Strong Plate Coupling Along the Nazca–South America Convergent Margin

Strong plate coupling along the Nazca–South America convergent margin

Giampiero Iaffaldano* Geophysics Section, Department of Earth and Environmental Sciences, Ludwig-Maximilians University, Hans-Peter Bunge Munich 80333, Germany

ABSTRACT complexity of the dynamic system by exploiting The force balance in plate tectonics is fundamentally important but poorly known. Here, isostasy and vertical integration of stresses in the we show that two prominent and seemingly unrelated observations—trench-parallel gravity so-called thin-shell approximation, although a anomalies along the Nazca–South America margin that coincide with the rupture zones of shortcoming arises from the need to parameter- great earthquakes, and a rapid slowdown of Nazca–South America convergence over the past ize the mantle buoyancy and fl ow that generate 10 m.y.—provide key insights. Both result from rapid Miocene-Pliocene uplift of the Andes shear stresses at the base of plates. At the same and provide quantitative measures of the magnitude and distribution of plate coupling along time, there has been great progress in our abil- the Nazca–South America margin. We compute the plate-tectonic force budget using global ity to simulate the circulation of Earth’s mantle models of the faulted lithosphere coupled to high-resolution mantle circulation models and at high numerical resolution (Bunge et al., 1997). fi nd that Andean-related plate-margin forces are comparable to plate-driving forces from the Such time-dependent Earth models account for mantle, and they have suffi cient magnitude to account for pronounced bathymetry variations radial variations in mantle viscosity (typically a along the trench. Our results suggest that plate coupling, gravity anomalies, and bathymetry factor 40 increase from the upper to the lower variations along a given trench are all controlled by long-term stress variations in the upper mantle), internal heat generation from radioactiv- portion of plate boundaries and that an explicit budget of driving and resisting forces in plate ity, bottom heating from the core, and a history tectonics can be obtained. For the convergent margin considered here, spatial variations in of subduction spanning the past 120 m.y., and the effective coeffi cient of friction associated with the distribution of lubricating sediments they provide a fi rst-order estimate of the internal entering the trench are, by comparison, of minor importance. mantle buoyancy forces that drive the plates; the models, however, do not account for the brittle Keywords: Andean uplift, plate coupling, gravity anomalies. nature of the faulted lithosphere and, specifi cally, for the contribution of plate-boundary forces INTRODUCTION anomalies (Fig. 2A). We computed these anom- to the stress balance. It is logical therefore to Plate tectonics (Morgan, 1968) is remark- alies by subtracting the regional-average trench- merge these two independent classes of models. able in that they explain the surface motion normal gravity profi le from free-air gravity data Using the global model for lithosphere dynamics of Earth with great accuracy (DeMets et al., (Sandwell and Smith, 1997). The trench-parallel SHELLS (Kong and Bird, 1995) combined with 1994), even though the budget of driving and gravity anomaly profi le along the Nazca–South three-dimensional (3-D) mantle circulation mod- resisting forces is poorly known (Forsyth and America margin is characterized by strongly els (Bunge et al., 2002), we have shown recently Uyeda, 1975). Mantle convection is commonly negative values, as large as −100 mGal, in the that late Miocene-Pliocene uplift of the Andes accepted as the engine for plate motion (Ricard central part close to the highly elevated Puna can account for the rapid Nazca–South America and Vigny, 1989), but the magnitude and distri- and Altiplano regions. In contrast, the northern convergence reduction over the past 10 m.y. bution of resisting plate-margin forces are less and southern parts of the trench both show a (Iaffaldano et al., 2006). clear. Short-term plate-motion changes on the positive signal. Trench-parallel gravity anomaly order of a few million years or less, which are gradients coincide with the occurrence of large MODELS AND RESULTS increasingly revealed through the comparison earthquakes—such as the great M 9.5 Chilean Global coupled lithosphere-mantle circulation of geodesy-based measurements (Dixon, 1991; event of 1960 (Barrientos and Ward, 1990) and models allow us to derive an explicit budget of Stein, 1993) and increasingly detailed paleomag- the recent M 8.0 Peru earthquake of 2007— plate-boundary forces along the Nazca–South netic reconstructions (Müller et al., 2008), repre- and are associated with substantial trench- America plate margin. Under the assumption sent a powerful probe to quantify these forces. parallel bathymetry variations (Smith and that plate-boundary forces along the margin are Since rapid plate-velocity variations are unlikely Sandwell, 1997). It has been suggested that the dominated by the recent uplift of the Andes, we to result from changes in the pattern of global largest earthquakes occur on portions of sub- used the SHELLS global model, which accounts mantle fl ow, which evolves on a much longer duction zones where plates are most strongly for the present-day topography as reported in the time scale, on the order of 150–200 m.y. (Bunge coupled (Kanamori, 1986); thus, trench-parallel ETOPO5 data set (National Geophysical Data et al., 1998), they must refl ect temporal varia- gravity anomalies might be indicative of lateral Center, 1998), and shear tractions taken from tions in plate coupling along a given margin. A variations in mechanical coupling (Stein and the aforementioned simulations of mantle fl ow prominent example is the 30% slowing of con- Wysession, 2003) along the plate margin. to compute equilibrium forces in the lithosphere. vergence between the Nazca and South America One way to estimate plate coupling is from We then performed a second simulation corre- plates over the past 10 m.y. (Fig. 1) inferred from computer simulations using global models of sponding to a paleoreconstruction of topography a variety of data (Norabuena et al., 1999). the lithosphere that include sophisticated rheol- of the Andes 10 m.y. ago (Gregory-Wodzicki, We propose that the slowing of convergence ogies and realistic plate confi gurations (Bird, 2000). The plate-boundary forces along the results from the same mechanism that causes 1999). The stresses involved in the dynamics Nazca–South America margin that correspond pronounced along-strike trench-parallel gravity of the lithosphere include the tectonic contribu- to the recent uplift of the Andes were obtained tion coming from regions of high topography, as the difference of the two simulations. It is which provide both horizontal deviatoric stresses worth mentioning that among others, one advan- *Current address: Department of Earth and Plan- etary Sciences, Harvard University, Cambridge, and vertical overburden pressure, and the shear tage of such an approach is that it allows us to Massachusetts 02138, USA: E-mail: iaffaldano@ stresses from buoyancies in the mantle. Typi- neglect, with reasonable confi dence, viscous eps.harvard.edu. cally, these models reduce the computational deformation within the Andean belt, since its

