Numerical Modelling of Arc–Continent Collision: Application to Taiwan

Tectonophysics 325 (2000) 23–42 www.elsevier.com/locate/tecto

Numerical modelling of arc–continent collision: application to Taiwan

J.-C. Tang *, A.I. Chemenda Ge´osciences Azur, UMR 6526, Universite´ de Nice-Sophia Antipolis et CNRS, 250 Rue Albert, Einstein — Sophia Antipolis, 06560 Valbonne, France

Received 10 September 1999; received in revised form 14 March 2000; accepted for publication 22 May 2000

Abstract

Two-dimensional finite element numerical modelling is applied to study the deformation and failure of the overriding plate during arc–continent collision (continental margin subduction). This plate has elasto-plastic rheology with strain weakening and contains a ‘volcanic arc’ with thinned and weakened lithosphere. The overriding plate deforms due to the normal and tangential stresses applied along the interplate surface. These boundary conditions represent the friction and pressure between the plates. The latter is due to the flexural rigidity of the subducting lithosphere and the buoyancy force generated by the subducting continental crust. The modelling shows that continental margin subduction results in increasing compression and failure of the overriding plate, which occurs along the surface dipping under the arc in either of two possible directions. The failure mode is largely controlled by the two competitive factors: the rigidity of the subducting plate and thickness gradient of the subducted continental crust. A high rigidity favors failure along an ocean-vergent fault, which is followed by a subduction reversal, while a high thickness gradient favors failure in the opposite direction, which is followed by a fore-arc block underthrusting beneath the arc. Both scenarios seem to have natural analogs. We consider one of them, the ongoing arc–continent collision in Taiwan, and argue that this process occurs according to the second scenario corresponding to the fore arc underthrusting. Wavelet statistical analysis of the seismicity distribution to the south of Taiwan has clearly displayed a shallow (0–40 km) zone of high density, coherently distributed seismicity beneath the Luzon Arc. This zone, interpreted as a lithospheric-scale fault, dips from the forearc basin to the east and corresponds to the initiation of the forearc block subduction. A self-consistent, combined mechanical–gravity–topography model is used to see whether failure of the overriding plate to the south of Taiwan can be ‘captured’ by this model. By ‘tuning’ different controlling parameters, we did not succeed in obtaining realistic topography and gravity field in a model where failure of the overriding plate was not allowed. Introduction of this failure and underthrusting of the forearc block under the Luzon Arc allowed us to fit both topography and gravity data. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: arc–continent collision; geodynamics; gravity anomalies; numerical modelling; seismicity distribution; Taiwan

* Corresponding author. Tel.: +33-4-92-94-26-06; fax: +33- 4-92-64-26-10. E-mail address: [email protected] (J.-C. Tang)

1. Introduction Fh, either extensional or compressional, can be sufficient to cause failure of the overriding plate Experimental (Shemenda, 1993) and numerical in the volcanic arc area, which is a weak zone. (Hassani et al., 1997) modelling of oceanic subduc- Failure under extension results in back arc rifting tion have revealed two principal stress regimes, and spreading. Deformation and failure of the characterised by extension and compression of the overriding plate under compression, corresponding overriding plate, respectively. The regime is defined to the compressional regime of oceanic subduction, by the flexural rigidity of the subducting plate and were studied both experimentally (Shemenda, by the forces acting on this plate, including the 1994) and numerically (Tang et al., in press). It pull force, Fpl, and the force of dynamic interaction was shown that if failure occurs, the resulting between the subducting lithosphere and the sur- lithospheric fault dips under the arc in either of rounding mantle, Fd (Shemenda, 1994). If these two possible directions (Fig. 2). Numerical tests forces and the rigidity were zero, the overriding with different boundary conditions, geometry, and plate would be in hydrostatic equilibrium, which rheologic structure of the overriding plate have means that the interplate pressure Pn (or interplate shown that the failure direction is largely con- normal stress) is equal to the hydrostatic pressure trolled by the distance, L, between the trench and =− Ph rogz and that there is no tectonic stress in the arc axis (Tang et al., in press): when < < the overriding plate (ro is the density of the 180 km L 230 km, the lithosphere fails along overriding plate; g is the acceleration of gravity; z the trenchward dipping fault; at L>230 km, the = = is the depth). When Fpl Fd 0, with a rigidity not failure occurs in the opposite direction. The mecha- ff ff equal to zero, Pn di ers from Ph. The di erence, nism ‘switching’ the mode of failure with variation = − sr Pn Ph, corresponding to the non-hydrostatic of L is associated with the flexural rigidity of the interplate pressure (normal stress) (Fig. 1), overriding plate and the wavelength of its bending. depends only on the subducting plate rigidity; the The arc/trench distance in subduction zones varies higher the rigidity, the greater the difference from ~150 to ~300 km and in most of them is between Pn and Ph. The integration of sr along about 200 km. Therefore, we conclude that the the interplate surface yields a tectonic (non- preferred mode of overriding plate failure during hydrostatic) pressure force, Fp, acting on the over- oceanic subduction is that which results in arc riding plate (Fig. 1). The horizontal component backthrust. of this force, Fh, produces compression of the Subduction of a continental margin can follow overriding plate. An application of the pull force either of the two regimes of oceanic subduction to the subducting plate modifies sr such that the and in both cases results in increasing compression horizontal component Fh of the pressure force can of the overriding plate and in lithosphere failure become extensional (can become oriented in the in the arc area (Chemenda et al., 1997). The force opposite direction) (Shemenda, 1993). causing an increase in compression during subduction of the margin is the buoyancy of a progressively thickened subducted continental crust. The non-isostatic interplate pressure (stress normal to the interplate surface) corresponding to this case roughly represents a superposition of the

