Depth-dependent geometry of margin-parallel strike-slip faults within oblique subduction zones *

Based on the principle that faults develop where shear stress is maximum, we determine the depth-dependent geometry of margin-parallel strike-slip faults within oblique subduction zones. Using an elastic half-space model for the south Chile subduction zone, we show that the geometry of a margin-parallel strike-slip fault as the Liquiñe-Ofqui Fault Zone (LOFZ), is vertical near the free surface and curved downwards, until reaching the subducting slab. This geometry is compatible with the observations of ref lectors on seismic data obtained from wide angle refraction studies in southern Chile. GPS measurements also support this curved geometry. We suggest that this curved pattern should occur on all margin-parallel strike-slip faults within oblique subduction zones worldwide.


Introduction
In oblique subduction zones, margin-parallel strike-slip faults accommodate part of the trenchparallel component of convergence.The presence of this type of faults, together with factors such as the obliquity angle (angle between the convergence vector and the normal to the plate boundary), the age of the subducting plate, the nature of the overriding plate and ridge subduction would control the degree of convergence partition (Fitch, 1972;Jarrard, 1986;Beck, 1991;McCaffrey, 1992McCaffrey, , 1996;;Nelson et al., 1994;Tikoff and Teyssier, 1994).The location of margin-parallel strike-slip faults has been attributed to weakening in the crust, due to the high temperatures associated with magmatism (Beck, 1983;Tikoff, 1998), however, only some of these faults coincide with volcanic arcs worldwide.Using a model of oblique convergence based on the f inite element method to the area of Sumatra, McCaffrey et al. (2000) suggest that the location of a margin-parallel strike-slip fault in the overriding plate is controlled by the stress distribution at the downdip end of interplate coupling across the megathrust.
Currently, the depth-dependent geometry of the LOFZ and other margin-parallel strike-slip faults that occur in different margins of oblique convergence worldwide, is still unknown.This paper seeks to clarify this topic, analyzing the three-dimensional distribution of shear stress inside the overriding plate obtained from an elastic half-space model of oblique subduction.

Methodology
Static shear stress within the crust depends on the loading source and the elastic parameters of the crust.The loading source is modeled here by a set of dislocations that represent the oblique subduction of a slab.The geometry of dislocations follows the geometry of subduction, but here we simplify it by having a constant dip angle.The upper portion of the subduction interface remains locked.This geometry follows the basic idea of Sieh et al. (1999) and Kanda and Simons (2010), as shown in f igure 2. Using the analytical expressions of Okada (1992) for an elastic, homogeneous, isotropic, and Poisson-solid half-space, the deformation produced by dislocations was calculated.
We are interested in f inding for any point on the overriding plate, the plane at which the marginparallel shear stress is maximum, which is given by: τxn=τxy ny+τxz nz=τxy sin(θ)+τxz cos(θ) (1) where x and y are the directions parallel and normal to the plate boundary, respectively, and z is depth, n is the normal vector to the plane of maximum margin-parallel shear stress at a given point, and θ is the angle between the surface and that plane (Fig. 2).The orientation of the plane is given by the angle θ that maximizes the value of |τxn(θ)|, for θ=(0:180°).

Results
The family of planes of maximum margin-parallel shear stress obtained by modeling the oblique subduction of the Nazca plate beneath South America in southern Chile, is shown in f igure 3. The model considers an oceanic plate of 20 km thick, dip angle of 15°, and depth to the downdip end of interplate coupling of 50 km.A convergence rate of 66 mm/yr and an obliquity angle of 18° were used (Angermann et al., 1999).
Considering a normal distance between the trace of the LOFZ and the Perú-Chile trench of 270 km (Fig. 1), we calculate the geometry of the LOFZ from the planes of maximum margin-parallel shear stress.The resulting LOFZ is vertical near the free surface and smoothly curved with increasing depth, until reaching the subducting slab (Fig. 4a).This geometry is compatible with the ref lector at the eastern end of the seismic ref lection profile at 38.2° S, shown in f igure 4b (Gross et al., 2007).
Relative motion along the resulting LOFZ should produce margin-parallel velocity on the surface, which can be compared with GPS measurements.We calculate the margin-parallel velocity on the surface, due to both: (a) oblique motion of the subducting oceanic slab, and (b) strike-slip motion on the resulting LOFZ.For these two sources, margin-parallel velocity on the surface were modeled and compared with GPS measurements for southern Chile, between 37°-40° S (Klotz et al., 2001;Ruegg et al., 2009;Moreno et al., 2011).Our model assumes that the LOFZ accommodates half of the strike-slip component of the relative motion between the Nazca and South America plates, and the fault remains locked up to 20 km depth (Fig. 5a).
In figure 5b, horizontal GPS velocities projected parallel to the margin, and margin-parallel velocities predicted by the model are plotted as a function of the normal distance from plate margin.It is noted that the GPS velocities are successfully reproduced by the model.A comparison between the observed and modeled velocity vectors, and corresponding residuals, are shown in figures 5c y 5d, respectively.

