greater ages of continental than oceanic commonwithin continentallithosphere. subductionzones are responsiblefor shallower intermediate For either type of lithosphere,both increasedthermal gradi- dips and thereforehigher strain classesin continentalsubduc- ent and greater crustal thicknesssubstantially decrease litho- tion zones. spheric strength [Vink et al., 1984]. The magmatic arc, characterizedby higher thermal gradients,decreased litho- Effect of Strike-Slip Faulting sphericthickness due to heating,and increasedcrustal thick- on Slip Vectors nessdue to plutonism,is thus by far the weakestportion of the overriding plate and most likely to accommodateeither Worldwide motion models [Minster et al., 1974; Chase, strike-slipfaulting or rifting [Beck, 1980]. For example,crust- 1978a; Minster and Jordan, 1978] utilize slip vectorsof shal- al temperaturesin Japan at 20-km depth are about 700ø-800ø low thrustingearthquakes as constraintson subductiondirec- near the arc, but only 100ø-150ø in the forearc [Uyeda and tion. However,if a forearcsliver plate is present,the slip vec- Horai, 1964], suggestingat least a factor of 10 differencein tors indicatemotion of the underthrustingplate with respect overallstrength (Figure 4 of Vink et al. [1984]). to the forearcsliver, not with respectto the major overriding In additionto strengthof the overridingplate and oblique plate. A detailedvector analysis of the important distinction convergence,a third factor is probably an important control betweenazimuths of theseand other convergencevectors is on strike-slipfaulting: couplingbetween the subductingand givenby Dewey[1980]. If convergenceis not stronglyoblique overridingpaltes. Of 14 subductionzones with low coupling and the strike-sliprate is low, resultingerrors will be minor. (strain classes1-3), only two or three have arc-parallelstrike- For example, a strike-slip rate which is 10% of the overall slip faults: Andaman, New Zealand, and possiblyIzu-Bonin. convergencerate causes a 5.2ø change in slip vector for Andaman and New Zealand both have very oblique conver- oblique convergenceof 30ø. For strike-sliprates that are a gence.It may not even be appropriateto include the Alpine larger percentageof the overall convergencerate, the effect Fault of New Zealandwith the other occurrencesof strike-slip can be substantial.For example,the presentstrike-slip rate on faulting,as it forms part of the boundarybetween two major the Median Tectonic Line of southwestJapan is only 0.5 plates,Australia and Pacific.As previouslydiscussed, the pres- crn/yr [Okada, 1971], but becauseconvergence is very slow ence of arc-parallelstrike-slip faulting in Izu-Bonin is uncer- (Table 1), an 8ø to 19ø error in inferredconvergence direction tain. Of 15 subductionzones with high coupling(strain classes betweenEurasia and the Philippineplate probably results. 5-7), only three or four lack strike-slipfaults: southeastand For most other subductionzones, geologic evidence of southwestMexico, Kamchatka, and possiblyJava. Conver- modernstrike-slip rates is very inexact.Another approach to gence in southeastand southwestMexico and Kamchatka is the estimationof strike-sliprates is analysisof slip vector nearly perpendicularto the trench, and presenceof arc- residuals,the differencesbetween observed slip vector azi- parallel strike-slipfaulting in Java is uncertain. muthsand predictedazimuths based on known major-plate Coupling is expectedto affect strike-slipfaulting, because motions.This methodmakes three important assumptions: (1) the shear traction along a potential strike-slipfault is a func- the slip vector indicatesrelative motion of the forearc sliver tion of the transversecomponent of the plate boundary cou- plate with respectto the underridingplate, (2) the relative pling force,not simplyof the convergencevector. This shear motion model used [e.g., Minster and Jordan, 1978] is not tractionequals the local stressdifference induced by the plate biasedby the fact that thesesame slip vectorswere inverted boundary (which is larger for better coupling)multiplied by without consideringpresence of sliverplates, and (3) slip vec- the sine of twice the angle betweenthe principal compression tors are not biasedby the velocity structureof the slab. The axis and the potentialstrike-slip fault (whichis largerfor more secondassumption is probably reasonablefor North Ameri- oblique convergence).If the product of these coupling and ca/Pacific,North America/Cocos,and South America/•Nazca obliquityeffects exceeds the strengthof the possiblefault zone, rotation poles, which are constrainedby global closurere- then activestrike-slip faulting is expected. quirementsas well as many slip vectorsthat are near perpen- Although the expectedcorrelation betweencoupling and dicular. However, uncertaintiesin Caribbean, Philippine, strike-slipfaulting is stronglyconfirmed by the data, an alter- SoutheastAsian, and Australian plate motions must be con- native explanationof this correlation is also likely. When sideredlarger than thoseassigned, because of possiblesystem- back-arcspreading occurs, arc-parallel strike-slip faulting is atic slip vectorresiduals along the subductionzones. The third usually not required to accommodatea portion of oblique assumptionis more difficult to evaluate.Velocity in the slab convergence.Instead, partitioning of obliqueconvergence can higherthan in the uppermantle can causesignificant errors in occur through a back-arc spreadingdirection that is not per- focal mechanismsolutions, particularly for thosedetermined pendicular to the trench [Dewey, 1980], as in the Andaman from local networks [Engdahl et al., 1977]. Evaluation of 242 JARRARD:RELATIONS AMONG SUBDUCTION PARAMETERS

TABLE 5. Slip Vector Residuals

Slip Vector Residual* PredictedStrike-Slip Rate, cm/yr 95% Conver- Confi- Obliquity? Focal Focal genceô 95% Subduction dence Mechanisms Mechanism Rate, Confidence Zone N X Limits 3• a Used;!: Sources{} cm/yr 3• Limits

South Kurile 24 6.6 9.0 3.8 28.2 0.6 SM' 42-65 $tauder and 9.2 1.1 0.5, 1.8 (42.5ø-44.7øN) Mualchin [1976] Central Kurile 21 2.9 6.4 2.9 26.4 0.7 SM' 21-41 $tauder and 9.1 0.5 0.0, 1.0 (44.8ø-47.0øN) Mualchin [1976] North Kurile and 18 0.7 8.7 4.4 0.8 2.4 SM' 2-15, 17-20 Stauder and 8.8 0.1 -0.6, 0.8 Kamchatka Mualchin [1976] (47.1ø-56.0øN) Aleutians 7 11.0 6.0 5.3 45.9 23.6 MJ: 21-27 Minster and 8.3 1.9 1.1, 2.7 (168øE-167.6øW) Jordan [1978] Alaska Peninsula 4 1.5 2.5 4.0 -15.2 1.7 MJ: 17-20 Minster and 6.8 0.2 -0.3, 0.7 Jordan [1978] Mexico 8 1.0 4.5 3.7 19.9 7.2 B: 4, 6, 7, 10, 13, Molnar and Sykes[1969], 7.2 0.1 -0.4, 0.6 20, 37, 39, 40, 42, Dean and Drake [1978], 52, 62 Chael and Stewart [1982], and Burbachet al. [1984] Ecuador and 5 11.4 14.1 17.5 22.6 17.3 P: 17-19, 23; S: 15; Pennington[1981], 7.7 1.6 -0.9, 3.7 Colombia C' 69 Sudrez et al. [1983], Chase [1978a] Peru 4 -7.7 12.5 19.9 -24.5 7.8 MJ: 107-109; C: 71 Minster and 8.7 -1.2 -4.0, 2.3 Jordan [ 1978], Chase [1978a] Chile 18 4.1 8.6 4.3 20.9 5.4 MJ: 110-127 Minster and 9.1 0.7 -0.0, 1.4 Jordan [1978] Sumatrall 7 27.9 ... 5.8 55.4 ... K: L1, L4, L9, L12, Kappel [1980], 6.8 3.6 3.1, 4.1 F7, F8, F10 Fitch [1972]

*Azimuth of slip vectorfrom focalmechanism minus predicted convergence azimuth from model RM2 of Minster andJordan [1978]. •-Azimuth perpendicularto arc minus predictedconvergence azimuth from model RM2 of Minster and Jordan [1978]. J;Lettersrefer to sourceto right in samerow. {}Referencesto Minster and Jordan [1978] and Chase[1978a] are not original sources;Minster and Jordan [1978] recalculatedslip vectors by rotating into horizontal plane; Chase[1978a] referencescite B. L. Isacks(in preparation)as source. ôFrom Minster and Jordan [1978]. IlSlip vector residualsand obliquity for Sumatra were determinedassuming that true convergencedirection is that of Java slip vectors(see text).

errorsdue to slab heterogeneityrequires detailed modeling in no attempt was made to correct other slip vectors, as the each region studied. Enqdahl et al. [1977] found that this correction is usually only about 1ø [Minster and Jordan, effect had a minor impact on slip directions from Kurile- 1978]. Kamchatka and a possiblysignificant impact in the Aleutians. The obliquity of convergence(Table 5) is here taken as the Thus slip vector residualsfrom any one region should be differencebetween the azimuth perpendicularto the arc and treated with some caution, while consistentpatterns among the major plate motion, where the latter is based on model differentregions are more trustworthy. RM2 of Minster and Jordan [1978]. In principle, it would be Table 5 and Figure 5 summarizeslip vector residualsfor preferable to use the azimuth perpendicularto strike-slip thosesubduction zones with well-constrainedplate motions: faults rather than the arc. However, fault locations are not Kurile-Kamchatka, Aleutian-Alaska Peninsula, Mexico, and alwaysknown; wherethey are known, they usuallylie along South America. Also shown are data for Sumatra, to be dis- the arc. cussedin the next section.All 10 segmentsconsidered have The relation betweenobliquity of convergenceand slip re- continentaloverriding plates, and all exceptKamchatka and sidualsis shown in Figure 5. Clearly, oblique convergence Mexico have activestrike-slip faults near their arcs(Table 4). causessystematic slip residuals,as expectedfrom the concept Most of the slip vectorsconsidered were included in the global of forearcslivers driven by obliqueconvergence. However, the inversionsof Minster and Jordan [1978] and Chase[1978a], 95% confidencelimits are often large; many more focal mech- but some newer data are included. The extensive data cover- anisms would be needed before one could draw conclusions age of Stauderand Mualchin [ 1976] for the Kurile-Kamchatka concerningeither the threshold amount of oblique conver- region allows subdivision of this zone into three latitudinal gencerequired for sliver plate motion or whether or not the intervals; Minster and Jordan [1978] use only a subsetof partitioning between oblique convergenceand strike-slip is theseresults, presumably to avoid extremelyheavy weighting affectedby parametersother than obliquity (e.g.,convergence of this zone in their inversion.When they are available from rate or slab age). Minster and Jordan [1978], correctedslip vectors are used, The rate of strike-slipmotion (Vss)of the forearcsliver with basedon the horizontalprojection of the slip vector.However, respectto the major overriding plate is determinedfrom the JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 243

CONV. OBL QU I TY -7

60- SUM ! ß I

ALU a ,

S.KUR •CKUR• I ECU I - I I--2 0

• i , , i • SLIP -•5 -•0 15 ao a5 :•0 RESIDUAL

•ALAI

-20 PERU

.

Fig. 5. Slip vector residual versusconvergence obliquity for subductionzones with both a reliably determined conver- genceazimuth and at least four slip vectorsof shallow underthrustingearthquakes. The slip residualis the angle between the mean slip vector azimuth and the convergencedirection. The convergenceobliquity is the angle betweenconvergence direction and the azimuth perpendicular to the arc. Horizontal lines are 95% confidencelimits; vertical lines are one standarddeviation. Data are from Table 5. Open circlesindicate subductionzones with no modern strike-slipfaulting; solid circlesindicate subductionzones with active strike-slipfaulting. Note that most points plot in the upper right or lower left quadrants;this suggeststhat oblique convergenceis causingstrike-slip displacement of the forearc, thereby biasing slip vectors.

simplegeometrical relation the Bering plate hypothesis,because the extensivenewer data from Kurile-Kamchatka [Stauder and Mualchin, 1976] show a V• = V tan O/(sin•b tan 0 + cos •b) good match of observed to modelled slip vectors. The Aleu- where V is the convergencerate betweenthe major plates,0 is tian mismatch and Kurile-Kamchatka match are readily ex- the slip vectorresidual, and •pis the obliquity of convergence. plicable as sliver plate responseto oblique convergence.More

Predicted strike-sliprates are small for the subductionzones generally, the effect of sliver, plates on slip vectors urges cau- of Table 5 (exceptfor Sumatra) and are generallyless than 1 tion in the use of global inversionsto test for the existenceof or 2 cm/yr (Figure 6). Includingthe 95% confidencelimits for uncertain plate boundaries,if slip vectorsconstitute an impor- the slip vector residuals,only South Kurile, Central Kurile, tant constraint in the test [e.g., Stein and Gordon,1984]. and Aleutian strike-sliprates are significantlynonzero at the 95% confidencelevel. However, of the sevenmean strike-slip Implicationsfor SoutheastAsian Plate Motions rates for subductionzones with known active strike-slip faults, all show predicted strike-slip directions(Table 5) consistent Basedon the conceptof slip deviationscaused by strike-slip with those observedin the field (Table 4). The slowestpredic- faulting, a reevaluation of Southeast Asia/India relative mo- ted strike-sliprates are in Kamchatka (0.1 +_0.7 cm/yr) and tions at the Sunda Arc is warranted. Although all global Mexico (0.1 _+0.5 cm/yr), the only two regionsof Table 5 with motioninversions can predict Eurasia/India relative mptions no known modern strike-slipfaulting. in the Sunda Arc, slip vectorsfrom this region were not'used Minster et al. [1974] noticed the systematicmismatch of in the inversions,because of possibleinternal deformation in observedto predictedslip directionsin the Aleutians,and they East Asia and Southeast Asia. Existence of a Southeast Asian hypothesizedthe presenceof a Beringplate to accountfor this plate, probably with a diffuse"plate boundary" within China, mismatch.Although this discrepancypersists in subsequent is implied by the work of Molnar and Tapponnier[1975]; they analysiswith more data, Minster and Jordan[1978] withdrew demonstrate that collision of India with Eurasia is causing 244 JARRARD' RELATIONSAMONG SUBDUCTIONPARAMETERS

CONV. OBLIQUITY

60-

_SUM

ALU

4o

• _1C. KUR , ßS. KURI i -I 'I '

sinistral i I i i - , • I I dexfrol I STRIKE-SLIP -3 -2 -i KAM , 4 RATE (cm/yr)

Z ALA , I '

PERU

Fig.6. Modernstrike-slip rates estimated from the slip vector residuals of Table 5 andFigure 5. Notethat rate of strike-slipmotion of forearc sliver plates appears to increasewith increasingly oblique convergence. Also note that the two smalleststrike-slip rates are for subduction zones with no known active strike-slip faults (open circles). All calculated offset directions(sinistral or dextral)are consistent with geological evidence ofmodern offset direction (Table 4). both strike-slipfaulting and crustalthinning in China.The with focal depthsgreater than 50 km were not usedin this plate'sexistence is confirmedby systematicdifferences be- calculationbecause of higherdispersion; including them does tween observedfocal mechanismsin the Sunda Trench [Fitch, not significantlychange the means.The two directionsare 1972; Kappel,1980] and predictedconvergence directions significantlydifferent at muchmore than the 95% confidence basedon Eurasia/Indiarelative motions. level. Predictedconvergence directions vary only slightlyalong The Sumatranslip directionis consistentwith predicted the Sunda Arc' N18øE at Andaman, N24øE at Sumatra, Eurasia/Indiamotions while the Javaslip directionis highly N23øE at Java, and N19øE at East Banda accordingto the discordant.Thus onepossible interpretation is that Sumatrais model of Minster and Jordan [1978] or N23øE, N28øE, part of the Eurasianplate but Javaand Bandaare not, with N27øE,and N24øE,respectively, according to Chase[1978a]. east-westextension implied betweenJava and Sumatra.Al- The "Indian"plate may actuallybe two platesthat have a thoughextension is recognizedin the southernSunda Straits smallcomponent of convergencealong their common bound- betweenthese islands [Huchon and Le Pichon,1984], there is ary, the NinetyeastRidge [Minster and Jordan,1978; Stein no evidenceof the required extensionnorth of the Sunda and Gordon,1984]. If so, predictedmotion between the Aus- Straits. tralianplate and Sunda Arc is about10 ø closer to north-south, An alternativeexplanation for the slip vectordiscrepancies basedon model A of Minster and Jordan [1978]. The predic- involvesthe effectof strike-slipfaulting on slip vectors.There ted motion at the northeast end of the Banda subduction zone is no evidenceof significantarc-parallel strike-slip faulting in impliesstrike-slip or extensionin this region ratl{er than the Java,except for a short segmentof unknownage in western- observedsubduction. An analysisof slab geometrybeneath most Java (Table 4). As the slip vectorsindicate convergence the Banda Arc led Cardwell and lsacks [1978] to conclude nearlyperpendicular to the trench(obliquity of 13ø),it is prob- that the convergencedirection is approximatelyNNW, about ably unlikelythat they are biasedby more than about 4ø 40ø + 20ø from that predictedfrom Eurasia/Indiarelative mo- clockwise(Figure 5) by strike-slipfaulting. Thus the true di- tions. rectionof convergencebetween Southeast Asian and Indian Kappel[1980] presents47 newand published focal mecha- plates at the Sunda subductionzone is probablyclose to nisms from the Sunda Arc. Of these, 19 are shallow under- north-south,a conclusionconsistent with Javaneseslip vectors thrustingsolutions indicative of interplatemotion. The mean and subductiongeometry of the Banda Arc. direction indicated by 5 slip vectors from Java is A further constraint that must be satisfiedby the inferred N1.0øW+ 6.7ø (95% confidence limits), and the mean of 7 slip north-southconvergence between the SoutheastAsia and vectors from Sumatra is N26.9øE + 6.8ø. Seven slip vectors Indian platesis convergenceall alongthe Andamansubdue- JARRARD: RELATIONS AMONG SUBDUCTION PARA'•• 245 tion zone. The Banda-Sunda-Andaman Trench curves north- the Sumatran forearc is substantiallylarger than that calcu- ward not only at its eastern(Banda) end but also at its west- lated for the other arcs of Table 5, consistentwith the highly ern (Andaman) end (Figure 7). The maximum Andaman reen- obliqueconvergence angle of about55 ø. The SemangkoFault trant angle of about 33ø between14 ø and 15øN would require (alsoknown as the BarisanFault or SumatranFault System) extensioninstead of subduction,if not for back-arc spreading is one of the mostgeomorphically obvious arc strike-slipfaults in the Andaman Basin and dextral strike-slipfaulting within in the world. Geologicevidence of both total offsetand offset the Andaman forearc. A vector diagram for 14ø to 15øN rates on the Semangkois contradictory[Page et al., 1979]; (Figure 7) indicatesthat the combination of India/Southeast the 20- to 25-km offset of Quaternary formationsfound by Asia (NIøW, about 6 cm/yr)' and Southeast Asia/Andaman Katili and Hehuwat [1967] indicatesa minimum rate of 1 [Lawyer and Curray, 1981] vectorsis sufficientto remove the cm/yr. Strike-slipmotion on the Semangkois accommodated need for extensionat the boundary and results in strike-slip to the westby transformfaults and back-arcspreading in the motion. Because seismic profiles indicate subduction here Andaman Sea.The 460-480 km of spreadingin the Andaman [Hamilton, 1979], an additional northward componentis re- Seasince 13 m.y.B.P. [Lawyerand Curray, 1981; Curray et al., quired, from strike-slip faults within the Andaman forearc. 1982] requiresan averagerate of dextral strike-slipfaulting These mapped strike-slipfaults [Curray et al., 1982] are cur- somewherein westernSumatra of 3.7 cm/yr, remarkably (and rently active, as indicated by focal mechanisms[Mukhopadhy- perhapscoincidentally) similar to the 3.6-cm/yrrate inferred ay, 1984]. However, neither the rate of subductionat 14ø to from slip vectors.Not all of the motion by either estimate 15øN nor the rates of motion on the strike-slip faults are need be accommodatedon 'the SemangkoFault alone, as known, and too few interplate slip vectors are available to other strike-slip faults have been mapped in the west Su- estimatethese rates. Furthermore,strike-slip faults appear to matran forearc(Figure 7, Karig et al. [1980]). However,some extend northward from northwest Sumatra into the North or all of the Sumatran forearc faults extend westward into Malay Peninsula, potentially complicating Andaman/Sunda strike-slipfaults in the Andamanforearc rather than into the motion comparisons.The offset direction of these faults and Andaman back-arc spreadingsystem [Karig et al., 1980; whether or not they are currently active is debatable [Hamil- Curray et al., 1982]. ton, 1979]. Thus although the geometryof the Andaman sub- Forearc Slivers and Terrane Motions duction zone is consistentwith north-south convergencebe- tween the Australian and SoutheastAsian plates, it does not Forearc sliver motion often accompaniesnormal subduc- precludea somewhatdifferent convergencedirection. tion; optimum conditionsare obliqueconvergence, strong in- North-south convergenceat the Sunda Arc, when compared terplatecoupling, and possiblya continentaloverriding plate. with the N18øE to N24øE India/Eurasia motion there,implies The importanceof forearc sliver motion for terrane displace- a significanteast-west component of extensionbetween Euras- ment stemsmore from its ubiquity than from its rates; half of ia and SoutheastAsia (Figure 7). This east-westcomponent is modern subduction zones possessforearc slivers, generally smaller,but apparentlystill significant,if the India plate actu- with strike-sliprates of lessthan 2 cm/yr. Prolonged periods ally comprisestwo plates' West India and Australia (Figure 7). of slightlyoblique subduction are likely to resultin substantial This extra component of eastwardmotion for SoutheastAsia terrane migration (e.g., 1000-2000 km in 100 m.y. at 1-2 is consistentwith, but not requiredby, the eastwardcompo- cm/yr). Several of the terranes of western North America, nent of China imparted by collision of India with Asia which have moved northward at rates of a few centimetersper [Molnar and Tapponnier,1975]. Determination of the South- year, may thereforehave been transportedas forearc slivers east Asia/Eurasia pole and rate of rotation is not currently rather than on oceanicplates [Beck, 1980]. possible;the one publishedpole, near 28øN, 97øE [Hamilton, Two factorswill limit comparisonsof observedto predicted 1979] compoundsthe problemsof predictedextension in the forearc sliver motions for the Tertiary and Cretaceous:(1) Banda Trench and of Javaneseslip vectormismatch. Indeed, it uncertaintiesin convergencerates and azimuthsand (2) uncer- is not even possibleto specifywith confidencethe northern taintiesin the partitioningof obliqueconvergence into strike- limit of the SoutheastAsia plate. However, the interpreted slip.The slip vectorresiduals of Table 5 suggestthat partition- east-westcomponents of extensionin both China and Sunda ing of the arc-parallelcomponent of convergenceinto strike- allow a tentative conclusionthat the SoutheastAsia/Eurasia slip variesfrom about 15% for 20ø obliquityto about60% for rotation pole is far enoughaway from the SundaArc to allow 60ø obliquity. However,confidence limits for theseestimates the convergencedirection in Java (NIøW +_6.7 ø) to be appro- are quite large, and the partitioning is likely to depend on priate also for adjacent Sumatra. friction at both the subductingand strike-slipinterfaces of the If the Australia/SoutheastAsia convergencedirection at Su- forearc sliver. matra is N IøW, then the Sumatran slip vector orientation of N26.9 ø +_6.8 ø, when combined with an approximate conver- STATISTICAL ANALYSIS gencerate of 6.8 cm/yr [Minster and Jordan, 1978], indicatesa Methods and Limitations strike-slip rate in Sumatra of 3.6 +_0.5 cm/yr. Of course,the SoutheastAsia plate may also have a north-south component The interrelationsof subductionparameters are a subjectof with respectto Eurasia; for example,if it is about 0.7 cm/yr, continuing controversy.We seek geologicallymeaningful or 10% of the 6.8 cm/yr assumed,then the estimateof strike- quantitative relationshipsbetween the dependentand inde- slip rate would also be in error by 10%. Such errors are pendentvariables of Table 1. Dependentvariables include the comparableto the 96% confidencelimits of 3.1 to 4.1 cm/yr strain regime and strike-slipfaulting in the overriding plate, on strike-sliprate, derivedfrom combiningthe 80% one-tailed arc-trenchgap, trench depth, Benioff zone length, and both confidencelimits for Java slip direction (NIøW +_2.3 ø) with shallow and deep dip of the subductingslab. Independent thosefor Sumatran slip direction (N26.9øE +_2.5ø). variablesthat have beenproposed as affectingthese dependent The inferred dextral strike-slipmotion of about 3.6 cm/yr of variablesinclude convergence rate and angle,absolute motion 246 JARRARD' RELATIONS AMONG SUBDUCTiON PARAMETERS

