All Supporting Information may be found in the online version of this article.
Corresponding author: F. Aron, Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY 14853, USA. (email@example.com)
 Geologists have long known that young normal faults are an important structural element of the Andean Coastal Cordillera, but their relationship to the subduction seismic cycle is still unclear. Some of the largest aftershocks of the 2010 Mw 8.8 Maule earthquake in central Chile were nucleated on upper plate normal faults, including the Mw 6.9 and 7.0 events of the Pichilemu earthquake sequence. We use the available coseismic GPS displacements, moment tensor sums, and slip distribution models for the Maule earthquake to compute the static strain and stress fields imposed on the upper plate by slip on the subduction interface. The extensional strains calculated from coseismic GPS and from a moment tensor sum of the Pichilemu events have similar orientations and orders of magnitude. The normal Coulomb stress increment (CSI) on the Pichilemu fault has maximum positive stresses as high as 4.9 MPa. Regionally, the Maule event produced a semi-elliptical, radial pattern of static extension and deviatoric tension (CSI > 1.5 MPa) along the Coastal Cordillera enclosing the rupture area. This elliptical pattern mimics the trends of the major upper-crustal structures. The static deformation field produced by a great subduction earthquake is an effective mechanism for generating permanent extension above the seismogenic zone, reactivating suitably oriented, long-lived normal faults. We suggest that the semi-elliptical outline of the first-order structures along the Coastal Cordillera may define the location of a characteristic, long-lived megathrust segment. This observation implies a persistence at least over the Quaternary of great subduction ruptures along the Maule segment.
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 On 27 February 2010, approximately 600 km of the Nazca-South America plate boundary ruptured to generate the Mw 8.8 Maule earthquake on the subduction megathrust beneath central Chile (Figure 1). Curiously, the two largest aftershocks were intraplate normal fault earthquakes with magnitudes of Mw 7.4 and 7.0, the first located in the outer rise of the downgoing oceanic slab and the second within the upper plate fore arc, directly above the rupture area (Figure 1 and section S.1 in the Supporting Information). In many parts of the Chilean Coastal Cordillera, where it overlies the zone of interplate seismogenic coupling, Neogene-Quaternary normal faults outnumber reverse faults, especially north of 33°S but also in the Maule segment [e.g., Allmendinger and González, 2010; Aron et al., 2012; Benado, 2000; Heinze, 2003; Katz, 1971]. The 2011 Mw 9.0 Tōhoku, Japan, subduction zone earthquake was also accompanied by a significant number of upper plate normal aftershocks [e.g., Lay et al., 2011; Toda et al., 2011a, 2011b]. How do upper plate normal faults relate to interplate boundary thrusting, and are there specific conditions that favor formation of normal faults?
 For the Chilean margin, a common answer to this question is that upper plate normal faults in the north are strictly related to subduction erosion [e.g., Armijo and Thiele, 1990; Von Huene and Ranero, 2003] and that any normal faults in the accretionary part of the Chilean fore arc, south of 33°S, are local features related to anticlinal folding above propagating thrust faults in the accretionary wedge [Melnick et al., 2006]. This common view, however, does not explain several key observations, including (1) local network seismic data that show that the Pichilemu fault cuts most of the crust [Farías et al., 2011], (2) existence of young normal faults in Paleozoic bedrock outside of the accretionary wedge, (3) normal fault focal mechanisms accompanying many great subduction earthquakes, or (4) the relatively common observation that upper plate faults have moved as both normal and reverse faults during their long-term history [Allmendinger and González, 2010; Melnick et al., 2006]. We suggest here a more nuanced explanation that acknowledges the profound influence that great subduction earthquakes, like the Maule megathrust, produce on the state of stress in the upper plate, even in accreting plate margins.
 We combine geophysical and geological data with principles of linear elasticity, dislocation theory, and Coulomb rock fracture criteria to explore how permanent upper plate deformation relates to release of elastic strain energy during great earthquakes. Modeling the infinitesimal static strain and stress fields imposed on the upper plate by the interplate megathrust, we provide a mechanical explanation for continental Mw 7.0 intraplate normal faulting triggered by the Maule earthquake. By comparing the coseismic and interseismic crustal deformation signals, we propose that cyclical unloading of the upper plate during great subduction earthquakes may generate a permanent, distinctive extensional pattern in the structural grain of the fore arc. This pattern may represent the average behavior over many thousands of subduction seismic cycles throughout the geologic time, and we suggest that might be used to identify characteristic, long-lived rupture segments.
2 Tectonic and Structural Settings
 Subduction zones are one of the most tectonically active provinces in the planet. The plate convergence forces, at least in the upper brittle part of the lithosphere, are transmitted to both plates in the form of shear stresses [Lallemand et al., 2005; Lamb, 2006; McCaffrey, 1994] on a “dual behavior” locking-slipping fault that constitutes the seismogenic portion of the plates interface (Figure 2) [Scholz, 2002]. The dual behavior is reflected in the seismic cycle. This can be divided into an interseismic period of full to partial coupling of the interface, with a duration in the scale of the hundreds of years for time intervals between events of magnitude >Mw 8.5 [e.g., Minoura et al., 2001; Rikitake, 1976; Satake and Atwater, 2007], and a coseismic-post-seismic period, minutes-to-months long [Reid, 1910; Scholz, 2002]. The later encompasses rapid slip on the subduction megathrust and continuous accommodation of strain due to aseismic afterslip and thrust aftershocks. The two periods of the seismic cycle differ in the time scale and in the direction of the applied shear, which is approximately opposite in sense (Figure 2). Post-seismic deformation has been recognized as increasingly important [e.g., Hu et al., 2004] but commonly has similar orientation to the coseismic deformation, and the two are indistinguishable in the geologic record, which is our main concern here.