Fig. 1. Non-hydrostatic interplate normal stress sr due to the subducting plate ﬂexural rigidity: compressional regime of oceanic subduction. Fp is the force caused by sr; H is the overriding Fig. 2. Two possible modes for the overriding plate failure. L plate thickness; z is the depth (after Shemenda, 1994). is the trench/arc-axis distance. J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 25

Fig. 3. Two equivalent settings of numerical experiments: (a) deformation of the overriding plate is caused by the buoyancy of the underthrusted crust of the continental margin. The subducting crust yield limit for normal load is 3.6×107 Pa; (b) the eﬀect of the subducted crust is simulated by the equivalent interplate normal stress sb calculated for the set-up in (a). = = × 3 3 = = = = rc rv 2.8 10 kg/m ; H 60 km; Lv 70 km; L 200 km; hc 15 km, where rc and rv are the densities of continental crust and the volcanics of the arc, respectively; Lv is the volcanic arc width; L is the arc axis/trench distance; hc is the thickness of continental crust at (under) the trench; h is the thickness of lithosphere in the arc. The volcanic arc is isostatically compensated. The density of the lithosphere is the same as that of the asthenosphere. The water depth is 4.5 km (see text for more explanations).

ff normal stress sb caused by the buoyancy (Fig. 3b) causes failure of this plate o shore of southern and the stress, sr, defined by the subducting plate Taiwan, along a west-vergent fault dipping under rigidity, as well as the pull force, Fpl, and the force the Luzon Arc. of dynamic interaction, Fd, of the subducted lithosphere with the surrounding mantle. The forces Fpl and Fd are neglected in this paper. The normal 2. Modelling set-up + stress, sb sr, and the interplate friction stress, tn , are applied to the overriding plate in numerical A one-layer overriding plate containing a vol- models to simulate the deformation and failure of canic arc with a thinned lithosphere floats upon a this plate. We obtained the same failure modes as Winkler (liquid) base with zero viscosity (Fig. 3a). for the compressional oceanic subduction regime. This plate has the same elasto-plastic rheology This time, the failure direction is mainly defined with strain weakening as in the experimental by two opposite torques caused by sb and sr, models of Shemenda (1994) (Fig. 4). The density respectively. Both failure modes are possible in of the plate is 3.3×103 kg/m3, the same as that of nature. The obtained results correspond well with the asthenosphere. The lithosphere is covered by the results from physical modelling of the same 4.5 km of water. The kinematic boundary condi- process (Chemenda et al., 1997) and are applied tion at the right edge (Fig. 3) allows no displace- to the ongoing subduction of the Eurasian conti- ment in the horizontal direction. At the left edge nental margin in Taiwan. Based on a wavelet of the model, the wedge of the elasto-plastic conti- statistical analysis of seismicity and on gravity nental crust is placed beneath the overriding plate modelling, we argue that the subduction of the along the interplate surface (Fig. 3a). The thick- Eurasian margin beneath the Philippine Sea Plate ness, hc, of the crust in the front of subduction 26 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

