Stresses and plate boundary forces associated with subduction plate margins

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. B8, PAGES 11,933-11,944, JULY 30, 1992

Stresses and Plate Boundary Forces Associated With Subduction Plate Margins

A. WI-IITTAKER •, M. H. P. Boa?T, AND G. D. WAGHORN •

Department of Geological Sciences, University of Durham, En91and

Primary tectonic stress in the lithosphere is predominantly caused by lateral density variations within the Earth and associated topographical loading. When such a stress system caused by major sublithospheric density anomalies is intersected by a weak zone which cuts across the lithosphere, plate boundary forces develop and modify the plate interior stresses. In this paper, finite element analysis is used to model the stresses and plate boundary forces associated with subduction plate boundaries, with dipping and vertical slabs extending to about 270 and 400 km depths having the subduction fault both locked and unlocked. In such regions, several types of horizontal deviatoric stress may occur, including (1) local compression in the trench-arc region caused by the dense sinking slab and the associated surface downflexure; (2) plate interior tension which occurs when this compression is intersected by a weak subduction fault; (3) local tension associated with thickening of the crust at the arc and elsewhere; (4) local tension in the back arc region produced by the underlying low density upper mantle; and (5) downbending stresses in the subducting slab, thermal stresses, and transmitted ridge push, which are not included in the modelling here. A gradient from compression in the forearc to tension in the back arc can be modelled in terms of these stresses when the fault is partially locked. It is, however, the intersection of the local compression (1) by an unlocked or partially locked subduction fault that modifies the plate interior stresses and gives rise to the slab pull and trench suction plate boundary forces. The state of stress in the interior of the overriding plate is also crucially influenced by back arc spreading where this occurs. Plate boundary forces have been evaluated for each of the models. It is shown that slab pull and trench suction may be of comparable magnitude.

INTRODUCTION

It has been recognized for some time that the subduction process can give rise to the slab pull force and to a more enigmatic trench suction force, which act to pull the subducting and overriding plates respectively toward the subduction zone [Forsyth and Uyeda, 1975]. These convergent plate margins can be associated with juxtaposed regions of compressional and extensional tectonics, such as the associa- tion of trench-arc compression and back arc extension characteristic of some subduction zones [Nakamura and Uyeda, 1980]. This paper aims to demonstrate that such local com- plications in the stress pattern can occur alongside the de- velopment of slab pull and trench suction plate boundary forces.

Plates are driven by the net torque which acts on them. For the simplified two-dimensional modelling of this paper, which neglects the Earth's curvature, this can be regarded as the net horizontal force. The driving force is in dynmnic equilibrium with underlying viscous drag and other resistances. If we wish to isolate the force acting on a plate at an individual plate boundary, it is necessary to reference it to a standard lithostatic pressure distribution, such as that of 80 Ma mature oceanic lithosphere. The force on a plate edge can then be determined by integrating the anomalous horizontal pressure with respect to depth [Lister, 1975]. This yields the force acting on unit horizontal length of the plate boundary, as "felt" by 80 Ma oceanic lithosphere in absence of intervening resistances.

1Now at SFK Technology Ltd, Milton Keynes, England. 2Now at BP Exploration Inc., Houston, Texas.

Copyright 1992 by the American Geophysical Union.

Paper number 91JB00148. 0148-0227/92 / 91JB- 00148505.00

The actual state of stress in the lithosphere is the superimposition of stress distributions of various origin, including surface and subsurface loading, thermal stress, membrane stress, and tidal stress. Subsurface loading includes loading due to lateral density variations both in the sublithospheric mantle and within the lithosphere. Much of the surface loading results from subaerial and submarine topography produced by flexural isostatic response to subsurface loads. Stress distributions caused by loading thus typically originate as the combined effect of associated subsurface and sur-

face loading. Loading stress distributions are of two types, bending stress and local isostatic loading stress. Isostatic loading stress is caused by subsurface and surface loading in local isostatic equilibrium as originally recognized by Bot• and Dean [1972] for passive margins and Ar•yushkov [1973] for more general crustal thickness variations. Where flexural isostasy applies, both isostatic loading and bending stresses occur. It is, however, the isostatic loading stress, and not the bending stress, which is relevant to the plate driving mechanism as indicated below.

The only one of these stress systems which is renewable [Bot• and Kusznir, 1984] and can dissipate tectonic energy at over 3x10 lø W (which is the rate of energy released by earthquakes) appears to be that due to sublithospheric loading in the mantle and the associated surface topography. Such deep loading can be renewed sui•iciently fast to keep up with the observed rate of tectonic dissipation as a result of inferred motions within the mantle beneath ocean ridges and convergent margins.

