Download Dynamic topography above retreating subduction zones

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 2␪ij ,
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).
REFERENCES CITED
Barker, P., 2001, Scotia Sea regional tectonic evolution: Implications for mantle
flow and palaeocirculation: Earth Science Reviews, v. 55, p. 1–39, doi:
10.1016/S0012-8252(01)00055-1.
Batchelor, G., 1967, An introduction to fluid mechanics: Cambridge, UK, Cambridge University Press, 615 p.
Cazenave, A., Souriau, A., and Dominh, K., 1989, Global coupling of earth
surface topography with hotspots, geoid and mantle heterogeneities: Nature, v. 340, p. 54–57, doi: 10.1038/340054a0.
Colin, P., and Fleitout, L., 1990, Topography of the ocean floor: Thermal evo744
lution of the lithosphere and interaction of deep mantle heterogeneities
with the lithosphere: Geophysical Research Letters, v. 17, p. 1961–1964.
Conrad, C., Lithgow-Bertelloni, C., and Louden, K., 2004, Iceland, the Farallon
slab, and dynamic topography of the North Atlantic: Geology, v. 32,
p. 177–180.
Enns, A., Becker, T.W., and Schmeling, H., 2005, The dynamics of subduction
and trench migration for viscosity stratification: Geophysical Journal International, v. 160, p. 761–775, doi: 10.1111/j.1365-246X.2005.02519.x.
Hager, B.H., 1984, Subducted slabs and the geoid—Constraints on mantle rheology and flow: Journal of Geophysical Research, v. 89, p. 6003–6015.
Harper, J.F., 1984, Mantle flow due to internal vertical forces: Physics of the
Earth and Planetary Interiors, v. 36, p. 285–290, doi: 10.1016/00319201(84)90052-9.
Kárason, H., and van der Hilst, R.D., 2000, Constraints on mantle convection
from seismic tomography, in Richards, M., et al., eds., The history and
dynamics of global plate motion: American Geophysical Union Geophysical Monograph 21, p. 277–289.
Kincaid, C., and Griffiths, R.W., 2004, Variability in flow and temperatures
within mantle subduction zones: Geochemistry, Geophysics, Geosystems,v. 5, doi: 10.1029/2003GC000666.
Lallemand, S., and Heuret, A., 2005, On the relationships between slab dip,
back-arc stress, upper plate absolute motion, and crustal nature in subduction zones: Geochemistry, Geophysics, Geosystems,v. 6, doi: 10.1029/
2005GC000917.
Laske, G., and Masters, G., 1997, A global digital map of sediment thickness:
Eos (Transactions, American Geophysical Union), v. 78, p. F483.
McClusky, S., Reilinger, R., Mahmoud, S., Ben Sari, D., and Tealeb, A., 2003,
GPS constraints on Africa (Nubia) and Arabia plate motions: Geophysical
Journal International, v. 155, p. 126–138, doi: 10.1046/j.1365246X.2003.02023.x.
Moresi, L., and Gurnis, M., 1996, Constraints on the lateral strength of slabs
from three-dimensional dynamic flow models: Earth and Planetary Science Letters, v. 138, p. 15–28.
Moresi, L., and Solomatov, V., 1998, Mantle convection with a brittle lithosphere: Thoughts on the global tectonic style of the Earth and Venus:
Geophysical Journal International, v. 133, p. 669–682.
Morgan, W., 1965, Gravity anomalies and convection currents: Journal of Geophysical Research, v. 70, p. 6175–6187.
Morra, G., and Regenauer-Lieb, K., 2006, A coupled solid-fluid method for
modeling subduction: Philosophical Magazine (in press).
Panasyuk, S., and Hager, B., 2000, Inversion for mantle viscosity profiles constrained by dynamic topography and the geoid, and their estimated errors:
Geophysical Journal International, v. 143, p. 821–836, doi: 10.1046/
j.0956-540X.2000.01286.x.
Reinecker, O., Heidbach, J., Tingay, M., Connolly, P., and Muller, B., 2004,
The 2004 release of the world stress map: http://www. world-stress-map.
org (October 2005).
Ricard, Y., Richards, M., Lithgow-Bertelloni, C., and Le Stunff, Y., 1993, A
geodynamic model of mantle density heterogeneity: Journal of Geophysical Research, v. 98, p. 21,895–21,909.
Royden, L.H., and Husson, L., 2006, Trench motion: Slab geometry and viscous
stresses in subduction systems: Geophysical Journal International (in
press).
Sandwell, D.T., and Smith, W.H.F., 1997, Marine gravity anomaly from Geosat
and ERS 1 satellite altimetry: Journal of Geophysical Research, v. 102,
p. 10,039–10,054, doi: 10.1029/96JB03223.
Stein, C.A., and Stein, S., 1992, A model for the global variation in oceanic
depth and heat flow with lithospheric age: Nature, v. 359, p. 123–129,
doi: 10.1038/359123a0.
Stern, R., Fouch, M., and Klemperer, S., 2003, An overview of the Izu-BoninMariana subduction factory, in Eiler, J.M., ed., Inside the subduction factory: Washington, D.C., American Geophysical Union Monograph 138,
p. 175–222.
Taylor, B., and Martinez, F., 2003, Back-arc basin basalt systematics: Earth and
Planetary Science Letters, v. 210, p. 481–497.
Tirel, C., Gueydan, F., Tiberi, C., and Brun, J.-P., 2004, Aegean crustal thickness
inferred from gravity inversion. Geodynamical implications: Earth and
Planetary Science Letters, v. 228, p. 267–280, doi: 10.1016/
j.epsl.2004.10.023.
Vanneste, L.E., and Larter, R.D., 2002, Sediment subduction, subduction erosion, and strain regime in the northern South Sandwich forearc: Journal
of Geophysical Research, v. 107, p. 2149, doi: 10.1029/2001JB000396.
Wheeler, P., and White, N., 2000, Quest for dynamic topography: Observations
from Southeast Asia: Geology, v. 28, p. 963–966, doi: 10.1130/0091-7613
(2000)28.
Manuscript received 12 December 2005
Revised manuscript received 19 April 2006
Manuscript accepted 25 April 2006
Printed in USA
GEOLOGY, September 2006