IND/SEA

ß ß

ß ß ß .¾ C.Lu IND/SI'A

IND/SEA

z o•*•

(71/,5,..0/2,,,, Z aJ•., I.[-0 4/0/'"'•/.,.¾en •.

I ND/SEA

0 Z

N ..U Z •" 0 0 -• • • z • <• > JARRARD: RELATIONS AMONG SUBDUCTION PARAMETEP.S 247 of overridingand underridingplates, slab age, and duration of absolute motion of the overriding plate, and almost all are subduction.At least three other independentvariables may be among the oldest subductionzones in Table 1. The noninde- important but are too poorly known to quantitativelyinclude: pendenceof observations(i.e., subduction zones) is therefore mantle flow patterns, width of the accretionary prism, and not only a reasonfor avoiding assignmentof confidencelevels width of the interface between overriding and underriding to regressions,but also (and more importantly) a fundamental plates. limitation of this analysis.Consequently, although the statis- Most theoreticalanalyses have yielded only qualitative and tical analysis is capable of determining the most likely re- often contradictoryrelationships, partly becausekey parame- lationships among variables for modern subduction zones, ters suchas shear stressbetween plates are poorly known. An none of these equationsshould be confidentlyused for other alternative approachis usedherein: empirical quantitative re- areas or times until their predictive value is confirmed on lationships are statisticallyderived, through application of independentdata for which both dependentand independent multivariate analysis to modern subduction zones. This ap- variables are known. proach is not meant to substitutefor theoretical analyses,but Becauseof the importance of including completelyindepen- to complementand perhapsfocus them. dent subductionzones with very different valuesfor individual Stepwisemultiple regressionanalysis is utilized to isolate variables,an attempt was made to includein Table 1 as many the primary independentvariables affecting each dependent different "normal" subduction zones as possible. Conse- variable. Unlike conventionalmultiple linear regression,step- quently, not all variablesare known for every subductionzone wise multiple regressioncan successfullycope with indepen- used. An alternative approach is used by most authors, in dent variablesthat are themselvespartly correlated.Stepwise which only subductionzones with no missingdata are used. multiple regressionfirst fits a linear regressionbetween the The stepwisemultiple regressionalgorithm usedherein for the dependentvariable and the most highly correlatedindepen- isolation of significant independent variables [Enslein et al., dent variable. Residuals to this relation are then correlated 1977] can utilize observationswith missing data. However, with all other independentvariables, and the variable with the resulting final correlation coefficientswere often found to be highest significantcorrelation is included in the regression optimistic when comparedwith an analysisof the same inde- equation. Inclusion of an additional independent variable pendent variablesomitting all observationswith any missing changesthe contributionsof any independentvariables al- data. Therefore missing data were allowed in the determi- ready in the equation.Thus it is possiblefor an independent nation of the significantindependent variables, but the final variable to enter the equation,gradually lose significanceas regressionequation is based on only those observationscon- other independentvariables enter the equation and account taining valuesfor both the dependentvariable and all of the for some of the same variance that it had accounted for, and selectedindependent variables. eventually be dropped from the equation becauseit is no Another factor that can lead to misinterpretationof signifi- longer significant.Examples of this phenomenonwill be dis- cancelevels for regressionsis the large number of hypotheses cussedin the modelssection; this behavior generally results testedby multiple regression.For example,if four dependent from correlationbetween independent variables. variables are each tested against five independent variables, The criterion for addition or subtraction of independent then one correlation significantat the 95% confidencelevel is variablesis an F test of their significance.In subsequentanaly- expectedby chance,even if no true physicalcorrelation exists sesan F of about 5 is generallyused, corresponding to signifi- among any of the variables.This problem is largely ameliora- cance at about the 95-99% confidence level for the 30-39 ted by raising the required confidencelevel to 99%. However, observationsin most regressions.The valuesof F are also given that not all observationsare independent(as previously given for the overall regressionand as a guide to the relative discussed),an even higher confidencelevel may be appropri- significanceof individual independentvariables. Significance ate. Alternatively,most readersmay preferto make a subjec- levelsof a given value of F and number of degreesof freedom tive decisionon the reliabilityof a correlation,based on exam- are availablefrom any statisticsbook; for the numberof nom- ination of a plot of dependentversus independent variables. inal degreesof freedom used here, F's of about 2.9, 4.2, 7.6, The regressiontechnique used here assumesthat valuesfor and 13.3 are significantat the 90%, 95%, 99% and 99.9% each independentvariable are perfectly known and that all confidencelevels. Assignment of confidencelevels to thesere- error is associatedwith the dependentvariable. This assump- gressionsis probablymisleadingly optimistic, because the indi- tion is clearly invalid for the data consideredhere, as all vari- vidual observations(i.e., subduction zones) used are not strict- ables in Table 1 have associated errors. Violation of this as- ly independent.Adjacent subductionzones often have very sumption leads to a calculated slope of the regressionline similar values for some or even most variables; thus the true which is lower than the slopeof the true relationshipbetween numberof degreesof freedomis impossibleto estimatebut is dependent and independent variables. This phenomenon is certainly less than implied by the number of observations most noticeablefor "noisy" data, in which less than 50% of used.As an extremeexample, suppose that our entire data set the variancein the dependentvariable is accountedfor by the consistedof 10 adjacent"segments" from the Marianasand i0 independentvariable(s) (e.g., Figure 12). For regressionequa- adjacent"segments" from Peru. Correlation betweenalmost tions with much higher correlations,such as most of those any two variableswould then be significantat greaterthan the shownsubsequently, this effectis subtle.The multiple regres- 95% confidencelevel basedon 19 (i.e., 20-1) degreesof free- sion techniqueused here is adequatefor isolation of the rele- dom, but in fact the true number of degreesof freedomwould vant independentvariables and approximatequantification of be closerto 1 (2-1). In contrast,the subductionzones of Table their effects. However, other more sophisticatedstatistical 1 were selectedon the basisof substantiallarge-scale segmen- techniquesare superior when both independentand depen- tation marking notable changesin at least some parameters. dent variables have associated known uncertainties, when Nevertheless,substantial similarities remain in some parame- these uncertaintiesvary between observations,and when the tersamong adjacent subduction zones. For example,the seven relationship between variables is nonlinear. Nonlinear re- subductionzones of South Americaall have nearly the same lationships(e.g., Figure 19) can significantlydegrade corre- 248 JARRARD' RELATIONS AMONG $UBDUCTION PARAMETERS lation coefficientsbased on linear regression.Although careful usuallyvalid; however,this generalizationmay not be true for examinationof regressionresiduals can reveal nonlinearre- slab dip. For example, the hypothesisthat strain regime is lationships,they can easily be missed. dependenton changesin slab dip [Furlong et al., 1982; Hager, Becauseregression is a least squaresprocedure, both the 1983] is not readily testablethrough theseanalyses. regressioncoefficients and correlationcoefficients are sensitive The variable that may have the longest responsetime is to extremeor anomalouspoints. Such points could be present deep dip, but little is known of its temporal variations. The in Table 1, either becauseof a misinterpretationby the orig- variable with the longestknown responsetim e is slab length, inal author of the value for a singlevariable for somesubduc- usually representingabout 10 m.y. of convergence.Most other tion zone or becausethe entire subductionzone is anomalous variablesappear to have changedvery little in the last 5 m.y. (e.g.,due to an unrecognizedplate boundary or subductionof Changesin absolute motion about 5 m.y. ago [Cox and En- an unsuspectedfragment of continentalcrust). In practice,the gebretson,1984] and in many spreadingrates 5-10 m.y. ago largenumber of subductionzones used here makes the contri- undoubtedly are a source of some variance when compared butionof a singleanomalous point generally minor. Neverthe- with slab length. Many current episodesof back-arc spreading less, regressionresiduals were carefully monitored and, as began about 5-10 m.y. ago. As previously discussedin the specificallynoted subsequently, residuals differing from the i'e- sectionon slab age, a correctionfor limited duration of back- gressionline by more than about 3 or 4 standarddeviations arc spreadingwas requiredfor four subductionzones when were usedas a criterion for excludinga subductionzone from calculating time since subduction of the slab tip. A similar a regression. correctionto convergencerates for thesesubduction zones is Allvariables were standardized prior to statisticalanalysis. applied to statisticalanalysis of slab length. With the possible Standardization involves subtraction of the variable mean exception of deep dip, the different measurementtimes and from each data poini, followedby divisionby the standard •esponsetimes of different variablesdo not appear to be an deviation. Standardizationserves two purposes:(1) computer obstacleto their reliable comparison. roundoff error is avoided, becausethe wide variations in mag- nitudes between variables are removed, and (2) the relative Correlation BetweenIndependent Variables importanceof regressioncoefficients for differentvariables is Correlation betweenindependent variables is probably the more evident.Resulting standardized regression equations are largest single reason for the profusion of models predicting then convertedback to the units of originalvariables. d.ependentvariables such as strainregime of the overriding Correlationpathways can sometimesbe usedto infer cause plateand slab dip. in theory,stepwise regression can •suc- and effectrelationships, with considerablecaution. As we will cessfullycope, with this problem,isolating the key independent seein the modelssection, the dependentvariable in one equa- variables.In practice,the degreeof successexpected for step- tion may be the independentvariable in anotherequation. For wiseregression depends on howstrongly correlated the inde- example,if A affectsB and B affectsC, then correlationsA/B, pendent variables are. For example, distinguishingbetween B/C, and A/C may all be significant,with probably the the independent variables convergencerate (Vc) and conver- poorestcorrelation between the three being the indirect path gencerate including back-arc spreading(Vc•,a) is difficult, be- A/C. When stepwiseregression is appliedto the predictionof cause their correlation coefficientis 0.72; distinguishingbe- C from A and B, B will be addedfirst to the regressionequa- tweenslab age at thetrench (As) and age of theslab tip (At)is tion. Because all of the correlation of A with C arises from A's nearly impossible,because the correlation coefficientis 0.93. effect on B, there should be little or no residual correlation of Becauseof correlation between independentvariables, the A with C after regressionof B on C. In another example, single independent variable showing the highest correlation supposeœ and F are two independentvariables that signifi- coefficientwith the dependent variable does not necessarily cantly predict H. One might concludethat variationsin œ and remain in the final regressionrelationship. For example, the F cause variations in H. Yet it is possiblethat unconsidered independent variable most strongly correlated with strain variable D causes variations in both F and unconsidered vari- regime is arc age. This implausible relationship arises from able G, with similar regressioncoefficients for D/F and D/G two factors' (1) South America includes some of the oldest due to somewhat similar but distinctive physical processes. arcs as well as the most compressiveenvironments, and (2) arc Then the true causeand effectrelations might be that œ and G age affectsintermediate dip (DipI). As subsequentsignificant causevariations in H, without eliminating the usefulnessof F independentvariables are added, arc age gradually drops out in the regressionequation. Similarly, if variablesI and J sig- of the equation and intermediate dip becomesmore impor- nificantlypredict L, the directcause and effectrelation might tant. be that I and J cause K which causesL. In the case of subduc- It is worthwhileto briefly examinethe correlationsbetween tion zoneparameters, a combinationof stepwisemultiple re- independentvariables, in orderto isolatethe correlationswith gressionand geologicinsight may isolate the mostlikely cause a physicalsignificance from thosethat are samplingartifacts. and effectpathways among available variables. However, cau- Table 6 lists the correlationsfor both the Chase [1978a] and tion is requiredand the possibilityremains that otherimpor- Minsterand Jordan [1978] motionmodels. The two are gener- tant variables were not included becausethey could not be ally similar,so here only the formerare mentioned. accuratelyquantified. Some correlationsare trivial, arisingfrom the fact that one Implicitin statisticalanalysis of subductionparameters is independentvariable is only a slightlymodified form of an- theassumption that all subductionzones are now in an equi- other. The correlation of 0.72 between convergencerate (Vc) libriumstate with respectto the variablesconsidered. This and convergencerate includingback-arc spreading (Vc•,a) is assumptionimplies that two conditions are met: (1) no signifi- dominatedby the many subductionzones with no back-arc cantchanges have occurred in anyvariable over the period of spreading.The very high correlationof 0.96 betweenshallow timerepresented by the variable with the longest response dip (DipS) and intermediatedip (DipI) is expected,since shal- time,and (2) no variableis primarilyaffected by the rate of low dip is measuredfrom the trench to 60-km depth and changeof anothervariable. The second condition is probably intermediatedip is measuredfrom the trench to 100-km JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS 249

TABLE 6. Correlation Between"Independent" Variables

DipI DipD As Ar Aa V• V•b• Vo• V• V• DipU

DipI 0.642 -0.039 -0.075 -0.536 -0.352 0.397 -0.316 0.011 0.103 0.734 DipD 0.642 0.139 0.104 -0.648 -0.568 0.124 -0.686 0.172 -0.215 0.608 A• -0.039 0.139 0.927 -0.375 0.168 0.350 -0.648 0.822 -0.468 -0.160 A, -0.075 0.104 0.927 -0.276 0.144 0.346 -0.509 0.572 -0.339 -0.121 A,, --0.536 -0.648 -0.375 -0.276 0.454 -0.014 0.742 -0.322 0.424 -0.267 -0.071 -0.113 0.291 0.249 0.350 0.704 0.490 0.458 0.118 -0.491 0.262 0.163 0.398 0.423 0.049 0.736 0.072 0.593 0.503 0.200 -0.160 -0.274 -0.324 -0.444 0.540 0.460 -0.006 -0.550 0.615 -0.054 v•, 0.054 0.144 0.551 0.525 -0.055 0.744 0.800 -0.250 -0.514 -0.415 v•, 0.386 0.168 -0.090 -0.130 0.102 0.204 0.579 0.330 -0.026 0.628 DipU 0.693 0.740 -0.034 0.035 -0.538 -0.300 0.223 -0.046 -0.285 0.709

Valuesbelow the blank diagonalline are from Chase[1978a]; valuesabove the blank diagonalline are from Minster andJordan [1978]. depth.The correlationof 0.93between slab age at the trench zoneswere approximately equivalent to the amountof litho- (As)and age of theslab tip (At)results from the generally slow spheresubducted during the last 10 m.y. Two possible reasons lateral changesin crustalage. Convergencerate, the sum of for this relationwere suggested: (1)a hiatusin spreadingprior absolute motions of the overriding and underriding plates, to 10 m.y.B.P. or (2) a 10 m.y. time constantfor resorptionof correlatesbetter with absolutemotion of the underriding plate the slab.The latter hypothesiswas preferred.Nevertheless, the (0.74)because that rate is generallyfaster. length of the Benioff zone in individual regionshas oc- Other correlationsbetween independent variables are more casionallybeen used to estimateduration of subduction.The geologicallyimportant. The correlation of 0.55 (or 0.82 for initiation of subduction in southwestJapan has been esti- Minster and Jordan) betweenslab age at the trench and abso- matedas 2 m.y.B.P. [Kanamori,1972-1, 3-5 m.y.B.P. [Kobay- lute motion of the underridingplate resultsfrom the slab pull ashiand Isezaki,1976-1, and 5 m.y.B.P. [Seno,1977] basedon force; a much higher correlationis found when the integrated slab length,though more likely it is considerablyolder. Be- effect of slab age along an entire plate boundary is considered causeof slab heating,the lengthof the Benioffzone can only [e.g., Forsyth and Uyeda, 1975]. A lower but still significant indicate a minimum duration of subduction. correlation of 0.29 between convergencerate and slab age More accurateconvergence rate data show the time since results from the previously mentioned effect of absolute subductionof the slab tip to be more variablethan originally motion of the underriding plate on convergencerate. In con- estimated(Table 1).Based on the subductionzones of Table 1, trast, convergencerate including back-arc spreadingis more the correlationbetween slab length and convergencerate is highly correlated (0.40) with slab age than is convergencerate 0.64. alone; as we will subsequentlysee, this resultsfrom the effect of slab age on the presenceof back-arcspreading. Slab Age A few correlationsare conceptuallyimplausible, suggesting Convergencerate aloneis inadequateas an explanationfor a sampling artifact. Absolute motion of the overriding plate variationsin slab lengthin Alaska [Lahr, 1975] or variations correlateswith both slab age (-0.32) and arc age (0.54). The in slabdepth along the SundaArc [Vlaar and Wortel,1976]. correlation with slab age is the oppositesign of what would be Vlaar and Wortel [1976] consideredthe alternativehypothesis expectedfrom the possibleeffect of trench suctionon the over- that slabage may controlmaximum focal depth. They recog- riding plate. Both correlations are dominated by South nized that the most relevantmeasure of slab age is age of the America and vanish when South American subduction zones slab tip at the time that it enteredthe trench (At), because are removed from the correlation. The same is true for the maximumfocal depth depends on the gradualheating of the correlation of 0.35 betweenarc age and convergencerate. slab. The correlationbetween this effectiveslab age and maxi- Regardlessof the sourceof correlation betweenindependent mum focaldepth was interpreted by Vlaar and Wortel [1976] variables,the presenceof thesecorrelations constitutes an im- as evidencethat the maximumpenetration depth of the slabis portant potential limitation to the reliability of empirical controlledby the effectof lithosphericage on gravitational equations between subduction parameters. The problem is instability.Subsequent studies recognize the slabtip as a ther- dealt with more successfullyby stepwisemultiple regression mal transition within the slab, with no implicationsfor total than by simple multiple regression.Nevertheless, all resulting depthof slabpenetration. empirical equations should be consideredtentative, pending Farrar and Lowe [1978] separatedthe influenceof conver- confirmation of their predictivevalue for other data. gencerate from slab age by demonstratinga correlationbe- tweenslab age and slablength along the Peru-Chilesubduc- MODELS OF SLAB LENGTH tion zone,a regionwith relativelyconstant convergence rate. ConvergenceRate Productof ConvergenceRate and Slab Age The deepestearthquakes in most Benioff zonesoccur within Both convergencerate and slab age affectslab length.The the subductingslab rather than at the contact with the over- quantitativerelationship between these parameters was im- riding lithosphere.The tip of the slab marks a transition from plicit in a plot by Defteyes[1972], who empiricallyshowed brittle to ductile deformationof the slab, a thermal responseof that many subductionzones have an approximatelylinear gradualslab heating['lsacks et al., 1968; McKenzie, 1969]. relationshipbetween slab age and time sincesubduction of the lsacks et al. [1968] noted a correlation betweenslab length slab tip. This relation was demonstratedtheoretically by and convergencerate and found that the lengths of Benioff Molnar et al. [1979]. The brittle/ductiletransition within the 250 JARRARD.' RELATIONS AMONG SUBDUCTION PARAMETERS