 The Nazca-South America plate boundary accounts for 16 out of 89 of all the earthquakes greater than Mw 8.0 ever recorded up to 31 July 2012 (source, U.S. Geological Survey (USGS)). Three of those are in the top 15, including the largest recorded in modern history (Valdivia Mw 9.5; Kanamori ). The 2010 Maule earthquake, which is the focus of this paper, is the sixth largest since 1900.
 The upper plate deformation in a “Chilean” type of subduction zone has been characterized as highly compressional [Uyeda, 1982] with compression parallel to the convergence vector as determined by plate boundary related earthquakes and fore-arc GPS data [Bevis et al., 2001; Brooks et al., 2003; Kendrick et al., 2001; Klotz et al., 2001; Klotz et al., 2006; Ruegg et al., 2002, 2009], which record strong coupling of the plates down to approximately 50 km depth [Bevis et al., 2001; Khazaradze and Klotz, 2003; Moreno et al., 2010; Moreno et al., 2011, 2012; Suarez and Comte, 1993; Tichelaar and Ruff, 1991, 1993]. In other words, the maximum long- and short-term compressive stresses in the continent are both approximately parallel to the convergence vector (Figure 2). In contrast, during the very short-term coseismic deformation, the portion of the fore arc above the rupture area extends in the direction of the megathrust rebound [e.g., Klotz et al., 1999; Klotz et al., 2006].
 Despite the highly compressive nature of the leading edge of the South American plate, a significant portion of the Central and Southern Andes, the outer fore arc (Figure 2), is dominated by kilometer-scale normal faults that run parallel and oblique to the plate boundary along the Coastal Cordillera (Figure 1). Structural studies documenting normal faulting are common north of the Maule rupture area [e.g., Allmendinger and González, 2010; Allmendinger et al., 2005; Arabasz, 1971; Armijo and Thiele, 1990; Benado, 2000; Delouis et al., 1998; González et al., 2003; González et al., 2006; Heinze, 2003; Loveless et al., 2010; Marquardt, 1999; Marquardt et al., 2004], but some evidence for extensional structures in the Maule region is also available [e.g., Aron et al., 2012; Cembrano et al., 2007; Gana et al., 1996; Geersen et al., 2011; Katz, 1971; Lavenu and Cembrano, 1999; Lavenu and Encinas, 2005; Lavenu et al., 1999; Melnick et al., 2006; Melnick, Bookhagen, Strecker, and Echtler, 2009; Wall et al., 1996]. Melnick et al. [2006, 2009] state that reverse faults in the Arauco Peninsula, at the southern end of the Maule rupture, seem to be relatively more abundant than the normal faults, especially compared to the Valparaíso Peninsula (northern end) and in general to the rest of the Coastal Cordillera. However, they also show a puzzling coexistence of normal and reverse faults and inversion of the structures.
 The normal fault-dominated structural style is active today and extends back in time to at least the Quaternary in the Maule region. For example, the Pichilemu normal fault shows evidence of successive offsets of a Pleistocene-Holocene? marine abrasion platform [Aron et al., 2012]. Some of these structures, like Pichilemu, may cut the upper crust all the way down until the plate interface, but others appear limited to just the upper crust [e.g., Allmendinger and González, 2010]. The long-term direction of extension along the outer fore arc (Miocene to Present) determined by these structures is approximately parallel to the convergence vector [e.g., Cembrano et al., 2007; Heinze, 2003; Lavenu et al., 1999], i.e., the orientation of the maximum compressive traction applied to the body during the time-dominant interseismic period (Figure 2). There are, however, distinctive regions, such as between Valparaíso and Pichilemu (Figure 1) or near the Mejillones peninsula, where these structures are more oblique to the continental margin.
 Published explanations of fore-arc normal faulting include the following: (a) changes in the flat-ramp geometry of the slab [Armijo and Thiele, 1990], (b) subduction erosion and underplating [Delouis et al., 1998; Hoffmann-Rothe et al., 2006; Von Huene and Lallemand, 1990; Von Huene and Ranero, 2003; Von Huene and Scholl, 1991], (c) crustal strain imbalance between the interseismic (accumulation) and the coseismic (release) periods that lead to plastic-permanent deformation [Klotz et al., 2006], (d) elastic flexure and bending moment tension of the plates during the period of fully coupling [Allmendinger and González, 2010; Delouis et al., 1998; González et al., 2003; Loveless and Pritchard, 2008; Loveless et al., 2010], and (e) an extensional static or dynamic stress field produced by the elastic rebound during a great subduction earthquake [Allmendinger and González, 2010; Delouis et al., 1998; Loveless and Pritchard, 2008; Loveless et al., 2010]. The last three hypotheses consider the earthquake cycle to be the driving mechanism for long-term deformation in the outer fore arc.
