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Dynamic topography above retreating subduction zones Laurent Husson* Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA ABSTRACT Dynamic topography provides a measure of stresses within the Earth’s interior. Dense slabs induce an upper mantle flow that deflects the surface of the Earth downward above them. By combining a simple theoretical (Stokeslet) model of subduction, gravity modeling, and seismic tomography, I show that a significant fraction (as much as 2000 m) of the topographic variations observed above the Scotia, Mariana, and Hellenic subduction systems appears to be dynamically induced by stresses related to the underlying subduction. Keywords: subduction, backarc basins, dynamic topography, Stokes flow. INTRODUCTION Dynamic topography provides fundamental information about the Earth for at least three reasons. First, it is a direct measurement of the stresses beneath the surface; above subducting slabs, it is critical in many respects, such as understanding seismic anisotropy. Second, as an observable, it informs us about the structure of the mantle. Third, it informs us about the nature of topography. Therefore, researchers have attempted to identify dynamic topography at a global scale (e.g., Hager, 1984; Cazenave et al., 1989; Colin and Fleitout, 1990; Ricard et al., 1993; Panasyuk and Hager, 2000), and have arrived at the controversial conclusion that the calculated magnitude of dynamic topography overestimates the magnitude that can be observed at the surface. There are, however, some areas associated with retreating subduction systems where the bathymetry developed on the overriding plate near the subduction boundary is deeper than in adjacent regions. A retreating subduction system indicates subduction boundaries where the trench is retreating above the asthenosphere, moving away from the extending overriding plate. Because these systems are of limited lateral extent, the dynamic stresses and the associated dynamic topography should vary across the system in a systematic and predictable fashion. Most attempts to quantify the dynamic topography compare the mean topographies above deep density heterogeneities (e.g., Conrad et al., 2004; Wheeler and White, 2000); I examine the lateral variations in dynamic topography above a given structure. An analysis of the bathymetry developed above several retreating subduction boundaries (East Scotia, Mariana, and Aegean Seas; Fig. 1) allows me to quantify the extent to which the dynamic stresses related to subduction influence the shape of the Earth. where ⌬vi is the mass anomaly associated with each point mass, g is gravitational acceleration, is viscosity, rij is the distance from each point mass to the observation point j, and ij is the angle between the vector ij and the direction of g. The normal stress on the upper free surface of a half-space can be calculated using the image technique (Morgan, 1965): Fzzij ⫽ 3⌬vi gzi3 , rij5 (2) where zi is the depth of the point mass body beneath the surface. Because inertial terms are negligible, stress does not depend on viscosity. If the surface is stress free, then there will be a deflection of the surface by a distance hij, such that (m – *) ghij is equal to Fzzij. The total Stokes flow is given by the sum of the Stokeslets; the total surface deflection Hj will be the sum of the deflections resulting from each point mass, hence MODELING DYNAMIC TOPOGRAPHY Stokeslets Approximation Viscous flow associated with bodies of heterogeneous density and random shape embedded within a Newtonian viscous fluid can be conveniently assessed using a Stokeslet approximation (Morgan, 1965; Batchelor, 1967; Harper, 1984). In this approximation, the density field is discretized into point masses. Each point mass i induces a elementary spherical flow (Stokeslet) for which the Stokes stream function is known and can be written: ⌿i ⫽ ⌬vi g r sin 2ij , 8 ij *E-mail: [email protected]. (1) Figure 1. Topography of East Scotia (A), Mariana (B), and Aegean (C) seas (wavelengths <50 km are discarded). Deflection of topography toward center of basins can be pointed out by circumscribing (dashed lines) areas deeper than arbitrary reference depth in overriding plates (A, 2500 m; B, 3000 m; C, 350 m). Isocontours are every 250 m. S. Am.—South American Plate; S.Scot—South Scotia. 䉷 2006 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. Geology; September 2006; v. 34; no. 9; p. 741–744; doi: 10.1130/G22436.1; 4 figures. 