TABLE 7. Slab Length Regressions

F Ratios

Velocity First Second RegressionEquation* Comment• Source:!: Regression Variable Variable R2 R

L s = 297.4 + 0.0747 x Vcx A t 1 M 127.6 ...... 0.831 0.911 L s -302.9 + 0.0671 x V• x Atõ 1 C 156.6 ...... 0.858 0.926 L s = 324.8 + 0.0634 x V• x As 1 M 71.0 ...... 0.732 0.856 L s = 364.6 + 0.0440 x V•ba x A t 1 M 34.3 ...... 0.569 0.754 L s - 368.8 + 0.0412 x V•bax As 1 M 34.4 ...... 0.570 0.755 L s = 399.9 + 0.0747 x V• x A t -4.31 x DipI 1 M 73.8 143.4 4.2 0.855 0.925 L s = 396.6 + 0.0669 x V• x A t - 3.91 x DipI 1 C 89.8 174.6 4.1 0.878 0.937 L s = 470.9 + 0.0649 x V• x As - 6.39 x DipI 1 C 45.7 88.6 6.2 0.785 0.886 L s - 219.3 + 0.0938 x V• x At 2 M 145.9 ...... 0.816 0.903 L s=229.9+0.0841 x V• xA t 2 C 127.8 ...... 0.795 0.892 L s = 458.7 + 0.0829 x V½x At -9.02 x DipI 2 C 103.4 ' 184.1 17.0 0.866 0.931 L s - 558.8 + 0.0710 x V• x As - 10.95 x DipI 2 C 163.1 292.1 37.7 0.911 0.954

*For units consistencywithin theseequations, velocities are in km/m.y. (i.e.,mm/yr); all other velocitiesin this manuscriptare in cm/yr. •'Comment 1: delete both subductionzones with missingdata and northeastJapan. Comment 2: all possibledata used in correlations; equivalent to deletingmissing data when only one term in regression. $C, Chase[1978a]. M, Minster and Jordan[1978]. Both revisedas indicatedin text. õPreferredmodel. slab is controlled by gradual conductive warming of the slab. Stepwisemultiple regressionusing the subductionzones of Therefore the length of the Benioff zone should be proportion- Table 1 confirms that V• x At is the best predictor of slab al to (1) the time since subduction of the slab tip, which is length. While the correlation coefficientsof slab length with controlled by convergencerate, and (2) the time required to V•, As, and At are 0.64, 0.72, and 0.69, respectively,the corre- heat the slab to the brittle/ductile transition, which is pro- lations with V• x As and V• x At are 0.90 and 0.89, respec- portional to the square of lithosphericthickness and therefore tively. Regressionequations based on V, x A, V, x As, V,ba also proportional to slab age. x At, and Vcbax As are given in Table 7. As we will subse- The exact theoreticalrelationship [Molnar et al., 1979] is quently see, • appearsto be preferableto V,•a.Use of At is theoreticallypreferable to As. However, it should be remem- L s = k x V• x A, bered that knowledgeof convergencerate is requiredfor the where L s is the length of seismicallyactive slab, k is a con- determinationof At. Thus convergencerate is implicitlypres- stant, Vc is the convergencerate, and At is the age of the tip of ent in both variablesof the product V, x At, complicatinguse the slab at the time it entered the trench. Molnar et al. [1979] of equation 1 of Table 7 for estimatingconvergence rates in measuredslab length and convergencerate along the direction modern subductionzones. Nevertheless,this equation is the of convergence;these parametersmay also be measuredper- preferredmodel. pendicular to the trench, as done herein, without affecting the The equationsgiven in Table 7 are based on only those constant k. subductionzones for which Ls, V,, and At are all known (i.e., Using slab age at the trench rather than effectiveage of the no missingdata), omittingnortheast Japan. As is evidentfrom slab tip, Molnar et al. [1979] estimated a value for k of 0.1, Figure 8, northeastJapan has an anomalouslylong L s. How- based on the following subduction zones: Aleutian, Kurile, ever,if two very deepepicenters of lchikawa [1966] are omit- Japan, Tonga-Kermadec, New Zealand, South America, Cen- ted, L s is reducedfrom 1480 km to 920 km, a length much tral America, and Lesser Antilles. In terms of the 39 subduc- more consistent with other subduction zones. This observation tion zone segmentsof Table 1, 14 were included in the analysis doesnot imply that the two epicentersare not part of a con- of Molnar et al. [1979]; two thirds of the 30 points usedcame tinuous slab, but rather that they should not be allowed to from four subductionzone segments.Other subductionzones undulyweight the entireregression line. were not used in the analysisbecause of uncertaintiesin rela- Regressionresiduals such as thoseevident in Figure 8 prob- tive plate velocities.$ugi and Uyeda [1984] showedthat seven ably result from a numberof factors,particularly the limited subduction zones with young slabs were generally consistent and varyingdurations of seismicactivity included in different with the relationshipof Molnar et al. [1979]. subductionzones, downdip gapsin seismicactivity causedby For most of the subductionzones consideredby Molnar et a transition from downdip tension to downdip compression, al. [1979] and $ugi and Uyeda [1984], slab age increases uncertaintiesin both V, and &, and temporalchanges in downdip, so that only minor errors are introducedby use of Somepossibly systematic patterns among regression residuals slab age at the trench rather than effectiveage of the slab tip. will be discussedin later parts of this section. Sykeset al. [1982] replotted the data of Molnar et al. [1979], This analysisdiffers from that of Molnar et al. [1979] in usingage of the slab tip for the Aleutians(the one region with severalimportant respects.First, a much larger number of possibly decreasingslab age downdip) in order to estimate subductionzones was used,thereby reducingthe weightingof Caribbean plate motion based on slab length in the Lesser Kurile, Tonga, Kermadec,and New Zealand subductionzones Antilles. Their adjustedAleutian points improve the fit to the from two thirds of the total data to 14% of the total data. overall relation of slab length versusthe product of conver- This changeinvolved inclusion of somesubduction zones with gence rate and slab age; the estimate of the constant k is lessaccurate convergence rates. However, it also reducedsen- unchanged. sitivity of the resultsto the 20% uncertaintyin slab age in the JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS 251

ßNJP ß Absent 1400 x Present, not Included in rote BACK-ARCo Present, SPREADINGincluded in r(3te

1200

1000

x o TON

MAR x ß o 8OO

ALA ß x o KER 600 ß NZL AKPß ß SUL ß ß ß ß 4OO ß s•. ß x ßß ONBR ß x o SCO (•) NHB • X o

2OO

ß=• CAS

2000 4000 6000 8000 10000 12000 14000 16000 V x At (km) Fig. 8. Cross plot of Benioff zone length versusthe product of convergencerate and age of the slab tip, for modern subductionzones. Note the better fit of subductionzones with back-arc spreadingto the overall trend when back-arc spreadingrate is excludedfrom V x At. Note also the nonzero intercept of the overall trend, which suggeststhat a constantrate of slabheating is not establisheduntil the slabhas passedthe upper portion of the overridingplate.

four subductionzones. Second,more recent and probably back-arc spreadingrates have not lasted as long as the time more accurateestimates of convergencerates and slab ages sincesubduction of the slab tip. This appearsto be true for the were used,changing most convergencerates and slab agesby Tonga, Kermadec, Marianas, and South Sandwich subduction about 20%. Third, separateanalyses of convergencerates with zones.However, as previouslydiscussed, calculated ages of the and without back-arc spreadingwere undertaken;for exam- slab tip for these four subductionzones have already been ple, the convergencerates of 6 and 9 cm/yr usedby Molnar et correctedfor the slower convergencerates prior to current al. [1979] for Kermadecand Tonga are revisedto 5 and 7.5 back-arcspreading. Furthermore, values of V• usedfor these cm/yr without back-arcspreading and 6 and 10 cm/yr includ- four zonesalso are correctedto slowertime-average values. ing back-arcspreading. Fourth, separateanalyses were under- Figure 8 indicatesthat use of V• rather than V• yields taken for As and At. Fifth, the possibilityof a nonzero inter- predicted slab lengths that are much longer than observed cept for the regressionline was included. And sixth, corre- lengths for South Sandwich and New Britain; a similar but lation of regressionresiduals with other relevant variableswas lessmarked relation is evidentfor Kermadecand Tonga. Al- examined.The utilizationin this analysisof convergencerates thoughNew Hebrideswas not usedin the statisticalanalysis and slablengths perpendicular to the trenchrather than paral- becauseof uncertaintyin V•, it also appearsto have a much lel to the convergencedirection does not significantlyaffect longer predictedthan observedslab length.This discrepancy the results. appears to be correlated with trench rollback rate. South In theory, convergencerate includingback-arc spreading Sandwich,New Britain, and New Hebrides have by far the (V•b,)is a more relevantparameter than convergencerate ex- largestrollback rates(6.6, 4.6, and 6.9 cm/yr, respectively)of cluding back-arc spreading(V•), becauseslab length should the subductionzones studied.The secondhighest group of dependon the time sincesubduction of the slabtip and there- rollback rates is Tonga, Kermadec,and Solomon(3.8, 2.9, and fore on the overallinjection rate into the mantle.However, V• 3.0 cm/yr),which lie at the bottom edgeof the overalltrend of is a consistentlybetter predictorof slab length than V•b, Figure 8. All other subduction zones have rollback rates of (Figure 8), whetherA s or At is used,whether rates of Minster less than 2.5 cm/yr. These cited rollback rates are for the and Jordan [1978] or Chase [1978a] are used, and whether Chase[1978a] model; the possiblepattern is not substantially individualcorrelation coefficient or overallregression quality changedfor the Minster andJordan [1978] model. of fit is considered.One possibleexplanation is that current The physicalmechanisms are elusivefor both anomalously 252 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS

TABLE 8. Earthquake Moment

F Ratios

Velocity First Second Number RegressionEquation Comment* Source, RegressionVariable Variable R2 Preferred

1 M w- 7.95- 0.0088x As + 0.134x V• 1, 2 R 16.2 12.4 12.6 0.643 0.802 2 M w'= 8.02- 0.0104x As + 0.143x V• 2 C 12.9 17.9 14.6 0.577 0.759 3 Mw' = 7.85- 0.0103x As + 0.172x V• 2 M 14.2 18.8 16.6 0.600 0.775 4 Mw' = 8.01- 0.0105x As + 0.159x V• 3 C 14.5 19.6 17.0 0.605 0.778 yes 5 Mw'= 7.88--0.0096 x As + 0.177x V• 3 M 15.8 18.0 18.9 0.624 0.790 yes

*Comment1: As from Ruff and Kanamori [1980]. Comment 2: total convergencerate. Comment 3: convergencerate perpendicular to trench. ?R, Ruff andKanamori [1980]. C, Chase[1978a]. M, Minsterand Jordan [1978]. Lattertwo revisedas indicated in text. short slabsassociated with back-arc spreadingand the possi- of a 50% increasein observedlength of the Lesser Antilles ble correlationof anomalouslyshort slabswith rapid trench slab resulting from using the length from McCann and Sykes rollback. One may speculatethat rapid trench rollback in- [1984] rather than that of Sykes and Ewing [1965]. The volves more efficient removal of heat from the portion of lengthsused here for Alaska and Alaska Peninsulaare based mantleadjacent to the slab,associated with increasedmantle on the same sources used by Molnar et al. [1979] but are convectiveflow. However, this speculationimplies that it is a twice as long. This difference apparently arises partly from coincidencethat predictedslab lengths are consistentwith ob- correction of profiles to an azimuth perpendicular to the servedlengths when V• is usedinstead of V•ba. trench by Molnar et al. [1979] and perpendicularto the strike A major differencebetween the resultsof this study and of Benioff zone contours in this analysis.The latter seemsless those of Molnar et al. [1979] is the nonzero intercept of the sensitiveto the modifyingeffects of the very wide accretionary regressionline (Table 7 and Figure 8). Interceptsof 200-400 prism on trench azimuth, but caution should be usedin either km result for statistical analysesusing V• x A,, Vcbax A,, V• approach, to avoid bias by Alaska to the entire best fit line. x As, and V• x As. Partly becauseof this, 100% of the The nonzero interceptis evidentbut not commentedon in the pointsin Figure 8 lie abovethe line determinedby Molnar et slab length plot of Sugi and U yeda [1984], which focusseson al. [1979], Ls - 0.1 x V• x As.The reality of a nonzerointer- subduction of young oceaniccrust. It is less evident in their ceptis evidentfrom Figure 8. However,caution must be exer- plots of maximum depth versusthe product of rate and age, cisedin interpretingthe interceptvalue, as data dispersion becauseof shallow dip of the slab beneath southwestJapan causesregression analysis to yield a slightly larger intercept and poor depth control for seismicityin Yap and Palau. than one would fit by eye throughany data. The relation of slab length to the product of slab age and The nonzerointercept does not conflictwith the theoretical convergencerate is both the most firmly basedin theory and analysisof Molnar et al. [1979]. It doessuggest that the ther- the strongestempirically constrained relationship of any pub- mal environment of the slab does not changefrom cooling to lished relationship between subduction parameters.Therefore heating exactly at the trench.Instead, the slab continuesto the equation of Molnar et al. [1979] has sometimesbeen used cool and "age"for a short time after subduction.The nonzero to estimate modern convergence rates from known slab interceptis probablythe sum of three relatedeffects: (1) the lengthsand slab ages [e.g., Molnar et al., 1979; Sykeset al., time lag betweensubduction and initiation of heating,(2) the 1982]. The validity of this approach is confirmed by the pres- additional time required for heating to counteractthis in- ent analysis.However, this analysisindicates that convergence creasein effectiveslab age, and (3) a slower rate of heating rates estimated from the equation of Molnar et al. [1979] during contactof the slab with the accretionaryprism and require substantialrevision. overridinglithosphere than during contact with the deeper Slab lengths for three subductionzones (Yap, Palau, and mantle. Tierra del Fuego) have never been determined, presumably Becausefrictional heating betweenthe slab and accretion- becausethey are too short. Rare shallowseismicity is observed ary prism is negligible,some cooling of the slab is likely in Palau, Yap [Katsumata and Sykes, 1969], and Tierra del during the early stagesof its subductionbeneath the accre- Fuego. All three regionshave very slow convergencerates and tionaryprism. Consequently, subduction zones with verywide young crust. Basedon the empirical equation of Table 7 relat- accretionaryprisms (e.g., Alaska, Alaska Peninsula,North Su- ing L s to Vc and As (since At is not known), predictedslab lawesi,southwest Japan, and New Zealand) tend to lie near lengthsfor thesethree regionsare only about 350 km. the upper bound of the group of pointsplotted in Figure 8. This generalizationis imperfect:the same is not true for IntermediateDip and the Product of Slab Makran, which has a very wide accretionaryprism, and the Age and ConvergenceRate positionof the North Sulawesipoint may also be biasedby Stepwiseregression indicates that length of the slab may be underestimationof convergencerate (as discussedpreviously more accuratelypredicted if intermediatedip (DipI) is includ- in the sectionon arc age). ed with Vcx At in the regressionequation (Table 7). An F test The nonzero intercept is not evident in the analysis of of the significanceof this additional variable indicates that Molnar et al. [1979] becausethree regionshad short observed DipI is highly significant( > 99.9% confidencelevel) when sub- and predicted slab lengths: Alaska, Central America, and duction zoneswith missingvalues are included in the analysis Lesser Antilles. The latter two regions show lower than and marginally significant(approximately at the 95% confi- averageevidence of a nonzerointercept in this analysis(lying dence level) when subductionzones with missing values are near the lower end of the clusterof points in Figure 8) in spite omitted. The significanceof the DipI term is also slightly JARRARD:RELATIONS AMONG SUBDUCTIONPARAMETERS 253