The stresses which give rise to plate boundary forces thus probably originate from surface and subsurface loading of the lithosphere. The relevant subsurface loading is mainly in the sublithospheric upper mantle. It occurs as low-density upper mantle, including upwelled asthenosphere beneath ocean ridges, and as dense subducting slabs beneath con-

11,933

11,934 WHITTAKER ET AL.: STRESSES ASSOCIATED WITH SUBDUCTION MARGINS

vergent plate margins. The surface loading is the isostatic response of the lithosphere to the primary subsurface loads.

This paper explores the main features of the stress distributions associated with subduction plate margins and demonstrates how the associated plate boundary forces originate. It develops and extends earlier work by Waghorn [1984], Whittaker [1988] and Bott et al. [1989]. A new set of models including crustal loading at the top of the overriding plate and subduction slabs which dip at both 45 ø and vertically is presented here and compared. Isoparamet- tic viscoelastic/elastic finite element modelling by the initial strain method has been used for the analysis of stress and deformation, as more fully described by Bott et al. [1989]. Surface loading is represented by boundary pressures, and anomalous subsurface loading is represented by body forces in the models. Faults are included using the dual-node tech- nique [Goodman et al., 1968]. The method used appears to be similar to that of Bischke [1974] except that here isostatic boundary forces have been automatically applied by modifying the stiffness matrix.

STRESSES ASSOCIATED WITH SUBDUCTION

It was shown by Waghorn [1984], Whittaker [1988], and Bott et al. [1989] that the downpull of the dense subducting slab and the associated trench and downflexure at the surface give rise to deviatoric compression above the slab. When this region of compression is intersected by a free subduction fault, then slab pull and trench suction develop in the subducting and overriding plates, respectively. Most of the models shown by Bott et al. [1989] were restricted to the surface lithospheric plates, with the downpull represented by a boundary traction. Two models, however, included the mantle down to 670 km with a 45 ø dipping slab extending to 400 km depth, one of these having the fault locked and the other having it free.

Here we present a more comprehensive series of models of the lithospheric plates meeting at a subduction plate bound-

ary and the underlying mantle down to 650 km depth. The models include dipping and vertical slabs extending to about 270 and 400 km depths, with the subduction fault being free or locked. In addition, a low-density upper mantle below the back arc region is included in the final models. The viscosity value adopted here for the lower lithosphere is a factor of 5 higher than that used by Bott et al. [1989] and is more in line with values generally used for modelling. However, 5 times more iterations are consequently needed to approach convergence.

The finite element grids used for dipping slabs and for vertical slabs are shown in Figure i•. The physical properties assumed are shown in Table 1. The anomalous densities are

referenced to the density distribution beneath the standard ocean floor at the right edge of the models and are thus superimposed on a laterally uniform suboceanic stress distribution. The 90-km-thick lithosphere consists of an elastic layer 30 km thick underlain by a viscoelastic layer 60 km thick with a viscosity 50 times that of the asthenosphere. Oceanic crust has not been included, but the upper 30 km of the overriding plate are assumed to be continental crust 400 kg/m 3 less dense than the mantle below. The viscosity increases by a factor of 10 below 400 km depth. The sinking slab has been assigned an excess anomalous density of 50 kg/m a except where the olivine-spinel transition occurs above 400 km depth, where it is 350 kg/m a. A subduction fault which may be locked or unlocked forms the top surface of the sinking slab. The models have been run for 500 time increments of 500 years each, that is 0.25 Ma. The low-density trench is not included in the loading to avoid excessive bending stresses, so that the slab is isostatically compensated entirely by downflexure.

The boundary conditions are as follows. The basal nodes at 650 km depth are constrained to zero vertical displacement but are free horizontally, having the effect of stiffening the resistance to subduction. The nodes at both edges of the lithosphere are constrained to zero horizontal displacement but are free vertically, thereby making it possible to measure

FINITE ELEMENT GRID FOR MODELS 3 AND 4

65O

0 Distance (km)

FINITE ELEMENT GRID FOR MODELS 7 AND 8

,

650

0 Distance (kin) 2400

2800

Fig. 1. The finite element grids used for the deeper subduction models 3, 4, 7, and 8. The grids for models 1, 2, 9, and 10 and models 5 and 6 only differ marginally. The central parts of the grids which are shown in the subsequent figures are outlined by the thicker lines.

