Ablative Subduction: a Two&Hyphen;Sided Alternative To

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. B6, PAGES 8877-8904, JUNE 10, 1992

Ablative Subduction: A Two-Sided Alternative to the Conventional Subduction Model

WINSTON C. TAO AND RICHARD J. O'CONNELL

Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

Subduction is conventionally modelled as a convergenceand overlapping of two semirigid plates; such a convergence is one-sided, in that one lithospheric plate descends while the other remains on the surface. We suggest an alternative model, one based on the dynamics of fluids. In this model, the viscous lower lithosphere flows downward, and the brittle upper lithosphere deforms in passive response. This process is potentially double-sided, for we find that even a buoyant plate can be dragged downward by a dense, descending neighbor. Thus an apparent overriding plate may be worn away by a process of viscous ablation, with the rate of ablation a function of plate buoyancy. We call this process "ablative subduction". Ablative subduction allows us to simply interpret observations concerning slab profiles, interplate seismicity, back arc tectonics, and complex processessuch as double subduction and subduction polarity reversal. In performing experiments modelling the evolution of simple, fluid "slabs", we find that slab profile is strongly influenced by ablation in the overriding plate. When ablation is weak, as when a buoyant continent borders the trench, deformable slabs adopt shallow, Andean-style profiles. These profiles develop over time from an initially steep shape. More vigorous ablation rates, as might occur in an ocean- ocean convergence,yield steeper, Marianas-style profiles. Thus differences between Marianas-style and Andean-style slabs may result from differencesin ablation rate and subduction duration. The occurrence of ablation might not be easily detected at depth, because material from subducting and ablating plates adhere closely as a single slab. These slabs show downdip deformations that are consistent with seismic focal mechanisms. Plate deformations associated with ablative subduction are also consistent with observed patterns of seismicity. In particular, the relative aseismicity of Marianas-style plate boundaries is consistent with the ablative model; we may thus explain how plates can converge aseismically, without requiring that these plates be decoupled. Ablation should be weakest in Andean-style subduction, although pulses of rapid ablation might lead to episodesof crustal shortening; in oceanic regions, the manifestation of ablation may depend upon tectonic regime. In an extensional area like the Marianas, ablation may be temporally self- limiting, and ablative cycles may explain conflicting observationsof tectonic erosion and accretion. In a compressionalregime, vigorous ablation might lead to observations of double subduction and subduction reversal. In each case, the behavior of the lower lithosphere is relatively simple; what varies is the rate of ablation and the response of the upper lithosphere.

1. INTRODUCTION ing plate may be consumedby a processof viscousablation. We find that this ablative model of subduction is consistent Subduction moves material from the surface, where we with major subduction-related observations,that it suggests can see it, into the mantle, where we cannot. Models de- a simple explanation for why continental and oceanic-style scribingthe processmust therefore rely on indirect lines of subduction zones differ greatly in observations of slab pro- evidence, the implications of which may not be unique. In file and surface tectonics, and that it may provide a means the standard interpretation, based upon early conceptions of interpreting complex tectonic processessuch as double of a simple, brittle lithosphere, subduction occurs as a sim- subduction and subduction polarity reversal. ple, one-sidedoverlapping of rigid tectonic plates. However, in the absence of direct measurements of relative plate con- Classical $ubduction: Assumptions and Problems sumption, other interpretations are possible. The underlying basis of any subduction model is that In this paper, we examine the plausibility of a two-sided, lithosphere created at mid-ocean ridges must somehow re- fluid-based model of lithospheric subduction, one based turn to the mantle. Early in the development of modern upon current views of lithospheric structure. Within this plate tectonic theory, this recycling was recognized to lie model, the viscous lower regions of the lithosphere flow at convergent plate boundaries, where patterns of topog- downward as a fluid, with the more brittle upper litho- raphy, seismicity, and volcanism suggested the descent of sphere deforming in passiveresponse. The asymmetry of surfacematerial [Benioff,1954; McKenzie and Parker, 1967; plate consumption is then determined by the asymmetry Morgan, 1968; Wilson, 1965; /sackseta/., 1968]. Though of plate buoyancy: when differencesin lithospheric buoy- the first depictions of this descent show material being re- ancy are great, as in a continental region like the Andes, movedfrom both sidesof a trench [Holmes,1944; Wilson, the bulk of the slab is composedprimarily of material from 1963],the one-sidedmodel came into favorby the late 1960s the denser plate. But when plate densities on either side [/sackseta/., 1968; McKenzie and Morgan, 1969; /sacks of the trench are more symmetric,subduction may in turn and Molnar, 1969] and provided an elegant means of re- be more two-sided. Hence what appears to be an overrid- lating the inclined profiles of seismic Benioff zones to the presence of nearby continental masses. In the model's sim- Copyright 1992 by the American Geophysical Union. plest form, the buoyancy of a continental plate enables it to Paper number 91JB02422. override denser oceanic lithosphere; forced downward by the 0148-0227/92/91JB-02422505.00 collision, the oceanic plate bends, generates thrust-faulting

8877 8878 TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION earthquakes as it scrapespast the overriding plate, and sinks of one plate beneath another), we must ascribethese dif- along the Benioff zone as a coherent slab. The place where ferencesto such secondary characteristics as absolute plate the subducting plate tilts downward is then marked by an velocities, relative convergencevelocities, or densities of the oceanic trench, and partial melting of slab material gives subductedplates [Cross and Pilger, 1982;Chase, 1978]. For rise to volcanism upon the overriding plate. A clear distinc- specific subduction zones, one or more of these mechanisms tion is thus made between overriding and subducting plates, can well apply on a case by case basis; however, the overall with the disposition of continental crust determining which differences between the two classesare so systematic as to plate will override; where ocean meets ocean, the presence suggesta more basic difference in dynamics, one based on of island arc material likewiseserves to define the overriding the character of the overriding plate. plate. Hence the classicalmodel ties together arc volcanism, Further problems arise in relating the dynamics of sim- oceanic trenches, interplate seismicity, and seismic Benioff ple plates to the dynamics of a layered lithosphere. It is zones, relating them all to the downward bending of a dense, currently thought that the lower portion of the lithosphere semirigid plate beneath a buoyant continent or island arc. behavesas a fluid over geologictime scales[Parsons and However, while the classical model may be used to inter- McKenzie, 1978]. Such a rheologywill inhibit subduction pret the most important aspects of subduction, we some- asymmetry: with uniformly solid plates, one plate might times have difficulty in applying it to details of slab and well slide completely over another; but if the lithosphere is plate dynamics. A notable difficulty concernsthe many layered, the top of a descendingplate should shear the vis- differences observed between continental and oceanic-style cous regions of its neighbor. This shear will tend to carry subductionzones (Figure 1): typically, oceaniczones of the material from the overriding plate downward. If the over- Marianas type show steep, deep slabs and tensional tecton- riding plate is continental, crustal buoyancy might minimize ics in the back arc region, while continental, Andean-style the subsequent loss of material; but if the plate is oceanic, areas contain extremely shallow slabs which underthrust then loss rates could perhaps be appreciable. For example, hundreds of kilometers of horizontally compressedcontinent we note that landmasses in western Pacific subduction zones [Uyedaand Kanamori,1979; Jarrard, 1986]. As the classical are typically sparse, appearing only as narrow island chains model makes no fundamental distinction between continent- lining one side of the trench; without great buoyant masses ocean and ocean-oceanconvergence (irrespective of overrid- to preservethem, the overriding plates in such regionsmight ing plate type, subduction should be but a simple passing be significantly ablated.

One-Sided Subduction Ablative Subduction

buoyant continent trench slowerthan overridingplate trench moves resists subduction with continent marginally buoyant dense ocean ocean and arc are sinks as before dense oceanic plate ablated, contribute to slab forms sinking slab

Fig. la. One-sidedversus two-sided (ablative) subductionmodels.

Fig. lb. Continentaland oceanicsubduction endmembers [from Uyedaand Kanamori, 1979]. TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8879

That ablative lossesmay be possibleis suggestedby labo- constraintsare requiredto keepthem at the surface[Gurnis ratory and numerical models of mantle convection: thermal and Hayer, 1988].While futureexperiments using more so- downwellingsin homogeneousNewtonian fluids are invari- phisticated rheologiesmay yet produce perfect subduction ably two-sided[Malkus and Veronis,1958; Chandrasekhar, asymmetry, the strong tendency for two-sided subduction 1961;O/son, 1984], as the descentof material on one sideof to occur in physicaland numericalsimulations suggests its a trench tends to drag along material from the other side; occurrence in nature as well. once thus entrained, even buoyant material may adhere to Even assumingthat completesubduction asymmetry is a sinkingslab and descendto great depths [Richardsand somehowmaintained in all subductionzones, there are dif- Davies,1989]. To removethis effectand produceone-sided ficultiesof interpretationin complexoceanic regions. A downwellings,slip zones have been introduced at the trench straightforward application of the rigid plate model often to mimic the effectof stress-dependentrheologies; to fully givesrise to unusualslab configurations (Figure 2), and fur- decouplethe plates, these slip zones must stretch from the ther complicationsarise in trying to explaintime-dependent Earth's surfaceto the baseof the lithosphere[Kincaid and changesin subductiongeometry. Particularly troublesome Olson,1987] or extendstill deeperinto the mantle[Gurnis is the issueof subductionpolarity reversal. In order for a and Hayer, 1988]. Even after the insertionof suchhetero- classicalsubduction zone to changedirection, subduction geneities,dense overriding plates still often sink, and further musthalt (perhapsin responseto an arc-arccollision), the