3 The Maule Earthquake
 Rapid moment tensor solutions published for the 2010 Maule earthquake show a Mw 8.8 thrust fault focal mechanism, with a centroid located at 35.85°S, 72.72°W and 35 km depth (USGS; http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010tfan/neic_tfan_cmt.php), or at 35.98°S, 73.15°W and 23.2 km depth (Global Centroid Moment Tensor (CMT) catalog; http://www.globalcmt.org/CMTsearch.html, Event name: 201002270634A). This megathrust earthquake filled the seismic gap from the 1835 earthquake [Darwin, 1845] and reruptured a segment that experienced a M 8 earthquake in 1928 [Beck et al., 1998; Campos et al., 2002; Kelleher, 1972; Lomnitz, 1970; Nishenko, 1985, 1991; Ruegg et al., 2002, 2009]. The Maule earthquake was located just north of the Mw 9.5 Valdivia earthquake in 1960. Inversions obtained from pre-earthquake geodetic data indicate that the seismogenic plate interface in the Maule area was strongly coupled up to the date of the event [Madariaga et al., 2010; Moreno et al., 2010; Ruegg et al., 2009].
 Most of the aftershocks Mw > 4.8 that followed the main shock reported by the Global CMT and National Earthquake Information Center (NEIC) agencies were thrust events that nucleated at the plate interface. However, approximately 19 yielded normal focal mechanisms with hypocenters located within the upper plate of the outer fore arc at depths varying between 12 and 20 km. An additional 15 normal mechanisms were located in the lower plate (outer rise) near the trench (Figure 1 and section S.1). The thrust earthquakes occurring after the main shock produce discrete slip that fills both the areas of low slip [Rietbrock et al., 2012] and the coseismically stressed areas on the plate interface, around the zones that concentrate most of the slip of the first motion (barriers). The normal earthquakes represent brittle intraplate deformation. It is notable that the outer rise earthquakes are located mostly along the traces of fracture zones in the subducting plate near the trench, at the north-central and southern parts of the segment (Figure 1).
 A cluster of upper-crustal aftershocks located near the northern end of the rupture area, the Pichilemu sequence [Arriagada et al., 2011; Farías et al., 2011; Ryder et al., 2012], started 6 days after the Maule earthquake and lasted for 269 days (Figures 1 and 3 and section S.1). This cluster can be divided into three groups according to the strike of the nodal planes and to the alignment of the individual events: (1) the NNE-NE, (2) the ~NS and (3) the NNW-NW sequences. Some of the epicenters and the nodal planes obtained from the moment tensor orientations of these earthquakes coincide with the location and strike of major faults of the Coastal Cordillera that appear in the 1-million scale Chilean geological map [SERNAGEOMIN, 2003]. Our recent field observations [Aron et al., 2012] indicate that these large aftershocks were nucleated in a 321°-striking, SW-dipping normal fault that nearly coincides with one of the structures of the Chilean geologic map (Figure 3). The maximum expression of the crustal normal fault cluster was on 11 March (12 days after the main shock) with Mw 6.9 and 7.0 events (12.9 and 16.3 km depth, respectively), which belong to the third sequence mentioned above (Figures 1 and 3).
4 Kinematics of the Pichilemu Events
4.1 Moment Tensor Summation in Pichilemu and GPS Strain
 Using data from the Global Centroid Moment Tensor catalog, we sum the moment tensors for the Pichilemu sequence which is dominated by the two main shocks, Mw 6.9 and 7.0 of 11 March 2010. The principal infinitesimal extension axis of the summed moment tensor has a trend and plunge of about 240°, 30° (Figure 4). Unlike the orientation, the magnitude of strain from a moment tensor sum is particularly dicey given the uncertainty surrounding the volume of the region affected by the earthquakes. We calculate strain for a range of volumes, from an unrealistically small 10 × 10 × 10 km3 to an unrealistically large 100 × 100 × 30 km3. In between those extremes, the principal extensional strain varies from about 10−5 to 10−4 (Figure 5).
 Coseismic GPS provides a different measure of strain, one restricted just to the surface on which the GPS stations lie. Because of the two-dimensional nature of the rupture area and the fact that Pichilemu lies at the northern end of the rupture, the traditional geophysical approach of constructing a 1-D transect of displacement versus distance does not work. Furthermore, there were no GPS stations within 55 km of Pichilemu, itself. Therefore, we invert the coseismic displacement field [Moreno et al., 2012; Vigny et al., 2011] for a distance-weighted, best-fitting displacement gradient tensor from which we extract the infinitesimal strain tensor [Allmendinger et al, 2009; Cardozo and Allmendinger, 2009]. The analysis shows that the highest extension magnitudes are located just to the south of Pichilemu (Figure 6). The regionally smoothed principal extension axis orientation is 80°–260°, with a magnitude of 1.4 × 10−5.
 Using just the seven nearest stations—three to the north and four to the south of Pichilemu (Figure 6)—we calculate a best fit principal extension axis oriented with an azimuth of 063°–243°, and a magnitude of 2.3 × 10−5 (Figure 6). As in the case of earthquakes, the magnitude of strain determined from GPS vectors is subject to several limitations: stations are not uniformly distributed, the strain is not homogeneous, and the magnitude depends on the length scale over which it is measured. Nonetheless, we note that the coseismic extension measured by GPS and the strain due to the Pichilemu earthquake sequence have very similar orientations and are well within an order of magnitude of each other (Figures 4 and 5).
4.2 Regional Strain Field
 Our second approach to the coseismic deformation caused by the Maule event is to calculate the infinitesimal strain field in three dimensions from discrete displacements of the upper crust (following methods described by Allmendinger et al.  and Cardozo and Allmendinger ). We use a distance-weighted least squares inversion to obtain displacement gradient tensors calculated over a regular grid. Note that the size of the grid only influences the visual smoothness of the solution but does not affect the magnitudes or orientations calculated.