Fig. 4. Stress–strain diagrams for the experimental and numerical lithosphere models. In the laboratory experiments, reported by Shemenda (1994) and Chemenda et al. (1997), the yield limit of the lithosphere for the normal load is 28 Pa, which = × 8 corresponds to ss 2.1 10 Pa in nature. In the numerical = × 8 = × 10 model, ss 1.8 10 Pa, Young’s modulus, E 2 10 Pa; the stress drop during the failure Ds=3.6×107 Pa; the strain soft- ening parameter k=0.3; Poisson’s ratio n=0.25. zone approaches zero at the base of the overriding plate. The crust has a density of 2.8×103 kg/m3, a very small yield limit (see caption to Fig. 3) and hence negligible flexural rigidity. A small yield limit is chosen in order to separate the effect of the buoyancy force from that of the flexural rigidity. The rigidity of the subducted lithosphere is incorporated into some models by addition of the Fig. 5. Three tested mechanical structures of the overriding interplate pressure, sr, shown in Fig. 1. To model plate. (a) The homogeneous plate has a notch and contains a the lithosphere deformation, we use the finite- volcanic arc. (b) The lithosphere yield limit reduces toward the element code, ADELI (Hassani, 1994). arc axis; (c) In addition to the arc weakening, the strength of The normal stress, sb, exerted by the subducted the model reduces toward the apex of the overriding wedge. crust on the overriding plate has been calculated ss is the yield limit of the lithosphere for the normal load. for every boundary finite element. The obtained discrete stress values are well approximated by a rheologic parameters as the lithosphere. The arc is linear function (see Fig. 3b) using the least-squares isostatically compensated and is 19.3 km thick, method. This stress applied to the model yields which yields an underwater topographic high of the same result as direct crust underthrusting 4.2 km. We consider that such average topography (Fig. 3a). The two settings in Fig. 3a and b are is representative of real subduction zones, although thus equivalent, but the use of stress, sb, in many this parameter has little influence on the modelling cases is more convenient. results. In reality, thinning of the lithosphere The weak zone associated with the volcanic arc causes its heating and hence reduction of the is introduced in three different ways in various lithospheric strength. The thermal structure of the tests (Fig. 5). In one set of experiments (not pre- lithosphere in the arc depends on many factors sented in this paper), we simply made a notch at and is the subject of much debate, particularly the base of the initially homogeneous plate. In between those working on the problem of arc another set of tests (experiments 1–10), we also volcanism (Schmidt and Poli, 1988; Furukawa, added an ‘arc’ composed of volcanics with a 1993). The problem with the lithospheric rheology density of 2.8×103 kg/m3 (Fig. 5a) and the same in this area is even more controversial. Without J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 27

× going into the details of this complex issue, we to sh H (see Fig. 3a). In order to cause the have introduced the weakening of the lithosphere, overriding plate failure, this plate has been suffi- as shown in Fig. 5b, and we tested the models with ciently weakened in the arc area by thinning and different degrees of lithospheric weakening toward reducing the lithosphere yield limit toward the arc the arc axis. Finally, we tested the effect of hetero- axis according to Fig. 5a and b. Failure (strain geneity of the overriding wedge (Fig. 5c). The localisation in a narrow zone) is accompanied by rheology of this wedge is unknown, but the general underthrusting of the lithosphere under the arc. tendency should be a strength reduction toward The numerical code can only model initial stages the subduction front where the wedge is normally of this process. Below, we describe a number of composed of strongly deformed and fractured representative trials. weak crustal/sedimentary material. Experiment 1. The set-up of this experiment corresponds to in Fig. 5b and is shown in Fig. 6a. The interplate normal stress sb corresponds to = = = 3. Results of numerical experiments hc 15 km; h 23 km; L 200 km (see Fig. 3 for notations). The yield limit of the lithosphere About 90 experiments have been conducted decreases by a factor of 2 toward the arc axis. under various conditions. In all cases, with or Subduction of the margin causes about 4 km without consideration of the subducting plate uplift of the overriding wedge apex (Fig. 6c), rigidity, the overriding plate undergoes compres- 220 m uplift at the arc axis, and a failure of the sion. The horizontal compressive force, Fh, is equal lithosphere along a continent-vergent fault. The

Fig. 6. Two experiments corresponding to the set-up in Fig. 5b (experiment 1) and Fig. 5c (experiment 1); the boundary conditions and the model geometry are the same in both experiments. The interplate normal stress, sb, is defined in Fig. 3 and corresponds to = = the subducted crust which is hc 15 km thick at the front of subduction; h 23 km (see Fig. 3a). The upper figure is a general view on the deformed model with zone of plastic strain localisation (failure). The lower figure shows the topography with respect to the model surface before deformation. (c) Superposed topography profiles obtained in the both experiments. (d) Zoom of the area shown in (c). CPD is cumulated plastic deformation. 28 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

= = × horizontal compressive force, Fh H sh 2.58 Experiment 3. Two models are tested (Fig. 7). 12 = 10 N m, where sh 43 MPa (Fig. 6a). Similar One is the same as in experiment 1 (set-up in experiments have shown that both sb and sh are Fig. 5b) and another has the same geometry but proportional to the subducted crust thickness, a constant yield limit (according to Fig. 5a). The hc. model in Fig. 7a is thus stronger than that in Experiment 2. The set-up corresponds to Fig. 5c. Fig. 7b. We applied the same interplate normal The boundary conditions and the failure mode stress to both models. This stress is 10% less than are the same as in the previous experiment that needed to cause failure of the weaker model (Fig. 6b). Fig. 6c shows the obtained topography used in experiment 1. The maximal difference in compared to that in experiment 1. The maximal topography between the models is about 30 m topography difference in the two experiments of (Fig. 7d). ~100 m is reached in the wedge apex (Fig. 6d). Experiment 4. One of the two tested models is The maximal normal stress needed to cause the same as the homogeneous model in the previ- failure of the model depends on the lithosphere ous experiment (Fig. 8a). The other model has weakening in the arc area (i.e. on the thinning and the same rheologic structure as the model in the rheologic structure of the plate in this area). experiment 1 (Fig. 6a), but the lithosphere thick- Both are poorly known. To estimate the effect of ness in the arc is increased by 10 km (Fig. 8b). these factors on the lithosphere deformation before This allows a larger interplate normal stress to the failure, we conduct the two following be applied without causing failure of the rheologi- experiments. cally weaker model. The maximum topography