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Fig. 2. Complexapplications of the classicalsubduction model. Proposed slab profiles south of Mindanao,Philip- pines [from Cardwell et al., 1980]. 8880 TAO AND O'CONNELL:AN ABLATIVEMODEL OF SUBDUCTION slab must detach from the formerly subductingplate, and ericlax,1972], North Sulawesi,which is •)ngoingand pro- subductionmust reinitiate on the oppositeside of the arc gressingtoward the SangiheArc [Hamilton, 1979; Silver (Figure3). Eachof thesesteps is problematic.That subduc- et al., 1983], and Halmahera [Hamilton, 1979; Card•vellet tion mightnot be easilyhalted is suggestedby the longevity al., 1980]. The Philippineregion in generalseems to have of continentalsubduction zones (over 200 m.y. durationin had west dipping subductionin the Paleogeneand east dip- the caseof Peru-Chile[Jarrard, 1986]) and by the restricted ping in the latter Neogene, and is currently undergoinga subductionof a buoyantcontinental margin that is appar- northward progressiveshift back to west dipping subduc- ently occurringnorth of the Philippines[Hamburger et al., tion [Le•visand Hayes,1980; Divis, 1980].Moreover, at least 1980].Moreover, in applyingthe classicalmodel, we assume one of these reversals,beneath Luzon in the late Oligocene, that the upper lithosphereis strongenough to controlover- seemsto have occurred without an arc-arc collision or any all plate dynamics;this strengthshould hinder both subduc- other apparentcause [Lewis and Hayes,1980]. tion reinitiationand the detachingof a slabfrom a formerly subductingplate. For thesereasons, we would expectsub- Ablative $ubduction duction reversalto be an extremely unusualevent. On the contrary, however,reversals of slab polarity appear to be It appears then that the classicalsubduction model, while rather common. They have been proposedin the New He- elegantlyapplicable to first-order observations,is not easily brides[Carney and MacFarlane, 1982], New Britain [Page extended to details of lithospheric dynamics and complex and Ryburn, 1977], SolomonIslands [Karig and Mature- oceanictectonics. We therefore ask if one can more simply interpret the subduction processusing a different conceptual framework. We can derive an alternative subduction model by reap- praising the dynamical role of the elastic upper lithosphere. In adapting the classical model to modern views of lithospheric rheology, we implicitly assumethat the lithosphere is so dominated by the strength of its uppermost layers that its overall behavior is platelike. This assumption might not be entirely warranted. The concept of plate rigidity primarily concerns the lithosphere's resistance to deformation along a horizontal plane; if this rigidity stems from an elastic rheology that is confined to the uppermost lithosphere, we can conceive of a situation in which the upper lithosphere is strong enough to impose platelike behavior in a horizontal direction, but too weak to control vertical motions in underlying viscous regions. Lithospheric consumption can then occur primarily as a fluid process,with the brittle upper lithosphere responding passivelyto viscousconsumption (b) from below. We call this dynamical endmember "ablative subduction", and sketch it in cartoon form in Figure 1. Here, the viscouslower lithosphere flows downward as a fluid, with descent rates varying as a function of plate density. The more dense of two plates thus "subducts", while the less dense of the pair "ablates". Such a plate convergencewill still leave a trench at the interplate boundary and a volcanic arc above the slab, but oceanic and continental subduction zones may differ in degree of ablation. If the ablating plate is extremely buoyant, as it would be if it were continental, then ablation rates will be low and subduction approximately one-sided. However, in a more symmetric, oceanic setting, ablation rates might be higher, so that the subducting slab will be composed of material originating on both sides of the trench. This ablative model of plate consumption provides a simple, alternative means of interpreting subduction-related observations. We therefore explore its implications in more detail. In section 2 of this paper, we perform a series of (d) simple numerical experiments simulating the behavior of an ablative subduction zone. We find that the ablative removal of even buoyant plate material may be a natural response to lithospheric convergence,and that buoyancy-controlled Fig. 3. Classicalmechanism for slab reversal. (a) and (b) When variations in ablation rate can strongly influence slab pro- buoyant masses(e.g., island arcs) collide, subductionat the original trench is halted. (c) The slab detachesfrom the old subducting files. In section 3, we consider how the model can be used plate, and (d) subduction reinitiates on the opposite side of the to interpret observed patterns of interplate seismicity. Fi- enlarged island arc. nally, in section 4 we examine how surface tectonic processes TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8881

might reflect the responseof the upper lithosphere to ongo- downwelling.) By measuringthe flux of material entering ing ablation at depth. the slab, we thus establish the trench motions appropriate for a purely ablative subduction zone. 2. NUMERICAL EXPERIMENTS Figure 4 shows the results of three runs. In the first, both plates are equally dense(Figure 4a); in the others,the We perform two sets of experiments, in which we model right-hand plate is either neutrally (Figure 4b) or moder- subduction as the foundering of a densefluid lithosphere. In ately (Figure 4c) buoyant with respect to the underlying the first, we ask whether small amounts of crustal buoyancy, mantle. As expected, symmetrically dense plates sink as such as would be associated with oceanic island arcs, would a symmetricalvertical downwelling(Figure 4a). We note, necessarilyprevent ablation's occurrence. In the second, we however, that a neutrally buoyant plate can also descend trace the development of simple ablative slabs and compare quite readily (Figure 4b). Even though sucha plate has no their profiles to those observed in nature. tendency to sink on its own accord, it is rapidly pulled down These experiments explore the endmember case of purely by shear coupling to the neighboring plate. Indeed, this cou- ablative subduction, in which the elastic strength of the up- .,,.-•1u.... .: ..... • ...... ,,1. • ...... uu•,,•,y buoyant material downward per lithosphere(comprising crust and uppermost mantle) in a processof viscousablation (Figure 4c). Thus plate does not control vertical motions in the plates. Lithospheric buoyancy does not preclude plate descent; instead, increas- consumption is then dominated by the fluid behavior of the ing buoyancy servesmerely to decreasethe rate of ablation viscouslower lithosphere (the part of the near-surfaceman- and thereby produce a displacement of the trench axis over tle that is more viscous than underlying material but is too time. warm to have an elastic rheology). Though this viscous layer might have different properties between continental and oceanicregions [Jordan, 1978], we assumefor simplicity that its rheology is everywhere uniform. We further assume T that this lower lithosphere is firmly attached to mantle and crustal layers overhead. Its ability to resist subduction is then largely determined by how much continental or island arc crust lies at the top of the plate (i.e., we assumethat continental or island arc material imparts an overall buoyancy to the lithosphereas a whole). > 0 -

Plate Buoyancy and Rate of A blation

In our first set of experiments, two plates of varying den- T sity convergeabove a homogeneousmantle. (The experimental model, which uses a two-dimensional, Cartesian ge- (b) ometry under periodic boundary conditions, is described in detail in Appendix A.) In these experiments,the viscous lower lithosphere appears as a uniformly thick layer Ap1 0 of Newtoninn fluid, over which a platelike horizontal veloc- Ap2 - 0 ity boundary condition is applied to mimic the effect of the elastic upper lithosphere. A single trench divides the lithosphere into two plates; material within the left-hand plate is of higher density than material within the mantle, while the T density of the right-hand plate varies between experimental runs. We initiate subduction by perturbing lithospheric fluid downward at the trench, after which we impose no further external guidance on the course of the experiment. The initially perturbed material flows downward, generat- ing a mantle circulation that in turn drives the plates toward the trench. We assumethat failure of the elastic lithosphere reflects removal of underlying material, in which case the requirement that plate consumption equals slab production Fig. 4. Plate buoyancy and lithospheric consumption. Two plates defines the trench migration speed: converge at a trench, marked by T; ridges lie out of view. The left-hand plate (shaded) is of constant density; the density of the -- Vl +c(v2 -Vl) (1) right-hand plate (open elements)varies betweenexperiments. (a) Plates of equal density form a symmetrical downwelling. (b) A -- + (2) neutrally buoyant plate (open) can be readily entrained downward by a dense neighbor (solid). (c) This entrainment can re- where vt is the trench velocity, v• ,v2 are the vector velocities moveeven buoyantmaterial (open) in a processof ablation. Plate of the overriding and subducting plates, and ')'1, ')'2 denote buoyancy thus does not preclude ablation, but reduces the abla- the massflux from eachplate into the trench. (The ablation tion rate and causesa lateral migration of the trench. Rectangles of constant area indicate the position of each density element (see parameter a indicates the relative contribution made by the Appendix A); Ap indicatesthe differencein density between plate ablating plate to the slab and ranges from a value of zero and mantle; a negative value of Ap indicates that plate material in the one-sided model to 0.5 in the case of a symmetrical is buoyant. 8882 TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION

AblationRate and SlabProfile any migrationmodel is not the trench'svelocity with respectto someabsolute reference frame, but its velocity with In the secondset of experiments,we examinewhether an respectto the mantlebeneath it. If the underlyingfluid con- ablative mode of subductioncan producerealistic slab pro- tains a backgroundflow, which we would expect in a con- files. As we have assumedin our model that the lithosphere vectingmantle overlainby movingplates, even a stationary displaysa predominantlyfluid behavior,it might be argued trench will producean inclinedslab; similarly,a mantle that that an ablative downwelling will not take on the slablike is flowing in the same direction as a migrating trench will forms observed in nature. We therefore trace the develop- reduce the effect of the migration. What should be noted ment of fluid slabs and examine the forms they adopt under is that in a one-sided subducting system with rigid plates, varying amounts of ablation. For simplicity, we begin each absolute trench motions and mantle flow fields are linked: if experiment with a uniformly dense lithosphere on either side the only way to speed up a trench is to speed up the entire of the trench and specify the ablation parameter c• in each overriding plate, then we may well find that the local flow experimentalrun. We alsoimpose a tenfold mantle viscosity generatedby plate-mantle couplingnegates much of the el- jump at 670 km, becausein performingexperiments with a fect of the velocityincrease (Figure 5). Henceunless plates variety of mantle viscosityprofiles, we find that a viscosity and mantle are completely decoupled,changes in the abso- increasewith depth is required to satisfy seismicconstraints lute migration of a one-sidedtrench need not produce cor- on slab deformation. Our resultssuggest that not only can respondingchanges in its effectivemigration. In an ablative weak slabstake on realistic forms, but their profileswill also system,however, variations in ablation rate can alter trench changewith both the rate of ablation and the duration of speedswithout affectingplate motions;as plate-driven flow subduction. is unaffected, there is then a one-to-one correspondencebe- Physical basis. Governing the development of our fluid tween absolute and effectivechanges in trench motion. By experimental slabs is the motion of the trench with re- directly controlling the effective migration of a trench, ab- spect to the mantle. In the framework of ablative subduc- lation may then exert a powerful control over the profile of tion, marked differencesin the buoyancy of continental and descendingslabs. oceanic overriding plates lead to marked differencesin abla- Results and Discussion. Results are shown for three ex- tion rate, in turn producing variations in the speed of trench perimentalruns, in which c• is set at 0 (Figure 6a), 0.15 motion (for a givenconvergence rate, increasingamounts of (Figure 6b), and 0.333 (Figure 6c). Figure 6a is thus the ablation will slow a trench until it effectively becomesa sta- classical, one-sided endmember, while Figures 6b and 6c tionary, symmetricaldownwelling.) As a migrating trench show the effects of low to moderate amounts of ablation in is essentially a moving conduit through which lithosphere otherwise identical settings. Each slab is shown at the same enters the mantle, grosschanges in its velocity will alter the stage in its development: in general, upper slab dips are path taken by sinkingmaterial and hencealter the shapeof initially steepand becomeshallower with time (Figure 7), the slab. An ablative style of subduction should therefore eventually achieving the mature, quasi-steady state forms lead to slab shapesand surface tectonics that systematically of Figures 6a, 6b, and 6c. In every case, lithosphere and vary with the buoyancy of the overriding plate. lower mantle viscositiesare 10 times that of the upper man- The idea of a link between trench migration and slab tle (higher lithosphericviscosities produce essentiallythe shape is not new. The basic concept, as proposed by same slabs), and density anomaliesare of constant mag- sasser[1971] and Hyndrnan[1972], and outlined by Cross nitude through space and time. For graphical purposes, we and Pilger [1982]and Garfunkelet al. [1986],is that a mov- have drawn the anomalies as linked rectangles of constant ing trench leavesbehind a trail of subducting material much area; as the distance between anomalies changesthrough as a fast-flying paratroop transport leavesbehind a trail of time, the width of each rectangle varies in inverse propor- parachutes. By producing a horizontal spacing between suction and reflects the local strain. The plotted thickness of a cessivelysubducted portions of the slab, trench motion leads slab thus indicates the amount of compressionor extension it to an inclined profile even though each slab element essen- has undergone in its descent. Trenches are labeled "T", the tially free-falls through the fluid mantle. Thus a stationary overriding/ablatingplates lie to the right of the trench, the trench should yield a vertical slab, and the role of migration subductingplates to the left, and the fluid associatedwith a is to reduce the dip. given plate is distinguished by shading. For comparison, we Ablative subduction modifies the basic model by effec- show in Figures 8 and 9 the slab profiles inferred from seis- tively slowing the migration rate for a given overriding plate mic observationsin a variety of subductionzones [Jarrard, velocity. If we assume that plates deform only at plate 1986; Rasmussenand Humphreys, 1988; James and Snoke, boundaries,then equations(1) and (2) giveus the migration 1990]. speedin any inertial referenceframe (of which the hotspot A comparisonof the experimental results in Figures 6a- referenceframe is a convenientexample). This seemingly 6c with the real-world profiles in Figures 8 and 9 showsthat minor adjustment to the migration model has several impli- variations in plate ablation can easily produce the entire cations. Though slab dips are in some casescorrelated with observed range of slab dips. Deep, steep, Marianas-style the absolutevelocities of overridingplates [Cross and Pilger, slabs with curved upper sections develop when the overrid- 1982],a moreglobal analysis shows the correlationto be rel- ing plate undergoesmoderate amounts of ablation(Figure ativelyweak [Jarrard,1986]. In the absenceof ablation,this 6c). Lesserablation rates cause the upperslab to straighten result implies that trench migration does not greatly affect and take on extremely shallowdips, producingChilean-style, slab shape. With ablation, the lack of a strong correlation shallow slabs extending severalhundred kilometers inboard is irrelevant,as migrationmay vary for a givenplate speed. of the trench (Figure 6b). This reductionof dip with de- Ablation also suggestsa way of easily controlling what we creasingablation acts most strongly on the uppermost por- call the "effectivemigration" of a trench. What matters in tions of the slab. Becausethe deep slab is lessaffected, re- TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8883