WHITTAKER ET AL.: STRESSES ASSOCIATED WITH SUBDUCTION MARGINS 11,935

TABLE 1. Values of Density, Young's Modulus, Poisson's Ratio, and Viscosity Used in Subduction Models 1-10

Layer Anomalous Young's Modulus, Poisson's Viscosity, Density, kg/m 3 Pa Ratio Pa s

Continental crust -400.0 0.90x l0 ll 0.25 elastic Top oceanic lithosphere 0.0 1.75 x 10 ll 0.27 elastic Lower lithosphere 0.0 1.75 x 10 ll 0.27 5.0x 1022 Ast henosphere 0.0 1.75 x 1011 0.27 1.0 x 102 Mantle transition zone 0.0 2.80x 10 ll 0.27 1.0x 10 22 Upper slab (normal) 50.0 1.75 x 10 ll 0.27 elastic Lower slab (normal) 50.0 1.75x10 ll 0.27 5.0X10 22 Upper slab (spinel) 350.0 2.80 x 1011 0.27 elastic Lower slab (spinel) 350.0 2.80x 10 ll 0.27 5.0x 10 22

the tectonic force exerted by the sinking slab at the edges of the models. The influence of ridge push and basal shear drag beneath the lithosphere are thus excluded in order to isolate the subduction effects. A continuous surface pressure has been applied to the upper surface of the overriding plate equal and opposite to the upthrust of the low-density continental crust, representing the topography of the continent relative to the ocean floor. This surface pressure is shown at the nodal points in the figures at the same scale as the deviatoric stresses.

The stresses are determined at the Gauss points of each element, but for simplicity of presentation the average stress is shown in the figures at the center of the elements. This means that the bending stress is averaged out, as the elastic upper lithosphere is only one element thick. It is assumed in the modelling that the out-of-plane principal stress is the arithmetic mean of the two in-plane principal stresses. This seems most appropriate in view of the high pressures within the Earth and is conceptually more satisfactory than plane strain for viscoelastic modelling. However, the results do not differ substantially from those using plane strain. Within the figures, compressions are denoted by solid lines and tensions by dashed lines. Displacement vectors are shown for the nodes bordering elastic elements and represent the displacements at the end of the run relative to the initial fixed Cartesian coordinate system as shown.

The models presented here are two-dimensional and cannot therefore take into account stress effects produced by irregular shapes of plates. They also suffer from two further unavoidable limitations. First, the method used cannot han- dle the bending of the lithosphere at the trench, and so the large bending moments are avoided by omitting the negative surface load associated with the seawater in the trench

and incorporating the downbend of the oceanic lithosphere in the finite element grid. The downpull of the slab is thus entirely compensated isostatically by the downflexure which it produces which is rather broader than an actual trench. Second, a more serious limitation is that an ongoing state of plate motion and subduction cannot be properly simulated, because the downdip motion is transient. This limitation is discussed later within the context of the dipping slab models 1,2, and 4.

Deviatoric stresses and elastic displacements for models 1 and 2 with a 45 ø slab extending to about 260 km depth are shown in Figure 2. Model 1 has a locked fault, and model 2 has a free fault. There are two contributions to the

deviatoric stresses in the surface lithospheric plates. First, there is the compressional stress system caused by the corn-

bined effect of the dense slab and the isostatic downflexure it

causes, which is modified when the subduction fault is free. Second, in the overriding plate the low-density continental crust and the associated surface topographical loading produce a superimposed deviatoric tension of about 25 MPa.

When the subduction fault is locked, as in model I (Figure 2), the downpull of the slab produces a surface downflexure which is opposed by isostatic forces. An approximate state of equilibrium is approached over the modelled time span, except that a dipping slab suffers rollback on a longer time scale toward a vertical attitude.

The main features of the deviatoric stresses in the upper elastic lithosphere of model I with the locked fault are as follows. Small horizontal deviatoric tensions occur in the sur-

face part of the subducting plate, but these die off toward the edge of the model. In the overriding plate, substantial horizontal deviatoric compressions of up to about 70 MPa occur above the subducting slab, but these give way to a small tension of about 25 MPa, which extends to the edge of the plate, caused by the low-density continental crust and the associated topographic surface load. Substantial downdip tension occurs in the elastic part of the sinking slab above 200 km depth, but this dies off toward the bottom of the slab, where deviatoric stresses are negligible. The displacements display a broad downflexure of the surface above the slab of the type suggested by Davies [1981], extending just beyond the slab on either side and reaching a maximum of 1.03 km. The sinking slab shows a substantial component of rollback, as exhibited by the displacement vectors.

When the subduction fault is free, as in model 2 (Figure 2), then both rollback and downdip sinking of the slab are occurring at the end of the 250,000-year run, although the downdip motion is slowing down. During the final 250-year time step in model 2, the downdip slab velocity is 8 mm/yr and the rollback velocity is 10 mm/yr. Thus the main de- viation of the modelled slab motion from actual subduction

is that the downdip velocity is up to an order of magnitude slower. However, with the shallow increase in viscosity at 400 km and the vertically fixed basal nodes at 650 km depth, the mantle beneath the slab is certainly much stiffer than in reality. As a result, the resistance to sinking is probably of the right order of magnitude, as supported by the good comparison with observations of changeover from downdip tension to downdip compression (see later section on comparison with observed stresses). Further work needs to be done on the factors affecting the slab resistance, but this is outside the scope of the present exploratory study.