10

R = .790

o

9

bJ

7 bJ

I I I 7 8 9 lO PREDICTED CUMULAT.IVE EARTHQUAKE MOMENT (From regressionon convergencerate and slab age) Fig. 9. Crossplot of cumulativeearthquake moment (M,•') versuspredicted Mw', basedon a regressionin which convergencerate and slab age are the independentvariables (Table 8). greater when Vcx At or •. x At is the primai'y independent quake magnitude with four possibleindependent variables' variable rather than Vcx As or V•b,x As. Intermediatedip is convergencerate, slab age, slab horizontal length, and slab more highly significantthan either shallowor deepdip. maximumdepth. They found that magnitude (Mw) of thelarg- The significantcontribution of DipI may arise from a com- est earthquake within 21 modern subductionzones is signifi- bination of two sources.First, shallowinitial dips are associ- cantly correlatedwith both convergehcerate and slab age. atedwith subduction zones with wide accretionary prisms. As Sixty-four percentof the total variancein M w was accounted previouslydiscussed, slab heatingmay be slowedduring pas- for by thesetwo variables(Table 8). Total convergencerates sagebeneath accretionary prisms, thus increasing slab length. were used[Minster et al., 1974],not includingback-arc Second,increasing mantle temperaturewith greater depth spreading. Significant correlations were also found between may lead to more rapid heating of steeplydipping slabsthan convergencerate and ma•ximumhorizontal extent of the slab of Shallowlydipping slabs [Toksb'z et al.,1973; Molnar et al., and betweenslab age and slabmaximum depth. A slightly 1979]. The latter possibilitywas suggestedby Lahr [1975] as better fit was achieved(R 2-- 0.71) when cumulativemoment ,. a contributing factor to the variations in slab length within the Mw'was used as the indepiendent variable instead of M w. Alaska-Aleutian region. Becauseincreasing ambient pressures Theseresults are not substantiallychanged when the revised in deeper, steeper slabs might counteract the temperature convergencerates and slabages of thisstudy are usedas effect, a more detailed analysisof temperatureand potential independentvariables (Figure 9). As shownin Table8, a temperature of the slab tip is required to evaluate the second slightly better fit was obtained when convergencecomponent possibility.Such an analysisappears warranted but is beyond perpendicularto the trenchis usedinstead of total conver- the scopeof this study. gencerate. The two ?atesare Similarfor mostsubduetion In viewof the marginalsignificance of DipI, currentlyit zones, and the improvement is not significant. RegressiOn may be more appropriate to utilize the regressionequation equationsusing convergencerates perpendicularto the trench that omits this variable. are pi'eferredherein, more for consistencyWith other analyses than for plausibility of physical mechanism.No significant EARTHQUAKE MAGNITUDE MODEL correlation of regressionresiduals is found with any other of In a statisticalanalysis similar to this study,Ruff and Kana- the possibleindependent variables of Table1. This suggests mori [1980] determined the correlation of maximum earth- that Ruff and Kanamori [1980] successfullyisolated the key 254 JAggngD: RELATIONSAMONG SUBDUCTIONPARAMETERS independentvariables. The possibilityremains that otherun- ficient detail is cited to allow the reader to evaluate strain consideredvariables have a significantbut secondaryinfluence classificationof individualsubdUction Zones. The compres- on M,•'; for example,sediment subducti0n may decreaseM,•' sion/extension continuum was subdivided into seven strain through a lubricating effect. classes.In contrast,several previous models are aimedonly at Ruff and Kanamori [1980] suggesta simplephysical model determiningthe cause of back-arc spreading.A critical as- to accountfor thesecorrelations. Convergence rate affectsthe sumptionis madeherein' the entire range of strainregimes in rate of horizontalslab migration,while slab age affectsthe overridingplates results from variationsin a few parameters. rate of vertical slab migration.The combinationof slab age Thus back-arcspreading and imbricatethrusting are assumed and convergencerate is thereforethought to determinea pre- to have the same cause.This assumptionis ultimatelyver- ferred trajectory for the shallow slab. The differencebetween ifiable only empirically;if it is incorrect,we shouldbe unable this preferred trajectory and the dip of the interfacebetween to account for a high proportion of the variance in strain overridingand underridingplates will directly affect the cou- regimesthrough multiple regression. pling and thereforemaximum earthquake magnitude. Thus The final differenceis the emphasison statisticaltests of increasedconvergence rate or decreasedslab age will increase •odels and on developmentof regressionequations. This ap- shear stressbetween overriding and underridingplates, given proachhas alreadybeen used by Ruff and Kanamori[1980] in that dip and roughnessof the interfaceare constant.No corre- a relatedanalysis of factorsinfluencing earthquake magnitude. lation of regressionresiduals with shallow dip was found in A complementaryaPProach has been followed by Crossand this analysis.This may suggestthat the conceptualbasis of the Pilger [1982], who examinedthe effectsof individual variables empiricalrelationship needs modification. onstrain regime in regionswhere only one variable changes. Only modelsinvolving the variablesof Table 1 are specifi- STRAIN REGIME MODELS cally tested.Several models account for back-arc spreadingin The primary controlsof strain regimein the overriding terms of mantle diapirismor inducedasthenospheric flow. In plate behind trenchesare still a subjectof activedebate, after general,these models have difficulty predictingthe observed more than a decade of proliferation of models.Most models temporal and spatial distribution of back-arc spreading. are qualitative and conceptual,rather than rigorouslyquanti- Taylor and Karner [1983] and Weissel[1981] reviewand tative and theoretical.Nearly all have been tested primarily critique many of these models, and those analysesare not through examinationof the correlationbetween strain regime repeatedhere. Instead it is assumedthat more detailedanaly- and one or more subductionparameters in currentsubduction sis of diapirism and asthenosphericflow modelswill be war- zones.The approach used here is similarin generalbut differs ranted only if the variablesof Table 1 fail to adequatelyac- in several details. count for observedregional variations in strain regime. First, more subduction zones are used than in previous analyses.This is consideredto be particularlyimportant in ConvergenceRate predictionof strain regime,because most proposedcausative A moderatecorrelation exists between convergence rate and parametersare correlatedwith each other.For exarnple, strain class(R = 0.52),with fasterconvergence corresponding Uyedaand Kanarnori [•1979-] have described the characteristics to more compressiveenvironments in the overridingplate of the two endpointsin the strain continuum,Marianas and (Figure I0). The measureof convergenceused here is compo- Peru-Chile.The highly extensionalMarianas has a steeply nent of convergenceperpendicular to the trench.Components dipping slab composedof very old lithosphere,absolute of convergenceparallel to the trench have an important motion of the overriding plate away from the trench, and impact on strike-slipfaulting in the overridingplate (seethe relativelyslow convergencerate. In contrast,highly compres- sectionon strike-slipfaulting) but may not affect the overall sionalPeru-Chile has a shallowlydipping slab composedof strain regime.However, azimuths of strain indicatorsare ap- youngerlithosphere, absolute motion of the overridingplate parentlyrelated to convergencedirection I'e.g., Nakamura and toward the trench,and rapid convergencerate. Clearly,deter- Uyeda, 1980; Cross and Pilger, 1982]. Back-arc spreading mination of which (if any) of thesefour parametersis control- rates are not included in convergencerates• as back-arc ling strain regime requiresexamination of subductionzones spreadingis consideredto be a manifestationof strain rather with very differentcombinations of theseparameters. BecaUse than a cause of strain. the number of modern subduction zones is limited, the corre- The mechanismfor an effect of convergencerate on strain lation between potential independentvariables may preclude regime is the possibleinfluence of convergencerate on shear reliableisolation of key variablesbased on modern subduction stressbetween the overriding and underridingplates. Dip of zones alone. the boundary betweenthe two platesis generallyshallow (10 ø A second difference between this analysis and previous to 30ø); consequently,an increasein convergencerate may analysesis the attempt to compileall proposedkey variables increasethe componentof horizontal compressiveforce at the for the samesubduction zones, so that thequality of different boundary. Changesin convergencerate occur every few mil- correlationscan be directlycompared. Impressive correlations lion years,a time scalecomparable to major changesin strain betweenback-arc spreading and absolutemotion of the over- regime. riding plate [-Chase,1978b•, slab age [•Molnar and Atwater, The correlationbetween convergence rate and strain regime 1978'],and the combinationof convergencerate and slab age is too poor for convergencerate to be the only causative [-Ruff and Kanamori, 1980] used different subductionzones factor. Thus most strain modelsthat invoke convergencerate and sometimeseven different picks for back-arc spreading, include at least one Otherprimary variable. These modelsare makingcomparison of the modelsdifficult. discussedin subsequentsections. A third differenceis the emphasishere on considerationof Jurdy [1979] has compared reconstructionsof plate mo- all available data for strain regime of each subduetionzone, tions within the Pacific Ocean to occurrences of back-arc includingapparently contradictory data. It is hoped that suf- spreadingover the last 80 m.y.A possiblecorrelation of back- JARRARD' RELATIONSAMONG SUBDUCTIONPARAMETERS 255

4 -- o o ß ß0 ß

z 3 o ß ß

--ß ß ß ß OO ß o

I I , I 6 8 10 12 Vc(crn/yr) Fig. 10. Crossplot of strainclass (Table 2) versusconvergence rate for modern subductionzones. Solid circlesindicate subductionzories for which both variablesare reliably known; open circlesindicate that one or both of the variablesis only approximatelyknown. Only solidcircles are usedin the regressionsof Table 9. Note that strainclass shows only a fair correlation with convergencerate.

arc spreadingwith highconvergence rates was found, opposite pressiveenvironments in three of theseregions, and the rela- to the correlationsuggested by Figure 10. However, someof tively young crust subductingat New Britain is associated the back-arc basinsconsidered in that analysismay not have with rapid back-arcspreading rather than simpletectonics. In beenformed by back-arcspreading; both Weissel[1981] and spiteof differencesin detail, the generalcorrelation of slab age Taylor and Karner [1983] considerthe problematicalorigins with strain regimeof Molnar and Atwater [1978] is confirmed of the SouthChina Sea,West PhilippineBasin, and Coral Sea. by this study. Jurdy [1979] concludesthat most back-arcspreading direc- The mechanismfor an influenceof slab age on strain regime tions are approximatelyparallel to convergencedirection, is probablyits effecton couplingbetween overriding and un- consistentwith observationsof most (but not all) modern derriding plates.The densityof oceaniclithosphere increases back-arcspreading. with age due to coolingand contraction,leading to increased gravitational instability and the well-known slab pull force. Slab Age Estimation of the crustal age of the transition from resisting A weak correlation exists between slab age and strain subductionto slab pull is hampered by uncertaintiesin key regime(R = 0.35),with increasingslab age correspondingto variables [e.g., Molnar and Atwater, 1978; England and more extensionalenvironments (Figure 11). Molnar and Atwa- Wortel, 1980-1,but it is clear that "young" lithosphereresists ter [1978] classified26 subductionzones into three strain subduction[Sacks, 1983], while subductionof old lithosphere classes:active back-arc spreading, simple, and Cordillerantec- is an important drivingmechanism of plate motions.Increased tonics.They found a much strongercorrelation between slab gravitational pull in old slabs probably reduceshorizontal age and thesestrain regimesthan is implied by Figure 11. compressionat the contactbetween overriding and underrid- There are apparentlytwo reasonsfor this discrepancy:ad- ing plates.And even yofinglithosphere is gravitationallyun- ditional subductionzones in Figure 11 and differencesin esti- stable beneath the eclogite transition (about 60 km, but see matesof slabage and particularlystrain regime. For example, Sacks [1983]). possibleCenozoic spreading in northeastJapan, western Aleu- Active back-arc spreadingrequires not just reduced hori- tians, Kuriles, and Java is lessrelevant than the current com- zontal compressionbut active tension.A possiblemechanism 256 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS

7 -

6 -

ß o o ß

•o 4- ß

3' oß ß

2-

0 , I I I I I I I I I I I I I I I 0 20 •0 60 80 I00 I•0 I•0 160

SLAB AGE(m.y.)

Fig. 11. Crossplot of strain class(Table 2) versusslab age at the trenchfor modernsubduction zones. See Figure 10 for an exp!anationof symbols.Note that strainclass shows only a poorcorrelation with slab age.

for this is age-dependentslab rollback, a hypothesissuggested Figure 12 indicates that absolute motions of subductionzones by Molnar and Atwater [1978] and developedin detail by with compressiveand neutral environments(classes 4-7) form Dewey[1980]. The path followed by any point in a subduct- a population that is significantly different from subduction ing slab is not parallelto slab dip; usuallyit is steeperthan zoneswith extensionalenvironments (classes 1-3). No corre- the slab dip, associatedwith a gradualseaward migration of lation between absolutemotiøn and strain regime is found the hinge line or trench axis. The necessityfor rollback was withineither of thesetwo groups. firstsuggested by Elsasset[1971], who noted that the gradual Thecorrelation is strong but not perfect. Of theeight sub-

Tertiary and Cretaceousshrinkage of the Pacific. Ocean re- duction zonesin Table 1 With the fastestrates of retreating quired subductionat an angle steeperthan slab dip. This ob- ("landward") absolutemotion, only four have active back-arc servationdoes not require active slab rollback driven by the spreading' Kermadec, Tonga, New Britain, and Marianas. gravitationalinstability of old lithosphere;alternative drivi,ng New Zealand and Izu-Bonin have extensional environments forces are a trench suction associated with mantle flow toward but no active back-arcspreading. The strain regimeand sub- the trenchand down the uppersurface of the descendingslab, duction history of the very short Palau and Yap subduction or absolute motion of the overriding plate driven by other zonesare uncertain,but back-arc spreadingis not occurring forcessuch as ridge push. Because theage dependence ofslab thoughabsolute motion of the overridingplate is rapidly re- rollback cannot be determined without considering absolute treating.Absolute motions for Makran, Alaska Peninsula,and motion of the overriding plate, further analysis of age- Nicaragua,though apparently retreating, are too closeto zero dependentrollback will followthe next section,absolute to be Consideredsignificant exceptions to the pattern. Of the motion. eight subductionzones with currentlyactive back-arc spread- ing, only New Hebrideshas an apparentlyadvancing overrid- Absolute Motion ing plate. However, the advancingPacific plate is clearly the Strain regimeis moderatelycorrelated (R = 0.69)with abso- overriding plate only for the northwestern New Hebrides, lute motion of the overridingplate. A possibleassociation of wherethe presenceof activeback-arc spreading is uncertain. compressivemountain building with seaward advancing abso- Activeback-arc spreading occurs behind the southeastern lutemotion and of back:arcSpreading with stationary abso- New Hebrides,where the plate configurationis too complex lute motionwas first suggestedby Wilsonand Burke[1972]. toeven reliably pick the• "overriding '•plate. • Hyndman [1972] independentlyproposed a rather similar The mechanismfor an effect of absølute motion on strain model, exceptthat back-arcspreading was thought to be as- regime is the concept of the downgoing slab as an anchor sociatedwith an overridingplate that is retreatingrather than which resistslateral motion. If the slab cannot readily move stationary. The global absolute motion model of Chase landwardor seawardbecause of the difficultyin displacing [1978a] confirmed the strong correlation between back-arc large amountsof mantle material,then the compressivestate spreadingand retreating absolute motion [Chase, 1978b]. of the overriding plate depends entirely on its absolute JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS 257

COMP. 7

ß ßaDo•RAIN =3.6+ 0.66xVa r z: O. 51 R = 0.7'1 ß •8o ß

Z 3

TENS. I '

-6 ABSOLUTE MOTION (cm/yr) Fig. 12. Crossplot of strainclass (Table 2) versusabsolute motion of the overridingplate. Positive absolute motion correspondsto trenchwardadvance of the overridingplate. Note that advancingoverriding plates are generally characterizedby a compressionalor neutral strain regime (classes 4-7), whileretreating overriding plates generally have an extensionalstrain regime(classes 1-3).

motion.Absolute motion away from the trenchwould require evidenceof back-arcspreading and major basincollapse sub- an equal rate of back-arcspreading; absolute motion toward sequentto 100 m.y. is lacking. the trench would require an equal rate of lithosphericfore- Major changesin absolute motion occur much less often shortening.To the extent that the slab can move laterally than the 5-10 m.y. time scale of major changesin strain throughthe mantle(through age-dependent rollback, change regime.Uyeda and McCabe [1983] suggestthat episodicback- in dip, or other causes),these predictions could be modified. arc spreadingat the marginof the Philippineplate may result The anchoringeffect of the slab is clearly relative and not from changesin absolutemotion of the Philippineplate, absolute.Actual foreshorteningin advancingupper platesis causedby collisionof buoyantfeatures along the Philippine muchless than absolutemotions, and Elsasser's[1971] obser- Trench. In other regions it is more difficult to envision a vation concerningthe shrinkingPacific Ocean indicatesthat mechanismfor episodicchanges in strain regimeassociated the slab often displacesmantle seaward. Dewey [1980] sug- with little changein absolutemotion, unless strain regime is geststhat the slab can only migrate seaward,but the rollback also affectedby another variable. For example,the combi- rates of Table 1 indicate that the Izu-Bonin and New Zealand nation of absolutemotion and secondaryflow inducedby slabs are currently moving landward.The short Yap and subductionmay accountfor episodicityof back-arcspreading Palau slabs, if present,must also be advancingrapidly [Jurdyand Stefanick, 1983]. The problemis exemplifiedby the through the mantle. Neogenechange from back-arcspreading to compressionin One possiblemechanism for temporarylandward advance northeastJapan [Nakarnuraand Uyeda,1980], which implies of the trenchaxis with little displacementof mantleis through a changein absolutemotion for all of Eurasia.Such a change steepeningof slab dip. This steepeningcan combinelandward hasnot beendetected [Morgan, 1980],though uncertainties in advanceof the upperslab with retreatof the lower slab,only Eurasianabsolute motions are perhapslarge enough to allow locallydisplacing mantle instead of forcinga large-scaleland- it. Rapid lateral changesin strainregime along a plate bound- ward horizontalflow of mantle. Gradual steepeningof the ary are also difficult to reconcile with a model in which abso- New Zealand Benioff zone over the last 15 m.y. has been lute motion is the only control on strain regime [Uyeda, inferred on the basis of patterns of arc volcanismin New 1984].For example,the Eurasianplate boundaryhas a rapid Zealand [Ballance,1976; Karnp, 1984]. changefrom class6 compressionin northeastJapan and class A more extreme example of rapidly retreating absolute 5 compressionin southwestJapan to class2 extensionin the motionwithout associated back-arc spreading comes not from Ryukyus. Similarly, Pliocene-Pleistocenevariations in exten- modern subduction zones but from the Cretaceous of North sion along the Tonga-Kermadec-NewZealand plate bound- America.If the absolutemotion model of Morgan [1980] for ary show no apparentrelation to lateral changesin absolute North America is even approximatelycorrect, then rapid motion of the Australianplate. back-arc spreadingtotaling about 5000 km must have oc- Absolutemotion of the overridingplate cannotaccount for curredbetween 180 m.y.B.P. and 70 m.y.B.P. in southwestern all modernoccurrences of back-arcspreading and compres- Alaska, as North America moved graduallynorthwestward. sion,nor can it accountfor variationsin strainregime within Evidenceof basin collapseabout 100 m.y. ago existsin the the broad groupingsof compressionalor extensionalenviron- vicinityof Mount Denali [Csejteyet al., 1982],but geologic ments. Nevertheless,of the possible independentvariables 258 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS consideredin this analysis,absolute motion of the overriding subductionzones with back-arc spreadingthan for those with- plateappears to be the bestsingle predictor of strainregime. out back-arc spreading.Too few examplesof back-arc spread- ing are available for a reliable fit of rollback rate to slab age, AbsoluteMotion and Slab Age but the apparent trend is for faster rollback with younger Molnar and Atwater [1978] first suggestedthe hypothesis slabs,the oppositeof the predictedtrend. Similarly, no corre- that strain regime may depend on both absolutemotion and lation of increasingslab age with increasingtrench rollback is slab age. The most extensional environments are thought to evident among subductionzones lacking back-arc spreading. result from the combination of a retreating overriding plate The latter observationdoes not disprovethe conceptof spon- and old slab, and the most compressionalenvironments result taneous age-dependentrollback, becauseVoa may mask the from the combination of an advancingoverriding plate and possiblecorrelation with age of V•. However, it suggeststhat young slab. Moberly [1972] had proposeda forerunnerof this spontaneousrollback, if real, is lessthan 2 cm/yr even in the hypothesis, recognizing that back-arc spreading may result oldest slabs. from a combinationof slab rollback and a retreatingoverlying The angle of descentof a point on the deep slab is readily plate. However, his model visualizedback-arc spreadingas a calculablefrom the deep dip, convergencevelocity including processpartially driven by flow of displacedmantle, rather back-arc spreading,and net rollback rate, assumingthat the than a passive responseto age-dependentslab rollback and deepdip is not changingwith time. Theseangles are tabulated absolute motion. in Table 1. Unfortunately, descentangles can only be calcu- A more rigorous vector analysisof the model is presented lated for 23 of the 39 subductionzones, primarily because by Dewey [1980]. The strain regime of the overriding plate is many subductionzones are too short for reliable estimation of thought to depend on the relative magnitudes of absolute deep dip. Furthermore, calculateddescent angles are quite motion of the overriding plate (Voa)and age-dependentslab sensitiveto the absolute motion model assumed, as evidenced rollback (V•).As in analysesin this paper, only the component by differencesbetween the Chase [1978a] and Minster and of absolute motion perpendicularto the trench is considered Jordan [1978] columnsof Table 1. relevant.If Voais advancing(toward the trench axis)and great- Figure 14 plots slab descentangles as a function of deep er than V•,compression in the overridingplate results.If Voais slab dip. According to the model of Dewey, all points should lessthan V, then extensionin the overridingplate results. lie within the envelopecorresponding to anglesbetween deep The Dewey [1980] model can be usedfor quantitativepre- dip and vertical. Subduction zones with older slabs should diction of strain regime only if we can estimate V, the sponta- plot closer to the horizontal line (correspondingto vertical neous rollback causedby gravitational instability of the un- sinking), and those with younger slabs should plot closer to derriding plate. It is important to distinguishthis rollback rate the diagonal line (correspondingto no spontaneousrollback). from the net rollback rate, which is the observed rate of ad- Although uncertaintiesin computed angle of slab descentare vance of the trench axis. The net rollback rate, which is equal large, no correlation between slab age and the two envelope to the absolute motion of the overriding plate plus any back- extremesis apparent.Several subduction zones lie significantly arc spreading rate, is hypothesizedto equal the spontaneous outside the predicted envelope.New Zealand and Izu-Bonin rollback rate when back-arc spreadingis present.Spontaneous lie significantlyto the right of the envelope, implying land- rollback can only move the trench axis oceanward,with a rate ward advance of the slab. Rollback rates in the Solomon and V•- V• cot DipD, whereDipD is the deepdip and V• is the particularly New Hebrides and South Sandwich subduction vertical sinking velocity, which is a function of the age- zonesare so rapid that descentangles of points on the slab are dependent gravitational instability of the slab. This model actually oppositein sign to the dip of the slab. makes several predictions that are readily testable with Unlessabsolute rates are substantiallyin error for the Solo- modern subduction zones: mon, New Hebrides, South Sandwich, New Zealand, and Izu- 1. All net rollback rates must be positive,i.e., trench axes Bonin subductionzones, downward gravitational force can be always move seaward. excluded as the only factor causing a differencebetween de- 2. Net rollback rates correlate with slab age for subduc- scentangle and deep dip. Descent anglesfor thesesubduction tion zones with back-arc spreading. zones seem to require an active horizontal force at 100- to 3. Net rollback rates for subduction zones lacking back- 400-km depth. The only plausible source of such a force is arc spreadingare faster than net rollback rates for subduction deep convectivemantle flow. Thus rather than spontaneous zoneswith back-arc spreading,if slab agesare comparable. rollback causing mantle flow, mantle flow may be causing 4. The angle of descent of a point on the deep slab is spontaneousrollback. always intermediate between the deep slab dip and vertical, The apparent dependenceof rollback rates on mantle flow with older slabsdescending at an anglecloser to vertical than (at least in some subductionzones) is discouraging,as we can younger slabs. never hope to know mantle flow patterns as well as relative or 5. The strain regimein the overridingplate is highly corre- absolute plate motions. Haqer and O'Connell [1978] have lated with slab age and absolute motion of the overriding modelled worldwide mantle flow resultingfrom mass flux be- plate. tween trenches and ridges; they discussthe uncertainties in Net rollback rates are tabulated in Table 1. Most are con- such models. The possible implications of such models for sistentwith the first prediction,but New Zealand, Izu-Bonin, predictionof deepdip are discussedin a subsequentsection. Yap, and Palau are clearly inconsistent,with large negative It is important to note that the relationship of slab dip to (landward)"rollbacks." Makran, Alaska Peninsula,Nicaragua, slab injection angle used here is markedly different from re- Marianas, and Sumatra have rollback rates that may be nega- lationshipsdetermined in previouspapers [Haqer and O'Con- tive but are not statistically distinguishablefrom zero. Net nell, 1978; Dewey, 1980]. This difference is subtle for many rollback rates are plotted as a function of slab age in Figure subductionzones but is quite large for some (e.g., Solomon 13. Contrary to prediction, rates are consistentlyhigher for and South Sandwich, Figure 15). The velocity of descent JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 259

lO BACK-ARC SPREADING ß ABSENT o PRESENT

4

rn _J ß ß ß _J ß ß o r• I I ß o

-r

Z

-2

ß 20 40 60 80 100 120 140 160 SLAB AGE (m.y.) Fig. 13. Cross plot of trench rollback rate versusslab age at the trench, for modern subductionzones. Note that the fastestrollback rates occur in subductionzones with back-arc spreading.Note also that modern subductionzones show no tendencytoward increasingrollback rate associatedwith increasingslab age. These observationsindicate that rollback rate is not controlledby a combinationof slab age and an advancingoverriding plate.