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(e) Fig. 5. Absoluteversus effective trench migration. The shapeproduced by sinkingslab elementsdepends upon the speedof the trench relativeto the underlyingfluid. Similar profilesmay result from (a) a fast trench and quiescentmantle or (b) a stationarytrench and a fastflowing upper mantle; in both casesthe effectivemigration rate is the same. (c) Conversely,a fast movingtrench may havezero effective velocity. (d) Plate motionsalter mantleflow fields unless completely decoupled. (e) In one-sidedsubduction, plate/mantle coupling will generatea flow associatedwith the trench's motion, thus limiting changesin effective migration. Even in the absenceof the global mantle flow in Figure 5/), this couplingwill result in steeperdips than producedin Figure 5a. $$$4 TAOAND O'CONNELL.' AN ABLATIVEMODEL OF SUBDUCTION

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Fig. 7. Transient stages of development. a -- 0.15, as in Figure 65, showing the initial descent of a near-vertical, curved slab, and subsequent straightening, kinking, and shallowing of dip to a quasi-steady state form. Fig. 6. Slab profilesgenerated with varying amountsof ablation; profilesare taken at the same stage of slab development,after flow fields. All that haschanged between experiments is the initial transients have disappeared. Trenches are marked by T; effectivetrench velocity, with the fastest migration occur- ridgeslie out of view. The subductingplate approachesfrom the left, the ablating or overridingplate from the right; solid slab ele- ringin the one-sidedcase of Figure6a andthe slowestin the ments are from the subducting plate, open elements are from the moderatelyablative Figure 6c. Any mechanismthat alters ablating plate. We have indicated the position of each density effectivetrench velocitieswill producea similar effect; we element with a constant area rectangle; the orientation of each have focusedon ablation becauseit suggestsa way in which rectangle showsthe local dip, while the heights and widths in- continent-oceanand ocean-oceanconvergence zones might dicate the strain accumulated by the slab over time. (a) a -- 0 (one-sidedsubduction); (b) a -- 0.15; (c) • -- 0.333. Low ab- behavedifferently. Potentially important mechanisms that lation rates yield shallow-dipping,kinked slab profiles;increased we have not consideredinclude global mantle flow and in- ablation leads to a straightening and steepeningof the profile. traplatedeformation behind a trench.Either may affect slab dipswithin a givenregion. However, global flow, whether duced ablation rates lead to kinked profiles in which shallow- drivenby surfaceplates [Hager and O'Connell, 1978] or by dipping upper slabs are joined to steep lower limbs. Curi- moregeneral convection within the mantle,does not ob- ously,strict one-sidedsubduction produces perhaps the least viouslydistinguish between different types of subduction common slab shape, one in which the uppermost slab virtu- zones. Plate deformation does make a distinction between ally underplatesthe continentfor severalhundred kilometers oceanicand continental overridingplates, but in the wrong beforeabruptly turning downward(Figure 6a). Sucha pro- sense:in the absenceof ablation, back arc deformation can file is consistent with proposed slab locations beneath Peru move a trench relative to the bulk of the overriding plate, (Figure9a) andthe U.S. PacificNorthwest (Figure 9b) but leadingto effectivelyfast trencheswhere there is backarc does not resemble the straight slabs found in typical sub- spreadingand effectively slow trenches where there is back ductioncartoons [e.g., Cox and Hart, 1986]. More common arc compression.As oceanicoverriding plates tend to be slabprofiles require the minor ablation ratesof Figure 6b. It extensional whereas Andean-style continents undergo com- is noteworthy how little plate lossis requiredto changeslab pression,plate deformationon its own shouldlead to shallow form: an ablation rate of a few percent turns the underplat- slabs in Marianas-style regions and steep slabs near conti- ing slab of Figure 6a into the moreconventional continental nents. Such a result is the opposite of what actually occurs. profileof Figure 6b, while a further increaseto 33% yields While back arc deformation may help determine slab dips the full-blown oceanic slab of Figure 6c. within a particular classof subduction(for example, the We stress that the varied slabs in Figure 6 are pro- shallow Peru-Chile slab is steepest where back arc compres- ducedwithout complicatingvariations in slab densities,slab sionhas beengreatest [Wdowinski et al., 1989]),it cannot strengths,plate driving forces,or externally imposedglobal produce the grossdifferences observed between continental T^o ANDO'CONNr. LL: AN ABLATIVEMODEL OV SUBDUCTION 8885

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Fig.8. Observed profiles ofsubducted slabs, taken from Jarrard, [1986]. Class 1subduction zones are predominantly oceanic; classes 6 and 7 are continental in nature. and oceanicsubduction zones. It seemsthen that if changes then the strongerof two convergingand subductingplates in effectivetrench velocityare to producesuch differences, shouldbe the more seismicallyactive. Observedslabs are these changesmust come from ablation. almostalways associated with cold lithosphere,while over- If ablativesubduction does occur, our resultssuggest that ridingplates are composed of weakercontinental, island arc, it might be difficult to detect. We seein Figure 6 that ma- or backarc material. If ablationwere to occur,the failure terial from ablating and subductingplates may adhere so of the weakoverriding plate may then be relativelysilent, closelyas to be seismicallyindistinguishable below about in whichcase we wouldobserve the deformationof onlythe 150 km. Nearer the surface,ablation appearsmainly as a morerigid subductingplate. If that werethe casein Fig- generalthickening of the overridingplate near the trench; ures6b and6c, only material from the left-handplates (solid the seismicityconsistent with suchdeformation may become area) would be visible. As an extreme but illustrative ex- lost in the diffuseseismicity commonly observed at shallow ample,we showin Figure11a a symmetricaldownwelling depths[Isacks and Baraganzi,1977] (Figure 10a). There (c• = 0.5), in Figure11b the samedownwelling with one is a suggestionof downwarpingin the overridingplate be- plate/slabinvisible, and in Figure11c the observedprofile lowthe BurmeseArc [Mukhopadhyayand Dasgupta,1988] of the Marianasslab [Creager and Jordan, 1986]. (Figure10b), and perhaps increased resolution may someday That the downwellingsin Figure 6 can resembleobserved settle the issue,but we suggestthat ablation may be inher- slabsis in someways surprising: whereas subducting litho- ently difficult to discernthrough seismicity: if, as is gener- sphereis generallyassumed to be strong(hence the term ally assumed,slab seismicityis indicativeof slab strength, "slab"),these downwellings have no strengthat all. Their 8886 TAOAND O'CONNELL: AN ABLATIVEMODEL OF SUBDUCTION

(• / o xoo 200 30DISTANCEo •0 ¸ (KM)5oo 600 7oo •oo (b)

Trench

e• OOoo-

100 _ ooe•eoOOOo. coo-•eo o00o ß ß c

IOOO..ele. oOoooo o -• - oOOcc l•lecOOOC: -oocOoe•e•.O¸00o o¸o-o.0ooe•o¸OOoo¸•e oo .ocoo e•eoOOOooo .... oCooo-l•.ooooo.o ß - 000oo e•eoOOOCo. . oo__ .... o.0 .... l•eOoOO0•'•O 0OOo...... o.e%•e. 0000oo¸oOoco o ...... e.-.oo-eeO-¸eO• • •00• . 500•oo_ _ • ?•20•'

(c)

Fig.9. Extremecontinental-style slabs: (a) Peru[from James and Snoke, 1990], and (b) Washingtonand Oregon [afterRasmussen and Humphreys, 1988]. (c) The one-sided subduction (a = 0) resultof Figure 6a is repeated for comparison. slablike forms arise not from a slablike resistance to defor- which has been broken and bent downward midway through mation,but from the sculptingaction of local mantleflow its descent. fields.In additionto generatingplausible profiles, these flow Finally, while we havefocused here on matureslab pro- fieldsalso produce downdip slab deformationsthat are con- files,the time developmentshown in Figure7 is of potential sistentwith frequentlyobserved seismic focal mechanisms significance.Oceanic subduction zones are thoughtto be [Isacksand Molnar, 1971]: as indicatedby the patternsof generallyyounger than thoseinvolving continents: the Marø thickeningand thinningin Figure 6, the downwellingsun- ianaszone, for example,is estimatedto be 45 m.y.old, while dergocompression at the trench,extension at intermediate the shallow slab beneath the Andes has been subducting for depths,and further compression as materialapproaches the over200 m.y. [Jarrard,1986]. This relativeyouth might ac- high-viscositylower mantle. Collectively,our resultssug- count for someof the steepnesscharacterizing oceanic slabs. gestthat flow-induceddeformation can account for muchof Our experimentssuggest that dips becomeshallower with a slab'sshape. They alsosuggest that inferringa slab'srhe- time, rapidly at first, then moreslowly, and it may be that ologyand behavior from its seismicprofile is not a straight- youngsteep slabs are displayingtransient behavior. Such a forwardtask; for example,if we were ignorantof the down- shallowingwould explainwhy arc-trenchdistances seem to wellings'true nature, we might examine the kinkedprofile of growwith subductionduration [Dickinson, 1973]: as sub- Figure6a anderroneously interpret it asa shallow,rigid slab duction progresses,the sourceregion for arc magmatism TAOAND O'CONNELL: AN ABLATIVEMODEL OF SUBDUCTION 8887

TRENCH AXES VOLCANIC LINE ! I • iOO [ IOO 200 !l I I'

200- o•.oo . oN%-q:•--o o•••• '• oo o• I '

Jade Mines Naga Chindwin Igneous Hills 8asm Complex .A./

N57W Indian plate Burma plate SS?E ! i i i i , , , i i , , ß ß ß ß o 'o ß o. "-, .•,. '• *

Sector I ' ' I I I I I I I I I I I t

a -- 0.333

, \

Fig.10. Observability ofplate ablation h (a) Earthquakecenters and original proposed slab profiles [from Isacks andBaraganzi, 1977]. (b) Proposeddownwarping ofBurma plate below Burmese Arc [after Mukhopadhyay and Dasgupta,1988]. A close-upofthe moderately ablative (a = 0.333)slab of Figure 6c is shown for comparison.

(a) (b) (c)

6OO

Fig. 11.Observability of plate ablation Ih (a) Profileof symmetricaldownwelling (a = 0.5). (b) Observedprofile if materialfrom one plate subducts aseismically. (c) Proposed profile of the Marianas slab [from Jarrard, 1986]. 8888 TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION might swing away from the trench as the dip of the slab decreases. It is also conceivable that ablation may slow a slab's evolution toward a shallow mature profile; in such a case, a lesserdegree of ablation than implied by our experiments might still yield steep dips in a region that is relatively young.