In model 2 the fault is unlocked with zero coefficient of


400

MODEL 1:300 KM DIPPING SLAB, FAULT LOCKED

ß

Deviatoric Stress

100 MPa

900 Distance (km) 2200

Displacement Vectors 2000 metre

. . . • • ,• • • I I IL/•_t_• ' .

ß . x.x• • . .

ß

ß •

400


MODEL 2:300 KM DIPPING SLAB, FAULT FREE Deviatoric Stress

ß

ß

ß J

ß

ß

400


Displacement Vectors m 2000 metre 0

ß • /'/ ....

ß

ß ... ß .

4OO


Fig. 2. Deviatoric stress distributions and displacement fields produced by model 1 (subduction fault locked) and model 2 (subduction fault free), with the top of a 45 ø slab extending to 260 km depth. The base of the lithosphere is marked by the dashed line and the upper elastic part of the lithosphere is outlined by the solid lines. The surface boundary pressures shown at nodal points simulate the excess continental surface loading relative to oceanic regions and are on the same scMe as the deviatoric stresses. Compressional deviatoric stress is represented by solid lines, and tensional deviatoric stress is represented by dashed lines. In some elements only the compressional stress is shown for clarity. The free subduction fault is marked by solid triangles on its upper surface. Properties assumed in these and subsequent subduction models are shown in Table 1.

friction. The effect of this is to superimpose a substantial horizontal deviatoric tension which extends out to the fixed

edges of both subducting and overriding plates. This has an element average of 64 MPa over 30 km depth range at the fixed edge of the sub ducting plate and of 70 MPa at the fixed edge of the overriding plate, where about 25-30 MPa can be attributed to the continental crustal loading effect and 40-45 MPa can be attributed to trench suction. Within

the sinking slab, downdip compression occurs near the bot-

tom as a result of viscous resistance to downdip motion at the end and along the lower surface, and the downdip tension near the top is consequently smaller than in model 1. Surface downflexure of the overriding plate is about 30% smaller than in model 1, but that of the subducting plate is larger. The displacement field demonstrates the motion of both plates toward the plate margin.

Models 3 and 4 (Figure 3) have the 45 ø dipping sinking slab extending to just over 400 km depth. The fault is locked


650

MODEL 3' 400 KM DIPPING SLAB, FAULT LOCKED Deviatoric Stress

. . ß +

ß ß + -{o +

90O Distance

Displacement Vectors

I • • • • • ...........

........

__: : ß . . . . . .

.

.

65O

2200

2000 metre .. ,


Fig. 3. The deviatoric stress distributions and displ&cem• •t fields produced by model 3 (fault locked) and model 4 (fault free), with the tope of a dipping subducting slab extendi•F to 400 km depth. The olivine-spinel transition within the slab and elsewhere is shown by a dashed line. Note tk•: • :he deviatoric stress scale differs from that in Figure 2.

in model 3 and free in model 4. Two major new factors in these models are (1) the increased length of the dense slab and the shallowing of the olivine-spinel transition within it, producing much increased downpull, and (2) penetration of the bottom of the slab into the top of the mantle transition zone, where the increase in viscosity by a factor of 10 increases resistance to sinking. As a result of the increased downpull of the longer slab outweighing the increased resistance to sinking, the lithospheric stresses and displacements produced by the subduction are much larger than those in models 1 and 2. Downdip compression affects the bottom of the sinking slab in models 3 and 4, although it is larger in model 4. In model 4 the slab pull tension at the fixed edge of the subducting plate is 122 MPa, and the tension at the fixed edge of the overriding plate is 111 MPa, of which at least 82 MPa is attributable to trench suction and the remainder to the thick, low-density crust. Both rollback and downdip velocity in model 4 are about twice those of model 2. This represents a trade-off between the increased downpull, which is about 4 times that of model 2 as a result of the high-density olivine-spinel region in the lower part

of the slab and the increased resistance to sinking as the higher-viscosity region below 400 km depth is reached.

Models 5-8 (Figares 4 and 5) correspond to models 1-4, respectively, except that the slab is vertical below 280 km depth. The contrasts are most strongly developed in the models where the slab reaches 400 km depth. The surface downflexure of the overriding plate and the associated region of compression are narrower than in the dipping slab models, especially for model 7 in comparison with model 3. How- ever, the magnitude of the stresses in the surface plates are closely similar for the vertical and dipping slabs of comparable depth extent. Rollback is not as well developed in the vertical slab models, although downdip velocities in models 6 and 8 with free faults are similar to those of the dipping models 2 and 4. Stresses at the fixed edges of the plates are marginally greater by about 6% in the deeper penetrating model 8 than in model 4 and are less by about 10-20% in the shallower penetrating model 6 than in model 2, indicating that the resulting plate interior stresses are not very sensitive to slab dip.