parallel to the slab dip is simply the total convergencerate at treme, with predicted slab sinking at a rate about double the the trench (V•s,or the convergencerate betweenoverriding rate that available slab enters the trench. Thus one must and underriding plates plus any back-arc spreading).The questionthe existenceof an additionalsinking component V• angleof injectioninto the mantle of a point on the slab (V•) is causedby rollback, except to the extent that increasedroll- the vectorsum of V•s(the velocityparallel to the slab)and Vsa back increasesconvergence rates. (the rollback rate of the trench axis, equivalentto the absolute Though the analysesabove have failed to detect evidenceof motion of the forearc). age-dependentrollback, both slab age and absolutemotion of As recognizedby Hager and O'Connell[1978], V/is equiva- the overridingplate may still control strain regimein the over- lent to the absolutemotion of a point on the underridingplate riding plate. Coupling at the contact betweenoverriding and (V•a).Both the angleand the rate of V•aare differentfor points underridingplates may be affectedby both slab age and abso- on the slab than on the unsubductedportion of the underrid- lute motion, with an increasein horizontal compressivestress ing plate. If one assumesthat the rate is unchanged[Hager possible due to either an increase in absolute motion or a andO'Connell, 1978], then the velocitytriangle V•s + Vsa= V•a decreasein slab age. However, when multiple regressionof doesnot close(Figure 15). For the Solomonexample, V•s is strain regime on both absolutemotion and slab age is under- underestimatedby about 30%, while for the South Sandwich taken, the resulting regressiondoes not account for signifi- example,no rate of subductionparallel to the slab or angleof cantly more of the variance in strain regime than does abso- injectioncan be reconciledwith the knownmagnitudes of Vsa lute motion alone (Table 9). In view of the significant corre- and V•a. lation of strain regime with both absolutemotion and slab age In the model of Dewey[1980], Vuafor the slabis incorrectly when consideredseparately, a strong covariancebetween the assumedto be parallel to the slab (Figure 15). Rollback is effectsof slab age and absolute motion is implied. We may thoughtto impartan additionaldownward component V• to a concludethat strain regime is not controlled by the combi- point on the slab.For the very steepdip and moderatelyfast nation of slab age and absolutemotion of the overriding plate. rollback in the Solomons,a near-verticalinjection rate of 35-40 cm/yr is implied; this rate is clearly inconsistentwith ConvergenceRate and Slab Age the 12-cm/yrrate at which lithosphereis enteringthe trench. Successfulprediction of earthquake magnitude, based on For the South Sandwichexample the discrepancyis lessex- convergencerate and slab age, was discussedin a previous 260 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS

120 - NEWHEBRIDES SANDWICH 110 - SOUTH

I00 - SOLOMON

9O

80-

70- Predicted Data Limits,

60 _ Rollback Hypothesis 50- ,• IIZU-BONIN 40-

.30-

20- NEWZEALAND

10 _ /

I I I 20 .30 40 50 60 70 8O 90

DEEP DIP

Fig. 14. Descentangle of the deepslab versusdeep slab dip, for modernsubduction zones. Solid symbolsindicate slabsolder than 70 m.y.; open symbolsindicate slabs younger than 70 m.y. Descentangles calculated from the global motion modelsof Chase[1978a] and Minster and Jordan[1978] are indicatedby circlesand triangles,respectively. Note that few deepslabs sink at an angleparallel to the deepdip (diagonalline); moreoften, they descend at an anglebetween the deepdip and vertical,as predictedby the rollbackmodels of Molnar andAtwater [1978] and Dewey[1980]. However, somedeep slabs sink at an angleshallower than deepdip or greaterthan 90ø . Also,no tendencyis seenfor opensymbols to plot nearthe diagonalline and closedsymbols to plot nearthe horizontalline. Both observationsare inconsistentwith a modelin whichgreater slab age gravitationally swings the descentangle toward vertical.

section.Although Mw and Mw' were the only measuresof ties in strain regime. However, some of the variance may coupling quantitatively analyzed by Ruff and Kanarnori also be due to different variables affecting Mw' and strain [1980], a similareffect of couplingon the strainregime in the regime. overridingplate may be present.Uyeda and Kanarnori[1979] When the semiquantitativestrain regime of this study is found a qualitativecorrelation between strain regimein the considered as the dependent variable, the independent vari- overridingplate and maximumearthquake magnitude. Ruff ables Vc and slab age are together a moderately successful and Kanarnori[1980] found that subductionzones with active predictor of strain regime (Table 9). With a correlation coef- back-arcspreading were generallyassociated with predicted ficient of 0.78, the combination of convergencerate and slab magnitudesof lessthan 8 from their regressionequation. They age accountsfor 62% of the total variance in strain regime. concludedthat back-arc spreadingis most likely in subduc- Thus these two variables together appear to be about as suc- tion zones with slow subduction of old slabs. cessfulas absolutemotion of the overriding plate in predicting This correlation between coupling (as measured by Mw') strain regime. Becauseboth slab age and convergencerate are and back-arc spreadingcan be extended to a more compre- somewhat correlated with absolute motion for the subduction hensive correlation between coupling and strain regime zones of Table 1, further analysis is required to determine (Figure 16). A moderate correlation between Mw' and strain which of the two relationshipsis the primary causal relation. regime (R =0.579) is improved to a good correlation In a subsequentsection we will see that significantimprove- (R = 0.694) if two extreme points are omitted. Some of the ment is achievedby adding a third variable (intermediatedip) variance in Figure 16 is undoubtedly attributable to the long to the strain regime equation based on convergencerate and recurrencetime betweenmajor earthquakesand to uncertain- slab age. SOLOMON SOUTH SANDWICH

Vuo vs• ' Vo• vs• Vu• ,r / // vø/r v,o __ SCOTI SOUTHAMERICA//

// // Vu• II/ Vi/ // Vs• • / // /

/ / vi /; / / v• ; /

; / / ; /

/

i

Vuo vso' * vo• vs•

PACIFIC V•(:Vuo)/ •• SCOTIA/• - ; Unsloble;ConnolClose v•

.

Vuo Vs• * Voo Vso Vuo

PACIFIC SOLO•O• SCOTI TH A•E•I /

VELOCITY VECTORS Vuo:U•OE•101•6 PLATEw.•.t. ABSOLUTE •E&F•A•E Vso: FO•EA•C SLIVE• PLATE w.•.t ABSOLUTE •EF. F•A•E :• Vus'UNOE•101•6 PLATEw.•.•.SLIVE• (:•OLLBAC•) Vi : SLAB I•JECTIO• w.•.t.ABSOLUTE •EF. F•A•E V• :VE•TICALSI•I•60UE TO •OLLBAC•

Fig. 15. Three differentmethods of determiningthe injection(or descent)angle of the slabinto the mantle.Note that the assumptionsmade by Dewey[1980] lead to extremelyhigh slabinjection rates in the Solomonand South Sandwich regionsand that the assumptionsmade by Hager and O'Connell[1978] breakdown in the SouthSandwich case of large Vs,.These two subductionzones are extremeexamples; more often,the differencesbetween the threemethods are much smaller. 262 JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS

TABLE 9. Strain Regressions

F Ratios

RegressionEquation Velocity First Second Third (Strain =) Comment* Source•' Regression Term Term Term R2 R

0.862 + 0.469 x V• 1 C 14.2 ...... 0.3717 0.610 3.71 + 0.706 x Voa 1 C 24.0 ...... 0.5003 0.707 4.07 + 0.429 x V•- 0.124 x DipI 1 C 17.6 17.8 13.5 ... 0.6042 0.777 6.25 + 0.619 x Voa- 0.106 x DipI 1 C 22.8 25.3 11.3 ..- 0.6652 0.816 1.95 + 0.519 x V•- 0.018 x A s 1 M 12.9 19.8 6.4 --- 0.5284 0.727 5.19 + 0.464 x V• -0.122 x DipI- 0.021 x As 1 C 25.1 34.5 21.9 16.4 0.7736 0.880 4.52 + 0.275 x V•- 0.105 x DipI + 0.459 x Vo• 1 C 24.2 9.6 15.2 15.4 0.7671 0.876 5.18 + 0.494 x Vc -0.130 x DipI- 0.018 x A s 1 M 26.7 37.4 26.1 13.0 0.7845 0.886 3.65 + 0.662 x Vo• 2 C 30.1 ...... 0.5092 0.714 3.95 + 0.468 x Vo• 2 M 35.6 ...... 0.5508 0.742

*Comment 1' delete 13 subductionzones with missingdata. Comment 2' all possibledata used in correlations'equivalent to deleting subductionzones with missingdata when only one term in regression. •C, Chase[1978a]. M, Minster and Jordan [1978]. Both revisedas indicatedin text.

Slab Dip The strain classesof this study exhibit a moderate inverse correlationwith shallowdip (R = -0.492), intermediatedip The Benioff zones of the highly compressionalAndes are (R =-0.570), and deepdip (R =-0.583). This apparently among the most shallowly dipping of modern subduction significantrelationship (Figures 17 and 18)is substantiallyim- zones.Indeed, in two segmentsof the Andes, Peru and Central proved if a single extreme point (the Solomon subduction Chile, the slab flattensat about 100-km depth and apparently zone)is excluded;the correlationcoefficients are then -0.549, travels horizontally along the lower surface of the South -0.633, and -0.670, respectively.However, examinationof American lithosphere. In contrast, subduction zones with Figure2 showsthat Benioffzone geometry cannot be theonly back-arc spreadinginclude some of the steepestslab dips.This factorinfluencing strain regime. apparent correlation has led several authors to infer that slab Correlationbetween dip and strainregime may arisefrom dip controlsstrain regimein the overridingplate. the effect of shallowdip on the degreeof couplingat the Low-angle subductionbeneath the Andes of Peru and Cen- contactbetween overriding and underridingplates [Cross and tral Chile [Barazangi and Isacks, 1976] is often consideredthe Pilger, 1982; Jarrard, 1984]. Resistanceto motion on this best evidencefor an effect of slab dip on strain regimein the interface is rS/sin Dc, where r is the shear stress,S is the overriding plate [e.g., Barazangiand Isacks, 1976; Megard and thicknessof the overridingplate, and Dc is the averagedip Philip, 1976; Pilger, 1981; Mercier, 1981]. The low-anglesub- alongthe contact.This relationshipmay greatlyunderestimate duction is thought to greatly facilitate the transmissionof the frictional resistancein the extremecase of very low angle compressivestress to the overriding plate, through increased subduction;for example, in Peru and Central Chile an inter- contact area between plates. Jordan et al. [1983] have thor- mediatedip of 13ø-14ø changesto near zero at about 100 km, oughly documentedthe associationbetween Benioff zone ge- wherethe underridingplate dragsalong the bottom surfaceof ometry and modern structural style in the Andes. However, the upper plate. Further, Dc is not equivalentto DipI, because structural style along the Andesis also clearly associatedwith the thicknessof the overriding plate, though usually not Paleozoicpaleogeographic features [Allrnendinger et al., 1983]. known,is Probably somewhat less than 100 km. Nevertheless, Thus it is possiblethat paleogeographicfeatures influence not it may be appropriateto use I/sin (DipI) as the independent only modern structural style but also the geometry of the. variable rather than DipI. However, for the shallow dips of subductedplate [Allrnendingeret al., 1983]. modernsubduction, the relationof sin (DipI) to DipI is nearly Laramide deformation of western North America is in linear, making it impossibleto distinguishbetween the two on many respectssimilar to modern Andean deformation [Jordan the basisof regressiongoodness of fit. Variations in both over- et al., 1983]. The Laramide orogeny was apparentlyalso as- riding plate thicknessand particularly shear stressare prob- sociatedwith very shallow slab dip basedon magmaticpat- ably much more important sourcesof the variancein Figure terns in the westernUnited States[Coney and Reynolds,1977; 17.Dip aloneis an inadequatepredictor of strainregime. Keith, 1978; Dickinsonand Snyder, 1978; Cross and Pilger, Shear stressat the base of the accretionaryprism is much 1978]. In New Zealand a gradual change from middle Mio- lower than at the baseof the overridinglithosphere. This dif- cene foreland deformation to the presentmildly extensional ferencewill tend to obscureany possiblerelationship between environmentwas similarlyassociated with a changefrom very dip and strain regime, becausetwo subductionzones with the shallow to moderate dip [Karnp, 1984]. A cause-and-effect same DipI may have very different widths of accretionary relationship between low-angle subductionand pervasivein- prism (e.g.,Alaska Peninsulaand Peru). Unfortunately,width traplate deformation in both the Andes and western North of the accretionaryprism is oftennot reliably known. America seemsrelatively well established,with the proviso The opposite relationship between slab dip and strain that one of the conditionsfavoring low-angledip may be the regime has also been proposedor implied. In his initial con- paleogeographiccharacter of the overridingplate. siderationof back-arcspreading, Karig [1971] suggestedthat Association between strain regime and the steeper dips one effectof back-arcspreading would be to decreasethe dip more commonly found in Benioff zonesis lesswell established. of the slab.In the model of Dewey[1980], slab age and abso- JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 263

lO

R--.579 All Reliable Data R =.694 Omit Java l& S. Chile ß S. CHILE I.d

z 9 (D o ß

8

I.d

ß JAVA

1 2. 3 4 5 6 7 Extension STRAIN CLASS Compression Fig. 16. Cross plot of cumulativeearthquake moment (Mw') versusstrain class,for modern subductionzones. Note the fair to good correlationbetween the two, which suggeststhat couplingbetween underriding and overridingplates is one factor controllingthe strain regimeof the overridingplate. Data dispersionis probably too high for couplingto be the only factor controllingstrain regime. lute motion of the overridingplate are the primary controls pendentvariables: convergence rate, slab age,and intermedi- on strain regime.Deep slab dip is also a factor in this model, ate dip. The resultingregression equation (Table 9), with a becauseit controls the amount of rollback causedby gravi- correlation coefficient of 0.88, accounts for 77% of the ob- tational sinking of the slab. A doubling of slab dip causes servedvariance in strain classes(Figure 19). The overall corre- about a 60% reductionin rollback for lithosphereof the same lation coefficientis higher (0.93) if subductionzones with in- age, substantiallyincreasing compressive stress whenever the completedata are includedin the analysis,but the more con- overridingplate is advancing.Ruff and Kanamori [1980] pro- servativeapproach of usingonly completedata is considered posedthat strain regimeis controlledby the effect of conver- preferable. gencerate and slab age on couplingat the interfacebetween Residuals to this regressionequation may be systematic the two plates.Convergence rate and slab age togetherdeter- (Figure 19). The data appear to be better fit by a curve than a mine a preferredtrajectory for the shallow slab; if this trajec- linear regression,possibly suggestingthat the seven strain tory is shallower than the dip of the interface, compression classes are not equally spaced points on the exten- results.The deeper dip of the slab, beyond the interface,is sion/compressioncontinuum. The regressionequation is much thought to be controlledby slab age, convergencerate, and better at accounting for variations in compressionalstates possibly other parameters. An inverse cor•'elation between than for variations in extensionalstates; it does not attempt to deepdip and compressionwould result,caused by the effectof accountfor variationsin back-arcspreading rotes within class convergencerate and slab age on both parameters.Thus the 1 zones. Ruff and Kanamori [1980] model predictsthat strain regimeis This relationshipcan be thought of as a small but signifi- positivelycorrelated with shallowdip and inverselycorrelated cant refinement of the previously discussedrelationship of with deep dip. Except for the observedinverse correlation strain regime to slab age and convergencerate. According to with deep dip, none of these predictionsis substantiatedby this model, slab age and convergencerate determinethe shear this study. stressat the plate boundary, while intermediate dip is a mea- sure of the contact area over which this stress acts. ConvergenceRate, IntermediateDip, and Either DipI is only an approximate measureof the most important Slab Age or AbsoluteMotion contact area, that betweenrigid lithospheresof the overriding Stepwisemultiple regressionindicates that the best predic- and subductingplates. That contactarea is not generallyde- tion of strain regimeoccurs with a combinationof three inde- terminable, because neither the width of the accretionary 264 JARRARD'RELATIONS AMONG SUBDUCTION PARAMETERS

7 -

6- ß ß ßß

ß ß ß O O

2-

ß ßß ß ß ß ß ß

0 i I I I o IO 20 30 40 SLAB INTERMEDIATE DIP(O-IOOkmdepth) Fig. 17. Crossplot of strainclass (Table 2) versusslab intermediate dip for modern subduction zones. See Figure 10 foran explanation of symbols.The correlation between the two is only fair, indicating that slab intermediate dip is not the only factorcontrolling strain regime of the overridingplate.

prismnor thethickness of theoverriding plate is knownfor resistingsubduction may resultin increasedcoupling with the most subductionzones. Sediments in accretionaryprisms are overridingplate and consequentcompression. oftenhighly overpressured [e.g., yon Huene, 1984] and deform To avoid acceleration,the forcesacting on the slab must at very low shearstresses (e.g., W.-L. Zhao et al., unpublished sum to zero. Englandand Wortel [1980] apparentlyassume manuscript,1986). We may anticipatethat the strainregime that the net forcefavoring or resistingsubduction is equalto equationwill ultimatelybe modifiedto includeconvergence the frictional and gravitationalforces involved in crustal thin- rate, slab age, width of the accretionaryprism, and width of ning(back-arc spreading) or thickening(thrusting) of theover- the lithosphericcontact zone. ridingplate. However, this net forcemay alsobe balancedby The successof convergencerate, slab age, and DipI in ac- frictionaldrag at the baseof the underridingplate or by countingfor variationsin strain regimedoes not imply that trenchsuction on the overridingplate. couplingand contactarea are the only two factorscontrolling Quantitativedetermination of the four forcesis plaguedby strainregime. The relativemagnitudes of the V• and As coef- major uncertaintiesin key parameters.However, at least a ficientsin the strain regimeequation are differentthan in the semiquantitativecomparison of the empiricalstrain equation equationfor earthquakemoment. Further, decreased coupling and the model of Englandand Wortel [1980] is warranted. doesnot accountfor the rapid rollback associatedwith back- The two majorforces whose variation may affect strain regime arc spreading(Figure 13). As previouslydiscussed, this roll- areslab pull and interface friction. back doesnot seemto be a simplefunction of slab age. An The slab pull forceis dominatedby a very strongdepen- additionalhorizontal force may be required;deep mantle flow denceon slabage' for example,100 m.y. old crusthas a factor and asthenosphericcounterflow [Toks6z and Hsui, 1978] are of 2 or 3 greaterslab pull than 30 m.y. crustat high conver- possiblesources of this force, but more model studies are re- gencerates (10 cm/yr) and a factor of 4 greaterfor slow con- quired to evaluatetheir contribution. vergence(3 cm/yr).This effect is augmentedslightly by the age Englandand Wortel [1980] present a theoreticalanalysis of dependenceof the weakerridge push force. A weakerbut still the ways in which these three parametersmay interact to strongdependence on convergencerate is expected ß fast con- affect the net force favoring or resistingsubduction at a sub- vergence(10 cm/yr)causes roughly twice the slabpull forceof ductionzone. This total forceis the sumof four forces:(1) the slowconvergence (3 cm/yr)for youngcrust, and 50% more for driving force from ridge push,(2) the driving forcefrom slab old crust.The observedrange in deepslab dips causes only a pull, (3) the resistingforce from frictiona t the contactbetween 40% range in slab pull. plates, and (4) the resistingforce from compositionalbuoy- In contrast,only shallowdip explicitlyaffects interface fric- ancy of the slab.England and Wortel [1980] hypothesizethat tion.For the rangeof shallowdips in modernsubduction a net force favoringsubduction might be expectedto lead to zones,the effectis nearlylinear' a doublingof dip decreases slab rollback and back-arcspreading. In contrast,a net force the interfacefriction about 50%. The possibleeffect of slab JARRARD'RELATIONS AMONG SUBDUCTION PARAMETERS 265

7 ,,.