3. RESPONSEOF UPPER LITHOSPHERETO ABLATION, INTERPLATESEISMICITY, AND SEISMIC MOMENT RELEASE RATES

We next consider how a two-sided mode of plate descent may affect the seismicity of convergent plate boundaries. Earthquakes along these boundaries typically possessfocal mechanismsthat are aligned with the upper slab; they are therefore interpreted within the classicalmodel as showing slip between subducting and overriding plates. Within the ablative model, we would interpret these earthquakes rather differently: rather than mark the simple passageof one plate beneath another, they may indicate how the elastic lithosphere respondsto the consumptionof underlying material. If the viscous lithosphere descendsin the manner of our experiments(e.g., Figure 4c), the upper lithosphericre- sponsemight take on a number of different forms. We would expect a simple behavior to be shown by the "subducting" plate (i.e., the morerapidly descendingof two plates): because the angle between plate and slab is relatively open, Fig. 12. Upper lithospheric responseto ablation of the lower litho- the elastic lithosphere may simply bend downward to follow sphere. As the viscouslithosphere (open) flowsaway as a fluid, the axis of the downwelling slab. However, a more complex the elastic lithosphere(solid) must deform in response.In the ab- response might be shown by the more slowly descending, lating plate, this responsemay take the form of (a) a downward bending,(b) crustalshortening, or (c) tectonicerosion. "ablating" plate: here, the angle between plate and slab is considerably more acute, and further complications can arise from the presenceof buoyant continental or island arc table exceptionto this trend is givenby the Aleutiantrench: crust. If the upper part of this plate is easily bent and not only is its effectiveseismicity much greater than that of possesseslittle buoyancy, it might still simply bend down- the other oceanicregions, but its valueof • is high even ward (Figure 12a). Alternatively,however, it may crumple with respect to continental zones. via crustal shortening(Figure 12b) or be worn away in a Within the classicalsubduction model, earthquakes at the processclassically referred to as tectonicerosion [Bloomer, top of the Benioffzone show either interplate slip (Figure 1983] (Figure 12c). Thus the upper lithosphere,whose de- 13a)or vigoroustectonic erosion (Figure 13b); in bothcases, formations should be responsiblefor the bulk of interplate the rate of seismicmoment release should ideally vary with seismicity,might respond to ablation in a variety of ways. the rate of plateconvergence, yielding consistent values of fl. This aspect of the ablative model may help explain why To explain the variationsseen in Table 1, we would there- rates of interplate seismicityvary widely from one subduc- foreinvoke a selectivedecoupling between plates in regions tion zone to another. The variations can be seenin Table 1, of extensionaltectonics and/or whereunusually dense litho- where we have tabulated the ratio of seismicslip rate to tec- sphereis subducted[Uyeda and Kanamori, 1979;Peterson tonic slip rate for a numberof major subductionzones [after and Seno,1984]. Thus amended,the classicalmodel can rea- Petersonand Seno,1984]. Seismicslip is the degreeof in- sonablyexplain much of the observedpattern. However,we terplate thrusting as inferred from rates of seismicmoment can also use the ablative model to devise a more fundamen- release; tectonic slip is that inferred from relative plate ve- tal explanation.If ablativesubduction occurs, then the dif- locities under the assumption of classical subduction. The ferentmoment release rates in Andean-styleand Marianas- ratio between the two is given by fi; • = I thus implies styleregions may reflectdifferences in ablationrate and up- that plate convergenceis entirely taken up by seismicslip per lithosphericresponse; in addition,we may further inter- along thrust planes, while a paucity of seismic release will pretthe activeseismicity of the Aleutiantrench as reflecting yield a value of fi closer to zero. Early studies of seismic a relatively rare occurrenceof true classicalsubduction. and tectonic slip rates had found a reasonable correlation We consider the Aleutian case first. The occurrence of between plate convergencevelocity and seismicmoment re- classicalsubduction in this regionis suggestedby the un- lease[Davies and Brune, 1971; Sykes and Quirtmeyer,1981], usualgeometry of the convergingplates. Here, wherelitho- but the more recentresults presented in Table I [Peterson sphereof Mesozoicage overthrustsyounger, early Cenozoic and $eno, 1984] showa surprisingdegree of variability. In material[Addicott and Richards, 1981], the overridingplate general, the relative seismicity of oceanic subduction zones is not only unusuallyold, but it is apparentlystronger and is far lessthan that of continental regions;indeed, moment more massivethan the plate that is being subducted. This releaserates in the classicMarianas-style zones (Marianas, geometryis uniqueamong major subductionzones (though Izu-Bonin, Tonga,and New Hebrides)are an orderof magni- it may be found in less well-developedareas such as the tude lower than rates in continental locales. However,a no- easternedge of the CarolinePlate [Hegartyet al., 1980]). TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8889

TABLE 1. Ratio of Seismic Slip to Plate Tectonic Slip in genic zone will then depend upon how the uppermost plate Continental and Oceanic Subduction Zones respondsto the removal of underlying material. If the upper plate undergoescrustal shortening, then there is still a sense Trench Length, km • of interplate slip, and earthquakes again should be present (Figure 13c). If ablation is accompaniedby a tectonic ero- Continental Zones sion of the elastic lithosphere, thrusting will also still occur Alaska 1350 0.77 (Figure 13d). However, if the upper layer of the ablating Kamchatka 1280 0.67 plate simply tucks downward at its leading edge, then the Nankai 750 0.50 relative slip betweenplates is substantiallyreduced (Figure Mexico 1150 0.38 Peru-Chile* 5300 0.37 13e) and subductionwill be comparativelyaseismic. Kurile 1210 0.36 We would therefore expect the seismicity of ablative sub- Columbia 650 0.33 duction zones to show a characteristic pattern. High rates Japan 650 0.24 of seismicmoment release should be found in Andean-style Cen. America 1580 0.10 zones: here, ablation rates will be reduced by continental Sumatra 1930 0.05 buoyancy, and observationsof crustal shortening [Isacks, Weighted mean 0.36 1988] and tectonic erosion[Stern, 1989] may accountfor any ablative lossesthat do occur. In contrast, the seismic- Oceanic Zones ity of Marianas-style zones might be comparatively weak: higher plate densities should foster higher rates of ablation, New Hebrides 1800 0.16 Kermadec 700 0.13 there is no observedcrustal shortening,and the young (and Tonga 1450 0.08 thus weak) overridingplates typically presentshould more Ryukyus 1300 0.05 likely bend downward than erode at the surface. Hence the Marianas 2150 0.01 observedaseismicity of Marianas-style subduction and the Izu Bonin 1240 0.01 Java 1800 0.00 activity of Andean regions may reflect varying degrees of buoyancy-controlled ablation. Weighted mean 0.06 Thus we can simply interpret the seismic observations in Table i if both classical and ablative modes of subduction Eastern Aleutians 1200 0.84 occur in different parts of the world. Such an interpreta- Western Aleutians 740 0.31 , tion is certainly not unique: as noted earlier, if we correlate After Peterson and Seno, 1984. • is the ratio between observed aseismicconvergence with a decoupling between converging seismicslip and the amount of slip expected from relative plate plates, we can reasonably account for the seismic data us- motions. "Weighted mean" is the average value of • over sev- ing the classicalmodel alone. The appeal of the ablative eral trenches,weighted by trench length. Trenchesare classedas model in this regard is that it permits us to assume a con- continental or oceanicaccording to tectonic style (Ryukyus) or becauseof crustaltype [Jarfatal,1986] of the overridingplate (all sistent degree of plate coupling worldwide. Consistent cou- others). In general,continental-style subduction zones have effec- pling may then be usedto simply explain severalother differ- tively higher rates of seismicitythan oceanic-stylezones, a pattern ences that exist between oceanic and continental subduction consistentwith the ablation and rolling under of oceanic forearcs. zones. For example, strong interplate coupling would ex- Note that the Aleutian zone is a significant exception to the rule plain why Marianas-style slabs, besidesdipping more steeply (see text). * • for Peru-Chileis the average• (weightedmean) over 5 than those beneath continents, also seem to descend to much trench segments. greater depths. The steepnessand deepnessof these slabs implies a rapidity of descent that is lacking in continental The overriding plates in most other subduction zones are areas. If plates are decoupled, then it is not clear how the most likely weaker, but more buoyant, than their subduct- character of the overriding plate can affect slab speeds. But ing neighbors, particularly when continents or young back if plates are coupled, then we would expect slabs dragging arc basins are found behind the trench. In such regions, along pieces of buoyant continental lithosphere to descend plate buoyancyseems to determine the identity of the over- more slowly than those joined to denser oceanic material. riding plate, a dependenceessential to the ablative model. Strong interplate coupling can also explain why we associate In contrast, the polarity of Aleutian subduction seems to compression with continents but extension with oceans: a arise not from the overriding plate's buoyancy, but from its shallow-dipping, one-sided slab that is shear-coupled to an mechanical resistanceto bending. Subduction in this region overriding continent should produce back arc compression, might then be best interpreted as a classicaloverlapping of while a steeply dipping ablative slab, by drawing material rigid plates. We should expect such a convergenceto be together from both sidesof the trench, shouldinstead induce seismically active. tension. In these respects, ablative subduction not only ex- Elsewhere however, in the majority of subduction zones, plains seismicobservations, but it provides a simple way of the ablative model may apply. In such regions, rates of seis- relating slab descentto the tectonics of the overriding plate. mic moment releasemay vary with both the rate of ablation and the behavior of the upper lithosphere. In a region of 4. TECTONIC IMPLICATIONS low ablation (as when a continentborders the trench), slip between buoyant and dense massesshould yield high rates We have seen thus far that an ablative subduction model of seismic moment release. But when ablation is significant, is dynamically plausible, that it is consistent with seis- there is little interplate slip within the viscous lower litho- mic observations, and that it can be used to explain why sphere(Figures 13c-13e). This absenceof slip is consistent Andean- and Marianas-style slabs are fundamentally differ- with the seismicity drop that generally occurs below a depth ent in profile. We now examine how the model may be used of 60 km [Petersonand Seno,1984]. Activity in the seismo- in the interpretation of surface tectonics. 8890 TAO ANDO'CONNELL: AN ABLATIVEMODEL OF SUBDUCTION

(b)

(d)

Fig.13. Ablution and interplate seismicity. (a)and (b) In classicalsubduction, thrust-faulting earthquakes show eitherthe slip between overlapping plates, or theerosion of theoverriding plate. (c), (d), and(e) In ablative subduction,though there is no localized shear or slip zone in the fluid lower lithosphere, earthquakes canoccur in theelastic upper lithosphere if crustal shortening (Figure 13c) or tectonic erosion (Figure 13d) occur. However, if ablutionisvigorous and the ablating plate turns downward (Figure 13e), interplate slip may be considerably reduced,and subductionmay then be relativelyaseismic.