The stresses in the surface plates are shown together for


650

MODEL 4:400 KM DIPPING SLAB, FAULT FREE Deviatoric Stress

100 MPa

illllllli&,= I- -i- /- . ß

ß

ß

4,-

* ' + -I- + ', 4"

900 Distance (kin) 22O0


o

ß . ß

ß

ß

ß ß

ß .

ß ß

650

2000 metre

900 Distance (km)

Fig. 3. (continued)

2200

most of the above models for comparative purposes in Fig- ure 6. Models I and 5 with locked fault show the local

compressire stress above the slab, which is almost equal in magnitude for both dipping and vertical slabs, although of marginally narrower horizontal extent above the vertical slab. In these two models (and all the other models), the continental crust of the overriding plate produces a small superimposed tension which extends uniformly to the edge of the model, and slightly reduces the compressions in the arc region. Models 3 and 7 with locked faults, which are not shown in Figure 6 (see Figures 3 and 5), only differ in the substantially larger compressions associated with the big- ger downpull of the deeper extending slabs. The effect of unlocking the subduction fault can be seen by comparing model 1 with model 2 and model 5 with model 6. In the

unlocked models, a uniform tension is superimposed on the stresses of both plates extending out to their edges and can- celling out the compressions in the arc regions. This tension is of closely similar magnitude for the vertical and dipping slabs of equal depth extent but is substantially larger for the deeper extending slabs.

Models 9 and 10 (Figure 7) illustrate the influence on the stresses of incorporating a back arc basin. Otherwise, mod-

els 9 and 10 are the same as models 1 and 2. The back arc

basin has a simulated water depth of about 3 km underlain by oceanic lithosphere. The excess elevation above the normal oceanic 5 km water depth is modelled by a surface pressure isostatically compensating the low-density mantle which extends from 30 km depth down to the top of the sinking slab. The density beneath the back arc basin is reduced by 50 kg/m a and the viscosity by a factor of a haft between 30 and 90 km depth, and the density is reduced by 25 kg/m 3 below 90 km down to the slab. Model 9 has a locked fault

and model 10 has an unlocked fault. In both models, horizontal tension is more in evidence in the back arc region than in the models without the back arc. In reality, the hot lithosphere beneath the back arc basin should mean that the elastic layer is thinner and thus that the tensional stress is amplified further in this region. Taking a stress situation intermediate between models 9 and 10, if the subduction fault is partially or spasmodically locked, trench-arc compression can grade into back arc tension.

In models 9 and 10, it is assumed that the strong upper elastic layer is unbroken in the back arc region. A different scenario will apply once back arc spreading is initiated, with the new presence of a divergent plate boundary producing

WHITTAKER ET AL.' STRESSES ASSOCIATEO WITH SUBDUCT•O• MARGINS 11,939

40O

MODEL 5:300 KM VERTICAL SLAB, FAULT LOCKED

ß

ß .

Deviatoric Stress

100 MPa

ß o

600 Distance (km)


ß . .

40O

1800

2000 metre


4OO 600

400

MODEL 6:300 KM VERTICAL SLAB, FAULT FREE Deviatoric Stress

. ' i

Distance (kin)


. .

1800

2000 metre


Fig. 4. The deviatoric stress distributions and displacement fields produced by model 5 (fault locked) and model 6 (fault free), with a verticM slab extending to 275 km depth. Stress scale is the same a• in Figure 2.

ridge push. The microplate between the spreading center and the trench would be expected to move rapidly toward the trench driven by a combination of ridge push and trench suction. On the other hand, the adjacent continental plate on the opposite side of the back arc basin will be subjected to a ridge push plate boundary force, rather than trench suction; thus a more compressional regime would be expected to apply when back arc spreading is active, and a more tensional regime when it is not. It is beyond the scope of this

paper to follow this up in detail, but the basic idea can be stated without need for supporting models.

COMPARISON WITH OBSERVED STRESSES

The results of the modelling are now compared briefly with observed stress distributions, with emphasis on the arc-back arc region. The observational evidence of thrust earthquakes indicates that a compressional stress regime ap-


65O

MODEL 7:400 KM VERTICAL SLAB, FAULT LOCKED Deviat, oric Stress

100 MPa



...............

ß ß ( I '

ß

650


Fig. 5. The deviatoric stress distributions and displacement fields produced the model 7 (fault locked) and model 8 (fault free), with a verticaJ slab extending to 400 km depth. Note the shMlowing of the olivine-spinel transition a• in Figure 3. The stress scMe is the same as in Figure 3.

proximately perpendicular to the trench is characteristic of most trench-arc regions, as shown on the world stress map of Zoback et al. [1989]. In contrast, the initiation of back arc spreading indicates that tension may occur in the back arc region. Nakamura and Uyeda [1980] showed that the stress grades from compressional in the forearc to tensional in the back arc in several arc regions including Japan, Alaska, and the Aleutians.

