Characterization of stress changes in subduction zones from space- and ground-based geodetic observations

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Spring 2017 Characterization of stress changes in subduction zones from space- and ground-based geodetic observations Bryan James Stressler University of Iowa Copyright 2017 Bryan James Stressler This thesis is available at Iowa Research Online: Recommended Citation Stressler, Bryan James. "Characterization of stress changes in subduction zones from space- and ground-based geodetic observations." MS (Master of Science) thesis, University of Iowa, Follow this and additional works at: Part of the Geology Commons

2 CHARACTERIZATION OF STRESS CHANGES IN SUBDUCTION ZONES FROM SPACE- AND GROUND-BASED GEODETIC OBSERVATIONS by Bryan James Stressler A thesis submitted in partial fulfillment of the requirements for the Master of Science degree in Geoscience in the Graduate College of The University of Iowa May 2017 Thesis Supervisor: Assistant Professor William D. Barnhart

3 Copyright by Bryan James Stressler 2017 All Rights Reserved

4 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL This is to certify that the Master s thesis of MASTER S THESIS Bryan James Stressler has been approved by the Examining Committee for the thesis requirement for the Master of Science degree in Earth and Environmental Science at the May 2017 graduation. Thesis Committee: William D. Barnhart, Thesis Supervisor Jane A. Gilotti Emily S. Finzel

5 ACKNOWLEDGEMENTS First and foremost, I would first like to thank my advisor, Bill Barnhart, for his constant support and guidance throughout my time as a graduate student and during the completion of this project. I would also like to thank my thesis committee members, Dr. Jane Gilotti and Dr. Emily Finzel, for useful critiques that contributed greatly to this manuscript. I am grateful to the Department of Earth and Environmental Sciences, University of Iowa, the Iowa Space Grant Consortium, and United States Geological Survey Earthquake Hazards Program Award No. G16AP00115 for financial support during my time as a graduate student. Finally, I would like to extend my thanks to all the staff, professors, and fellow graduate students at the University of Iowa and to my family and friends for enduring support and encouragement throughout the duration of this project. i

6 ABSTRACT Temporally and spatially clustered earthquake sequences along plate boundary zones indicate that patterns of seismicity may be influenced by earthquake-induced stress changes. Many studies invoke Coulomb stress change (CSC) as one possible geo-mechanical mechanism to explain stress interactions between earthquakes, their aftershocks, or large subsequent earthquakes; however, few address the statistical robustness of CSC triggering beyond spatial correlations. To address this, I evaluate the accuracy of CSC predictions in subduction zones where Earth s largest earthquakes occur and generate voluminous and diverse aftershock sequences. A series of synthetic tests are implemented to investigate the accuracy of inferred stress changes predicted by slip distributions inverted from suites of geodetic observations (InSAR, GPS, seafloor geodetic observations) that are increasingly available for subduction zone earthquakes. Through these tests, I determine that inferred stress changes are accurately predicted at distances greater than a critical distance from modeled slip that is most dependent on earthquake magnitude and the proximity of observations to the earthquake itself. This methodology is then applied to the 2010 Mw 8.8 Maule, Chile earthquake sequence to identify aftershocks that may be used to perform statistically robust tests of CSC triggering; however, only 13 aftershocks from a population of 475 events occurred where confidence in CSC predictions is deemed to be high. The inferred CSC for these events exhibit large uncertainties owing to nodal plane uncertainties assigned to the aftershock mechanisms. Additionally, tests of multiple published slip distributions result in inconsistent stress change predictions resolved for the 13 candidate aftershocks. While these results suggest that CSC imparted by subduction megathrust earthquakes largely cannot be resolved with slip distributions inverted from terrestrial geodetic observations alone, the synthetic tests suggest that dramatic ii

7 improvements can be made through the inclusion of near-source geodetic observations from seafloor geodetic networks. Furthermore, CSC uncertainties will likely improve with detailed earthquake moment tensor catalogs generated from dense regional seismic networks. iii

8 PUBLIC ABSTRACT Earth s largest magnitude earthquakes occur in subduction zones, where tectonic plates converge and one plate slides beneath the other. In these settings, earthquakes commonly trigger tsunamis, extensive aftershock sequences, and in some cases, subsequent large earthquakes. Therefore, it is important to understand the physical mechanisms that allow earthquakes to interact (how one earthquake potentially triggers another) to properly assess and mitigate the associated hazards, as well as to constrain the state of stress in the Earth s crust. The goal of this project is to test if static stress changes can lead to earthquake triggering by using aftershocks of the 2010 M w 8.8 Maule, Chile earthquake as a statistically robust proxy for larger triggered earthquakes. Stress change triggering stipulates that an earthquake changes the stress state on nearby faults and brings them either closer to or further from failure. To test this, it is crucial to first assess the limitations of resolving earthquake source properties in subduction zones using the tools that are commonly available to geodesists (GPS and satellite radar observations). Using synthetic tests to simulate subduction zone earthquake scenarios, it is determined that earthquake magnitude and proximity of observations to the earthquake dominate the accuracy of the inferred stress changes. These tests are applied to the Maule earthquake sequence and only 13 aftershocks are identified for confident predictions of stress changes. Due to the small sample size of aftershocks and large stress change uncertainties the stress change triggering hypothesis cannot be adequately tested without improved coverage of geodetic observations, which can be made possible with the addition of seafloor instrumentation in global subduction zones. iv