 To see the complete upper plate kinematic field, we combine the observed GPS with the slip vectors on the fault patches from the different published Maule slip models in a South America fixed reference frame. The displacements utilized were the following: (a) the coseismic static GPS displacements published by Vigny et al.  and Moreno et al.  (Figure 6); and (b) slip vectors from the finite fault models published by G. Hayes et al., (all unpublished data, 2010; refer to section 3 for web sites) (section S.2). These three slip models were chosen to avoid circular calculations because they are only based on seismic data and not GPS data.
 In this way, we constrained the inversion of the applied displacements from above and below the deformed body, i.e., the outer fore-arc wedge. The inclusion of the interface slip distribution not only constrains the three-dimensional displacement gradients but also offers much better resolution for the strain calculation in the volume above the rupture area.
 Like the GPS vectors, alone, the inversion of coseismic GPS displacements and static fault slip displacements show a widespread volume of a positive extensional field, covering the entire fore arc above the Maule segment (Figure 7 and section S.3). The models produced a radial pattern of static extension (predominantly trench-perpendicular) and semi-elliptical pattern of shortening axes enclosing the rupture area and the zones of maximum slip (Figure 7 and section S.3). We return to this pattern in the discussion section.
5 Coulomb Stress Increment
5.1 Theoretical Background
 We also take a static mechanical approach to determine the coseismic deformation field by using an analytical solution based on Volterra's theory of dislocations [Volterra, 1907]. This theory was first developed to study earthquakes by Steketee  and completely defined by Okada . The fault plane is represented mathematically as a dislocation in an infinite, homogeneous elastic half-space. The shear vectors on the source fault (or megathrust), or distributed slip vectors in the case of finite discrete fault models, produce opposite displacement couples of the blocks separated by the dislocation and generates an elastic perturbation or distortion of the material surrounding the discontinuity (Figure 2). This process is expressed in an internal displacement field [Okada, 1992].
 The determination of the coseismic internal deformation field using theory of dislocations and subsequently the Coulomb stress increment or Coulomb stress change (hereafter CSI) resolved on receiver faults (like Pichilemu) has been extensively and successfully utilized to assess how the coseismic stress transfer affects the structures near the source fault and how it triggers new earthquakes (aftershocks) around the source [e.g., Chinnery, 1963; Das and Scholz, 1981; Freed, 2005; Harris, 1998; King et al, 1994; Lin and Stein, 2004; Oppenheimer et al, 1988; Press, 1965; Stein, 1999; Stein et al, 1994; Toda et al, 2011]. A brief summary of the mechanical theory behind these methods is given in the Supporting Information (section S.4) of the article.
 Here we produce coseismic forward models of the static CSI on the Pichilemu receiver fault and coincident nodal planes of the Mw 6.9 and 7.0 normal events of 11 March (Figures 1 and 3 and Table 1; see also section S.1). Also, we compute the strike of “optimally oriented” normal faults on horizontal grids at different depths covering the entire fore arc above the Maule rupture area. The optimal orientation is defined by the maximum value of CSI modeled at each grid element, which is also shown in our results as color contoured maps, along a normal slip vector with rake = −90° (section S.4.1).
Table 1. Input Parameters Used in Our Mechanical Modeling
Pichilemu Receiver Normal Fault Parameters (Rake: −90°)c
U W c
Publications by Delouis et al. , Lorito et al. , Vigny et al. , and Moreno et al. . Web open sources by G. Hayes, A. Sladen, and G. Shao (all unpublished data, 2010) Synthetic interseismic locking (or backslip).
E, elastic modulus; ν, Poisson's ratio (Lamé constants parameters).
T D, top tip line depth; U W c, coordinate of upper west corner. The fault was subdivided in an 8 (L) by 4 (W) grid.
 Because the determination of coseismic slip is an inverse algebraic problem with no unique solution, we test all the available finite fault models that have published the slip distribution data (papers by Delouis et al. , Lorito et al. , Vigny et al. , and Moreno et al. ; and web open sources by G. Hayes, et al., all unpublished data, 2010) (section S.2). Models for great ruptures that are based only on teleseismic data do not reliably solve for the slip distribution [Pritchard et al., 2007]. Although our calculations use all the fault slip models mentioned, we prefer the fault slip models which are based on a much more comprehensive data matrix for the slip inversion (i.e., models by Lorito et al. , Moreno et al. , and Vigny et al. ). The Lamé constants were determined using average values for upper-crustal materials of elastic modulus and Poisson's ratio [Turcotte and Schubert, 2002]. The static coefficient of friction (μ′) was set following the criteria adopted by Byerlee  and Sibson  for preexisting faults and intact rocks (Table 1; see Supporting Information for mathematical details about how the material properties parameters relate to the CSI on receiver faults). The selection of the nodal plane, location, and dimensions of the Pichilemu normal receiver fault, which cuts through the entire upper plate, were based on the information reported in the Chilean geological map [SERNAGEOMIN, 2003] and in our field observations [Aron et al., 2012] (Figure 3).
 The receiver fault was subdivided into 32 patches to obtain more precise and detailed calculations of the CSI distribution on the fault plane and to avoid that possible singularities in the calculation of the CSI near the source slip model would be included in the complete fault plane average (Figure 3). We assumed no external stress acting on the elastic half-space to assess exclusively the coseismic deformation.
 Somewhat similar analyses of CSI have been carried out by Farías et al.  and Ryder et al. . Our approach differs in that we compute alternative models offering a statistical range of possible solutions; we model the reactivated structure in detail and include an analysis of GPS and moment tensor data, lacking in these other articles. Moreover, in the following sections, we provide a mechanical comparison to the interseismic period and a regional perspective about the genetic relation between the structural grain of the fore arc and the seismic cycle.