Fig. 7. Two experiments corresponding to the set-up in Fig. 5a (experiment 3a) and in Fig. 5b (experiment 3b); the boundary conditions % are the same as those in the previous experiments except for the interplate normal stress, which is reduced by 10 (0.9 sb) to prevent failure of the weaker plate in (b). The model geometry is the same as in the previous experiments. (c) Superposed topography profiles obtained in both experiments. (d) Zoom of the area shown in (c) where the difference D between two profiles is maximum. CPD is cumulated plastic deformation. J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 29

Fig. 8. Two experiments corresponding to the set-up in Fig. 5a [experiment 4a, (a)] and in Fig. 5b [experiment 4b, (b)]. The boundary conditions in these experiments are the same as those in the previous experiments except for the interplate normal stress, which is increased to 1.2sb. The model in experiment 4a is the same as that in experiment 3a and does not fail under this interplate stress. To prevent failure of a ‘rheologically’ weaker plate in experiment 4b, its thickness in the arc is increased to 33 km (instead of 23 km in experiment 3b). (c) Superposed topography proﬁles obtained in both experiments. CPD is cumulated plastic deformation.

difference between two models occurs at the arc at the arc axis. The other conditions are the same axis and is about 100 m. as those in experiment 1. The deformation of the The above (and many other) experiments show lithosphere results in an almost 7 km deep trench that the plate deformation and failure direction and 2 km non-isostatic forearc elevation (Fig. 9a). = are not very sensitive to the rheologic structure of Horizontal stress, sh 43 MPa, causes failure of the the arc and forearc area. This is an important plate along the trenchward-dipping fault. conclusion as the lithosphere rheology in these Experiment 6. The interplate normal stress is + areas is unknown and should be complex. Unless equal to sb sr, where sb is taken from experi- specified otherwise, the structure of the model in ment 1, and sr is from the previous experiment the following experiments corresponds to Fig. 5b. to simulate the contribution of both the sub- Experiment 5. This experiment, reported by Tang ducting crust buoyancy and the subducting et al. (in press) corresponds to the subduction of a lithosphere rigidity. A compressive stress, = ffi rigid oceanic lithosphere. The interplate non- sh 77 MPa, is su cient to cause failure of the hydrostatic normal stress, sr,isshowninFig.9a 40 km thick lithosphere (Fig. 9b). Failure again (see also Fig. 1). The overriding plate is 22 km thick occurs along a continent-ward dipping fault. 30 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 31

Experiment 7. The interplate non-hydrostatic fact, the result depends on the trade-off between normal stress is zero, and the deformation occurs two opposite torques caused by sb and sr. sb under the constant interplate friction stress, tn causes a clockwise and sr a counter-clockwise (Fig. 9c), which is estimated to be of the order rotation of the forearc block; accordingly, sb of 10 MPa (e.g. Tichelaar and Ruff, 1993). In favors failure along the continent-vergent fault = this experiment, sh 48 MPa. A smaller tn value and sr along the continent dipping fault. tn ‘works’ ffi results in a smaller sh, but the su ciently weak- in the same direction as sr. The numerical results ened lithosphere always fails along the continent- are in good agreement with experimental modelling ward-dipping fault. of the same process by Shemenda (1994) and Experiment 8. In this experiment, the constant Chemenda et al. (1997). The numerical approach tangential stress is applied only to the interplate is more efficient in testing various conditions con- surface between 20 and 50 km depth (Fig. 13), trolling the failure direction and thus defining the corresponding to the seismogenic zone (Tichelaar later evolution of the deformation. This evolution, and Ruff, 1993). The failure mode is the same as however, cannot be modelled by the technique that in experiment 7. used above. Such a modelling has been done Experiment 9. Now, we superpose the interplate experimentally (Chemenda et al., 1997, in press) stress from experiment 1 (sb) and the interplate and has shown that failure along the ocean-verging = friction stress tn 15 MPa. These stresses applied fault results in a subduction reversal, while failure separately cause lithosphere failure in opposite in the opposite direction is followed by a forearc directions (Figs. 6a and 9c). Applied together, block subduction beneath the arc. Both scenarios tn and sb result in failure along the continent- seem to have natural analogues. For example, vergent fault (Fig. 9e), which implies that in this structural (Snyder et al., 1996) and GPS (Genrich case, the effect of the interplate normal stress et al., 1996) data clearly show that the subduction produced by the buoyant margin is more impor- of the Australian continental margin under the tant than that of the friction. The failure direction Banda arc near Timor resulted in a subduction does not change when tn is increased twice. reversal. Below, we consider another example of Experiment 10. The difference between this test the ongoing arc–continent collision in Taiwan and and the previous test is that we add the stress sr argue that in this area, the overriding plate fails from experiment 5 (Fig. 9a). The interplate fric- along the continent-verging fault. = tion is: tn 15 MPa, and the result is shown in Fig. 9f. 4. Geodynamic setting of Taiwan The experiments that we have presented show that the overriding lithosphere failure mode Along the Luzon–Taiwan segment of the con- depends largely on the flexural rigidity of the vergent plate boundary, the Eurasian Plate sub- continental margin and on the thickness of the ducts under the Philippine Sea Plate carrying the subducting continental crust (hc in Fig. 3a). In Luzon volcanic arc (Fig. 10). The Philippine Sea