Uyeda and Kanamori [1979] classified trench-arc regions into tensional systems with active back arc spreading (Mar- iana type) and compressional systems without it (Chilean type). They interpreted the distinction as due either to the degree of lithospheric coupling at the plate contact or to the anchoring of the subduction slab in the stationary mantle relative to the overriding plate motion. England and Wortel [1980] attributed compressire stress in the trench-arc region to the shearing stress on the plate boundary exerted by the subducting plate. Froidevaua: et al. [1988] also attributed

the distinction between Mariana and Chilean arcs to the

degree of coupling at the plate boundary. The modelling of this paper similarly emphasizes the im-

portance of coupling of the plates at the subduction fault in controlling and varying the stress in the arc region. How- ever, a new important factor is introduced, namely, the local compressire stress system in the trench-arc region produced by the sublithospheric loading of the subduction slab and the modification of this when it is cut by a fault. It becomes much easier to understand compression in the trench-arc region with this new factor.

The modefling indicates that most of the observed features of the stress patterns in trench-arc-back arc regions can be explained by superimposition of some or all of the following stress systems: (1) large local compressional stress dominating the overriding plate above the slab when the fault is locked or partially locked (models 1, 3, 5, 7, and 9); (2) a supplementary and fairly uniform tensional stress sys-

WHITTAKER, ET AL,: STRESSES ASSOCIATED WITH SUBDUCTION MARGINS 11,941

650 6(

650

MODEL 8:400 KM VERTICAL SLAB, FAULT FREE Deviatoric Stress

100 MPa

ß ß + -/- + + ß . .

)0 Distance (km) 1800



Fig. 5. (continued)

tem occurring in both surface plates and extending into the plate interiors when the fault is unlocked (models 2, 4, 6, 8, and 10); (3) a local tension due to the low-density relatively thick crust occurring in continental and island arc regions (all models); and (4) a substantial local tension occurring where anomalous low density mantle overlies the slab in the back arc region (models 9 and 10), which may be annulled when back arc spreading is active. To these should be added two other contributors which are not modelled in this paper: (5) pervasive transmitted compression from ridge push; and (6) bending stresses, especially locally in the downbending slab.

Major compressive stress in arcs depends in the models on the fault being temporarily or partially locked (models 1, 3, 5, 7, and 9), with the value depending on the magnitude of the slab downpull and superimposed ridge push. Two further important factors which have not here been taken into account may be the dip of the subduction fault through the lithosphere and the occurrence of transmitted ridge push compression. The models suggest a slightly narrower belt

of compression over nearly vertical slabs such as below the Marianas than above dipping slabs such as that of Japan (compare models 3 and 7). Where back arc spreading is inactive such as in the Japan Sea, the models account for a transition from arc compression to back arc tension when the subduction fault is partially locked (intermediate situation between models 9 and 10) or is unlocked with superimposed ridge push (not modelled).

The modelling shows that the fault must be unlocked to develop appreciable back arc tension, but it must be locked to give large compression in the forearc region of the type needed to explain the great thrust earthquakes. The mod- elllng shows a stress gradient from forearc to back arc region, but it does not show how large forearc compression can co- exist with large back arc tension. Superimposition of ridge push does not help, as this would equally affect both regions in as much as it is transmitted across the subduction fault. It is possible that there may be other relevant factors not included in our simple modelling which account for this inconsistency. Alternatively, the subduction faults may be-

11,942 WHITTAKER ET AL.: STRESSES ASSOCIATED WITH $UBDUCTION [VIAHGINS

MODEL 1:300 KM DIPPING SLAB, FAULT LOCKED o

9O 0

Deviatoric Stress 100 MPa

28OO

MODEL 2:300 KM DIPPING SLAB, FAULT FREE o

9o o

100 MPa

28O0

MODEL 4:400 KM DIPPING SLAB, FAULT FREE

90

100 MPa

28O0

MODEL 5:300 KM VERTICAL SLAB, FAULT LOCKED o

90 0

100 MPa

24O0

MODEL 6:300 KM VERTICAL SLAB, FAULT FREE o

9o

100 MPa

2400

MODEL 8:400 KM VERTICAL SLAB, FAULT FREE o

-:- 90 0 Distance (km)

100 MPa

2400

Fig. 6. The near-horizontal deviatoric stresses in the surface lithospheric plates, extending over the whole width of the models, shown for models 1, 2, 4-6, and 8. The stress and distance scales are identical for all the models to enable easy comparison. Note that the vertical scale is exaggerated.

come temporally locked at intervals, with the large thrust events occurring during such episodes.