5.2 The Interseismic CSI Analysis
 To explore the potential of the interseismic deformation field to generate fore-arc permanent extension compared to the coseismic field, we simulate a simple dislocation model of the Maule segment throughout an interseismic period of 150 years, which falls within the recurrence times of subduction earthquakes estimated for the Andes [e.g., Comte and Pardo, 1991; Lomnitz, 1970; Nishenko, 1985, 1991]. We based our simulation on a “backslip” model [Savage, 1983], hypothesizing that the finite upper plate deformation field over Maule is created by shear stress transfer at the plates interface (Figure 2). This external shear acts constantly during the entire interseismic cycle due to the interplate locking and the continuous plate convergence.
 Here we present a synthetic semi-2-D approximation of the subduction interface along the Maule segment, divided into three segments with variable strike, which mimics the trend of the trench (section S.2 and Figure S.9). This approach does not include the sophisticated interseismic coupling models of Moreno et al. . Although crude, our model is consistent with the overall interseismic stress field determined by other methods which consider second-order effects such as strain rate, rheology inhomogeneities, elasto-plastic and viscous behaviors of the material, and thermal effects near the volcanic arc [e.g., Yáñez and Cembrano, 2004]. The mathematical specifications and theoretical foundations behind our approach are explained in section S.4.2.
 The upper tip line of the plate interface lies on the trench axis (~4.5 km depth), and we extend the full-to-partially coupled zone (>25%; see Figure S.12) down to the seismogenic zone depth (~50 km), in agreement to the reported data for Maule [Khazaradze and Klotz, 2003; Métois et al, 2012; Moreno et al., 2010, 2012; Ruegg et al., 2009; Suarez and Comte, 1993; Tichelaar and Ruff, 1991, 1993]. We used a constant value of 18° for the dip angle of the three segments (Figure 2 and Figure S.9) based on the recent world slab model contributed by Hayes et al. . The interseismic slip deficit vector has a rake of −77° and a maximum magnitude of 9.75 m (6.5 mm/year over 150 years), according to the Nazca-South America convergence vectors reported for the latitudes of Maule [Angermann et al, 1999; Kendrick et al., 2003; Norabuena et al, 1999]. The plate interface was discretized in 11 downdip elements and 13, 19, and 13 along-slip elements for the south, central, and northern segments. In our reconstruction, we avoid superposition of elements and gaps of patches on the subduction interface (Figure S.9). Similar to the coseismic modeling, the calculation of the upper plate stress field and the CSI on the intraplate faults uses the material properties listed in Table 1; we imposed no external fields to assess specifically the interseismic deformation generated by the stress transfer at the plates interface. Our use of dislocations and CSI to determine the stress field assumes that interseismic deformation is a result of a static mechanics and not dynamics over the 150 years of slow shortening.
 For the coseismic and interseismic periods, both calculations—the internal deformation field and the CSI—were run with the Matlab code Coulomb 3.2., developed by the “Team Coulomb,” USGS.
5.3 Results from the Maule Seismic Segment
5.3.1 The Pichilemu Normal Fault
 The coseismic stress tensor, resolved in the rake direction of the normal fault responsible of the Pichilemu aftershocks (CSI along a −90° rake), encourages slip on the structure (Figure 8). For all the models tested (Table 2), we obtained positive values of CSI ranging from a minimum of 0.13 MPa to a maximum of 9.30 MPa (note that the very high negative value showed in Table 2 is clearly a model artifact). The maximum values are some of the highest CSI estimations reported in any study and agree with maximums estimated by Ryder et al. . However, the lower left corner of the modeled Pichilemu fault almost intersects the slip area of the subduction megathrust; it is possible that the CSI calculation on the patches of that corner are biased by singularities caused by proximity to the source (Figure 3). To avoid this potential artifact, we omit some of the Pichilemu fault patches from the calculation to produce a more realistic estimate of a CSI maximum value of 4.87 MPa and the same minimum value as before (fifth to seventh columns or “safe area” in Table 2).
Table 2. Summarized Results of the Coseismic CSI Resolved on the Pichilemu Normal Faulta
Finite Source Fault Model
Max All (patch)
Min All (patch)
The Pichilemu fault was subdivided into 32 patches (4 along dip by 8 along strike, see Figure 5). Maximum, minimum, and average CSI values are for the entire set of results (second to fourth columns) and for the “safe area” (fifth to seventh columns) explained in the text.
 To extend these results to the entire fore arc, we calculate the CSI and strike of the optimally oriented normal faults over a horizontal grid divided into 30 by 30 km elements, at different depths, covering the region affected by the Maule earthquake (Figure 9a). Our resulting preferred fault orientation and stress magnitude are similar for each of the input slip models and calculation depths so we show the regional model using the slip distribution by Vigny et al. , computed for 10 km depth (Figure 9a) (and relegate the remaining models to section S.6). As in the analysis of the Pichilemu fault, the regions of very high CSI near the trench (both positive and negative) are caused by singularities where the source slip model intersects the calculation surface. Near the toe of the upper plate wedge, a region in the submarine portion of the fore arc shows negative values of CSI (Figure 10a). The negative stress field suggests enhanced development of reverse faulting in the region overlying that part of the subduction zone, which experienced an up-dip decrease in slip on the seaward side of the slip maximum, generating a negative slip gradient. This result agrees with the observations of Melnick et al. .