Fig. 9. Six experiments (experiments 5–10). (a) Experiment 5. Deformation of the overriding plate during oceanic subduction. The interplate normal stress, sr, corresponds to compressional subduction regime (see Fig. 1). The upper ﬁgure presents the deformed model with zones of plastic strain localisation. The lower ﬁgure shows the topography with respect to the model surface before + deformation. (b) Experiment 6. The interplate normal stress is sb sr, where sb is from experiment 1 (Fig. 6a), and sr is from = experiment 5 (Fig. 9a). (c) Experiment 7. Deformation of the lithosphere under the interplate friction stress, tn 30 MPa, constant = along the interplate surface. (d) Experiment 8. Constant interplate friction, tn 60 MPa, is applied to the same model as in the previous experiment model between 20 and 50 km depth. (e) Experiment 9. Both interplate normal stress, sb, and interplate friction, = tn, are applied to the overriding plate. sb is from experiment 1 (Fig. 6a), and tn 15 MPa. (f ) Experiment 10. The boundary conditions + = along the interplate surface are sb sr and tn 15 MPa; sb is the same in experiment 1 (Fig. 6a); sr is the same in experiment 5 = (Fig. 9a), and tn 15 MPa. CPD is cumulated plastic deformation. 32 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

Fig. 10. Geodynamic situation around southern Taiwan (modified after Huang et al., 1992). G–G∞ corresponds to the bathymetry and gravity profiles used in this paper. S–S∞ corresponds to the seismic profile in Fig. 19e. LVF is the Longitudinal Valley Fault; SLT is the South Longitudinal Trough. TT is the Taitung Trough.

Plate moves toward the Eurasian Plate at a rate collisional prism. At this latitude, the Asian margin of more than 7 cm/yr. (Seno et al., 1993; Yu et al., has already been underthrusted (Reed et al., 1991; 1997). To the south of about 21°N, the subduction Liu et al., 1992). Further to the north, the conti- of the South China Sea Plate beneath the active nental subduction is more advanced. The arc– Luzon arc is taking place along the Manila trench continent collision is thus propagating to the south, (Taylor and Hayes, 1983; Hayes and Lewis, 1984). with the collision front being somewhere between This is a typical intra-oceanic subduction zone 21.25 and 22.65°N (Lundberg et al., 1992, 1997; (Liu et al., 1998). Near 21.25°N, the Manila trench Huang et al., 1997). North of 22.65°N, the Luzon disappears, and the Luzon arc becomes inactive, arc overrides the collisional prism along a litho- while rapid plate convergence continues in this sphere-scale east-dipping fault, the Longitudinal region and results in the formation of the Taiwan Valley Fault (Fig. 10). This fault is not mapped J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 33 offshore to the south where the Philippine Sea tor; and Y1 is the conjugate Fourier transform of Plate also undergoes an intense deformation and Y. KY should be finite, so the wavelet has a zero shortening (Huang et al., 1992; Lundberg et al., mean, which implies that only the seismicity distri- 1997) as indicated by the seismicity (Wu et al., bution contrast is taken into account, while a 1997; Kao et al., 1998) and GPS data (Yu et al., constant level signal is removed. The filter size, a, 1997). The GPS data yield a shortening rate of is chosen empirically by testing various a values about 5 cm/yr between the Luzon arc and southern to obtain the most clear pattern: we chose a= Taiwan. This shortening results in the formation 2.5 km, which means that the calculated wavelet ffi of the Huatung Ridge (Fig. 10), which is made up coe cient is attributed to every 2.5 km side-size ffi of the deformed sediments of the forearc basin cube. This coe cient can be considered as measure (Lundberg et al. 1997). of strain (slip) localisation within the lithosphere. The seismicity concentration zone clearly seen in-plane (Fig. 11a) is also well displayed in the 4.1. Seismicity pattern seismicity sections processed by the wavelet method (Fig. 12). The localisation of deformation The deep lithospheric deformation around begins near 21.5°N and becomes more intense to southern Taiwan can be inferred from the seismi- the north (there is no localisation to the south of city distribution. The most prominent feature of this latitude). According to the above mechanical the seismicity pattern in this area is a narrow, modelling results, we interpret this pattern as a almost linear seismicity concentration zone along progressive failure of the Philippine Sea Plate and the western border of the Luzon arc (Fig. 11a). the displacement along the formed fault. This fault The cross-sections in Fig. 11b and c show the deep dips eastward under the Luzon arc to 30–40 km geometry of this zone, which appears as an east- depth. Such a dip direction coincides with one of dipping swarm beneath the arc. The Wadati– the nodal planes of the focal mechanism solutions Benioff zone, corresponding to the subducted in this region (e.g. Kao et al., 1998). The failure Eurasian Plate, can also be identified. In order to and hence the forearc block underthrusting start obtain a clearer pattern, we apply a statistical near 21.5°N. This location therefore corresponds method based on a three-dimensional wavelet to the beginning of the Taiwan arc–continent transform to analyse the seismicity spatial distribu- collision. tion (Ouillon et al., 1995; Bethoux et al., 1998). A The seismicity data thus support the model of family of filters (wavelets) are used to decompose Philippine Sea Plate failure and the underthrusting a seismicity distribution function and are derived of the forearc block beneath the Luzon arc. from a mother function, Y, which is the second Subduction of this huge block should have impor- derivative of the Gaussian function: tant geological consequences and therefore should be seen in geological records. Unfortunately, the = − 2+ 2+ 2 − (x2+y2+z2)/z Y(x, y, z) (3 (x y z ))e (1) situation in this area with intense active deforma- where x, y, and z are the Cartesian co-ordinates. tion, rapid erosion, and sedimentation is very ffi A family of this mother function is defined as complicated. For this reason, it is di cult to = constrain deep lithospheric deformation based on Ya(x, y, z) Y(x/a, y/a, z/a), where a is the filter size, corresponding to the spatial scale of analysis. the surface observations, although there are some A wavelet coefficient is defined as: geological arguments in favor of the forearc block subduction (Malavieille et al., in press). Below, we attempt to gain additional insights into this issue = −3/2 CI(x, y, z, a) 1/[KYa PPPI(u, v, w)Ya from the gravity data.