Depth-DepenDent geometry of margin-parallel strike-slip faults within oblique subDuction zones
The effects that variations in model parameters have on the margin-parallel velocities on the surface, and root-mean-square (RMS) response, are shown in f igure 6.Among the parameters involved in our calculations, are (a) the depth to the downdip end of interplate coupling, (b) the dip angle of subduction, and (c) the percentage of the margin-parallel component of oblique convergence accommodated by the LOFZ.
In f igure 6a, we can see that the margin-parallel velocity decreases as the downdip depth decreases.
The main effect of the dip angle is to shift the curve towards the trench as the dip angle increases (Fig. 6b).
Variations in the strike-slip rate and locking depth of the LOFZ, have similar effects on the calculated margin-parallel velocities.Considering a locking depth of 20 km, the percentage of the margin-parallel component of oblique convergence accommodated by the LOFZ varied between 0-100% (Fig. 6c).Changes in the slab thickness have little effect on the results.Our preferred model, with an oceanic plate of 20 km thick, dip angle of 15°, depth to the downdip end of interplate coupling of 50 km, and the LOFZ accommodating half of the strike-slip component of oblique convergence, provides the lowest RMS of 2.22 mm/yr (Fig. 6).

Discussion
Currently, the depth-dependent geometry of marginparallel strike-slip faults within oblique subduction zones, is still unknown.Based on a model of oblique convergence for southern Chile, we propose that the LOFZ, a transpressional dextral strike-slip structure parallel to the Nazca-South America plate boundary, has a curved geometry in depth, as shown in figure 4a.We note that this geometry is in agreement with the easternmost reflector of the seismic reflection profile obtained by Gross et al. (2007), from wide angle refraction studies at 38.2° S (Fig. 4b).Although the nature and origin of this reflector is still unclear, the authors noted the spatial coincidence of the extrapolation to the surface of this reflector and the trace of the LOFZ.The other areas of high reflectivity observed in the prof ile, would be consistent with the geometry of the planes of maximum shear stress obtained by our model: East-and west-dipping planes to the left and right of the downdip depth limit, respectively (Fig. 4).
As both plates collide, the value of shear stress at each plane increases at the same rate as the convergence rate.As shear stress increases and the plane breaks, friction coefficient is reduced on such plane and it is likely to be the place of future rupture.Which of all planes initially breaks depends on several factors, including the temperature profile, its particular composition and past history of deformation.Considering the earthquake cycle, with complementary coseismic and interseismic periods both having maximum shear stresses near the downdip depth, it is likely that the planes reaching close to this downdip zone are best candidates to develop as long term faults.The effect of temperature on friction, would promote the development of faults along planes distant to this downdip zone.

Conclusion
Here we show that for any oblique subduction zone, the depth-dependent geometry of a potential margin-parallel strike-slip fault, is vertical near the free surface and smoothly curved with increasing depth, until reaching the subducting slab.This geometry is consistent with observations of ref lectors for southern Chile, in relation to the LOFZ (Gross et al., 2007).
In addition, we model the crustal deformation due to the combined effect of oblique motion of the Nazca plate plus strike-slip motion along the LOFZ, and compare with GPS observations in southern Chile.The parameters of both oblique subduction and strike-slip fault are determined by minimizing the difference between model results and observations.Along the subduction interface, we assume a plate velocity of 66 mm/yr and an obliquity angle of 18°.The preferred model considers an oceanic plate of 20 km thick, dip angle of 15° and depth to the downdip end of interplate coupling of 50 km.The LOFZ remains locked up to 20 km depth, and accommodates half of the strike-slip component of oblique convergence.
FIG.2.Cross section of geometry of oblique subduction for a homogeneous elastic media, with dislocations surrounding the brittle oceanic plate.x and y are the directions parallel and normal to the margin, respectively; z is depth; h is the plate thickness; δ is the dip angle of subduction; zd is the depth to the downdip end of interplate coupling.At any point p, θ is the angle between the surface and the plane (normal to vector n) at which margin-parallel shear stress (τxn) is maximum.
FIG. 5. A. Geometry of the best-fit model.This model considers both oblique motion of the subducting slab and strike-slip motion along the resulting LOFZ.zl is the locking depth for the LOFZ.Other notations are same as figure 2. The LOFZ accommodates half of the margin-parallel component of plate convergence.Observed versus modeled margin-parallel velocities between 37°-40° S, in B cross section, and C map view.D. Residual velocities obtained by subtracting the model from the GPS velocities.
FIG. 6. Margin-parallel velocities and RMS, obtained for different values of: A. downdip depth limits; B. dip angles; and C. percentages of margin-parallel component of oblique convergence accommodated by the LOFZ.