741 Figure 2. A: Map view of theoretical dynamic topography above slab. ␦ ⴝ 40 kg mⴚ3, * ⴝ 1030 kg mⴚ3, ⴝ 1.2 102t Pas. White solid contours give shape of a slab (50 km isocontours). See text for details. B: Residual topography of East Scotia Sea after thermal subsidence, isostatic correction for sediment loading (sediment density s ⴝ2500 kg mⴚ3), and ⴚ1800 m (depth of edges of ridge) have been removed. Only negative elevations are color-coded to emphasize similitude with theoretical predictions. Horizontal scales are different. Isocontours every 250 m. Hj ⫽ z , 冘 r 3⌬v ( ⫺ *) 3 i i i 5 ij (3) m where m denotes the density of the mantle and * either that of the air or of the seawater, depending on the geologic setting. Theoretical Results Subduction of a slab into the asthenosphere can be simulated by embedding a dense sheet of finite width within a viscous fluid of lower density. The Stokeslet approach requires that the fluid have uniform viscosity. The assumption that the slab has the same viscosity as the asthenosphere may limit our ability to fully understand the convective processes associated with subduction (Morra and Regenauer-Lieb, 2006). For example, with this model, trench retreat is the only way to have nonvertical slabs. However, the effective rheology of subducting slabs may be low (Moresi and Gurnis, 1996), and this simple choice gives a starting point to examine how subduction generates dynamic topography. There are few models of subduction that can provide for dynamically consistent trench motions (e.g., Enns et al., 2005; Royden and Husson, 2006), but a migrating trench can be mimicked in the Stokeslet approximation by specifying that the point masses that make up the dense sheet in the foreland have zero velocity until they become sufficiently close to the trench, at which point they are allowed to move in response to the Stokeslet flow. In this paper I assume that points in the foreland must be closer to the trench than a distance equal to half the width of the slab. This has the same effect as the somewhat ad hoc yield stress criterion found in other dynamic models (e.g., Moresi and Solomatov, 1998; Enns et al., 2005). This allows the trench to be freely distorted (the mantle flow controls trench shape) and to migrate toward the foreland. In practice, an assemblage of point masses that collectively forms a slab of finite specified width describes the initial sine-shaped slab geometry. Each point mass induces a Stokeslet and these are summed to determine the flow (which includes the slab). For simplicity, the stream function for slab motion is computed in an infinite space (note that this approximation breaks down for the most shallow elements). The resulting flow is used to compute the evolving shape of the slab and the location of the trench until steady state is reached. Dense point masses are considered to drive the flow only within the upper mantle and are removed from the model when they reach the base of the upper mantle at 670 km depth. Figure 2 shows model slab geometry and dynamic topography for a slab in steady-state subduction; at the trench the slab is 100 km thick and 600 km wide. The trench migrates to the 742 Figure 3. Observed (solid line) and modeled (from seismic tomography and bathymetry, dashed line) minimum residual topography (top) and gravity anomalies (bottom) along ridges of East Scotia (left) and Mariana (right) basins. Gravity anomalies from solid Earth only (dotted lines, top) and from seawater only (absolute value, dashed lines, top). Discrepancies between observed and modeled bathymetry are second-order chemical variations and uncertainties in tomographic data. z—dynamic topography; 円⌬g円—absolute value of the gravity anomaly. right at ⬃6.5 cm yr⫺1 for ⌬ ⫽ 40 kg m⫺3 and ⫽ 1.2 1021 Pa s. The surface trace of the trench is gently curved, concave toward the overriding plate, and the curvature of the slab increases with depth. This simple model reproduces most of the subduction features. Dynamic topography generated above the slab reaches its greatest value of ⬃1500 m at a distance of ⬃300 km from the trench. Note that H linearly scales with ⌬ (equation 3). Dynamic topography decreases from its maximum value toward the sides of the subduction system, indicating that the pressure of fluid flow is more negative above the center of the slab than above the edges. The maximum gradient in dynamic topography is located ⬃100 km (⬃/6) inside the edges of the slab. EVIDENCE OF NON-ISOSTATIC TOPOGRAPHY The East Scotia, Mariana, and Aegean Seas are above three narrow subduction zones. Because their tectonics are comparable to the theoretical example described here, all three should exhibit topographic signals consistent with the model dynamic topography shown in Figure 2. Observed Bathymetry The East Scotia Sea (Fig. 1A) is a well-developed backarc basin that has opened since ca. 10 Ma (Barker, 2001). The trench is ⬃600 km wide and is migrating east at ⬃60–70 mm yr⫺1 (Lallemand and Heuret, 2005, and references therein). Figure 2B shows the residual topography computed by subtracting expected depth as a function of seafloor age (cooling model of Stein and Stein, 1992; ages from Vanneste and Larter, 2002; Reinecker et al., 2004). An isostatic correction has been applied to account for sediment loading (data from Laske and Masters, 1997). A datum at 1800 m given by the depth of the edges of the ridge after correction has subsequently been subtracted (Fig. 2B) in order to evaluate the minimum residual topography. In map view it is quite similar to the theoretical results shown in Figure 2A. In addition, the basin shows an overall ENE tilt (largely hidden by the arc) toward the center of the trench. The depth of the spreading ridge decreases by ⬃1500 m