© 2008 The Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. GEOLOGY,Geology, June June 2008; 2008 v. 36; no. 6; p. 443–446; doi: 10.1130/G24489A.1; 4 fi gures. 443 for the associated mass anomalies. Our predicted trench-parallel resisting force anomalies display a similar behavior. Gravity and resisting force anomalies along the trench are highly correlated at the 90% confi dence level (Fig. 2C). In Figure 3A, we plot the observed trench- parallel bathymetry anomalies obtained by subtracting the average trench-parallel bathymetric profi le from the digital elevation model ETOPO5. The trench-parallel gravity (Fig. 2A) and bathymetry (Fig. 3A) anomalies are in excellent agreement, an inference suggested earlier by Song and Simons (2003): negative gravity anomalies correspond to deeper-than- average bathymetry, whereas positive anomalies correspond to bathymetry that is shallower than the average. We note that the age of the Nazca ocean fl oor varies between 20 and 50 m.y. old along the margin (Müller et al., 1997), and that a simple half-space model of plate subsidence due to lithosphere cooling would predict ocean depth variation of ~1 km, accounting for only 25% of the observed bathymetric variations. Figure 1. Comparison of past (10 m.y.; red) and present-day (blue) motion of Nazca (NZ) and We tested whether the magnitude of plate- South America (SA), derived from paleomagnetic (red) and instantaneous geodetic observa- coupling forces arising from our simulations was tions (blue). Velocity vectors reveal a 30% convergence reduction from 10 to 7 cm/yr over the suffi cient to explain the observed bathymetry past 10 m.y. Timing suggests a co-evolution of increased plate-coupling forces and Andean signal by solving for an analytical solution of the uplift. Plate boundaries are in black; continents are in gray. Plate abbreviations: AF—Africa, AN—Antarctica, CA—Caribbean, CO—Cocos, PA—Pacifi c. thin-plate differential equation for a semi-infi nite oceanic plate, tectonically loaded on one side (see inset in Fig. 3B). We assumed a Young’s modulus growth is included in our simulations not as a as the trench-parallel gravity anomalies. That is, of 20 GPa, Poisson ratio of 0.25, and an elastic time-evolving process but rather as initial and we subtracted the average resisting force along thickness in the range 25–30 km, consistent with fi nal stages. We found that the average resist- the margin from the local plate-boundary forces published estimates (Caldwell et al., 1976). We ing force upon the Nazca plate from gravita- in our simulations. Along the central portion of used the analytical solution to compute vertical tional spreading of the Andes is on the order of the margin, we found strongly positive force bending of the Nazca plate under the action of 3.7 × 1012 N/m, a value comparable to results anomalies, as high as 3 × 1012 N/m, whereas our predicted force anomalies. We also accounted from previous, two-dimensional (2-D) studies negative anomalies prevail in the northern and for gravitational restoring forces from the denser (Husson and Ricard, 2004). Integrated over the southern parts. Figures 2A and 2B reveal a asthenosphere, as well as for intrinsic bathy- total length of the plate boundary (5300 km), the remarkable correlation of trench-parallel gravity metric variations related to the cooling of oceanic net average force equals 2 × 1019 N. The along- anomalies and plate-boundary forces predicted lithosphere. Predicted bathymetry anomalies are strike variation of the Andean-related plate- from Miocene-Pliocene uplift of the Andes in shown in Figure 3B. We mapped the lack and boundary forces is more interesting. For ease our model. The gravity signal shows pronounced excess of mass expressed by computed bathyme- of comparison, we treated the plate-boundary short-wavelength spatial variations from positive try anomalies into predicted gravity anomalies by forces due to Andean uplift in the same manner to negative values suggestive of a shallow origin integrating a Bouguer gravity formula for water