Ablution in Andean Subduction Zones tions of tectonic erosion in the Andean zone, which appears to takeplace at a rate of 1%-5%[Stern, 1989]. The low-ablution endmember of the ablative model is Conversely,the surfaceresponse to Andean-styleablution Andean-stylesubduction, in which a large continentcom- mightat timesbe morecomplex. So longas continental prisesthe overridingplate. Here, the ablativemodel can crust is well attached to material below, ablution can be gov- be mostsimply applied, for as continentsare not platelike ernedby tectonicerosion, and subduction may then take on in their behavior(and in somecases may be modelledas a classicaloutward appearance. But if the lowerlithosphere thin viscoussheets [England and McKenzie,1982]), their is not firmly attachedto overlyingcrust, then it may con- rheologyis well suitedto ablativeconsumption. What can ceivablydelaminate from the buoyantpart of the plate. In preservecontinents, and createthe impressionof classical suchan event,the ablativeremoval of the viscouslithosphere subduction,is a combinationof crustalthickness and buoy- cansuddenly increase in vigor.As thisablution need not be ancy.The presenceof a thick, buoyantcontinent imparts a localizedabout the trench, it might then yield a thickening significantdegree of buoyancyto the overridingplate as a andlateral shortening of the continentalcrust (Figure 14). whole. If plate buoyancygoverns the flux of materialinto Sucha processwould explain certain anomalies of slabpro- the slab(Figure 4), ablutionrates can be severelycurtailed file that are found in the Andean subduction zone. Here, solong as crustand lower lithosphere are firmly joined. the Peru-Chile slab varies in profile along strike, and dis- Giventhe apparentfluidity of continentalcrust, the sur- playsa markedsteepening where it passesbeneath a zone faceappearance of Andean-styleablution can be relatively of pronouncedcrustal shortening (Figure 15 [Isacks,1988]). simple.Since continental crust is buoyant,it shouldnot de- Within the ablative model, we might interpret the crustal scendunless dragged downward by sinkingmaterial; since shorteningas a surfaceresponse to a pulseof ablutionin it is weak,the descent of a givencrustal element will notdi- the lowerlithosphere. This temporarytransition to vigor- rectlyaffect more distant regions. Thus continental crust ousablution might then be reflectedin the observedlocal should not descenduntil it is virtually in contact with steepeningof the slab. the subductingplate. As crustalablution is thenlocalized Ablution in Marianas-Style$ubduction Zones within the immediate vicinity of the trench, the consumption of a fluid continentcan take on the appearanceof classi- Intermediate,time-varying ablution would be expectedto cal tectonicerosion. Ablution can thus accountfor observa- occurin Marianas-stylesubduction zones. Such regions are TAOANDO'CONNELL: ANABLATIVE MODELOFSUBDUCTiON 889•

(c)

crustFig.14.(solid)Crustal should delamination limit ab and ßlateral shortening a I subcrustallithosphere(or•,•la_tlø, n,and subducti(•n(l• nnø.r_malA.n_deansubduction, thebuoyancy ofc thenproducea region ofcrustal shortening overlyingbe an....rapidlyanomalously removed. ,u ms•anidtysteep (c)slab. Theforms resulting in the

o -5• W•ST•N •N•UNE AL•P•NO

' •S PRE•RDi• S•ER•sPAMP•N •

•0 I •Jg.15.Propoaed profi]e•• •heA•deA• •ubduc•1o• - .- overliesalocally steepsegmentof the slab. zone [trom Isacks, 1988] 'The w•es• partofthe Altiplano 8892 TAO Arid O'Cor•r•ELL: Ar• ABLATIVE MODEL OF SUBDUCTION

MARIANA TROUGH MARIANA ISLAND MARIANA FORE-ARC MARIANA TRENCH PACIFIC PLATE --'• ARC 453 454 456 ' - 458 459 460 461 452 Alamagan island Magellan Seamounts

4.5-5.8 k/ 3.3-4.3 k/s 5.3-5,9 k/s

I----- 50 km------I

_•-'•rocksIsland fromarccrust, contemporary including volcamsm and from older, rifted, volcamc arcs. k/s denotes seismicvelocity, kdometers per

Fig. 16. Physiographicdiagram and crustal structure acrosspart of the Marianas subductionzone [from Hussong et al., 1981]. The active arc overliespart of the back arc basin, the forearc is composedof island arc material, evidence of subsidence is found in the trench wall, and deep refractors within the overriding plate dip towards the trench. characterized by periods of back arc quiescenceinterspersed with pulses of back arc spreading, the latter often begin- ning with a rifting of the islandarc [Karig, 1972; Taylorand Karner, 1983]. Theseextensional pulses, by splittingthe arc crust) • (crust in two, might limit the accumulationof large buoyant masses and prevent the development of Andean-style asymmetry. However, the periodic creation of fresh back arc material will also ensure that plate densities do not become overly symmetric: in these regions, the mature Pacific plate typically lies to one side of the trench, with much younger and warmer back arc basins on the other. Extensional subduction zonesthus occupy a middle ground between the extreme plate asymmetry of an Andean-style region and a symmetric convergenceof mature oceanic plates. The intermediate nature of Marianas-style subduction should lead to the formation of a subduction zone that is clearly asymmetric but which features a more steeply inclined slab than is found in Andean regions. Given that weak, young back arc basin material makesup much of the overriding plate, we would expect ablation to be accompa- nied by a rolling under of the overriding plate edge. This rolling motion would be consistentwith the previously dis- cussed seismic moment release pattern, and would also account for observations of near-vertical normal faults in the Marianasforearc [Mrozowski and Hayes,1980], as well asfor an apparent trenchward dipping of deep seismic refractors within the Marianas forearc [Latraille and Hussong,1980] (visiblein Figure 16 [fromHussong et al., 1981]),and for seismic and tectonic evidence of surficial tension between the Marianastrench and back arc basin [Hussongand Sin- ton, 1980; Hussongand Fryer, 1981] (sucha tensionmight Fig. 17. Slowing of Marianas-style ablation over time: as ablation proceeds, island arc material is gradually emplaced within the arise from bending of the forearc or from coupling between forearc (Figures 17a and 17b) [after Bloomer, 1983]. When this descendingforearc and slab). island arc material enters the trench (Figure 17c), its buoyancy Left alone, the rate of ablation in a Marianas-style sub- should reduce or inhibit the rate of ablation. duction zone should tend to decrease over time. The reasons are summarized in Figure 17. Becausethe distance between subsidingas they cool. This processwill gradually replace arc and trench shouldremain more or lessconstant (barring the initial oceanic forearc with one composed of island arc changesin slab dip), an observeron the overridingplate basement. (The most recently erupted rocks will then lie will see the active arc move in a back arc direction as fore- near the active arc while the oldest will be found close to arc consumption continues. Becauseof this motion, a given the trench.) As this basementwill be both warmer and com- arc volcano will eventually become inactive, to be replaced positionally less densethan the original oceanic forearc, its by new volcanoesin the former back arc region. Over time, entry into the trench should reduce the rate of ablation. inactive arc fragments will then approach the trench, per- Just such a progressionseems to have taken place in the haps wearing away under surfaceweathering processesand Marianas. Deep Sea Drilling Project (DSDP) drillings and TAO AND O'CoNNELL: AN ABLATIVE MODEL OF SUBDUCTION 8893 seismic studies of the Marianas forearc indicate that it is ment, underestimate the peak rates of ablution. If arc ma- composedof island arc basement[Meijer, 1980; Hussonget terial eventually enters a trench, then we will have lost all a/., 1978; Bloomer and Hawkins, 1980; Latraille and Hus- record of both subduction and ablution at the time of the song,1980], upon which lie manylarge seamounts of possibly arc's creation. Thus vigorous ablution will tend to remove igneousorigin [Hussong and Uyeda,1980]. This arc-derived evidence of its occurrence. Such a consumption of arc ma- basement showsthe expected age progressionof increasing terial might be used to explain why arc age estimates vary agetoward the trench, with early Oligocenerocks lying mid- widely between continental and oceanic arcs: when we com- basin[Mrozowski and Hayes, 1980], and an Eocenearc com- pile arc ages(taken from Jarpard[1986]) by subductiontype, plex appearingwithin the trenchwall itself [Bloomer,1983]. we see that continental volcanic arcs are typically several Moreover, the modern Marianas arc overliesyoung back arc times older than their oceaniccounterparts (Table 2). If basinmaterial (Figure 16), a geometrythat can result only arc ages are used to constrain the duration of subduction, from a rearwarddisplacement of arc volcanism.(Elsewhere, as they are typically used within the classical subduction the Scotia(South SandwichIslands) and Tongasubduction model, this pattern is not easily explained. The remarkable zonesare similarly sited [Barker and Hill, 1981; Weissel, youth of many oceanic zones may reflect a greater ease of 1981],and the West MarianasRidge, a formersite of Mar- subduction initiation in oceanic regions, but it is curious ianas arc volcanism, also lies atop the rifted forearc of the that even the oldest oceanic zones are comparatively young. olderPalau-Kyushu Ridge [Taylorand Karner, 1983].) The Possibly, oceanic subduction is simply short-lived, but there character of the Marianas arc and forearc is thus consistent is no obvious reason why the presence of a continent should with the occurrence of ablution in the past. In turn, a recent so emphatically increasesubduction duration. Indeed, given slowingor cessationof ablution is suggestedby evidenceof the apparent resistanceto subduction displayed by Andean- accretionin the southernpart of the Marianas [Karig and style slabs, one might expect the opposite correlation be- Ranken, 1980], by the survivalof arc material dating back tween duration and crustal type. more than 32 m.y. in the nearby islands of Guam and Palau [Meijer,1980], and by signsthat forearcconsumption in the TABLE 2. Arc Ages middle Marianas took place primarily between 42-45 m.y. and 25-30 m.y. ago [Bloomer,1983]. Additionally,we note Trench Arc Age, m.y. that the zone's current 200-km arc-trench gap is unusually Continental Zones wide [Karigand Ranken,1980] and that the underlyingslab profile is much flatter near the Earth's surfacethan it is at Columbia 242 depth (Figure 8 [Jarpard,1986]). Suchcharacteristics can Chile 226 Ecuador 226 result from a decreasein ablution (and/or an increasein Peru 226 back arc spreading),for the consequentincrease in effective Cascades 175 trench migration will lead to a shallowingof the upper slab. SW Japan 175 Within the ablative model, we would therefore ascribe the Alaska 160 Alaska Peninsula 160 shape of the modern Marianas slab to fairly vigorous ablu- Kamchatka 153 tion in the past (whichwill havegiven the profileits overall T. del Fuego 150 steepdip) and to a morerecent slowing or cessationof fore- NE Japan 115 arc consumption serving to fiatten the near-surfacepart of Andaman 100 the profile. Additionally,if a givenMarianas-style subduc-' Mid. America 100 Mexico 90 tion zone is fairly young, then some of the slab's steepness Kurile 82 might be a holdoverof its youth (Figure 7), with ablution Ryukyu 55 helping to slow the slab's evolution toward an increasingly Makran 46 shallow shape. Sumatra 27 What is not clear is whether ablution in the Marianas it- New Zealand 21 Aegean 11 self was ever strong enough to maintain a stable, steep slab profile. Estimates of Marianas forearc consumption rates rangefrom a steady0.15-0.3 cm/yr [Beccaluvaet al., 1980] Oceanic and Transitional to a 0.3-0.5 cm/yr pulseof 12-20 m.y duration [Bloomer, Central Aleutians 56 1983]. Comparedwith the modern Marianas convergence Lesser Antilles 48 velocityof some8-10 cm/yr [Fryereta/., 1990],such rates Marianas 45 are much lower than what our experiments suggest is re- Izu-Bonin 45 Palau 45 quired to produce steep, mature slabs. While convergence Yap 45 velocities might have been lower during the height of the Kermadec 30 ablativepulse (if, for example,the ablutiontook place dur- Scotia 30 ing a period of inactive back arc spreading)and while our Java 27 experiments probably overstate the required degree of ab- Tonga 24 Sangihe 13 lution by not including the effect of other slab-steepening New Britain 8 mechanisms,it seems unlikely that such a weak rate of ab- New Hebrides 8 lution can of its own maintain a steep slab. If these estimates Solomon 8 representthe maximum amount of ablution in the Marianas North Sulawesi 7 forearc, we would therefore suggestthat ablation's chief role Philippine 6 has been to help retard flattening of the slab profile. From Jarpard, 1986. Oceanic arcs are generally much younger Alternatively, it is conceivablethat current consumption than arcs on continents; this age distribution is consistent with an estimates, which are based on patterns of surviving arc base- ablative recycling of island arc material. 8894 TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION

If, however, arcs can be entirely consumed,then the youth pectedto lack both the inherentasymmetry of Andeansub- of modern oceanic arcs does not imply a corresponding duction and the extension-influenced, intermediate charac- youth of subduction. Episodes of vigorous ablation would ter of Marianas-style zones. Plate consumption might then then remove records of ancient subduction, biasing arc ages take place in a symmetrical fashion, producing surface ef- toward anomalously low values. Such a consumption would fects that are difficult to interpret within the framework of explain the curious nature of the North Sulawesislab: while classicalone-sided subduction. A possibleexample of such a the arc-derived age of subduction in North Sulawesiis 7 :t:4 region is the tectonically complex area about the Philippine m.y., the tip of the slab appears to have been subducted Islands. some 15.3 m.y. ago [Jarrard, 1986]. Assumingthese es- In an ablative convergence of symmetrical plates, the timates are not grossly in error, they would suggest that lower lithosphere should descendas a simple, near-vertical geologic evidence for the earliest phase of North Sulawesi downwelling(Figure 4a). If sucha slab yields arc volcan- subduction has been lost. ism, magma originating in the slab will tend to rise through Arc consumption would also help explain why apparent or near the center of the convergencezone, accumulating at hiatuses are found in the arc magmatism of Marianas-style the surface as a centrally located island arc. This linear, areas. For example, arc volcanism in the Marianas zone buoyant mass may be further augmented by continental or seemsto have been minimal between 20 Ma and 30 Ma, with arc material brought in from elsewhere. Because such an anothergap appearingfrom 5 to 9 Ma [Scottand Kroenke, arc will be kept warm by active volcanism, and because it 1980]; likewise,a minimum in Ryukyusvolcanism has also will not suffer the rifting that occursin extensionalzones, it beenreported for the period21-49 Ma [Bowinand Reynolds, should be more likely to survive than its Marianas counter- 1975]. Within the framework of the classicalmodel, the part. By accumulatingin the center of the convergence,this origin of these gaps is unclear. Because the minima often arc may then considerablycomplicate the surfaceresponse coincide with pulses of back arc spreading, it has been sug- to an essentially simple ablative downwelling. gested that back arc spreading and arc volcanism are in- The simplest geometry is that of double subduction, herentlyasynchronous processes [Scott and Kroenke,1980]. whereby a central landmass is bounded on either side by However, this suggestionconflicts with the synchroneity of convergingsubducting plates. Examplesof suchdouble sub- spreading and arc volcanism that is displayed by more mod- duction might be found in the Philippines[Rangin et al., ern back arc spreadingregions [Karig, 1980]. Ablation can 1988] and Caribbean [Larue, 1989], and its occurrenceis reconcilethese conflicting observations:if arc magmatism is also consistent with the occurrence of anomalous seismicity continuous,episodes of vigorous ablation, perhaps linked in behind Costa Rica (G. EkstrSm, personalcommunication, some fashion to back arc spreading, might produce apparent 1991) (Figures18a-18c). gaps in the record. A second possibility is that of time-varying subduction, If ablation can be episodic, then we have an alternative in which subduction appears to oscillate about a centrally explanation for the steepnessof Marianas-style slabs. It is located arc. The mechanism behind such an oscillation is conceivable that these slabs neither remain stable nor be- shown in Figure 19. If for some reason the upper litho- come monotonically more shallow with time; instead they spherefails in an initially asymmetricfashion, a singletrench might fiatten and steepenwith alternate periods of accretion will form to one side of the central landmass(Figure 19a). and ablation. Such an episodicity must remain speculative Hence, while ablation removes the lower lithosphere in a until more experiments are performed, but its occurrence roughly symmetric fashion, the surfaceappearance is that at least seems possible. We have proposed that Marianas- of a conventional one-sided subduction zone. Because of style ablation will be self-limiting, as over time the forearc this surfaceasymmetry, the arc will try to migrate toward basin will incorporate buoyant massesof warm arc-derived the apparent subducting plate. This movement will carry basement. This suggestion is consistent with observations the active trench away from the vertical axis of the vertical of anomalously high and variable rates of heat flow in the slab, and the top of the slab will come to lie beneath the fore-arcbasins of East and SoutheastAsia [Anderson,1980]. inactive side of the arc (Figure 19b). If ablation-induced Of interest is what happenswhen this forearccools, for with stressesthen cause the overlying plate to fail, subduction coolingwill come a rise in plate density. Resurgentablation will appear to wane on one side of the arc while strengthen- may then consume the arc-derived forearc, induce a tem- ing on the other (Figure 19c). In this way, subductionwill porary steepeningof the slab, and perhaps even accentuate have apparently changeddirection, with a brief appearance back arc spreadingby increasingtensile stresseswithin the of double subduction in the shift from one polarity to the overriding plate. Eventually, this resurgencewill also foster other. Sucha processwould be consistentwith the observa- a renewed migration of the arc, and a warm, arc-derived tion that most recently reversedarc systemsare associated forearc might then redevelopto start the cycle anew. Thus with extremelysteep slabs [Karig, 1972], and it suggestsa ablation in Marianas-style subductionzones is potentially mechanismfor spontaneousreversals of subductionpolarity complexin its effects,and the ablative model allows for dy- that does not require an arc or continent collision to have namic feedbacksrelating slabs to arcs, forearcs, and back occurred. (As noted earlier, a spontaneousreversal seems arc spreading basins. to have taken place about the Philippine island of Luzon [Lewisand Hayes,1980].) A blation in Philippine-Style SubductionZones A third possibilityis again of subductionreversal, the re- versalsoccurring in straightforwardresponse to changesin We would expect ablative subduction to adopt its most rates of ablation. If the asymmetry of plate density changes extreme form when plates of similar character converge in overtime, through either arc collisionor a more gradual al- a compressionaltectonic regime. Such plates would be ex- teration of plate character, then a simple redistribution of TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8895

120 •

•0• N Aclive$ul)cluc hon Inactivesubcluctmn Thrust

P. Panoy

SOUTH N.P.8. North' Polowon block CHINA SEA C.R Cocjoyon R,dge

130 •

CEœ FEES SEA

Fig. 18a. Double subduction. Proposed tectonics in the Philippines, showing linear island chains bounded on either side by subduction[from Rangin et aI, 1988].

88kin

Fig.18b. Proposed cross section across the Mona Passage, near Puerto Rico [after Larue, 1989]. relative ablation rates may sut•ce to "swing" a slab from adjacent slabs of opposite polarity. Such a slab geometry one polarity to the other (Figure 20a). If this swingingof has been proposedin the Molucca Sea south of the Philip- the slaboccurs at differenttimes along different sections of pines(Figure 20b [afterAddicott and Richards,1981]). The the trench, then a single trench will appear to overlie two conventionalexplanation for this feature would be that two 8896 TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION

axis of max vertical stress

1 ON "

8N 86W 84W/ 8œW

09...,..:•d•.• • 0 ..:••83 max vertical stress

Fig. 18c. Anomalous earthquake beneath Costa Rica. Earthquake , 042291 lies above the plane of the slab and may be interpreted as indicating a shallow thrusting from the north ((•. EkstrSm, personal communication, 1991).

oppositely migrating subduction zones have passedby each (b) other; an explanation in the ablative framework would be that what appears to be two slabs is in fact a single downwelling that has not wholly reversed its dip. Thus in addition to double subduction, the ablative model allows for two dynamically plausible modes of subduction polarity reversal. In both mechanisms,the lower lithosphere smoothly descendswhile the upper lithosphere respondsdis- continuously. Given the apparent frequency of subduction reversals,this aspect of the model is a significantstrength. Within an ablative framework, we can interpret complex tectonic processes as a response of the Earth's brittle surface to simple viscousablation below; this conceptualdecoupling between surface and interior is a major distinction between the ablative and classicalmodels. In the classicalmodel, we must directly relate what we see at the surface to processes and geometriesdeep underground. This requirement causes complicationswhen we considercomplex tectonics (Figure 2, repeatedas Figure 21a), complicationsthat disappearwhen Fig. 19. Apparent reversals in subduction polarity: a near- we relax the conceptual link between surface and interior symmetrical, vertical "slab" exerts a downwards pull on the mate- (Figure 21b). rial directly above it; if this pull can break the elastic lithosphere and crust, an island arc may oscillate about the axis of the slab. (a) An arc bounded by a single trench will move toward the ap- 5. CONCLUSIONS parent subducting plate. This motion puts the passive side of the arc over the slab, where vertical slab-induced stressesare highest; We see that an alternative view of subduction, one based (b) plate failure might then create a transient stageof double sub- on the viscous consumption of the lower lithosphere, is an duction. (c) As the new trench experienceshigher stressesthan does the original, subduction may then appear to undergo a spon- appealingway of modellingthe majority of the Earth's con- taneous change in polarity. At all times, subduction of the lower vergencezones. If we considersubduction not as an overlap- lithosphere proceeds simply and smoothly. ping and slidingof rigid plates,but as a processmore akin to the downwellingof a convectingfluid, then we can easilyand simply explain variations in slab shape, interplate seismic- a fluid and the more brittle surface layers then breaking up ity, observationsof tectonicerosion, double subduction, and to suit. subduction reversal, all with a single, simple model. While An integral aspect of the ablative model is that it allows these phenomenaand observationscan also be explained for a two-sided mode of lithospheric descent. While some within the classicalframework, the required mechanismsare loss of overriding plate material has long featured in geo- often lesselegant. For dynamicalreasons, we suggestthat chemical models as a means of recycling continental crust classicalsubduction best applies to regions like the Aleu- into the mantle [C•illuly,1971; Jacobsen,1988], such "tec- tians (i.e., thoseareas in whichoverriding plates are strong tonic erosion" has generally been considered dynamically enoughto controlthe subductionprocess). In the remaining unimportant. We suggestthat ablative lossesof the viscous convergencezones, which are far morenumerous, subduction lithospheremay at times be significant, and that these losses may be ablative, with the lower lithospherefalling away as may influencethe evolution of a subducting slab's profile. TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8897

Fig. 20a. Subduction reversal through changes in ablation rate: a stable subduction zone with c• -- 0.333 has its ablation rate suddenly upped to c• -- 0.667, reversing the dip of the slab.