×(x−u, y−v, z−w)dudvdw (2) 5. From mechanical model to gravity model where CI(x, y, z, a) is the convolution of the seismicity density function I(u, v, w) in the point Our aim is to develop a ﬁrst-order density =∆ 1 3 −3 3 (u, v, w); KY Y (K) K d K, K is the wavevec- structure model of the initial collision zone to the 34 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

Fig. 11. Seismicity around southern Taiwan. (a) Superposed seismicity map (earthquakes of magnitude M>3 between 0 and 30 km depth located by the TTSN and CWBSN during 1974–1997) and simpliﬁed free-air gravity anomaly map from (Sandwell and Smith, 1997). The latter shows only the areas with positive anomaly (shaded) to delineate the Luzon arc. (b, c) Seismicity cross-sections. J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 35

Fig. 12. Seismicity profiles processed by the wavelet method (see text for explanations). The profile positions are shown on the simplified gravity map (the same as those in Fig. 11). The gray scale corresponds to the wavelet coefficient defined by Eq. (2). south of Taiwan which would be consistent not topography is maintained by the rigidity of the only with gravity and topography data, but also lithosphere and is caused by the non-hydrostatic with a mechanical model of collision. (tectonic) stress in the lithosphere. We will analyse Any topography can be presented as having both components separately, starting with the non- two components, isostatic and non-isostatic. The isostatic topography. The profile that will be isostatic topography is caused only by density treated is shown in Fig. 10 (G–G∞). The gravity variations with the assumption that the lithosphere calculations are based on the mechanical (numeri- rigidity is zero. On the contrary, the non-isostatic cal ) model and consist of four steps, or four 36 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 approximations. In all cases, we neglect the flexural additionally uplifted for about 90 m in the arc rigidity of the subducting continental margin and axis, which corresponds to the non-isostatic com- represent the subducted Eurasian plate only by ponent. The forearc topography has two compo- low-strength crust. The set-up of this model is thus nents as well: the non-isostatic component, due to similar to that shown in Fig. 3a. The only differ- the deformation and uplift of a constant (mantle) ence is that the geometry of the interplate zone is density overriding wedge, and an isostatic compo- now constrained by the seismicity distribution nent, due to the presence of low-density under- along the chosen profile (Fig. 11c). The Asian thrusted crust. The calculated and measured crustal thickness to the west of the subduction topographies are very different in the forearc front is calculated, based on the assumption that (Fig. 13b), while the gravity curves show a much the lithosphere here is in isostatic equilibrium and better fit (Fig. 13c). This implies that the obtained that the crustal density is 2.8×103 kg/m3. The topography is close to the non-isostatic component crustal thickness progressively decreases from of the topography along the chosen profile. The 14.3 km in the trench to near 5 km (close to the isostatic topography component is unrealistically oceanic crust thickness) near the bottom of the small. The reason is an excessively high (mantle) overriding plate (Fig. 13a). The overriding plate density of the overriding wedge in the model, has a rheologic structure corresponding to Fig. 5a which in reality contains both low-density crust and is too strong to fail under the conditions and sediments. Therefore, the second approxima- shown in Fig. 13a, so we will first test the model tion in the gravity modelling involves incorpora- without failure. The topography generated in this tion of the crust into the overriding plate model. model is shown in Fig. 13b. The topography in As the Philippine Sea Plate is oceanic, we intro- = = × 3 3 the arc has two components. The principal compo- duce ho 6 km thick, roc 2.8 10 kg/m dense nent is the isostatic component because the arc oceanic crust layer (Fig. 14) by replacing the equiv- was introduced initially as a completely compen- alent upper mantle layer of thickness, hm,in sated feature. During the deformation, the arc was the previous model, as shown in Fig. 15a:

Fig. 13. Mechanical–gravity model: first approximation. (a) Set-up of mechanical model corresponding to Fig. 3a; (b) calculated and = × 3 3 = = × 3 3 measured topography profiles; (c) calculated and measured free-air anomaly profiles. rm 3.3 10 kg/m ; rc rv 2.8 10 kg/m ; = × 3 3 rw 1.0 10 kg/m . J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 37

Fig. 14. Mechanical–gravity model: second approximation. The diﬀerence from the ﬁrst approximation model in Fig. 13a is the incorporation of the oceanic crust using the isostatic principal described in the text and illustrated in Fig. 15a. The oceanic crust = × 3 3 density, roc 2.8 10 kg/m .

= = hm (roc/rm)ho 0.85ho. In this way, we increase the sedimentary layer, removing the equivalent only the isostatic topography component, leaving amount of the mantle material. The thickness of the non-isostatic component the same. Both calcu- the sediments (and hence of the removed lithosphe- lated topography and gravity anomaly in this case ric mantle) is calculated to obtain the observed correspond better to those observed (Fig. 14c and bathymetry (Fig. 16c). Then, we compute the grav- d), but the calculated topography in the forearc is ity anomaly for this model, which has proved to still very different from the measured data. This is be fairly different from the observed anomaly in not surprising as the model does not contain low- the forearc (Fig. 16d). density sedimentary material of the accretionary To determine the reason for this discrepancy, prism in the forearc area. Therefore, the third we have varied three parameters: thickness at approximation consists of incorporation of the depth of the subducted Eurasian crust, and thick- sedimentary material in the forearc area (Fig. 16). ness of the sedimentary and crustal layers in the The procedure is similar to that used in the second forearc. By doing this, we do not succeed in fitting approximation and is based on the isostatic prin- both the bathymetry and gravity data in the same ciple (Fig. 15b). We kept the forearc crustal thick- model. For example, an increase in the subducting ness the same as in the previous test and added crust thickness results in a higher uplift of the 38 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

nent, which is not taken into account in the model. This topography could be due to the interplate friction or non-hydrostatic normal stress caused by the rigidity of the subducting plate. Introduction of interplate friction generates con- siderable negative non-isostatic topography and hence a negative gravity anomaly in the frontal most part of the overriding plate (Fig. 9c and d). Therefore, the interplate friction will not solve the problem; instead, it will generate an intense negative anomaly in the frontal part of the overriding wedge where the observed anomaly is almost zero. Introduction of flexural rigidity of the subducted lithosphere results in the non-isostatic uplift of the forearc (frontal arc) (Fig. 11) and hence an even Fig. 15. Schemes explaining the introduction of the oceanic higher calculated anomaly in this area. Therefore, crust (a) into the second-approximation model in Fig. 14 and we proceed to a fourth approximation in gravity of both the crust and the sediments (b) into a third-approxima- modelling, which consists of the introduction of tion model in Fig. 16. (a) The upper layer of the ‘mantle’ over- plate failure in the arc and consequent underthrust- riding plate model in Fig. 13a is replaced by the crustal density ing of the forearc block, which also modifies the = layer such that ho (rm/roc)hm. (b) An additional hm thick non-isostatic topography. We returned to the ini- mantle layer is replaced by the sedimentary density layer such that h =(r /r )h . r =2.4×103 kg/m3. tial mechanical model in Fig. 13 and reduced the s m s m s lithospheric strength according to Fig. 5b to allow the lithosphere to fail and the forearc block to overriding wedge in the mechanical model and underthrust the arc. Compared to the model with- hence in a still higher calculated anomaly in the out failure, the topography in this case is character- forearc. Reduction of this thickness reduces the ised by ~600 m subsidence at the western arc foot anomaly but not sufficiently. The problem is that and 190 m uplift at the arc axis (Fig. 18). The the subducting crust thickness cannot be changed above procedure of isostatic topography ‘building’ at the front of the subduction zone as it is con- has been applied to this new model. The result is strained by the topography. Down along the shown in Fig. 19. It appears that both the calcu- interplate zone, the subducting crust in the model lated topography and the gravity anomaly fit the is already thin, and its thickness approaches that observed data. Unfortunately, there are no avail- of the oceanic crust. Therefore, we do not have able seismic data that would allow us to check on much freedom in reduction of the subducting crust the obtained deep structure of the overriding thickness (it cannot be thinner than the oceanic wedge. The only published seismic profile in the crust). In the forearc area, the variation of both study area is shown in Fig. 19e, and this is consis- crustal and sedimentary thickness so as to keep tent to a first approximation with the superficial the topography constant does not have a signifi- structure of the model in Fig. 19d. The accretion- cant effect on the gravity anomaly. Fig. 17 shows ary prism in the model is very small, and the a model in which the crust is completely absent in forearc sediments are not part of the prism in its the forearc. The calculated gravity anomaly does classical definition. [It is often supposed (e.g. Reed not differ significantly from that in Fig. 16d. et al., 1992) that the whole forearc (forearc block) Therefore the relative thickness of the crustal and is an accretionary prism.] sedimentary layers is not well constrained by the gravity data. These tests lead to the conclusion 6. Conclusion that the cause of the discrepancy between the calculated and observed gravity field in Fig. 16 is The numerical modelling presented here shows an additional, non-isostatic topography compo- that during subduction of the continental margin, J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 39