 Most of the onshore fore arc above the rupture, however, is highly affected by a coseismic tensional field consistent with the infinitesimal strain analysis (compare Figures 7 and 9a). This widespread field extends down to the plate interface. The volume of continent in and around the Pichilemu sequence, approximately 7.5 × 105 km3, was highly stressed, with positive values of CSI on optimally oriented normal faults exceeding 1.5 MPa (Figures 9a and 10a). The coseismic stress field encourages normal faulting oriented subparallel and oblique to the plate boundary in all of the onshore fore arc. Like the strain field (Figure 7), the maximum values of CSI, all greater than 1.0 MPa, on optimally oriented normal faults are concentrated along the Coastal Cordillera (Figure 9a). The strikes of these idealized faults form a semi-elliptical pattern around the zones of maximum slip on the finite fault models (Figure 9a and section S.6). The modeled normal faults at the southern end are mostly oblique with respect to the continental margin striking ~NE, subparallel to the margin along the center of the rupture and again, oblique at the northern end striking ~NW (Figure 9a). More importantly, many mapped upper plate normal faults coincide in orientation with the model fault traces (Figure 11 and section S.7); at the northern and southern ends of the segment, mapped faults show bimodal patterns in the structural grain with some striking subparallel to the modeled structures and some subperpendicular (Figures 1 and 11 and section S.7). The orientation of the Pichilemu fault fits well with the modeled strikes.
 We also modeled the optimal orientations and CSI magnitude for thrust and strike-slip faults in the upper plate. With the exception of a few small areas, reverse faulting is retarded by the coseismic stress field, and strike slip is enhanced but the CSI is generally much smaller than the estimations for normal faults along the Coastal Cordillera.
 In contrast to the coseismic deformation, the interseismic field suppresses normal faulting in the majority of the upper-crustal wedge (Figures 9b and 10b). The finite CSI on optimally oriented normal faults yields a negative field over the entire upper plate (Figure 9b) for a 10 km calculation depth (30 by 30 km each grid element). Along the outer fore arc, normal faults are negatively stressed by Values <−0.125 MPa, and at depths greater than 10 km, the CSI reaches values <−0.5 MPa (Figure 10b).
 Additionally, for most of the Coastal Cordillera the optimal modeled strike of the normal faults is nearly orthogonal to the plate boundary (Figure 9b). In fact, the calculated orientations and negative CSI magnitudes imply that permanent reverse faults in the upper plate should strike nearly parallel to the trench. The reverse faults mapped by Melnick et al. [2006, 2009] fit the interseismic pattern very well. The small positive stressed area located on the continent, in front of the northern and southern bends of the plate boundary (Figure 9b), may be caused either by the change in geometry of the slab or by a model artifact.
 Similar to the coseismic modeling, a small portion at the toe of the upper plate wedge near the trench behaves in an opposite way than the rest of the fore arc, showing positively stressed zones for normal faulting. In this case, the up-dip low coupling zone of the plates interface generates a positive gradient of backslip and presumably, extension in the upper plate (see Figures 2 and section S.4.2).
6.1 Permanent Coseismic Extension
 Much of coseismic extension documented here is accommodated by elastic rebound, but part was produced by the permanent reactivation of the normal faults in the Pichilemu region (Figures 4 and 5 and Table 2). To generate a Mw 7.0 earthquake, almost the entire plane that we modeled should have ruptured with 0.5 m of average slip, a nontrivial coseismic deformation considering the surface area of this structure (70 by 35.4 km) and the surface area of the megathrust (~600 by 200 km) (Figure 3 and Table 1). The principal extensional axes obtained from both the moment tensor summation of earthquakes in Pichilemu and from the coseismic surface GPS coincide in orientation and magnitude of strain (Figures 4 and 5). The similarity in magnitude is significant because it suggests a nontrivial plastic response to coseismic extension. The Tōhoku subduction earthquake was likewise followed by significant upper plate normal fault aftershocks [Lay et al., 2011; Toda et al, 2011a; Toda et al, 2011b], suggesting a plastic component to coseismic rebound.
6.2 Interseismic Versus Coseismic Deformation
 CSI calculations have been used elsewhere in the Andean Cordillera to suggest that the interseismic deformation field, caused by the stress transfer at the locked interplate surface, produces tension at shallow crustal levels (< ~2.5 km depth), which could load the normal faults and bring the structures to fracture [Loveless and Pritchard, 2008; Loveless et al., 2010]. These interseismic estimations for CSI accumulation near the surface reach maximum values of about 0.5 MPa on fixed, homogeneously oriented normal faults, over a 1 km depth horizontal grid and during a ~100–150 year interseismic period. Below this depth, the CSI becomes negative for normal faulting.
 Our simulation for the Maule segment indicates that normal faulting is mostly suppressed along the Coastal Cordillera during the interseismic period (Figures 9b and 10b). The only possible region of interseismic fore-arc extension along the Coastal Cordillera is restricted to a shallow and small region, not deeper than ~1 km, where the CSI is close to 0 (Figure 10b). Large intraplate normal faults generally nucleate at levels deeper than 5 km [Jackson and McKenzie, 1983; Jackson and White, 1989; Jackson, 1987; Jackson et al, 2008; Scholz, 1988, 2002]. Likewise, the hypocenters of the sequence of normal aftershocks that followed the Maule earthquake range between 12 and 30 km depth (see section S.1).