6 -

5 -

z • 3-

I--

J ,.,,

o 0 I0 20 30 40 50 60 70 80 90 SLAB DEEP DIP Fig. 18. Crossplot of strainclass (Table 2) versusslab deep dip. SeeFigure 10 for an explanationof symbols.The correlationbetween the two is poor, indicatingthat deepslab dip probablyhas no effecton the strainregime of the overridingplate.

age and convergencerate on shearstress at the interface[Ruff emergefrom stepwiseregression all operate in directionscon- and Kanamori, 1980] was not specificallyconsidered by the sistent with the hypothesisthat coupling is the dominating model of Englandand Wortel [ 1980]. influenceon strain regime. The model of Englandand Wortel [1980] thereforepredicts A possiblysurprising result of this stepwiseregression is the that the empirical strain regimeequation should show a very absenceof absolute motion of the overriding plate, particu- stronginverse correlation with slab age, a stronginverse cor- larly becausethis variable showsthe highestindividual corre- relation with convergencerate, a moderateinverse correlation lation with strain regime. As the three other variables are with deep dip, and a moderateinverse correlation with shal- gradually added to the regression,the contribution of absolute low dip. The signof the slab age and shallowdip correlations motion gradually sinks to a nonsignificantlevel. This results is as predicted,though the slabage term is lessdominant than from the correlation of absolute motion with the three other expected.The sign of the convergencerate correlationis the independent variables: inverse correlations with intermediate oppositeof model prediction.This conflictis presentnot only dip and slab age and positive correlation with convergence for the empiricalstrain regimeequation, but also for the em- rate. The mechanismfor all three of these fair to poor corre- pirical earthquakemoment equation. lations is obscure,if indeed they are even real. The combined The proposedrelationship between strain regimeand resist- effect of these correlations on the stepwiseregression is too ance to subductioncan also be tested by a crossplotof slab large for the statisticaltechnique to unambiguouslyisolate the age versusvertical sinking rate [Englandand Wortel, 1980]. variablesaffecting strain regime. On such a plot, a line correspondingto a resistingforce of An alternative stepwiseregression endpoint suggeststhat 8 x 10•2 N/m was thought [Englandand Wortel, 1980] to strain regime is affectedby convergencerate, intermediatedip, separate extensional and compressionalsubduction zones. and absolute motion of the overriding plate. The regression Figure 20 showsthat this expectedpattern is poorly displayed equation (Table 9), with a correlation coefficientof 0.88, ac- by the data of Table 1. Differencesbetween Figure 20 and the counts for 76% of the observedvariance in strain class(Figure correspondingfigure of Englandand Wortel [1980] are pri- 19). This fit is as high as that achieved by the combination of marily attributed to the substantialimprovements in strain convergencerate, intermediatedip, and slab age. Thus multi- classificationsand the greaternumber of subductionzones in variate analysisis capable of indicating that two of the three the presentstudy. variables affectingstrain classare convergencerate and inter- One may tentativelyconclude that couplingat the interface mediate dip; it is not capable of distinguishingwhether abso- betweenplates is more important to strain regimein the over- lute motion or slab age is the third variable. riding plate than is slab pull. Theoreticalcalculations cannot Two observationssuggest that slab age is more likely than predict the effect of slab age and convergencerate on shear absolute motion to be the third variable. First, nearly all of stressat this boundary. However, the three parametersthat the empirical subduction relations previously discussedin- 266 JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS

7 - (a) R a = .767 neutral, while continental overriding plates are more often R = .876 compressionalthan extensional(Table 1). This correlationis a 6 - sampling artifact, resulting from three factors: (1) strain regimeis affectedby DipI (as discussedabove), (2) DipI is affectedby duration of subduction,and (3) continentalover- riding plates have much longer subduction durations than

el ß oceanicoverriding plates. The latter two factorsare explored more thoroughly in the next section.

b.I > SLAB DIP MODELS n,' b.I cn The factors influencing slab dip are not yet known with certainty. The searchfor the primary causesof slab dip vari- I ations has been hamperedby four limitations: (1) changesin dip with depth within each subductionzone, (2) limited data concerningpaleodips, (3) correlation betweenpossible causa- 0 1 2 3 4 5 6 PREDICTED STRAIN CLASS tive factors,and (4) unknown valuesfor parametersin theoret- from: SC =4.52 + .275 x Vc -.105 x Dip]:+.459 x Voa ical models. Almost all subductionzones show a gradual steepeningof the Benioff zone with increasing depth, at least to 100- to THRUSTING 7 (b) * * Ra= .774 200-km depth (Figure 2). Thus the dip of a Benioffzone is not R = .880 readily characterizedby a singlevalue. It is probablyinappro- 6 priate to use the average dip of the entire Benioff zone to characterizeslab dip, becausethe searchfor factorscontrolling slab dip is then contaminated by factors controlling slab length. In this paper, slab dip is parameterizedinto three somewhat arbitrary measures:(1) DipS, the average shallow dip to 60-km depth, (2) DipI, the average dip for the more intermediatedepth range of 0 to 100 km, and (3) DipD, the more constantdip of the deeperslab, generally in the interval from about 150 km to 400 km. It has been suggestedthat there is no correlation between shallow dip and deep dip •[Karig et al., 1976], indicatingthat entirelydifferent causes BACK-ARC SPREADING may be responsiblefor Dips and DipD. However, Dips and DipD are moderately correlated (R--0.560) and therefore probablynot independent.Apparently either someof the same

PREDICTED STRAIN CLASS factorscontrol both deep and shallow dip, or either deep or from SC= 5.19 +.464XVc-.122x DIP[-.O21xAs shallowdip is partly controlledby the dip of the other part of Fig. 19. Cross plots of strain class(Table 2) versuspredicted the slab. strain class.Predicted strain classesare basedon regressionsin which Analysisof deep slab dips is entirely limited to presentBe- the independentvariables are convergencerate, intermediate dip, and nioff zones. This limitation may be serious, as we cannot either(b) slabage or (a) absolutemotion of the overridingplate. Both assume a priori that observed present deep dips are in an regressionresults are very successfulin accountingfor modernvari- ations in strain regime.Analysis of modern subductionzones cannot equilibrium state rather than a state of constantmajor change. determinewith confidencewhether slab age or absolutemotion is the Suchan assumptionmay be safelymade only a posteriori,if it third causalvariable. See Figure 10 for an explanationof symbols. is found that observeddeep dips can be accurately predicted Note the possibilitythat the data in eachplot would be betterfit by a from independent variables that change only gradually (e.g., curve than by the linear fit used.This observationmay suggestthat the strain classesare not equally spacedpoints along the continuum l/c, Vo,,or As). Paleodip estimationis possiblefor DipI, based from extensionto compression. on potassium content of ancient arc volcanics [Dickinson, 1972; Lipman et al., 1972] or correlation betweenBenioff zone depth and other measuresof arc composition [Keith, 1978]. volve some combination of convergencerate, slab age, and However, these paleodip estimatesmust be treated with cau- intermediatedip. Absolutemotion is consistentlyabsent from tion, as factors other than Benioff zone depth can have major theseother relations,though each statisticalanalysis included impact on arc composition [Gill, 1981; Glazner and Supplee, absolutemotions of both overridingand underridingplates as 1982; Foden, 1983]. potentialindependent variables. Second, Mw', which is affected The problem of correlationbetween possible causative vari- by slab age and convergencerate, is correlatedwith strain ables is not unique to dip models, as previouslydiscussed. It class.Neither observationproves that slab age, rather than is, however,more severefor dip and strain regimemodels than absolute motion, affectsstrain class.Thus neither of the two for some other models (e.g., slab length) becausequalitative regressionequations can be accepteduntil they are both tested relationships to more potential independent variables are on other (presumablypre-Quaternary) data. plausible. Strain regimesof modern subductionzones are indirectly Quantitative theoretical models of slab dip have met with correlatedwith crustal type in the overridingplate. All over- very limited successbecause key parametersaffecting flow and riding plates composedof oceaniccrust are extensionalor force balanceswithin the mantle are too poorly known. Slab JARRARD' RELATIONSAMONG SUBDUCTION PARAMETERS 267

160 -

2

140 - 5

120 - i 5?

RESISTING 100 _FORCE OF 8xlOiZN/m

_

80-

_ 4

60- 5 4 - • 6?27? I•(n• 40-

?0- 6! 6 6 I•

I I I I I I I I I I I 2 4 6 8 10 12 VERTICAL SINKING RATE (cm/yr) Fig. 20. Crossplot of slabage versus vertical sinking rate of the slab.The strainclass of eachsubduction zone is indicatedby a numberbetween 1 and7; questionmarks indicate less reliable data. According to themodel of Englandand Wortel[1980], strain class is expectedto increasefrom the upper right to thelower left of theplot. The linerepresenting a resistingforce of 8 x 10•2 N/m was thoughtto separateextensional (classes 1-3) from compressional(classes 5-7) subductionzones. Note the poor fit of the data to this predictedpattern.

dip modelsare thereforelargely dependent on empiricalcorre- be useful as an indicator of stresswithin the slab [Laravie, lation to possibleindependent variables. Given reliable em- 1975]. pirical correlations,it may then be possibleto placelimits on appropriate theoreticalmodels. For example, Hager and ConvergenceRate O'Connell [1978] modelled mantle flow patterns based on Luyendyk [1970] suggestedthat convergencerate may be three different sets of viscosityassumptions and compared an important control of slab dip, basedon examination of the their results to observedslab dips as a test of these assump- Tonga, Kermadec, Java, and Kamchatka-Kurile subduction tions. zones.Faster convergencewas thought to causeshallower dip, following the relation sin (dip)- sinking rate/convergence Radius of Curvature rate. Similarly, Roeder [1975] proposedthat convergencerate Subduction-relatedbending of a part of the earth'sspherical changesmay cause dip changes.However, Tovish and Schu- lithosphericcap imposesinternal stresses on the slab.The slab bert [1978] compareddeep dips to convergencerate for most dip that minimizesinternal stress is simplytwice the radiusof of the subduction zones of Table 1 and found little correlation curvatureof the plate boundary [Frank, 1968]. Benioff zone betweenthe two for convergencerates of lessthan 10 cm/yr. geometrymay thereforebe analogousto a dent in a ping pong The presentanalysis confirms this result: a small positivecor- ball, exceptthat in the ping pong ball the radius of curvature relation between Vcb, and dip is found, and a small inverse is free to changein responseto the imposeddip, whereasthe correlation between Vcand dip is found (Table 6). These corre- shape of an overriding plate imposesa radius of curvature lations do not disprove the relationship proposed by Luy- which may control slab dip. Severalstudies have soughtto endyk [1970]; if it is valid, sinking rate must be much more establishan empiricalrelationship between radius of curvature variable than originally suggested. and dip [Aoki, 1974; DeFazio, 1974; Laravie, 1975], usually usingradius of curvatureof the trenchrather than of the arc Slab Age and averagedip of the entire Benioffzone insteadof shallow South America has both shallowerdips and younger sub- or deepdip. Tovishand Schubert[1978] showedthat the cor- ducted lithosphere than many western Pacific subduction relation betweenarc radius of curvature and deep dip is poor. zones.Because older lithosphereis more gravitationally unsta- In this analysis,logarithm of radius of curvatureis used,be- ble than younger lithosphere,it might be expected to sink cause both the distribution of radii of curvature and uncer- more rapidly, causinggreater dips. Wortel and Vlaar [1978] tainties in individual RC's are approximately log normally suggestedthat dip variations along South America may be distributed. The conclusionof Tovish and Scht•bert[1978] is caused by variations in slab age. Similarly, Barazangi and not changedby the presentstudy (R = 0.100 for DipS, R = lsacks [1979] suggestedthat the youth of the slab beneath -0.256 for DipD). Though Frank's [1968] relationship is Peru is one possiblecause of flat subductionthere. Jordan et clearlynot a primary controlon slabdip, the relationmay still al. [1983] indicated a possibleassociation between decreasein 268 JARRARD: RELATIONS AMONG $UBDUCTION PARAMETERS

SLAB DIP cidence.First, the hypothesizedLate Tertiary slab steepening inferred from patterns of andesitic volcanism [Coney and Reynolds,1977; Keith, 1978] appearsto be an artifact of lati- DIP = 41.7 + .167 x AGE - 2.27 x RATE tudinal sweep in the location of volcanism [Glazner and Supplee,1982]. Second,because of Benioff zone curvature 121•' ' '•' i:ß Chili e24 '•S. Chile18 (Figure 2), the physicalsignificance of averageBenioff zone 10[' NE Japanß % .... Kamchatka•©Peru16 03 / 27% ;•oß , ß38 u'O dip is not obvious.A more appropriate dip for comparison ß 47 Kuri•es ' ß ß ,.,t[ Tonkaa • --,- C' America•45 L;OIOITIDlal with locations of andesiticvolcanism is DipI, the averagedip •., 0•,,,,• Java '•Ox ß...... ,.;,, e34 / '• ß50Kermadec Sumat..r_a54 ...... • to 100 km. However, Table 6 shows that the correlations of LU6 55 • e36 ß17 DipI with As, V•, and Vcba are negligible.This decreasein •lzue'•8onin'•e•NewZealand Ryukyus Alaska quality of fit may be partly attributable to the increasein I--[-M•ri6a7nas ø"•,.5'O • -] number of subductionzones analyzed and improvedestimates n-41Ma.,,•anas •.NewHee51•rides• I of dip, V•, and As. Perhaps more important is the changefrom averageBenloft zone dip to DipI. 0 •:•'e2"n Thermal modelling of the flexural rigidity of the subducted 160 140 120 100 80 60 40 20 0 slab has been used to infer a different dependenceof DipI on AGE, m.y. convergencerate and slab age [Furlong et al., 1982], with greaterDipI resultingfrom slower V• or youngerAs. Based on Fig. 21. Observeddips for a subsetof modernsubduction zones, thermal modelling of each of 12 subductionzones, a different shownon a crossplot of total convergencerate versusslab age [Jar- rard, 1984]. Diagonallines indicate the regressionplane of predicted relationshipof dip to V• and As was found for six subduction dips. The good fit of observedto predicteddips seenhere is not zones with continental overriding plates than for six oceanic confirmedby the reviseddata of Table 1. ones. Furlong et al. [1982] find an overall correlation coef- ficient of 0.9 between observedand predicted dips. Becauseof the small number of subductionzones analyzed, a more rigid test of this hypothesisrequires thermal modellingof each sub- dip from North Chile to Central Chile and decreasingslab duction zone omitted from the original analysis.Such a test is age;they noted,however, that the evenyounger slab beneath not attempted here, partially becauseit has not been possible South Chile is not shallowlydipping. When all the subduction to successfullyreproduce shallow dips, initial effectiveelastic zones of Table 1 are considered,the correlationsbetween slab thicknesses,or even convergencerates for the examplesde- ageand both DipI and DipD are negligible(R < 0.3, Table 6). scribedby Furlong et al. [1982]. The hypothesizedeffect of convergencerate and slab age is not expectedto accuratelyfit ConvergenceRate and Slab Age the form of a regressionequation, but a good fit of DipI to the Increasein gravitational instability with slab age suggestsa productof convergencerate and slabage is predicted.Subduc- possiblemodification of the relation proposedby Luyendyk tion zones with continental overriding plates show no corre- [1970]: sin (dip)= k x As/V•,. This simple geometrical re- lation of DipI with •b, x As (R = 0.06), Vcba (R = 0.07),or As lationship indicatesthat the dip dependsonly on the amount (R = --0.08). Subductionzones with oceanicoverriding plates of sinking that accompaniesa given period of convergence showno correlationwith Vcba x As (R = -0.12) but fair corre- and that this sinking rate is proportional to slab age. How- lationswith As (R = -0.51) and Vc•a(R = 0.58).The apparent ever, no correlationof A•/V•. is found with either the sine of correlationwith Vc•ais the inverseof that predictedby the DipD (R = 0.14) or the sineof DipI (R = -0.24). A somewhat model of Furlonget al. [1982]. Similar correlationsare found similar relationship was suggestedby Ruff and Kanamori using• insteadof Vc•a.Thus no confirmationof the modelof [1980]. They noted that Benioffzone maximum depth is mod- Furlonget al. [1982] is found in the much larger data set of erately correlatedwith slab age and that maximum horizontal Table 1. extent of the Benioff zone is moderately correlated with con- vergence rate. ConvergenceRate, Slab Age, and Basedon the subductionzones tabulated by Ruff and Kana- Absolute Motion mori [1980], Jarrard [1984] found throughmultiple regression Crossand Pilger [1982] suggestthat slab dip is controlled that by four factors:absolute motion of the overridingplate, con- DipA = 41.7 + 0.17 x As- 0.23 x Rate vergencerate, slab age, and subductionof aseismicridges. The possibleinfluence of subductionof aseismicridges is discussed where DipA is the averagedip of the entire Benioff zone and in a subsequentsection. Cross and Pilger [1982] also suggest Rate is the convergencerate, not just the component perpen- that accretionplays a secondaryrole in modifyingshallow dicular to the trench, excludingback-arc spreading.This em- dip; accretiontoo is discussedin a subsequentsection. pirical relationship,with a correlation coefficientof 0.717, is In the model of Crossand Pilger [1982], both increased shown in Figure 2!. Jarrard [1984] tested this equation by convergencerate and decreasedslab age cause shallower dip, using Late Cretaceousand Tertiary variationsin As and Rate as in the modelsjust discussed.Absolute motion is also hy- for western North America [Engebretson,1982] to generate pothesizedto affectdip, with rapid trenchwardadvance caus- predicteddips. Comparisonof thesepredicted dips with those ing a shallowerdip throughoverriding of the subductedslab. independentlydetermined by Keith [1982], on the basis of A similareffect of advancingabsolute motion on shallowdip locations of dated andesiticvolcanism, shows a strong agree- was suggestedby Dewey[1980]. Both studiesinfer that re- ment (Figure 22). treating absolutemotion of the overriding plate has no effect Two lines of evidence indicate that this apparent confir- on dip. Lliboutry [1974] hypothesizedthat dip is dependent mation of the relationship of Jarrard [1984] is only a coin- on absolute motion and rate of vertical sinking. If vertical JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 269

PREDICTED DIPS & COMPRESSION 161 • 60. 50•- COMPARISONOF DIP ESTIMATES 50 /I 40- / / / /

30 */

20 - ee / / / - o • 2e 10 / / / / f I I I I 10 20 30 40 50 160 140 120 100 80 60 40 20 0 DIP (FROM VULCANISM) SLAB AGE (m.y.) Fig. 22. Application of the dip relationshipof Figure 21 to the predictionof Late Cretaceousand Tertiary dips for westernNorth America [darrard, 1984]. (Left) Changesin convergencerate and slab age from 90 m.y. to present,overlain on the regressionplane of correspondingdips; numbersin boxesare dips independentlydetermined by Keith [1978] based on dated arc volcanism.(Right) Cross plot comparingdips of Keith [1978] with predicteddips based on slab age and convergence rate.