The observed state of present-day stress in plate interiors is almost everywhere compressional except in uplifted regions [Zoback et al., 1989]. However, the models indicate tension which is greatest and most extensive when the subduction fault is free (models 2, 4, 6, 8, and 10). The dis- crepancy can be accounted for by our neglect of ridge push which applies at the opposite edges of nearly all the present plates. However, these models demonstrate how tension may in the past have been prevalent in continental plates when they were bordered by subduction on opposite sides, thus explaining the occurrence of extensive continental tensional regimes in the geological past when the continents were more concentrated than at present [Bott, 1982].

As pointed out earlier, comparison of the modelled stresses within the sinking slab with observed stresses inferred from focal mechanism solutions can only be partially valid because of the anomalously slow modelled downdip velocity and the anomalously stiff boundary condition at the base of the model and because transmitted ridge push is not included. However, both these models and the previous slab models of Neugebauer and Breitma•ler [197'5] do show broad agreement with the observed patterns of stress in subducting slabs, explaining the downdip stress pattern in terms of downpull of the dense sinking slab and the resistance to downdip motion, especially at its end.

Izackz and Molnar [1971], reviewing focal mechanism solutions in slabs, showed that the stress axes are mostly par- allel to the seismic zones which delineate the slab, with downdip compression dominating below 300 km depth. At shallower depths, solutions include both downdip tension and downdip compression. Subsequent work using much larger data sets has generally confirmed this pattern. For instance Zhou [1990] showed that downdip tension generally gives way to downdip compression in the slabs of the north- west Pacific and Tonga-Kermadec regions, with the neu- tral zone of changeover occurring within the depth range of 100-250 km. Schneider and Sackz [1987] showed that downdip tension predominates to 200 km depth in the contorted Nazca slab below southern Peru despite local bending effects.

All our models show downdip orientation of the stress axes in agreement with observations. The models with a locked subduction fault show downdip tension decreasing to about zero at the bottom of the slab. This is because the downdip velocity is negligible so that there is no significant resistance to sinking at the bottom end. The models with a locked subduction fault thus do not agree with observed slab stresses, indicating that present-day subduction faults have not been locked for long enough to halt downdip motion. The models with an unlocked subduction fault all show downdip tension at shallow depths giving way to downdip compression at greater depths. In the models, the changeover takes place


40O

MODEL 9: BACK ARC, FAULT LOCKED

I I I I I ' •, '7' '.•'•X • •

/,

ß

Deviatoric Stress

-- 100 MPa

ß

4OO


MODEL 10: BACK ARC, FAULT FREE Deviatoric Stress

. . . .' ••/• • • •' : . 900 Distance (km) 2200

Fig. 7. The deviatoric stress distributions produced by model (fault locked) and model 10 (fault free), which are identical to models 1 and 2, respectively, except for the incorporation of back arc basin supported by an underlying low-density mantle.

at about 150 km depth for the 270 km slabs (models 2 an, 6) and at about 250 km for the 400 km slabs (models 4 and 8). Not too much significance, however, should be placed on the broad agreement with observations, as the resistance to downdip motion at the end of the slabs may be fortuitously close to the actual value as a result of trade-off between the

anomalously slow downdip velocities and the anomalously stiff boundary conditions at 650 km depth.

ESTIMATES OF THE PLATE BOUNDARY FORCES

It has been demonstrated in the models presented that the plate boundary forces develop as a result of the intersection of a primary isostatic loading stress system in the lithosphere by a region of weakness. At subduction zones, the weakness is the subduction fault. The shearing stress is reduced or even effectively annihilated within such zones or planes of weakness. This can be regarded as giving rise to a supplementary traction on the plate edge. In the finite element method, the shearing stress on the fault plane is removed by application of appropriate equal and opposite forces on each pair of dual nodes. The vertical components give rise to local lithospheric flexure, and the horizontal components are effectively the plate boundary forces, which produce stresses which penetrate, as demonstrated, into the adjacent plate interiors.

An estimate of the plate boundary force acting on the plates in the models presented can be made by using the chosen type of standard reference lithosphere at the edge and constraining the edge nodes to zero horizontal displacement, as described by Bott et al. [1989]. Integration of the stress difference with respect to depth at the edge gives the required estimate. The plate boundary forces have been referenced to a 5 km deep ocean basin representing oceanic lithosphere of about 80 Ma age. The results are shown in Table 2, together with an estimates of the ridge push force for comparison.