from the edges to the center of the basin, consistent with model dynamic topography (Fig. 3A). Without development of dynamic topography, or variations in chemical or thermal GEOLOGY, September 2006 properties of the underlying mantle, the ridge axis is expected to exhibit an approximately uniform depth along its length. Lateral conduction of heat across the edge of the basin (at the ends of the spreading ridge), as well as the poloidal vs. toroidal flow, would be expected to create colder mantle and deeper seafloor near the edge of the basin (Kincaid and Griffiths, 2004), opposite to what is observed. In my interpretation, depth variations along the spreading ridge are a direct measure of the minimum dynamic topography due to subduction. The Mariana subduction zone has developed largely since 3–4 Ma (Fig. 1B; Stern et al., 2003, and references therein), as the trench migrates eastward at rates of ⬃60–70 mm yr⫺1 (Lallemand and Heuret, 2005). The trench is 1000 km long and the backarc oceanic basin is narrow (⬍⬃300 km). Along the eastern side of the Mariana basin, a volcanic arc overlies a large portion of the basin, making it impossible to map a residual topography as in the Scotia Sea. However, the depth of the backarc spreading ridge still contains information about possible dynamic topography. As in the Scotia Sea, the ridge axis deepens away from the edges of the basin by more than 1000 m (Fig. 3B), similarly consistent with the basin center being dynamically deflected downward. The Hellenic subduction zone (Fig. 1C) is an ⬃1000-km-wide segment of the African slab. The trench currently moves southwestward at ⬃35–40 mm yr⫺1 (McClusky et al., 2003). The Aegean upper plate consists of thinned continental crust, although arc-parallel extensional structures are no longer very active. In the southern part of the Aegean Sea, the Cretan trough forms an ⬃2000-m-deep depression. Measured crustal thicknesses are 20–26 km (Tirel et al., 2004, and references therein), which should correspond to an isostatically compensated bathymetry that is close to sea level. This suggests that a dynamic depression of the seafloor with a magnitude in excess of 1000–1500 m may be present in the Cretan trough region. However, unlike the oceanic backarc basins, where observed bathymetry can be readily referenced to oceanic depths of comparably aged lithosphere, continental basins have no obvious reference level with which to estimate dynamic topography. Nevertheless, the magnitude and distribution of apparent excess depth in the Aegean Sea region is comparable to that observed in the East Scotia and Mariana basins. Seismic Tomography, Gravity Anomalies, and Dynamic Topography The theoretical model presented here yields dynamic topography that is comparable to what is observed within the described systems. In order to account for density and thickness variations as well as idiosyncrasies in the geometry of the Scotia, Mariana, and Aegean slabs, I use seismic velocity anomalies to estimate the arrangement of the density anomalies within the upper mantle. To a first approximation, the difference ⌬V, between the observed and the average seismic velocities at a given depth can be used as a proxy for the density anomalies at depth, where the density anomalies are linearly related to ⌬V by a factor p/⌬V. I use P-wave velocity anomalies computed from the three-dimensional grid of Van der Hilst (as updated from Kárason and van der Hilst, 2000) and assign mass anomalies, ⌬v ⫽ ⌬VP v, ⌬VP (4) to each Stokeslet cell, where v is the volume of each cell. The conversion factor p/⌬Vr is deduced from free-air gravity anomalies (Sandwell and Smith, 1997). Free-air gravity anomalies are computed for each area using the entire set of point masses derived from the seismic velocity structure and the observed bathymetry. The conversion factors that provide the best fits are 24.5, 23, and 18 kg m⫺3/% for the Scotia, Mariana, and Aegean seas, respectively, if no uniform background, long-wavelength value is added. These converGEOLOGY, September 2006 Figure 4. Dynamic topography induced by solid Earth density anomalies, in East Scotia (A), Mariana (B), and Aegean (C) seas. Relative densities are inferred from seismic tomography and conversion factor /al⌬V is deduced from gravity (see text). Isocontours every * 250 m. Dashed lines outline inferred dynamic topography of Figure 1. S. Am.