sinking rate dependson convergencerate and slab age [En- Mantle Flow gland and Wortel, 1980], then the model of Lliboutry [1974] is Observed plate motions require net mantle flow from sub- similar to that of Crossand Pilger [1982], except that higher duction zones to ridges. Hager and O'Connell [1978] have convergencerate would causesteeper rather than shallower modelled global flow patterns based on current massfluxes at dip. ridges and trenches and three different sets of viscosity as- Cross and Pilger [1982] documentedthe possibleeffect of sumptions. Resulting flow directions at subduction zones can these three independentvariables through examination of re- be comparedwith descentangles of subductedslabs, based on gions in which only one of the three variables changes.For the assumptionthat deep dip is controlled by mantle flow. A example, a shallowingof dip from southwestMexico to south- good fit of observedto predicted descentangles can then be east Mexico may be attributable to the 1.3- to 1.4-cm/yr faster taken as an indication that deep dip is controlled by mantle convergencein the latter. The gradual dip shallowing from flow. north to south along the South Sandwich subduction zone Based on 10 subductionzones, Hager and O'Connell [1978] [Brett, 1977] may be attributable to the much younger litho- find that observeddeep dips correlate with dips predicted by sphere in the southern half of the slab than in the northern their "Cathies" model with a correlation coefficient of 0.91. half. Much shallower dips in Mexico compared with Nicara- The "Cathies" model has constant viscosity throughout gua may be related to the differencesin absolutemotion of the almost the entire mantle, with a narrow low-viscosity layer North American and Caribbean plates. just below the lithosphere.Their model effectively predicts An alternative approach to determining the importance of both the polarity of subductionand the amount of dip' thus these three variables to slab dip is multiple regression.With both seismicand predicted dips go from 0 to 180ø. For seven DipD as the dependent variable, absolute motion of the over- of the ten subductionzones considered, the overriding plate is riding plate (Voa)is the most important of these three possible continental,thereby precludingsubduction of the oppositepo- independent variables. With an F of 5.5, Voais marginally larity. For consistencywith other tests of causesof dip, it is significant and accounts for 19% of the observed variance in probably more appropriate to consideronly amount of dip DipD. Virtually zero (F < 0.1) residual correlation with con- rather than both polarity and dip. The correlation between vergencerate and slab age is found. The correlation with Voa Observedand Cathles predicted dips is then0.78. results almost entirely from the fact that South American sub- Two factors indicate that a revised analysis of the consist- duction zones have both a rapid advance in Voaand shallow dips;the Solomonsubduction zone, with a rapidadvance in ency of flow models with observed dips is warranted. First, Voaand the steepest DipD, conflictswith the SouthAmerican newer data on Benioff zone geometry changesome deep dips. For nine of the ten subductionzones, the deep dips of Table 1 data and substantially degradesthe correlation. The major are within 10ø of those used by Hager and O'Connell [1978]. difference between South American and Solomon deep dips For New Zealand the difference is 21 ø, because Adams and occurs despite generally similar convergencerates, slab ages, Ware [1977] showedthat the dip estimate of Ansell and Smith and absolutemotions of overriding plates. [1975] was biased by faster velocities in the slab. A more With DipI as the dependentvariable, all three of the varia- significantrevision is in the transformationbetween descent bles Voa,Vc, and As showvery low correlations;Voa, the bestof angle and deep dip. As discussed in the section on strain the three, has a correlation coefficientof only -0.160 (Table regime models and shown in Figure 15, Hager and O'Connell 6). It therefore appears unlikely that the primary controls on [1978] apparently incorrectly assumed that the rate of abso- either DipI or DipD are convergencerate, slab age, and abso- lute motion of the underriding plate is the same for the slab as lute motion of the overridingplate. for the unsubductedportion of the plate. 270 JARRARD.'RELATIONS AMONG $UBDUCTIONPARAMETERS

Correlation of the descent angles of Table 1 with predicted ridge collision and both uplift and deformation of the accre- descent angles based on the Cathies model yields correlation tionary prism (W. R. McCann and Haberman, unpublished coefficientsof 0.417 and 0.414 for the Chase [1978a] and Min- manuscript, 1986). Several authors have suggestedthat shal- ster and Jordan [1978] motion models, respectively.The fit is low dips along portions of the South American margin may much better for the constant mantle viscositymodel of Hager result from aseismic ridge subduction [e.g., Kelleher and and O'Connell [1978]: 0.742 and 0.724, respectively.Com- McCann, 1976; Barazangi and lsacks, 1979; Pilger, 1981; Pen- paring the two models by fit to individual subductionzones, nington,1981]. Evidencefor dip shallowingin other subduc- six of the ten show a better fit to the constant model, two tion zonesdue to aseismicridges is summarizedby Crossand show a better fit to the Cathies model, and two show approxi- Pilger [1982]. No evidencehas been found for anomalously mately equal fits. However, descentangles for two subduction steep subduction of the deeper slab in such regions; in fact, zones are highly tentative and not even shown in Table 1. only below 60 km does the anomalouslyshallow subduction Estimated descentangles for New Hebrides (114ø for Chase of Peru and Central Chile becomeevident. Thus a major dis- [1978a]; 118ø for Minster and Jordan [1978]) are highly de- crepancyappears to exist betweenexperimental geochemistry pendent on the uncertain velocitiesfor this region, though a and the hypothesizedeffect of aseismicridges on slab dip descentangle of > 90ø seemslikely. The descentangle of 6ø below 60 km. Crossand Pilger [1982] suggestthat either the usedfor Peru assumesa deep dip of 5ø; this dip determination transformation to eclogitedoes not occur for aseismicridges requires a relaxation of the requirement that deep dips be or the aseismicridge is shearedaway from the slab. However, .measuredfor portions of the slab deeperthan 150 km. suchshearing would presumablyoccur above 60-100 km and Most analyses indicate that a constant viscosity mantle is less likely than a mantle with a low-viscosity asthenosphere would still leave an anomalouslythick crustal root. [e.g., Richter and McKenzie, 1978]; the correlation coefficient In summary, aseismicridge subduction probably has a sub- of 0.4 between observed and predicted dips suggeststhat stantial impact on the accretionary prism. Effects on both mantle flow is not the primary control on deep dip. An analy- intraplate and interplate earthquakes have also been amply ,is of more than ten subduction zones seems warranted, but demonstrated [Kelleher and McCann, 1976; Barazangi and such an analysisis not possiblefrom the figures shown by lsacks, 1979]. A possiblerole of aseismicridge subductionin modifying slab dip has been demonstrated.However, quanti- Hager and O'Connell [1978]. tative evaluation of this effect must await reconciliation with The flow models of Hager and O'Connell [1978] do not experimental geochemicaldata and isolation of the factors includethe possibleeffect of densitycontrast of the downgo- controllingdip of normal oceaniclithosphere. ing slab on either flow or slab dip. Tovish et al. [1978] mod- elled corner flows associated with the slab and found that Accretion,Arc Age, and Mantle Flow pressuresinduced by flow generally act to lift the slab, off- The uppermost portion of the Benioff zone may be flattened settingthe tendencyof gravity to make the slab vertical.As by an accretionary prism [Karig and Sharrnan,1975; Karig et dip is decreased,a dip is reachedbeyond which these pressure al., 1976]. Gravity modelling indicates that the load of the forcescannot be balancedand the only stableconfiguration is accretionaryprism is sufficientto depressthe overriding plate a dip of about zero.This may explainthe lack of dipsbetween [Karig et al., 1976], thus modifying both Dips and DipI. Ac- l0 ø and 25ø [Tovish et al., 1978]. Further, this result implies cretion cannot be the only factor affecting shallow dip, as that the substantial dip variation along South America may substantialdip variationsoccur even among subductionzones not reflect much differencein whateverfactors primarily con- with virtually no accretionaryprisms. trol dip. Karig et al. [1976] tabulated the widths of accretionary prisms for many subduction zones. However, recent DSDP Aseismic Ridges sitesin forearcsoften yieldedsurprising and major revisionsin the widths of accretionaryprisms [e.g., yon Huene, 1984]. Un- Subductionof aseismicridges is occurringor about to occur fortunately,only a few forearcshave beendrilled as yet. In the at several of the subductionzones consideredin this study: absenceof either deepdrilling or very high quality multichan- Roo Rise (Java), Izu-Bonin Ridge (southwestJapan), Pratt- nel profiling, estimationof the location of the transition from Welker Chain (Alaska Peninsula), Carnegie Ridge (Ecuador), crust to accretionaryprism is often hazardous.Consequently, Nazca Ridge (Peru), San FernandezRidge (Central Chile), and no estimatesof width of the accretionaryprism are includedin Tiburon Ridge (LesserAntilles). Aseismic ridges are also sub- Table 1. ductingseveral hundred kilometers away from the transectsof Nevertheless,it appears safe to concludethat certain sub- Table 1 for somesubduction zones: Louisville Ridge (Tonga- duction zones have particularly wide accretionary prisms: Kermadec), Oki-Daito Ridge (Ryukyu), Marcus-Necker Sea- Alaska [Jacob et al., 1977], Alaska Peninsula [Jacob et al., mounts (Izu-Bonin), and Emperor Seamounts(Kamchatka). All of these ridges are likely to have greater than normal 1977], Makran [Farhoudiand Karig, 1977; White, 1979], New crustal thicknesses[Kelleher and McCann, 1976; Derrick and Zealand [Katz, 1982], North Sulawesi [Silver et al., 1983a], Watts, 1979]. Kelleherand McCann [1976] suggestedthat the Java-Sumatra-Andaman[Hamilton, 1979], Kamchatka [Dick- increased crustal thickness of aseismicridges decreasesthe inson, 1973], LesserAntilles [Bqu-Duval et al., 1981], south- gravitational instability of the slab, thereby decreasingslab west Japan, Aegean, and Cascades.Examination of Table 1 dip. At a depth of about 60 km the basalt of oceaniccrust showsthat thesesubduction zones are consistentlylower in undergoesa phase transformation to eclogite [Ahrens and both Dips and DipI than nearly all other subductionzones; Schubert,1975], with a correspondingmajor increasein den- low-accretionPeru and possiblylow-accretion South Chile sity. Therefore aseismicridge subductionis predictedto cause are notable exceptions.No correlation of the high-accretion a shallowing of dip above 60 km and a steepening of dip subductionzones with DipD is expectedor observed.Because below 60 kin. accretionaffects shallow dip but is difficult to quantify, sub- The effect of aseismicridge subductionon the accretionary duction zoneswith higher accretionare omitted from subse- prism is dramatic, with a strong associationbetween aseismic quent regressionsin which DipI is the dependentvariable. It JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 271

TABLE 10. Dip Regressions

F Ratios

Velocity First Second RegressionEquation Comment* Source•' Regression Variable Variable R 2 R

DipD = 32.3 + 0.939 x Dipi$ 1 ß.. 16.8 ...... 0.412 0.642 DipD = 46.4 + 0.604 x DipI - 0.0653 x A a 1 ß.. 13.6 6.1 6.5 0.542 0.736 DipD = 34.2 + 0.838 x Dipi- 1.21 x Voa 1 M 11.4 14.2 3.9 0.498 0.706 DipD- 31.6 + 0.972 x DipI 2 ß.- 16.9 ...... 0.424 0.651 DipD = 37.3 + 0.814 x DipI 3 ß.. 13.6 ...... 0.392 0.626 DipI - 35.2- 0.081 x A• 1 ß.- 22.1 ...... 0.538 0.733 DipI = 41.7- 1.64x (A,O•/2 1 ß-- 31.8 ...... 0.626 0.791 DipI = 42.8- 1.92x (A•)a/2$ 4 ß.- 64.3 ...... 0.791 0.889

*Comment 1: all possibledata used in correlations;equivalent to deleting subductionzones with missingdata when only one term in regression.Comment 2: delete New Britain. Comment 3: delete South America; eliminatesall correlation with Vo•.Comment 4: delete Colombia and Middle America. •'M, Minster and Jordan [1978]. Revisedas indicated in text. $Preferredmodel. should be noted, however,that an appreciableeffect of accre- With DipD as the dependentvariable, both DipI and arc tion on DipI is probable even among the nominally "low age show approximatelyequally high correlations(0.64 and accretion" subduction zones. This currently unknown accre- -0.65, respectively).No other potential independentvariable tion contribution is expectedto degrade the quality of fit of of Table 1 showsa significantprimary correlation with DipD. DipI to any other factorsthat control dip. However,the quality of fit of DipD to DipI and arc age is Dickinson[1973] compiled estimatesof arc-trench gap and comparable to the fit achieved for a small subset of subduc- arc age for many of the subductionzones of Table 1. He found tion zonesby the constant-viscositymantle convectionmodel an approximately linear relationship between the two vari- of Hager and O'Connell[1978]. Arc ageis unlikelyto directly ables and concludedthat arc-trench gap tends to increaseat a affectDipD; more likely,arc ageaffects DipI, and the trajec- rate of about 1 km/m.y. A similar pattern of increasingarc- tory initiated by DipI has a strong impact on DipD. With trench gap with time is often found within individual subduc- DipI as the primary independentvariable, there is a small tion zones [Dickinson,1973]. A combination of accretionand residualcorrelation with arc age, but this residualcorrelation retrogrademotion of the arc (of unknowncause) was suggest- is entirely attributable to South American subduction zones ed as the factors causingthis relationship. (Table 10). Because arc volcanism nearly always occurs above the In summary,regression analysis indicates that the primary portion of the Benioff zone that is about 125 km in depth, factorscontrolling average dip to 100-km depth (DipI) are arc-trench gap bears a very close relationship to DipI accretionand duration of subduction(i.e., arc age).A gradual (R =-0.824, and R = 0.907 for 1/tan (DipI)). If the corre- shallowingof DipI with time is predictedfor most subduction lation betweenarc-trench gap and arc age is significant,then zones, becauseduration of subductionwill always increase either (1) arc age affectsarc-trench gap, which affectsDipI, or with time (unlessarc polarity reversaloccurs) and accretion (2) arc age affectsDipI, which affectsarc-trench gap. The latter will usuallyincrease with time (thougherosion may occur). seemsmuch more plausible. Becausethe width of the accretionaryprism is often unknown, When multiple regressionis applied to prediction of DipI a singleregression equation combiningthe two effectsis not for the subset of subduction zones with "low" accretion, the attempted.Deep dip is probably a result of DipI and mantle most significantcorrelation is with arc age (Aa).The resulting convection:the slabtrajectory established at shallowdepths is regressionequation (Table 10),with a correlationcoefficient of modified at greater depth by mantle flow patterns.Because -0.73, accountsfor only 53% of the variance in DipI. With estimatesof presentmantle flow patternsare highlydependent the exceptionof Dips and DipD, no other potential indepen- on viscosityassumptions, it is not currentlypossible to reli- dent variable showsa significantcorrelation with either DipI ably establishthe impact of mantle flow on DipD or includeit or regressionresiduals. The relationshipbetween DipI and Aa with DipI in a regressionequation predicting DipD. may not be linear; a better fit is observedfor the squareroot Other variablesoften considered to affectslab dip (e.g.,con- of •l a (Table 10 and Figure 23). Seventy-ninepercent of the vergencerate, slab age,and absolutemotion of the overriding variancein DipI for "low-accretion"subduction zones is ac- plate)do not showany systematicrelationship to either DipD counted for by a regressionon the squareroot of arc age, if or DipI. A subsidiaryrole of one of thesevariables cannot be two anomalouspoints (Colombia and Middle America) are excluded,however. It was not possibleto combinearc age and omitted. accretionin a singleequation to predict DipI, nor to combine The conclusionthat arc ageis the primaryvariable of Table DipI and mantle flow in a singleequation to predict DipD. 1 affectingDipI is unchangedif all subductionzones are con- Thereforethe possibilityof a significantresidual correlation to sidered,rather than just the "low-accretion"subduction zones. another variable could not be fully investigated. The correlation coefficientis degradedfrom -0.73 to -0.54, The mechanismfor a decreasein dip with increasingdura- because variance in DipI associatedwith accretion is no tion of subductionis not known with certainty.Gradual thin- longer even partly removed.With the exceptionof Dips and ning of the lithosphereof the overridingplate with time is DipD, regressionresiduals show very low correlationwith all implied. Whether this thinning is a result of active abrasion other possibleindependent variables. [Smith,1976] or of frictionalheating [Dickinson, 1973] is diffi- 272 JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS

ß

30- ß • -

t-- o ß ß '• o ß • c• •0- o ß I.l.i O ß •: o ß

i,i _

Z • O 10 o

i i i i SO • ISO ZOO ZSO DURATION OF SUBDUCTION (m.y.) Fig. 23. Crossplot of intermediateslab dip wrsusduration of subduction,as indicatedby maximumage of arc-related rocks.Solid circlesare subductionzones with narrow or moderatea

cult to determinewithout a better knowledgeof the shear plate.Possible contact within the depthrange from about60 stressesand strengthof the overridingplate. In the very old km to the baseof the overridingplate is not determinable, arcsof South America,active erosion of the overridingplate is becausethese depths are belowthe brittle/ductiletransition in required by the fact that the oldest arc is at or seawardof the the overridingplate. presentcoast [James, 1971]. This erosionaffects even the up- Jischke[1975] examinedthe physicsof stresses-involvedat permostpart of the SouthAmerican overriding plate and does thecontact between plates and concluded that nonhydrostatic notnecessarily imply erosion-related shallowing of dip. pressure force and Viscousshear force are sufficient to main- The better regressionfit achievedby the squareroot of Aa, tain contactdown to the baseof the overridingplate. Flexural comparedwith a linear fit to Aa,suggests that gradualheating rigidityof the slabwill alsoact to minimizedip and maintain of the overridingplate may be the primary factor causing contact.However, our knowledgeof someforces acting on the shallowingof dip with time. The temperatureof the top sur- slabis insufficientto permit reliabledetermination of the rela- face of the slab is independentof slab age upon enteringthe tivemagnitudes of all forces.The empirical correlation of DipI trench, and the slab acts as a heat sink rather than a heat with accretion and arc agesuggests that the dominantforces sourcewithin the zone of contact with the overridingplate are buoyantat depthsless than the baseof the overriding [FUrlonget al., 1982]. Thereforethe causeof heatingof the plate. Apparently, horizontal forces associatedwith conver- overridingplate is likely to be friction at the interfacebetween gencerate and verticalforces associated with age-dependent platesrather than heat from within the slab.Consequently no negativebuoyancy of the slabare insufficientto affectDipI, correlationbetween DipI and slab age is expected.However, thoughthey can affect both earthquakemagnitude and stress subductionof a spreadingcenter is expectedto involve accel- in the overridingplate. eratedheating of the overridingplate and thereforeanoma- A gradualshallowing of DipI is usuallybut not invariably lously shallow DipI. Unfortunately,ridge crest subduction accompaniedby an increasein arc-trenchgap. In New Zea- alsoimplies little or no Benioffzone, so that this predictionof landthe arc hasmoved seaward during the Neogene[Kamp, the model is not readily testable. 1984]. Similarly,a major Laramidelandward migration of This modelfor DipI is very differentin mechanismfrom volcanismin westernNorth Americawas followed by a swing modelsdiscussed in precedingsections. All of the previous back toward the trench [e.g., Coneyand Reynolds,1977; models(e.g., V•, A s, Vo•,and aseismicridges) implicitly treat the Keith, 1978]. In both cases,near-horizontal.subduction of the cross-sectionalshape of the overridingplate as a point in- Portionof the slabdeeper than about 80-100 km apparently denter.In contrast,if accretionand arc agecontrol DipI, then occurred.Thus the generalvalidity of the DipI andDipD the slab mustfollow the leadingedge of the overridingplate, relationsmay not be invalidatedby theseobservations; the regardlessof other forcesacting on the slab.Earthquake epi- subhorizontal slab could result from the combination of shal- centers strongly suggestthat contact is usually maintained lOwDipI and mantle flow. In Newzealand the shallow DipI down to at least 60-km depth. The difficultyin precisely1o- presumablyresulted primarily from the very wide sedimentary caringthe top of the slab at shallowdepths is a consequence prism,because the subductionwas newly established. In con- of this contactand resultantearthquakes within the overriding trast, Laramide subduction beneath western North America JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS 273