 Field studies carried out by González et al. , Loveless and Pritchard , Allmendinger and González , and Loveless et al.  in the Atacama Desert show minor reverse reactivation on the NS and trench-oblique structures of the Coastal Cordillera. Likewise, Melnick et al. [2006, 2009] describe reverse reactivation of normal faults on Santa Maria Island and in the Arauco Peninsula at the south end of the Maule rupture (Figure 1 and section S.7.1). Our field data from the Pichilemu region also documents centimeter- to meter-scale reverse faults, mostly oriented NS, cutting Pleistocene-Holocene? sedimentary sequences, subsidiary to the NW-striking normal faults of the region [Aron et al., 2012]. Our interseismic model is consistent with these field data as the magnitude of stress obtained is small (CSI ~ |0.5| MPa) compared to the coseismic period, with optimal orientation of reverse faults mainly NS (Figures 9b–10b).
Loveless and Pritchard  and Loveless et al.  proposed that coseismic deformation generated by the 1995 Antofagasta Mw 8.1 earthquake in northern Chile could trigger both, normal and reverse intraplate faulting in the Coastal Cordillera depending on the slip distribution on the megathrust. The coseismic CSI calculated for the Maule earthquake shows that reverse faulting in the subaerial part of the fore arc is unlikely during a subduction earthquake. Six out of the seven finite fault models generate vast regions of values of CSI greater than 1.5 MPa on optimally oriented faults over the outer fore arc, all the way to the subduction interface (Figures 8 and 9a–10a and section S.6). Positive CSI averaged across the Pichilemu fault ranged from 1.2 to 3.2 MPa with maximum CSI values of 2.3 to 4.9 MPa (Figure 8 and Table 2). Reverse faulting can indeed be triggered by the megathrust, but it is restricted to the toe of the continental wedge, along the submarine portion of the outer fore arc. In this region, the negative slip gradient of the rupture induces compression in the upper plate and likely reactivation of thrust “splay faults.” This result is consistent with recent observations reported for the Maule earthquake region [Melnick et al., 2012] and for other subduction ruptures [e.g., Plafker, 1967]. Additionally, as described below, preexisting oblique faults striking towards the center of the rupture zone may also be reactivated if they are very near failure already.
6.3 Breaking the Fore Arc
 The CSIs that we have documented are probably not sufficient to make very many new large structures, but in the fore-arc basement we have abundant evidence of preexisting planes of weakness, like the Pichilemu fault. Those preexisting planes may be the result of older Cenozoic tectonics produced during Andean subduction or they may well take their heritage from tectonics affecting the Paleozoic basement of the fore arc [e.g., Lavenu and Encinas, 2005; Yáñez et al, 1998]. Regardless of the origin of the fractures, only those that are suitably oriented in the stress fields related to current subduction processes will be reactivated and thus will have marked topographic expression or structural relief.
 The permanent deformation of any particular place along the fore arc should represent a combination of coseismic normal faulting and interseismic reverse faulting behaviors. Local variations in interseismic coupling and coseismic slip on the megathrust, as well as the availability of suitably oriented planes of weakness, will probably determine which style is more prevalent. In general, interseismic reverse fault reactivation will mostly occur on planes parallel or subparallel to the margin, although strike or oblique slip on extremely weak planes might also occur. For coseismic deformation, normal displacement may occur on faults parallel to the margin in the center of the rupture segment; at the ends of the rupture segments, faults oblique to the margin and at a high angle to coseismic extension direction are likely to be reactivated as in Pichilemu.
 Other than the Pichilemu structure and the Arauco Peninsula, fault activity and kinematics is not well known for the Maule rupture area. Based on the normal aftershocks that follow the Maule earthquake (Figure 1, Table S.1, and Figure S.1) and on analogous examples elsewhere in the Coastal Cordillera [e.g., González et al., 2006; Heinze, 2003] and along the Maule rupture area [e.g., Aron et al., 2012; Gana et al., 1996; Katz, 1971; Lavenu and Cembrano, 1999; Lavenu et al., 1999; Wall et al., 1996], it is likely that the principal structural style, at least above the northern half the Maule segment, is extensional and active, although reverse faults also exist. Reverse faults coexisting with larger scale normal faults along the Coastal Cordillera [e.g., Melnick et al., 2006, 2009; Moreno et al, 2008] may reflect the permanent signature of the compressive interseismic period as well as coseismic splay faults in the toe of the accretionary wedge [Melnick et al., 2012]. Alternatively, surface normal faults described by Melnick et al.  may represent coseismic normal fault reactivation of faults with documented interseismic reverse activity [Melnick et al., 2006, 2009] as there was no documented co/post-seismic reverse fault seismicity associated with the structure.
 Why were other preexisting intraplate faults not triggered by the Maule earthquake, at least with magnitudes large enough for focal mechanisms to be calculated? In northern Chile, recent work by Cortés et al.  suggests that upper plate fore-arc normal faults have recurrence intervals more than one order of magnitude longer than the plate boundary seismic cycle. Thus, if subduction earthquakes are responsible for the permanent upper plate extension, many cycles are necessary to accumulate shear loading and break the Coastal Cordillera or reactivate upper plate normal faults. The coseismic loading of a single event, mostly controlled by the slip distribution on the megathrust, is not homogeneously distributed over the fore arc (Figures 9a–10a), contributing to possible variations in the recurrence times for the different intraplate faults.