—South American Plate; S.Scot—South Scotia. sion factors yield excess densities of ⬃35–60 kg m⫺3 in the areas that might be occupied by subducted material, in the range of typical lithospheric density anomalies. Figure 3 shows the best-fit model freeair gravity, computed from VP anomalies and bathymetry, and the observed free-air gravity anomalies, along profiles that follow the spreading-ridge axes in the Scotia and Mariana backarc regions. Dynamic topography is implicit in the model free-air anomalies because the observed bathymetry, which is used in the calculation of model values, has dynamic topography embedded within it. Both the observed and model free-air anomalies decrease toward the center of the backarc basins. This is consistent with a positive contribution to the gravity from a dense slab at depth partially counteracted by a negative contribution from dynamic topography at the surface. This can be scaled by noting that a point mass at depth z will generate a gravity anomaly that scales like z /(z2⫹d2)3/2 while the dynamic topography generated by the same point mass scales as z /(z2⫹d2)5/2 (d is the horizontal distance at surface level from above the point mass). This generates a longer-wavelength, lower-amplitude positive component and a shorter wavelength, larger amplitude negative component to the gravity. Maximum cancellation of the primary anomaly by the secondary therefore occurs above the point mass, i.e., in the center of the basin. The density structure used to compute the model free-air gravity anomalies was also used to compute an explicit dynamic topography, using the same conversion factors for each area from equation 3. This is compared to the residual topography in the Scotia and Mariana basins and to the observed topography in the Aegean Sea (residual topography is difficult to compute for continental areas). A constant value corresponding to an unknown sum of background, large-scale mantle flow and relative position of the 0% Vp is implicitly added from the model values (600 m, 2000 m, and ⫺2000 m for the Scotia Sea, Mariana Sea, and Aegean Sea, respectively). In map view (Fig. 4), the maximum value of dynamic topography is located ⬃170 km, ⬃230 km, and ⬃280 km behind the Scotia, Aegean, and Mariana trenches, respectively, suggesting that the Scotia slab is the steepest slab and the Mariana is the flattest. In the East Scotia region the maximum dynamic topography is predicted to occur 743 beneath the volcanic arc that largely hides it. Because the ridge obliquely intersects the edge of the deflection, the profile mostly features a northward tilt. Beneath the Mariana basin, the dynamic topography can only be observed along the ridge axis due to the location of volcano-sedimentary edifices east and west of the ridge, but the fit between observed and model topography along the ridge is good. Within the Aegean region, the largest model dynamic topography occurs in the southern Aegean and beneath the Cretan Sea, reaching a magnitude of ⬃2 km. Thus, although it is not possible to compute a residual topography for the Aegean region, the model topography is in good agreement with total observed topography, suggesting that most of the deep bathymetry in the south Aegean could be dynamically maintained, and not due to an isostatic compensation of a thinned crust. CONCLUSIONS This study gives evidence for the signature of sinking slabs on the topography developed above them. A theoretical model of subduction, inversion of ␦VP seismic data, and observations of gravity and bathymetry data above several subduction systems show that slabinduced mantle flow is a prominent control on the topographic signal in the vicinity of subduction boundary. This results in a curved shaped characteristic of retreating trenches and a depressed topography above the slab. Downward deflection of the surface topography for these retreating subduction zones is expected to be 1000–2000 m below that of the surrounding areas. The discrepancies between dynamic topography computed here and observed residual topography are primarily attributable to chemical anomalies (although significantly less than those suggested by Taylor and Martinez, 2003), to uncertainties in the seismic data and subsequent conversion to density anomalies, and to the approximation made on the viscosity. Elasticity of the upper plate plays a minor role because the wavelength of the deflection is much larger than the typical length scale for elastic flexure of the lithosphere. Because of complications arising from large-scale mantle flow and mantle viscosity variations, the dynamic topography can only be clearly observed in particular areas, but any narrow retreating subduction system should yield its signature. For example, it can be inferred in the Lau, Manus, Caribbean, or Calabrian basins, but complex prerifting geodynamical events or multiple ridges make it difficult to isolate the dynamic signal. Unlike other studies, I analyzed topographic variations within individual tectonic systems. Because they are small-scale tectonic systems, independent of large-scale mantle circulation and viscosity variations, a joint analysis of their bathymetry, tomography, and gravity shows that these subduction zones feature a dynamic component in the topography comparable to theoretical predictions. These results suggest that dynamic topography probably contributes to net topography in other locations where it is difficult to observe, and this raises the question of whether dynamic topography remains elusive only because isostatic processes hide it. ACKNOWLEDGMENTS This work originated from the enthusiasm of Wiki Royden. I thank ChangLi and R. Van der Hilst for providing tomography data, and two anonymous reviewers. This work was funded by National Science Foundation grant EAR0409373 (Medusa project). 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