as should occur in oceanic zones, effective trench migration will be hindered. The progressive flattening of a slab is thus slowed, and steep profiles can be stable when moderate ablation occurs. In addition, the pattern of deformation undergoneby fluid slabs, be they ablative or one-sided, is consistent with frequently observed seismic focal mechanisms if the mantle's viscosity increases below 670 km: at the surface is compression, at intermediate depths there is extension, and at the bottom of the upper mantle there is again compression. Buoyancy-controlled ablative subduction can thus account for many fundamental characteristics of oceanic and continental-style slabs. If ablative subduction does occur in oceanic regions, it might not be readily discerned through patterns of seismicity. In the lithosphere and uppermost mantle, the deformation associated with moderate ablation is consistent with observed seismicity patterns, while at greater depths, ablated material adheres closely to the downgoing slab and might not be easily resolved. The relative aseismicity of Marianas-style convergence,however, is consistent with the ablative model: if ablation occurs here, then a rolling under of forearc basins might allow even seismically coupled plates to converge aseismically. What should control the character of an ablating oceanic subduction zone is the region's overall tectonic regime. In an extensional regime, ablation is self-limiting, and subduction might go through cyclesof accretion and moderate ablation. Fig. 20b. Proposed plate boundary in the Molucca Sea south of the (If suchcycles occur, then the consumptionof arc material Philippines: the north-south trench between Sulawesi and Halma- might destroy evidence of previous phasesof subduction and hera shows a slab reversal from west dipping near Mindanao to ablation.) With compression,the convergenceof oceanic east dipping farther south near Kepulauan Sula [after Addicott plates can lead to vigorous ablation, double subduction, and and Richards, 1981]. observations of apparent subduction reversal. In each case, the behavior of the lower lithosphere is relatively simple; The slabs within the ablative model are not slablike in a what varies is the rate of ablation and the response of the rheological sense. Instead, we assume their behavior to be upper lithosphere. predominantly that of a fluid. Our experiments show that Thus, while ablation is not easily proven, its incorporation slab strength is not necessaryto explain the shapesof seismic into a model of subduction can simplify the interpretation of Benioff zones. Even completely fluid downwellingscan take conflicting and complex observations. It suggestsa unified on realistic shapes, particularly if plate consumption can at model for almost all convergence zones, is consistent with times be double-sided. In Andean-style regions, where con- modern views of a partly fluid lithosphere, and elegantly tinental buoyancy inhibits ablation of the overriding plate, explains slab profile variations and various problematic sur- subduction can be approximately one-sided. Rapid effective face processes. The model thus invites further exploration trench migration will then encourage the gradual develop- to determine its range of applicability, its limitations, and mentof a fiat-lying,kinked slab. With higherablation rates, its implications. 8898 TAO AND O'CONNELL: AN ABLATIVEMODEL OF SUBDUCTION

CELEBES COTABATOSANGIHE TALAUO PHILIPPINE PHILIPPINE BASIN TRENCHRIOGE RIOGE TRENCH BASIN

$OUTHEAS'• AN PLA1 // PHILIPPINE --- ,7'/

00600 / /I400 I 200I I O0I I 200I I 4OO DISTANCE. KM

(b)

Fig. 21. (a) Classicalinterpretation of slab profilessouth of Mindanao,Philippines [from Cardwellet al., 1980]; repeated from Figure 2. (b) An example of an ablative interpretation of the same region.

APPENDIX A: EXPERIMENTAL MODEL and are not at all certain. Rather than base our experi- In our numerical experiments,subduction is modelled as ments on a particular view of the Earth, we instead adopt the foundering of dense material. These experiments are a more neutral, simple model, wherever possible choosing essentiallyexperiments in fluid flow, in that the sinkingof experimental parameters that will best illustrate ablative slab material drives internal flow within the mantle, and the effects. The greatest simplifications involve the rheologies mantle flow in turn drives the surfaceplates and distorts the of the plates and slabs and the number of forcesdriving the slab as it sinks. plates. Since internal strength will hinder a slab's response Ideally, our experimental model would incorporate de- to changingstresses, we model slabs as fluid downwellings tailed rheologiesand forcesidentical with thosein real sub- which differ from the mantle solely through their greater duction zones,but in practice, the propertiesof plate, slab, density. In effect, our slabs are so broken in the process and mantle are themselvesthe subjects of active research of subduction that they cannot resist the effects of mantle T^o ^ND O'CONNELL: AN ASL^TIVE MODEL Or SUBDUCTION 8899 flow. While real slabs are likely to be more viscous and hence lithosphere from the upper mantle and the upper from the strongerthan surroundingmaterial [Zhangeta/., 1985],the lower mantle (material may freely passthrough the transi- rheology we use maximizes a slab's responseto changes in tions). In all the experiments,the lithosphericviscosity is the mantle flow field that may arise from migration. Such a 10 times that of the upper mantle (higher lithosphericvis- rheologyis also consistentwith the very seismicityof slabs, cositiesdo not producesignificantly different results). The which indicates that they deform as they descend, and with fluid associated with the lithosphere is of usually of higher both modellingconsiderations [Hager and O'Conne//, 1978; density than fluid belonging to underlying regions; in the Begis, 1986] and detailed studiesof slab morphology first experimental set, we set the lithosphere lying to one ardini and Woodhouse,1984, 1986; Fischer et M., 1988], side of the trench at different relative densities, while in the which suggestthat a slab's strength does not prevent its be- remaining experiments the lithosphere has a constant den- ing sculpted by mantle flow. As it is not clear how much of sity throughout. As this dense lithospheric fluid sinks, it a slab's observed profile is governed by its internal strength generates a flow field through the entire box. To determine and how much by fluid flow, our study then has the addi- its path of descent, we make use of what is normally a nu- tional goal of determining to what extent flow effects alone merical limitation: because a computational scheme cannot may account for slab shape. For the lithospheric plates, we distinguish between mass concentrated at a point and mass adopt the standard division of the lithosphere into elastic distributed within the model's spatial resolution limit, the and viscousportions [Jordan, 1978] and model the viscous flow generated by a continuous dense fluid is indistinguish- lower portion as a layer of high-viscosityfluid atop the man- able from that generated by closely spaced point masses. tle. Rather than explicitly include the elastic upper por- We therefore treat the high-density lithosphere as a collec- tion, we impose a platelike velocity boundary condition on tion of point density anomalies, each anomaly representing the flow atop the viscous lithosphere; this condition mimics the excessmass of a region of cold lithosphere. In its initial the nonlinear behavior of a rigid upper lithosphere strong state, our model thus contains a row of evenly spaced, uni- enough to maintain platelike motion within plate interiors form point anomalies, all lying 45 km below the surface of but weak enough to fail abruptly at the boundaries. So that the fluid. From these density elements, we calculate the flow flow beneath the trench is not distorted by arbitrarily cho- field using a quasi-analytic method discussedin Appendix sen plate velocities, we set the surface velocities to reflect B, then use the flow field to advect the anomalies through the motions of plates that are driven by the flow surround- successivetime steps. ing a sinking slab. This choice of dynamically consistent Our experiments proceed as follows: starting with the plate velocities forms the third major simplification in the uniform row of lithospheric anomalies, we select initial po- model, in that we neglect potentially significant plate forces sitions for a ridge and a trench. At the trench, we perturb a suchas ridge-push[lithospheric-thickening,which will drive single anomaly downward to initiate subduction, then step the plates faster, and collisional resistance, which will slow the model through time by following a simple set of instruc- them. tions (Appendix B): with each time step, we calculate the The model we use is shown in Figure A1. Its geome- flow field generatedby the densityanomalies (Appendix B), try is two-dimensional Cartesian, with periodic sidewalls, a paying due attention to density-driven motions of the sur- platelike surface boundary condition at the top, and a free- face plates (Appendix C); anomaliesare then advectedto slip condition representingthe core-mantle boundary at the new positions along the streamlines. From the surface plate bottom. Within this periodic box, a Newtonian viscousfluid velocities, we determine the migration speeds of the ridge represents material of the upper mantle, the lower mantle, and trench: the ridge moves at the vector average of the and the viscousportion of the lithosphere. In the present ex- plate velocities(the conditionfor symmetricalspreading), periments, we scale the box to span 2900 km in the vertical the trench in accordancewith equation (1); thesemigration direction and 5800 km in the horizontal; flow is evaluated velocities are used to shift the ridge and trench in prepara- on a grid numbering 65 points across and 33 down, yield- tion for the next time step. (In the first experimentalset, a ing an effective spatial resolution of about 90 km. Viscosity is determined by measuring the flux of material that passes transitions at depths of 90 km and 670 km distinguish the through a horizontal plane lying one grid level beneath the base of the viscouslithosphere; in the second,we specify the

Platelike Surface Velocities value of a for each run.) Finally, if anomalieshave moved apart at the ridge, we emplacenew (constant-magnitude) 0 km Ridge Trench T]1 anomalies to represent the production and fast cooling of "[]1[[ 1! [] • • [[l[;[l[f •1 I [[1•[I I [•l]•llllfl I f •[I II[11•[I • •[•l•'[l]'[l 90 km- fresh lithosphere. Densityanomalies inplate •n•l• •2 670 km- The simplicity of the instruction set points out an important aspect of our model: after the initial, single displacement that begins subduction, the density anomalies freely FluidMantle •• •3 advect without further guidance. No attempt is made to force them downward at the trench, to pin them to the surface elsewhere, or to force them to move together as a plate or slab. Platelike motion comes from the velocity boundary

2900 km Free-slipBottom Boundary condition, which in practice tends to entrain anomalies in a near-surfacehorizontal flow; if an anomalydoes begin a de- 0 km 5800 km scent,it is becauseit has encountereda downwellingin the Fig. A1. Geometry and rheologiesused for numerical experiments. overallflow field (in practice,such downwellings occur where •1 = 10•2 in all experiments. In the first set of experiments, platesconverge). At all times,anomalies are mechanically r/3 = r/2; in the secondset, independentof one another,and the "slabs"they form are 8900 TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION

effectively nothing more than regions of strengthlessdense body force Apg arising from a density perturbation Ap un- fluid, freely moving with the vagaries of mantle flow. Col- der gravitational acceleration g. lectively, these anomalies show the development of simple, To solve these equations, we express fluid stresses and easily deformed slabs beneath migrating trenches; by run- velocities as the real part of a discrete Fourier series:

ning the experiment with varying values of c•, we may see N how ablation can influence the course of that development. f(x,Z) = Re•-•fn(z)e (A4) n----0 APPENDIX B: STRUCTURE OF THE NUMERICAL CODE where x is the horizontal axis; z is the vertical, with z = 0 We solve for the flow field in a sequential manner. In at the top of the fluid and z = i at the bottom; k• is the the initial time step, all density anomalies but one lie in wavenumber,given by k• = 2•rn/L; N is the maximum a uniform sheet near the top of the fluid; the remaining number of terms retained (N = 32 in the presentexperi- anomaly is displaced downward at the trench to initiate ments);and f (x, z) is eitherthe verticalvelocity vz, the hor- subduction.We calculatethe flow (AppendixC) that these izontal velocity vz, an element of the nonhydrostatic stress anomalieswould generate when placed under a zero-velocity tensor rij, the nonhydrostatic pressurep, or a density per- top boundary; this flow field is stored, and the shear trac- turbation Ap. Finding the solutionto equations(A1)-(A3) tions at the base of the viscouslithosphere are used to deter- then becomesa matter of solving for the Fourier coeffcients mine dynamicallyconsistent plate velocities(Appendix D). f,•(z). The plate velocities are then used in a secondcalculation, in Followingthe methodof Hayer and O'Connell[1981], we which we determine the flow produced by plate motions in combineequations (A1)-(A4) into a vectorequation for each the absenceof density anomalies. Adding the density-driven fourier mode: and plate-driven flow fields together gives us the complete du flow field. d-•- Au+ b (A5) Our next step is to advect the anomaliesthrough the flow field. We determine the streamlines passing through each whereu is the array[Ul, U2, U3, U4] T, givenby anomaly and move the anomalies along them. This advec- Ul -- -ikvz tion proceedsuntil the fastest moving anomaly has travelled U2 ---- kvz a distance equivalent to half a grid spacing, at which point (A6) i the advection is halted until a new flow calculation is per- U3 formed. Each time step is therefore of variable length. 2r/0 Last, we use the dynamically consistent plate velocities 1 U4 to determine the trench and ridge migration velocities: the 2r/0 ridge travels at the vector sum of the plate speeds, while b is the array [0,0,-iApg/2qo,O]T for eachof m density the trenchvelocity is givenby equations(1) and (2) in the anomalies,of vertical thickness A7 and located at depth 7, text. We assumethat plate speedsremain constant within a and A is the matrix time step and simply multiply the migration speedsby the duration of the time step to obtain the new plate boundary 0 -k 0 0 ' positions. A= 0k 0 0 2k1•7'-k (A7) APPENDIX C: MATHEMATICAL DEVELOPMENT 0 2r/*k k 0