9O

8O

7O ß ß

ß ß ß ß ß ß

C3 40

aJ 30

2O

10

i i i i 50 tO0 150 200 250 DURATION OF SUBDUCTION (rn.y.) Fig. 24. Crossplot of deepslab dip versusduration of subduction.The crustaltype of the overridingplate is indicated by trianglesfor continentalcrust, squares for transitionalcrust, and circlesfor oceaniccrust. Open symbolsindicate less reliabledata than solidsymbols. Subduction zones with continentaloverriding plates have generally shallower deep dips than thosewith oceanicoverriding plates, probably because they are older. occurred beneath an old arc with an accretionaryprism of continental overriding plates had a mean DipD of 53ø, while unknown width. thosebeneath oceanic overriding plates had a mean dip of 65ø. The Laramide and New Zealand exampleshighlight an The mantle down to about 400 km exhibits systematicdiffer- oversimplificationof the model. The 100-km depth selection encesin shear velocity betweenoceanic and continental litho- for DipI does not have a unique physical significance;it is sphere [Sipkin and Jordan, 1980]. Furlong et al. [1982] hy- merely a compromisebetween the 100- to 150-kin depth of pothesize that the differencesin DipD may indicate that origin of arc volcanism and the 50- to 100-km thicknessof mantle material propertiesaffecting DipD may also differ be- overridingplates. Unfortunately, the thicknessof the overrid- tween suboceanic and subcontinental mantle. ing plate is usuallynot accuratelyknown. One would expect, The differencein DipD for slabs beneath continental and however,that the baseof the overridingplate is the depth at oceaniclithosphere is confirmedby the larger number of sub- which accretionand duration of subductioncease controlling duction zonesin the presentstudy. Only one subductionzone dip and mantle flow begins to have an effect. Dip change with a continental overriding plate (Middle America) has a above the base of the overridingplate may be possibleonly deep dip steeperthan 55ø; crustal type in the Nicaragua por- when the overridingplate is graduallyheated or abraded. tion of Middle America is not known with certainty. Only one The apparent associationbetween paleogeographyand subductionzone with an oceanicoverriding plate (LesserAn- both low-angle subduction and segmentation in South tilles) has a deep dip shallower than 55ø. The median DipD America may be speculativelyexplained by the DipI and beneath continental overriding plates (40.5ø ) is much lessthan DipD models above. Duration of the present period of the median DipD beneathoceanic overriding plates (66ø). Andean subduction is constant from Peru to South Chile. The difference in DipD for slabs beneath continental and However, the variable Paleozoic subduction and structural oceanic lithospheredoes not necessarilyimply a differencein historiesin the four segmentsmay have permittedvariations sublithosphericmantle properties.Instead, the differencemay between these segmentsin amount of late Mesozoic and Ce- be an artifact, causedby differencesin duration of subduction nozoic abrasionof the overridingplates. The result is slight betweencontinental and oceanicsubduction zones. In the pre- differencesin DipI. As Tovishet al. [1978] have shown,there cedingsection we showedan apparent dependenceof DipI on may be a critical dip beyondwhich pressureforces cannot be accretion and duration of subduction and dependence of balanced and near-horizontal subduction occurs. Because of DipD on DipI and mantle flow. Thus DipD also correlates the long duration of subduction(and thereforeabrasion) and with duration of subduction (Figure 24), though this corre- the landward mantle flow beneath South America, these sub- lation does not imply a primary causal relationship.Because duction segmentsmay be near the critical dip. Such specu- duration of subduction is greater for nearly all continental lation is hazardous,however; it must be rememberedthat the overriding plates than for oceanicones, deep dips are gener- preferredmodels for dip are neither as quantitative nor as ally shallower beneath continental plates (Figure 24). The ex- successfulas modelsfor someother subductionparameters. cellent correlation betweenDipD and crustal type in the over- riding plate thereforemust be treatedwith caution. Crust of OverridingPlate In an examinationof DipD for 16 subductionzones, Fur- Tm•NCH DE?TH MODELS long et al. [1982] noted a possiblecorrelation between deep Maximum trench depth is stronglycorrelated with regional dip and the crustaltype in the overridingplate. Slabsbeneath seafloor depth away from the trench [Grellet and Dubois, 274 JARRARD.' RELATIONS AMONG SUBDUCTION PARAMETERS

R =.TT

-1-

z i,i

i,i

I I I I I I 2_. 3 4 5 6 PREDICTED RELATIVE TRENCH DEPTH (Km)

from- Ad=-.81+.0185 x As + ß .0816 x Dip]: Fig. 25. Comparisonof relativetrench depths with thosepredicted from a regression(Table 11) in whichthe indepen- dent variablesare slab age and intermediatedip.

1982; Hilde and Uyeda, 1983]; this obviouscorrelation is re- suggestthat marginal basin subductionmay result in anoma- moved by analyzingonly relative depth (Ad), the difference louslydeep trenches because of compensationof nonequilibra- betweenmaximum trenchdepth and regionalcrustal depth. ted subductedlithosphere within the mantle of theseregions. Causesof variations in Ad have only recently been investi- Statisticalanalysis of the larger number of subductionzones gatedin detail.Meiosh [1978] and Grellet and Dubois [1982] of Table 1 confirmsthe correlation of Ad with both slab age correlated trench depth with convergencerate. Grellet and (R = 0.57) and total subduction rate Vcba (R--0.45 for the Dubois[1982] found that trenchdepth changes along 8 of 11 models of both Minster and Jordan [1978] and Chase subductionzones showed positive correlationswith conver- [1978a]). Relative tren.chdepth is also moderatelycorrelated gencerate changes,though regression coefficients were quite with intermediate slab dip (R = 0.52). As suggestedby Hilde different for different subduction zones. They also found a and Uyeda [1983], the correlationwith subductionrate arises correlation betweenAd for eight subductionzones and con- largely or entirely from the correlation between slab age and vergencerates. Both Melosh[1978] and Grelletand Dubois subduction rate. When the slab age correlation is accounted [1982] suggestthat this correlationmay result from viscous for by stepwiseregression, the residualcorrelation with Vcba is flow in the lower lithosphereof the subductingplate. Hilde degraded (R =0.32 for the Minster and Jordan model; and Uyeda [1983] suggestan alternativeexplanation for this R = 0.29 for the Chase model) while the residual correlation correlation:age of the subductingslab affectsboth Ad and with DipI is improved to 0.61. When both As and DipI are convergencerate. Thus the correlationof Ad with convergence then includedin the regression,the residualcorrelation to Vcba rate is interpretedby them as simplyanother confirmation of is insignificant(R--0.07 for the Minster and Jordan model; the effectof slabpull on convergencerate [Forsythand Uyeda, R = 0.14 for the Chase model). Other possibleindependent 1975; Carlson et al., 1983]. variablesshow no significantcontribution to Ad. A strong correlation has been found betweenmaximum Stepwiseregression therefore indicatesthat relative trench trench depth and age of the slab at the trench [Grellet and depth (Ad) is affectedby slab age at the trench and the dip of Dubois, 1982; Hilde and Uyeda, 1983]. Grellet and Dubois the interfacebetween overriding and underridingplates (DipI). [1982] fit a curve to all subductionzones analyzed. In con- An increasein either As or DipI appearsto causean increase trast,Hilde and Uyeda[1983] fit a straightline to half of their in Ad. The overall correlation coefficientis 0.77 (excluding subduction zones and consider the other half to be anoma- subductionzones with missingdata), indicatingthat thesetwo lous. Most of these anomalous subduction zones are subduct- independentvariables account for 60% of the variancein Ad ing lithosphereof marginalbasins. Hilde and Uyeda [1983] (Figure 25). Hilde and Uyeda [1983] have suggestedthat sub- JARRARD' RELATIONS AMONG SUBDUCTION PARAMETERS 275

z LLI ß o

LU 2

o ß

IO 2o ;50 SLAB PULL FORCE (1012N/m) Fig. 26. Comparisonof relative trench depth with local slab pull force; the latter is calculatedfrom slab age, conver- gence rate, and deep dip as describedin text. Solid symbols,based on more reliable data than open symbols,are subduction zones used for determination of correlation coefficient.

duction of marginal basin lithosphere is associated with matesof physicalconstants, anomalouslydeep trenches.No suchrelationship is indicated Fs = KlS3Vcbasin (DipD)[1 - exp(Kz/SZVcba sin (DipD))] by Figure 25; nor is it evident in the analysisof Grellet and Dubois [1982]. This discrepancyis attributable to variations whereV•, a is in km/m.y.,K1 = 2.37 x 106, K 2: - 1.74x l0 s, in crustalages assumed by differentinvestigators. and S is the thicknessof the lithosphere,determined from The heightand wavelengthof the outer rise of the subduct- ing plate are well fit by a simpleelastic flexural model, partic- S - 8.19(As)•/2 ularlywhen effective age of the lithospher•is consideredin- for As < 70 m.y., or steadof true age [McNutt, 1984]. Effectiveage, which can be S = 91.3 - 74.9 exp (-A•/62.8) estimated from basementdepth, is often less than true age becauseof lithosphericreheating. Relative trench depth might for A > 70 m.y. Englandand Wortel [1980] do not include also be expectedto be flexurally controlled.However, the ob- back-arcspreading rate in convergencerate. Becausethe criti- servedpositive correlation between Ad and .dsis the opposite cal velocityparameter is verticalsinking rate into the mantle, of the inverse relationship expectedfrom a simple flexural V•a is consideredhere to be more appropriatethan V•. model. Hilde and Uyeda [1983] suggestthat this apparent Accuratedetermination of Fs is not possible,due to major contradiction is explicable in terms of variations between uncertaintiesin many physical parametersrequired for the trenchesin amount of effectiveload on the subductingplate. determination of K• and K2. Nevertheless,the equations The effectiveload on the plate includesboth the load due to abovepermit a generalestimation of the relativemagnitudes the overridingplate and that due to the slab pull. Only if the of trenchpull amongdifferent subduction zones. Based on the effectiveload is relatively constant in different trenchesis an valuesof V•a, DipD, and .ds in Table 1, calculatedslab pull inverserelationship between Ad and slab age expected.If re- forcesare plotted as a function of Ad in Figure 26. The corre- gional variations in slab age causemuch larger variations in lation between the two is better than the correlation between slab pull force than in flexural rigidity, then a positive corre- Ad and .ds and similar to the regressionof Figure 25. The lation betweenAd and slab age can result [Hilde and Uyeda, hypothesisthat trench depth is directly correlatedwith slab 1983]. pull [Hilde and Uyeda, 1983] is thereforeconsistent with this The slab pull force per unit length of trench segment(Fs) analysis. was derivedby Richterand McKenzie [1978] and modifiedfor Slab pull forceon the portion of underthrustingplate at the a nonverticaldip of the slab by England and Wortel [1980]. trenchaxis is directednearly parallel to the slab and therefore Following England and Wortel [1980] and using their esti- subhorizontally.A more relevantforce to the effectiveload on 276 JARRARD: RELATIONS AMONG SUBDUCTION PARAMETERS

R = .84

5

4

ß o

o ß 2 -- ß ß ß

o ß ß

1

2 4 6 8 10 12 14 Fssin(DipI) (1012N/m) Fig. 27. Comparison of relative trench depth with vertical componentof the slab pull force at the interfacebetween plates. The latter is calculatedfrom slab age, convergencerate, deep dip, and intermediatedip as describedin text. Solid symbols,based on more reliable data than open symbols,are subductionzones used in regression(Table 11). Note the similarity to Figures25 and 26 but smallerdispersion than either. the slab may be the vertical componentof slab pull beneath (variables)were determinedfor each of 39 modern subduction the overridingplate. This verticalforce, which is equal to the zone segments.Not all parametersare known for every sub- productof Fs and sin (DipI), is plottedas a functionof Ad in ductionzone. Stepwiseregression analysis was applied to por- Figure 27. The correlationcoefficient of 0.84 is substantially tions of this data set,in order to determineempirical quantita- better than that for the stepwiseregression above. This corre- tive equationsindicating the most likely cause-and-effectre- lation is consideredto be very good, in view of the fact that lationships.Table 11 summarizesthe final empiricalequations individual estimatesof vertical componentof trench pull are which result from this analysis.Published models were tested subjectto the combineduncertainties of physical"constants" primarily through regression,but also through a comparison and four variables:Vcba, As, DipI, and DipD. of model-based predictions with the observed variations Althoughvertical component of trenchpull is influencedby amongsubduction zones. This analysisis not meant to substi- Vcba,As, DipI, and DipD, it is stronglydominated by As and tute for theoretical analyses,but to complement them and DipI. Thus the stepwiseregression (Figure 25) and physical perhapsfocus them. model (Figure 27) are consistent.We concludethat relative A surprisingresult of this analysisis that most of the depen- trench depth is controlledby flexure of the underthrusting dent variablesare accountedfor by one or more of only three plate. Variationsin relativetrench depth arise primarily from independentvariables: convergence rate (Vc or Vc•a),slab age variationsin the loading effect of the verticalcomponent of (As or At), and intermediatedip (DipI). Though absolutemo- the trenchpull forcebeneath the overridingplate. tions of the overriding and underridingplates were included For regions with wide accretionaryprisms, this loading as potential independentvariables in all stepwiseregressions, effectis generallyconcealed beneath the accretionaryprism. In only one possiblysignificant relationship was found: a corre- suchregions the trenchaxis is only slightlyloaded by accre- lation of absolutemotion with strain regime.Duration of sub- tionary prism; the near-horizontalslab there has negligible duction (Aa) only affects one dependent variable, DipI. The vertical componentof slab pull. Most of theseregions have dominance of convergencerate, slab age, and DipI has two already been excludedfrom Table 1 and the analysisabove implicationsfor future research:(1) developmentof theoretical becauseof the dominatinginfluence of sediments. physical models will be aided by the knowledge that these three independent variables are the primary factors control- CONCLUSIONS ling subductioncharacteristics; and (2) if valuesfor the depen- Modern subduction zones constitute a rich data source for dent variablesare known for a subductionzone, the indepen- the determination of relations among subductionparameters. dent variables can be estimated by solution of simultaneous Based on a detailed review of the literature, 26 parameters equations. JARRARD'RELATIONS AMONG SUBDUCTION PARAMETERS 277

TABLE 11. PreferredEmpirical Models

F Ratio

Variable First Second Third Predicted RegressionEquation Comment* Regression Variable Variable Variable R 2 R

Slab L s = 302.9+ 0.0671 x V, x At 1, 2 156.6 156.6 ...... 0.858 0.926 length Ls = 396.6+ 0.0669x V• x At - 3.91 x DipI 1, 2 89.8 174.6 4.1 '.. 0.878 0.937 Earthquake Mw'= 8.01-0.0105 x As + 0.159 x V, 14.5 19.6 17.0 ... 0.605 0.778 moment Strain strain= 5.19+ 0.464x V, - 0.122x DipI - 0.021x As 25.1 34.5 21.9 16.4 0.774 0.880 class Interme- DipI = 42.8- 1.92x (Aa)•/2 3 64.3 64.3 ...... 0.791 0.889 diate dip Deep dip DipD = 32.3 + 0.939 x DipI 4 16.8 16.8 ...... 0.412 0.642 Arc-trench gap = 51. + 81.4/tan (DipI) 147.7 147.7 ...... 0.822 0.907 gap Trenchrelative Ad = -0.81 + 0.0185x As + 0.0816x DipI 15.4 18.7 13.3 '-' 0.595 0.772 depth Ad - 0.36+ 2.87x 10-•3 x Fs x sin(DipI) 60.4 60.4 ...... 0.707 0.841 *Comment1' deleteNE Japan.Comment 2' forunits consistency within this equation, velocities are in km/m.y.;all othervelocities in this tableand text are in cm/yr.Comment 3' deleteall subductionzones with wide accretionary wedges; also delete Colombia and Middle America. Comment 4: also possiblecorrelation with mantle flow.

An excellentcorrelation (R = 0.93) is found betweenBenioff affectedby slab age and intermediateslab dip. The vertical zone length and the productof slab age and convergencerate. componentof the slabpull foi'cein the vicinityof a trenchis On the basis of a conductiveheating model, Molnar et al. dominatedby thesetwo variables.This verticalforce, in con- [1979] predictedsuch a correlation' however,the present junctionwith the load of the overridingplate, determines the analysis results in substantial modification of their relation- flexuraldeflection of the underridingplate and therebythe ship.Slab heatingis muchslower during passage beneath the depth of the trench. accretionaryprism and overridingplate than when the slab is Developmentof empiricalequations for the predictionof adjacent to deepermantle. This equation can be Usedto esti- intermediateand deepslab dip is hamperedby limitedknowl- mate either slab age or convergencerate, when the other vari- edgeof two keyvariables' width of theaccretionary prism and able and slab length are known. Significantsecond-order ef- mantleflow patterns. Nevertheless, intermediate dip is clearly fects on Benioff zone length may result from width of tlie stronglydependent on widthof the accretionaryprism. When accretionaryprism, trench rollback rate, and slabdip. subductionzones with moderateto narrow accretionary Uncertaintiesin determination of forces acting on both prismsare analyzed,a dependenceof intermediatedip on du- overriding and underridingplates have preventedsimilarly ration of subduction is found. The correlation coefficient precisetheoretical analyses of strainand strike-slipfaulting in (R = 0.71) is degradedby two factors'(1) variableaccretion the overridingplate, maximum earthquakemagnitude, and amongthe subductionzones used and (2) uncertaindurations slabdip. The strainregime of the overridingplate cannoteven of subductionfor manysubduction zones. Intermediate dip be accuratelyquantified. However, one can classifyindividual shallowswith increasingduration of subduction,due to abras- subductionzones into one of sevenstrain classes,along a ion and/orheating of the overridingplate. Arc-trench gap is continuumfrom stronglyextensional (back-arc spreading) to almostentirely controlled by intermediatedip. Deep slab dip stronglycompressional (active folding and thrusting).Stepwise is affectedby themantle trajectory established by intermediate regressionindicates that these semiquantitativestrain classes dip (R = 0.64),but this trajectoryis probablymodified by can be accountedfor with an accuracyof about + 1 class mantleflow patterns.Unfortunately, mantle viscositiesare not (R = 0.88) by the combined effect of three variables' conver- known with sufficientprecision to permit reliableestimation gencerate, intermediateslab dip, and either slab age or abso- of mantleflow patternsfor all subductionzones. Stepwise lute motion of the overridingplate. Other observationssug- regressionindicates that convergencerate, slab age, and abso- gest that slab age, not absolutemotion, is the third variable. lute motion of the overridingplate have little or no direct However, data from modern subduction zones cannot unam- effecton slabdip. biguouslyisolate this third variable. The studyof strike-slipfaulting in the overridingplate is Convergencerate and slabage affect strain regime through less amenableto regressionanalysis. Nevertheless, several their effecton couplingbetween plates. This effectis confirmed physicalinsights result from a globalsurvey of strike-slip by a high correlation(R = 0.78) of maximum earthquake faultingbehind subduction zones. The combination of oblique magnitudewith the combinationof convergencerate and slab convergenceand strongcoupling between overriding and un- age [Ruff and Kanarnori,1980]. The physicalmechanism of derridingplates causes the developmentof sliverplates, with intermediatedip affectingstrain regime is less certain; two iheforearc separated from the remainder of theoverriding possibilitiesare (1) stressin the overridingplate dependson plateby a zoneof arc-parallelstrike-slip faults. Modern offset the contactarea betweenplates, which is proportionalto in- directionsare nearly always consistentwith the senseof termediatedip, or (2) intermediatedip affects the astheno- obliqueconvergence, and strike-slipfaulting is almostexclu- spheric return flow and therefore affectsshear traction on the sivelyconfined to compressive(strain classes 5-7) subduction baseof the overridingplate. zones.The locationof thestrike-slip fault(s) is generallyalong Relative trench depth, the difference between maximum the arc, whichis the portionof ihe overridingplate that is trenchdepth and depthof the nearbyabyssal plain, is strongly weakestdue to highthermal gradient, thin lithosphere,and 278 JARRARD'RELATIONS AMONG SUBDUCTIONPARAMETERS thick crust. Two thirds of modern subduction zones with an Allmendinger,R. W., V. A. Ramos, J. E. Jordan, M. Palma, and B. L. overriding plate composedof continental crust exhibit active Isacks, Paleogeography and Andean structural geometry, north- west Argentina, Tectonics,2, 1-16, 1983. strike-slip faulting near the arc, while only one fifth of oceanic Alvarez, W., D. V. Kent, I. Premoli-Silva, R. A. Schweickert, and R. overriding plates have similar faulting. The mr/ch more A. Larson, Franciscan Complex limestone deposited at 17ø south common occurrenceof strike-slip faulting in continental litho- paleolatitude, Geol. Soc.Am. Bull., 91, 476-484, 1980. sphere than in oceanic lithosphere is a consequenceof the Ansell, J. H., and E.G. C. Smith, Detailed structure of a mantle greater strengthof oceaniclithosphere. Once a strike-slipfault seismiczone using the homogeneousstation method, Nature, 253, 518-520, 1975. hasbeen established due to obliqueconvergence, subsequent Aoki, H., Pressureeffects on the deformation of slabs descending stressis readily accommodatedalong this zone of weakness, below island arcs,J. Seisrnol.Soc. Jpn., 27, 110-119, 1974. resulting in dip-slip, reverse faulting, and transpressionalor Arabasz, W. J., Geological and geophysicalstudies of the Atacama transtensionalfaulting. Lateral relative motion of a forearc Fault Zone in northern Chile, Ph.D. thesis,275 pp., Calif. Inst. of Technol., Pasadena, 1971. sliveroften causes compression and mountain building at the Arthurton, R. S., G. S. Alam, S. Anisuddin-Admad, and S. Iqbal, leading edgeand crustal extensionat the trailing edge. Geologicalhistory of the Alamreg-Mashki Chah area, Chagai Dis- Though focal mechanismsof shallowunderthrusting earth- trict, Baluchistan,in Geodynamicsof Pakistan,edited by A. 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