6.4 Long-term Strain Markers and Seismic Segmentation
Loveless et al. [2005, 2009] suggested that the semi-elliptical pattern of coseismic cracks in the Atacama Desert in northern Chile delineates the long-term, average behavior of rupture segments. We postulate that a semi-elliptical map pattern of normal faults might likewise indicate average rupture segments (Figures 11 and 12). As geologists studying features that develop over a million year or more, and thousands to tens of thousands of earthquake cycles, we define an “average rupture segment” as one that, over geologic time, tends to rupture repeatedly. Thus, the accumulation of permanent deformation of the upper plate should reflect that average behavior. This view is quite different from the more typical geophysical view of a single earthquake cycle, a characteristic earthquake, or historical record spanning two or three events. On the scale of just a few events, segments may shift around, or only parts of segments will rupture (as with the case of the 1928 earthquake of the northern part of the Maule segment), and from time to time extremely large events may rupture several segments. The long-term, permanent record of deformation of the upper plate should smooth out that short-term behavior and reflect features of the upper plate that tend to control segmentation.
 With this concept in mind, we ask the question of whether there is an identifiable average behavior in this part of the Chilean fore arc and, if so, whether the Maule rupture may be relatively close to the average segment. The answer, at this point, is a qualified “maybe yes.” Maule mostly ruptured an oblique bend in the coastline between south of Valparaíso to the Arauco Peninsula, overshooting the peninsula by a small amount (Figure 1 and section S.2). Others have already postulated that peninsulas might control long-term segmentation [e.g., Song and Simons, 2003; Wells et al, 2003]. At a more detailed scale, we have calculated the misfit between known normal faults in the Coastal Cordillera of the Maule segment and the ideal semi-elliptical pattern calculated from the slip models (Figure 11). This exercise is hampered by lack of detailed geologic mapping and disagreement by existing coworkers over the quality of the existing mapping and significance of known normal faults. Given these uncertainties, the modeled semi-elliptical pattern is in good agreement with faults of known normal displacement (e.g., Pichilemu) and with faults that arguably may have normal component of slip (Figure 11 and section S.7). Note that if the rupture segments are long-lived, at the boundaries there should be a bimodal population of faults (Figure 12), and to evaluate the goodness of fit for a single segment, faults produced by adjoining segments should not be included. This is the case with the southern and northern ends of the Maule segment (Figures 1 and 9a; Figure S.29), which coincides with the boundary of the 1960 Mw 9.5, Valdivia earthquake [Cifuentes, 1989; Kanamori, 1977; Plafker and Savage, 1970] and the segment which ruptured in 1906 Mw 8.6 and 1985 Mw 7.8 Valparaíso earthquakes [Barrientos, 1988; Christensen and Ruff, 1986; Comte et al., 1986], respectively.
 It is probable that the largest, frequently repeated earthquakes are responsible for the majority of the fore-arc, upper plate deformation. For the Maule rupture region, it appears that, on average over geologic time, and consistent with recent observations made by Moreno et al. , great subduction earthquakes tend to rupture the same segment repeatedly. However, definitive test of the concept in Figure 12 must await better and more complete mapping of the Chilean Coastal Cordillera.
 We have demonstrated that the static coseismic deformation field imposed in the upper plate by a great subduction earthquake is an effective mechanism for generating convergence-parallel permanent extension above the seismogenic zone. This large and widely distributed extensional field is consistent with the large upper plate normal aftershocks generated by the Maule earthquake and probably the normal aftershocks that followed the Tōhoku earthquake as well. Long-lived normal faults in the outer fore-arc wedge are likely reactivated whenever the slip on subduction megathrust segments is appropriately oriented to provide the proper loading conditions.
 The semi-elliptically oriented coseismic stress field generated by slip on the Maule megathrust mimics the semi-elliptical outline of the first-order normal faults along the Coastal Cordillera. The interseismic deformation field produces convergence-parallel shortening and enhanced minor reverse faulting in the upper crust, which agrees with geological observations of the fore arc. As upper plate normal faulting is suppressed during the interseismic period, recurrence of discrete events like great subduction earthquakes probably plays a major role in the genesis of permanent extensional provinces along the leading edge of noncollisional convergent margins.
 Such architectural patterns may be persistent over many thousands of cycles in the region overlying the Maule rupture zone. A hypothesis meriting further testing is that the semi-elliptical outline of the first-order structures along the Coastal Cordillera may indicate the cyclic accumulation of slip on segments that tend to rupture repeatedly over geologic time, thus enhancing the morphological and structural expression of appropriately oriented faults. The 2010 Maule earthquake may be representative of the average great earthquake in this segment.
 We are grateful to many colleagues in Chile, the United States, and Perú for enhancing our understanding of these processes, including Matt Pritchard, Tony Ingraffea, Erik Jensen, Jack Loveless, Jason Phipps-Morgan, Carlos Benavente, Bryan Isacks, Amanda Baker, Kristopher Baker, and Bill Barnhart. Muawia Barazangi's continuous insistence encouraged us to elaborate this article, and he contributed with a meticulous review of the manuscript. We are grateful to the two anonymous JGR reviewers for their careful and constructive comments on an earlier version of our manuscript. Our field campaigns in Chile and Perú have been helpfully assisted by Felipe Astudillo, Camilo Rojas, Violeta Véliz, Pamela Pérez, Raquel Arriaza, Rodrigo Gomila, Gloria Arancibia, Diego Mackenna, Nicolás Pérez, Bárbara Aron, and Sonia A. Martínez. Our work in the Andean fore arc has been supported by National Science Foundation grants EAR-0738507 and EAR-1118678 and Cornell University. Aron's PhD studies are funded by CONICYT Beca Chile (2009, Chilean Government). Finally, we acknowledge the “Team Coulomb” (USGS) for having made the Coulomb 3.2. code freely available to everyone.