The ridge push force given in Table 2 is the average of the values given by D ahlen [1981] and by Fledout and Froide-

vaux [1983], and it is referenced to 80-100 Ma oceanic lithosphere. The slab pull and trench suction forces are negative and are generally substantially larger than ridge push. At first sight it is surprising that slab pull and trench suction are of comparable magnitude, but with the adopted free boundary conditions at the edges of the asthenosphere, this is to be expected; partition of the boundary force between slab pull and trench suction may be strongly affected by pressure gradients associated with flow in the asthenosphere. The calculations show that the ibrces do not depend greatly on the dip of the subducting slab (although this may be affected by asthenospheric pressure associated with rollback). How- ever, they are approximately proportional to the downpull of the slab and thus on its depth extent. The calculations indicate that a net force of around 6 to 12x1012 N/m acts on unit length of the lithosphere along the strike direction of the plate boundaries of a hypothetical two-dimensional plate to move subducting and overriding plates from ridges toward trenches.

CONCLUSIONS

1. Large local deviatoric stresses are produced in the strong upper lithosphere by major density anomalies in the sublithospheric mantle and associated surface topography, such as occurs at ocean ridges and trenches. When such a stress system is intersected by a plane of weakness which cuts across the lithosphere, then the resulting modification of the tractions on the adjacent weak plate boundaries gives rise to the plate boundary forces, which produce pervasive supplementary stress systems in the adjacent plate interiors. The actual state of stress within the plates is a superposition of stresses produced by plate boundary tractions, by the various resistances to plate motion, by lateral variation of the density-depth distribution within the lithosphere, and by associated bending of the lithosphere and thermal anomalies, etc.

2. At subduction plate boundaries, local horizontal deviatoric compression occurs above the sinking slab (trench- arc region) and resalts from loading stress produced by the dense slab and the associated flexural depression. When these compressire stresses are intersected by an unlocked subduction fault, slab pull and trench suction develop to pull the plates toward the trench and to give rise to superimposed tensional stresses within the adjacent plate interiors. Additional tensional stress occurs within the overrid-

ing plate due to crustal thickening beneath the arc and the adjacent continental regions. A further tensional stress system is associated with a typical back arc basin as a result of the low-density upper mantle beneath. There are also large bending stresses associated with lithospheric flexure, but these average to zero in a vertical section through the lithosphere. Where the subduction fault is partially locked, compression in the trench-arc region may give way to tension in the back arc region and beyond, although radical modification occurs if there is back arc spreading. The state of stress in both plates is critically dependent on whether the subduction fault is locked or unlocked, giving scope for major variations of plate interior stress dependent on the exigencies of subduction and back arc spreading.

3. The magnitude of the plate boundary forces produced at convergent plate margins have been estimated by fixing the edges of the lithosphere in the models and calculating


TABLE 2. Plate Boundary Forces Acting on Unit Length of Plate Boundary as Estimated for the Models With Fixed Edges and Free Faults

Type of Boundary Slab Dip Slab Depth, Model Plate Boundary Force, km 10 l• N/m

Ridge push - - - +2.4 Slab pull 45 ø 260 2 (Figure 2) -4.8 Trench suction 45 ø 260 2 (Figure 2) -4.2 Slab pull 90 ø 275 6 (Figure 4) -4.1 Trench suction 90 ø 275 6 (Figure 4) -3.7 Slab pull 45 ø 400 4 (Figure 3) -9.3 Trench suction 45 ø 400 4 (Figure 3) -8.1 Slab pull 90 ø 400 8 (Figure 5) -10.0 Trench suction 90 ø 400 8 (Figure 5) -9.2

Plate boundary forces are referenced to approximately 80 Ma oceanic lithosphere and are positive when they produce compression.

the tectonic force at these edges, which have been assigned standard oceanic structure for this purpose. At subduction boundaries, the slab pull and trench suction forces are found to be of comparable magnitude, but this situation may be vitiated by pressure gradients in the asthenosphere. The slab pull and trench suction forces appear to be insensitive to the dip of the slab in the models, but as expected they are approximately proportional to the total downpull and thus to the depth extent of the slab. They are substantially larger (and of opposite sign) to ridge push by a factor of 2-4.

Acknowledgments. Most of the computations were done on the VAX at the Geophysics Division, DSIR, Wellington, New Zealand, •ud we are grateful to the director and to D. J. Wood- ward for provision of the facilities and assistance with them. The paper has benefitted from comments by J. M. Jurdy and an anonymous referee. We are also grateful to the director of the University of Durham Computer Centre for computing facilities.

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M. H. P. Bott, Department of Geological Sciences. University of Durham, South Road, Durham DH1 3LE, England.

G. D. Waghorn, BP Exploration Inc., Sage Plaza One, 5151 San Fe!ipe, P.O. Box 4587, Houston, TX 77210.

A. Whittaker, SFK Technology Ltd, Amstral House, Mill Court, Wolverton, Milton Keynes MK12 5QP, England.

(Received December 19, 1989; revised August 1, 1990;

accepted November 19, 1990.)

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Stresses and plate boundary forces associated with subduction plate margins