Analytic Solution with r•* = r•/r•o, and r•o as some referenceviscosity. The solution is then We calculate fluid flow by combining an analytic propagator solution with a numerical finite difference scheme. The m analytic development closely follows that used by Hayer and u(z)-- P(z, z0)u(z0) + ZP(z, 7i)b(7i)A7i (A8) O'Connell[1981], with a few changesto increasethe flexibil- i--1 ity of the solution, while the numerical part of the method with the propagator matrix involves a modification of a standard relaxation code. The flow in our experiments takes place in two dimen- c o Sl* o sions and is assumed to be periodic along the horizontal 0 C 0 S/rl* (A9) axis, with a spatial wavelength of L. For flow in an in- P(z-zo) = 7'S 0 C 0 compressibleNewtonian fluid at zero Reynoldsnumber, the 0 •*S o C governingequations are the continuity equation, the consti- -s -c -Cl,f -Sl* tutive equation, and the equations of motion: + LAz C S S/•7' C/•* V.v = 0 (A1) -v*C -v*S -S -C v*S v*C C S r = 2U• - pI (A2) whereC = cosh(kAz), S = sinh(kAz), and Az = (z- zo).

V. r + f = 0 (A3) Incorporation Into Relaxation Method where v is the fluid velocity, • is the stress tensor, r/ is Although the propagator gives us an analytic solution the viscosity,• is the strain rate tensor, p is the nonhydro- for the flow field, this solution is difficult to evaluate at static pressure,I is the identity matrix, and f is the vertical high wavenumbers. For a fixed Az, differencesbetween TAO AND O'CONNELL: AN ABLATIVE MODEL OF SUBDUCTION 8901 cosh(kAz) and sinh(kAz) becomevanishingly small with boundary conditions. We may therefore make Az arbitrar- large values of k•, and the propagator becomes singular. ily small by increasing the number of grid levels, thereby Because our boundary conditions are split between the sur- keeping cosh(kAz) and sinh(kAz) small enoughto avoid face (z = 0) and the bottom (z = 1) of the fluid, a solution singularities at even high values of k. Any remaining nu- for the complete set of boundary conditions requires that we merical errors are then minimized by the error correction of propagate from z -- 0 to z - 1. As we thus cannot set Az the relaxation method and distributed throughout the grid. to an arbitrarily small value, a straightforward evaluation of A further benefit of this method involves the vertical place- the solution is intractable. ment of densityanomalies: because equation (A8) yieldsan To overcome this difficulty, we combine the propagator exact expression for an anomaly's effect upon the flow at with a numerical finite difference algorithm to evaluate the different depths, the depth resolution of the anomaly is in- solution. The technique we use resembles a standard re- dependent of vertical grid spacing, and we may freely place laxation scheme for solving two-point boundary value prob- density elements at intermediate depths between grid levels. lems. Such methods are stable, ideally suited to problems in which the solution contains dying and growing exponentials APPENDIX D' PLATELIKE VELOCITY CONDITIONS (suchas appearin our hyperbolicsines and cosines)and are efficient in memory use when performed on a digital com- To calculate the horizontal velocity at the top of the fluid, puter. Additionally, relaxation methods are well-developed, we use a method discussedby Hager and O'Connell [1981] and fast, standardized routines have been developed for their and by Gable et al. [1991]. Surfacevelocities are platelike, application. We therefore use a standard relaxation code and the dynamically consistent plate velocities are defined [Presset al., 1986]but alter it to incorporatethe propaga- as those which add no energy to the system. To find the tor. dynamically consistentplate velocities, we require that the In a conventional finite difference method, we essentially forcesacting upon each plate must sum to zero. The plate replace the differential equation speedat which velocity-dependentand velocity-independent forcesbalance is then the desired velocity. du The forces which may act upon a lithospheric plate are d-•- Au (A10) varied; proposedforce mechanismsinclude ridge-push,ther- with the finite difference equation mal thickeningof the lithosphere,slab-pull, slab-resistance, An collisional resistance, transform fault resistance, trench suc- = Au (All) tion, and mantle drag [Forsythand Uyeda, 1975;Hager and or, O'Connell, 1981]. In our model,only mantle drag and a form of slab-pull/trench suction appear. These forces are not Au- AuAz (A12) parametrizedin the fashionof forcebalance studies [Forsyth Starting at a known value of u (e.g., at the boundaries), and Uyeda, 1975];instead, they are fluid dynamicalforces we may then use equation (A12) to find successivevalues arising from the sinking of density anomalies and the resultof u at discrete grid points. Such a solution is dependent ing shear coupling between plate and mantle. Propelling upon on the spacingbetween grid points Az, with an in- the plates is a slab-induced, velocity-independent force that creasingdegree of error associatedwith increasing values depends upon the shape and size of the subducting slab. of Az. The standard relaxation method attempts to mini- This slab-induced force differs from the conventional slab- mize these errors and distribute them evenly among the grid pull mechanismof Elsasser[1969], wherein subducting litho- points through an iterative processof error correction;with sphere acts as a stressguide directly coupling the descent of each iteration, the solution at each grid point then relaxes the slab to the horizontal motion of the subducting plate. toward a value in keepingwith the finite differenceequation As the slabsin our model are fluid and strengthless,there is and boundary conditions. A strength of this method is its no such mechanical coupling. Instead, the sinking of dense stability, as errors are not allowed to grow over successive material generates a local circulation about the slab, which grid points. Drawbacksinclude the errors implicit in the in turn drives plate motions through a coupling between finite differenceapproximation and the need for successive lithosphereand mantle [Hager and O'Connell, 1981]. As iterations to approach the solution. such coupling does not distinguish between subducting and By incorporating the propagator matrix P into the re- overriding plates, the resulting plate force is a form of both laxation scheme, we retain the stability advantagesof the slab-pull and trench suction. Retarding the plates is mantle standard method but increasethe accuracy and speed. As drag, which is produced by shearing between the plate and the propagatoryields an exact expressionfor the changein those portions of the mantle which are not strongly driven u for a givenAz, we may rewrite equation(A8) as by the local slab circulation. We calculate this force directly from the flow field; in practice, however, its strength varies directly with plate speed and size. Az Au=((P- I)) uAz (A13)Potentially important mechanismsthat we have neglected We see then that the finite difference matrix A in equation include lithospheric thickening and collisional resistance;we (A12) may be replacedby ((P- I)/Az), a substitutionthat omit these and others to avoid complexity. Thermal litho- makes the equation exact and independent of grid spacing. spheric thickening adds a driving force that depends largely The solution may then be obtained in a single iteration, upon the spreadinghistory of the system prior to the begin- and stability problems are avoided for the following reasons: ning of the experiment; the effect of this mechanism may be with the relaxation code, the propagator is used only to approximated by adding a constant, arbitrary driving force relate the flow at adjacent grid levels, and it is no longer to each plate. Collisional resistance, as well as other plate- necessaryto propagate from z -0 to z - i to solve for the boundary forces,depends upon the rheologiesand processes 8902 TAO AND O'CONNELL: AN ABLATIVEMODEL OF SUBDUCTION

in effect at a particular plate boundary; its contribution is Benioff, H., Orogenesisand deep crustal structure: Addi- to add a poorly constrained retarding force to each plate. tional evidencefrom seismology,Geol. Soc. Am. Bull., The combined effect of these various mechanisms is to add 65, 385-400, 1954. a force of unknown or arbitrary magnitude and sign to the Bevis, M., The curvature of Wadati-Benioff zones and the force balance on each plate. Such an addition will have an torsionalrigidity of subductingplates, Nature, 323 52-53, impact on plate velocities and suggestsa future course of 1986. study; for now we seek the simplest model and include only Bloomer, S. H., Distribution and origin of igneous rocks mantle drag and slab-induced forces. From the landward slopes of the Marianas Trench: Im- To determine the force componentson each plate, we note plications for its structure and evolution, J. Geophys. the linearity of the equations governingthe flow and decom- Res., 88, B9, 7411-7428, 1983. pose the flow field into density-driven and traction-driven Bloomer, S. H., and J. W. Hawkins, Gabbroic and ultramafic components. The former is the flow produced by density rocks from the Mariana Trench: An island arc ophio- anomalies sinking beneath a stationary surface; the latter lite, in The Tectonic and GeologicEvolution of South- is the flow driven by surfaceplates moving over a homoge- eastAsian Seasand Islands,Part 2, Geophys.Monogr. neous fluid. We first calculate the density-driven flow, then Set., vol. 27, edited by D. E. Hayes, pp. 294-317, AGU, integrate the shear stress along the base of the lithosphere Washington, D.C., 1980. to determine the effective driving force di on each plate i. Bowin, C., and P. H. Reynolds, Radiometric ages From We next calculate the flow field associated with the motion Ryukyu Arc region and an Ar-40/Ar-39 age from bi- of a single plate j at a velocity vj - 1, then determine, for otite dacite on Okinawa, Earth Planet. Sci. Left., 27, eachplate i, the integratedshear stress T/j causedby the 363-370, 1975. motionof plate j. Repeatingthe processfor eachplate gives Cardwell, R. K., B. L. Isacks, and D. E. Karig, The spatial us a matrix T, for which Tij is the forceexerted on plate i distribution of earthquakes,focal mechanismsolutions, by the motion of plate j. The force balancerequirement on and subducted lithosphere in the Philippine and north- each plate then gives the expression easternIndonesian islands, in The Tectonicand Geologic Evolution of SoutheastAsian Seas and Islands, Part 1, T-V=-D Geophys.Monogr. Set., vol. 23, edited by D. E. Hayes, pp. 1-35, AGU, Washington, D.C., 1980. where T is the matrix of T/j, V is the array of unknown Carney, J. N., and A. MacFarlane, Geologic evidence bear- plate velocitiesvj, and D is the array of density-drivenshear stressesdi that are to be matched. Solving this matrix equa- ing on the Miocene to recent structural evolution of the New Hebrides Arc, the evolution of the the India-Pacific tion yields the dynamically consistentplate velocities. plate boundaries, Tectonophysics,87, 147-175, 1982. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Sta- Acknowledgments. This work was supportedby NSF grant bility, pp. 9-75, Oxford University Press, New York, EAR 8708477 and NASA grant NAG5-840. We are grateful to 1961. Bruce Buffett, Carl Gable, Richard Holme, and Joann Stock for Chase, C. G., Extension behind island arcs and motions critiquing our manuscript, and to Dennis Hayes for providing relative to hot spots, J. Geophys.Res., 83(Bll), 5385- maps of the western Pacific. We especially thank B. H. 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