Figure 2. A: Observed trench-parallel gravity anomalies (TPGAs) along Nazca–South AB C America (NZ/SA) plate margin (see text). Anomalies as high as ±100 mGal vary rap- idly from north to south along margin and suggest shallow origin of gravity signal. B: Predicted tectonic force anomalies due to rise of Andes (see text for details). Force anomalies are obtained by subtracting average resisting force along margin from local plate-boundary forces in our simulations. Note strongly positive force anomalies, as high as 3 × 1012 N/m, along central portion of margin, whereas negative anomalies prevail in northern and southern parts. Black dots indicate large (Mw > 8.0) earthquakes reported since 1555, which occurred in regions of moderate to low coupling between subducting and overriding plates. C: Com- parison of along-trench profi le of gravity and tectonic force anomalies. Profi les correlate at 90% confi dence level.

444 GEOLOGY, June 2008 AB C

Figure 3. Trench-parallel bathymetry anomalies observed (A) and predicted (B) from analytical plate-bending model (see text and inset) using tectonic forcing computed from our models. Predicted magnitude and spatial pattern of bathymetry anomalies are in excellent agreement with observations. C: Observed (gray) and predicted (blue) gravity anomaly profi les along Nazca–South America (NZ/SA) plate boundary. Predicted gravity anomalies were computed by integrating a Bouguer formula for density of water against crust along bathymetry-anomaly profi les predicted from our simulations. Profi les correlate at 90% confi dence level, implying that gravity anomalies and plate-coupling variations along convergent margin are associated with recent growth of Andes (see text). against crust along the computed bathymetric fi elds: one is associated with homogeneous margin are unlikely to provide a simultane- anomaly profi le of the Nazca plate. Our predic- friction along the trench, and the other features ous explanation for the observed convergence tions of the gravity signal are in excellent agree- increased friction in the sediment-starved por- record, the bathymetry anomalies, and the ment with the observations (Fig. 3C). tion of the trench between 13°S and 30°S. Our trench-parallel gravity anomalies along the results show that the convergence velocity is Nazca–South America plate boundary. Instead, DISCUSSION rather insensitive to the assumed friction coef- these observations are best explained by large Our results raise an important question: Could fi cient, and that one requires a friction value as topographic features, such as the high plateaus there be other mechanisms capable of provid- high as 0.4 to result in a convergence reduction in the central Andes. We speculate, however, ing a simultaneous explanation for the observed compatible with observations (shown in green that friction-generated variations in trench- slowing of convergence over the past 10 m.y. and in Fig. 4). Such a high value, however, is close to parallel plate boundary forces might explain the pronounced gravity and bathymetry signals the prediction from Byerlee’s law for failure of moderate trench-parallel gravity anomalies in along the margin? For instance, the amount of materials (shown in blue), and it is much larger other regions of plate convergence where high seafl oor sediments varies substantially along the than the commonly accepted limit for conver- topography is not a dominant feature. trench (Mooney et al., 1998). Sediment thickness gent margins of 0.1 (shown in red). Theoretical Our results suggest that variations of mechan- in the northern and southern parts of the margin 2-D studies of the Andean orogeny (Sobolev ical coupling along the plate boundary are the is higher than 1500 m, whereas the central part, and Babeyko, 2005) reveal in fact that friction origin for the peculiar shape of the South Ameri- between 13°S and 30°S, the margin is sediment- coeffi cients higher than 0.1 would produce slab can margin, with its strong indentation near the starved. It has been suggested that a lack of sedi- break-off, thus stopping the subduction process. Puna and Altiplano Plateaus. Paleomagnetic ment infi ll may be responsible for stronger plate From this, we conclude that frictional varia- evidence indicates that rotation in the Bolivian coupling by increasing the effective coeffi cient of tions along the Nazca–South America plate orocline occurred over the past 7–9 m.y. (Rousse friction along the central, sediment-starved portion of the trench (Lamb and Davies, 2003). This Figure 4. Predicted Nazca–South America would result in higher resisting stresses in these (NZ/SA) convergence reduction for a range of regions (Kohlstedt et al., 1995), which would assumed friction coeffi cients along sediment- oppose convergent motion. starved plate boundary between 13°S and We test this hypothesis in Figure 4. Because 30°S. Friction values smaller than 0.1, which is a commonly accepted limit for trench fric- we lacked a direct relationship between the tion (see red line), cannot explain observed amount of sediment infi ll and the friction coef- convergence reduction (see green line). To fi cient, we computed plate coupling and associ- explain observed 30% velocity reduction solely ated convergence velocity for a range of friction through frictional variations along sediment- starved portion of margin, rather high friction coeffi cients in the sediment-starved part of the values, close to 0.6 (see blue line—Byerlee’s trench. Specifi cally, we computed and then sub- law for failure of materials under stresses tracted from each other two equilibrium force- larger than 200 MPa), are required.

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