Fig. 16. Mechanical–gravity model: third approximation. The difference from the second approximation model in Fig. 14a is an incorporation of the sedimentary layer according to Fig. 15b. The oceanic crust thickness is kept the same as in Fig. 14. the overriding plate can fail in the volcanic arc area occurs along the continent-vergent fault. Statistical along a fault dipping under the arc in either of two processing of the seismicity distribution clearly possible directions. The failure direction depends reveals a shallow (0–40 km) seismicity concen- on the trade-off between two opposite torques tration zone dipping eastward under the Luzon arc acting on the forearc block and caused by the to the south of Taiwan. This zone is interpreted as normal and tangential stresses exerted by the sub- corresponding to the ongoing Philippine Sea Plate ducting plate along the interplate surface. High failure and underthrusting of the forearc block flexural rigidity of this plate favors failure along under the arc. According to the seismicity data, the continent dipping fault. Interplate friction ‘works’ failure front is currently located near 21.5°N. in the same direction. Increase in the thickness of Considering this conclusion, we chose a profile in the subducting continental crust favors failure in the area of the supposed initial underthrusting of the opposite direction. Failure of the lithosphere in the forearc block and looked at whether this process either direction seems to be likely in reality and is could be captured by a simple self-consistent com- followed by the underthrusting of the lithosphere bined mechanical–gravity–topography model. It under the arc. An analysis of ongoing arc–continent was shown that the forearc block underthrusting collision in Taiwan shows that in this region, failure was necessary to fit both topography and gravity 40 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

Fig. 17. Mechanical-gravity model: extreme case. The diﬀerence from the previous model in Fig. 16 is that the crustal thickness in the forearc is supposed to be zero (the isostatic topography component is only due to the thick sedimentary layer).

data in the same model. To obtain this result, we had to assume that the flexural rigidity of the subducted margin would be small. Similar conclu- sions have been made by other workers stating that stretched lithosphere at some margins remains weak for a long time following rifting (e.g. Watts, 1988). In Taiwan, this time period was not very long as the subducting Chinese margin underwent extension and rifting in the Middle Oligocene to Lower Miocene (Taylor and Hayes, 1980, 1983), which Fig. 18. Topography profiles in the two models. One model is terminated about 12 Ma before subduction of this that shown in Fig. 13a (set-up corresponds to Fig. 5a). This margin under the Luzon arc. Another conclusion model is so strong that failure does not occur in the arc area. that follows from the modelling is that the interplate The second model differs from the first model only by the rheo- friction in the studied area should be small. This logic structure of the overriding plate, which corresponds to Fig. 5b. This plate is weaker, and the compression generated can be explained by a large amount of very weak by the subducted crust is sufficient to cause plate failure and and hydrated sediments of the margin dragged to underthrusting of the forearc block. depth by the subducting plate. J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42 41

Fig. 19. Mechanical–gravity model: fourth approximation. The difference with the third approximation model in Fig. 16a is an incorporation of the plate failure (c and d), which causes a change in the non-isostatic topography according to Fig. 18. (e) Interpreted seismic profile along the line S–S∞ in Fig. 10 (simplified from Reed et al., 1992). TWT denotes the two-way time.

Acknowledgements the proceeding of seismic data. We thank J. Che´ry for the code to calculate the gravity anomalies and Thisworkhasbeendoneintheframeworkof S. Lallemand for the bathymetry data acquired the I.F.T.-N.S.C. cooperation (Insitute Franc¸ais a` during the ACT cruise. The seismic data are from Taipei and National Science council of Taiwan). the Central Weather Bureau of Taiwan. We thank J.-C.Tang received a grant from CNOUS, France C. Beaumont and S. Ellis for the constructive review and the Ministry of Education at Taiwan, ROC. We and A. Lomax for assistance with the English. This acknowledge N. Be´thoux for her contribution on is a Ge´osciences Azur contribution # 304. 42 J.-C. Tang, A.I. Chemenda / Tectonophysics 325 (2000) 23–42

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