9 TABLE OF CONTENTS LIST OF TABLES... vi LIST OF FIGURES... vii 1. INTRODUCTION METHODS Synthetic Tests Synthetic Models Inversion Strategy SYNTHETIC TEST RESULTS Inverted slip distributions CSC distributions CSC Accuracy-Distance Thresholds MAULE EARTHQUAKE Data & Modeling Synthetic Tests Coulomb Stress Change Analysis DISCUSSION Synthetic Tests- Accuracy of CSC Predictions Maule CSC- Uncertainties and Interpretations Strategies to improve the accuracy of CSC predictions CONCLUSION REFERENCES FIGURES TABLES APPENDIX- SUPPLEMENTAL FIGURES v

10 LIST OF TABLES Table 1: ALOS-PALSAR acquisitions spanning the 27 February 2010 M w 8.8 Maule earthquake Table 2: Final Coulomb stress change predictions for the 13 aftershocks selected from the RMT catalog from Hayes et al. [2013] vi

11 LIST OF FIGURES Figure 1: Synthetic test setup Figure 2: Synthetic observations and inverted slip distributions for synthetic M w 8.0 and M w 8.5 earthquakes Figure 3: CSC maps predicted by slip distributions informed by dense onshore (InSAR & GPS) observations for a synthetic M w 8.0 earthquake Figure 4: Correlation between known and inferred stress changes Figure 5: Φ distributions for stress changes predicted for each M w 8.0 scenario Figure 6: Critical distance (D c ) methods and results Figure 7: Observations and inferred co-seismic slip distribution of the 2010 M w 8.8 Maule earthquake Figure 8: Maule earthquake synthetic test set up and inverted slip distribution Figure 9: CSC sensitivities to model parameters Figure 10: Correlation between the inferred stress changes predicted by several published slip distributions and the slip distribution derived in this study Figure 11: CSC predictions and uncertainties for different uncertainty magnitudes vii

12 1. INTRODUCTION Global subduction zones produce Earth s largest magnitude earthquakes, posing significant hazards to nearby population centers from ground shaking, tsunamigenesis, landslides, and the triggering of subsequent earthquakes. Sequences of large megathrust earthquakes have been observed to occur in close proximity in time and space, which suggests that these earthquakes may interact through stress changes [e.g., Sieh et al., 2008; Hughes et al., 2010]. A possible explanation for the spatial and temporal correlation of these earthquake sequences is triggering by means of Coulomb stress change (CSC). CSC theory stipulates that slip on a fault (the source fault ) imparts static stress changes to the surrounding lithosphere, which in turn modifies the state of stress on nearby faults ( receiver faults ) and may bring them closer to (encourage) or further from (discourage) failure [King et al., 1992; Harris, 1998; Steacy et al., 2005]. CSC is defined as: CSC = τ + μ σ! (Equation 1) where τ is the change in shear stress, μ is the effective coefficient of friction, and σ! is the change in normal stress. The components of CSC are resolved onto a receiver fault with a specified location, orientation, and slip direction. To date, the majority of CSC studies have demonstrated strong spatial correlations between inferred static stress changes and subsequent aftershocks and large earthquakes (or lack thereof) in continental strike-slip environments, such as southern California, the North Anatolian fault zone, and New Zealand [King et al., 1994; Stein et al. 1997; Hardebeck et al., 1998; Toda et al., 2005; Barnhart et al., 2011; Zhan et al., 2011]. In these regions, near-fault geologic (rupture maps, known fault geometries and regional structure), seismologic (high-precision earthquake catalogs, finite rupture kinematics), and geodetic observations (Global Positioning Systems, space-based imaging geodesy) provide 1

13 excellent constraints on the geometry and locations of both the initial earthquake source and potential receiver faults that accommodate stress changes. However, few studies have addressed the statistical robustness of CSC models in such a way that a cause of earthquake triggering can be inferred beyond spatial correlations. This problem largely arises because there are not enough earthquake sequences with potentially triggered events (such as the Landers-Hector Mine, California earthquake sequence) to statistically assess if earthquakes are triggered by static stress changes, what percentage of earthquakes may be triggered via static stress changes, or if this behavior may vary within and between different plate boundary zones [Freed & Lin, 2001]. One possible means to address these questions is to use large populations of off-fault aftershocks as a corollary to triggered events. Given a high-quality catalog of aftershock regional moment tensors (RMTs) and locations, an earthquake slip distribution could then be used to assess the degree to which off-fault aftershock mechanisms and locations are statistically consistent with static stress triggering. An additional limitation of CSC studies is that their accuracy is dependent on earthquake source models that are often inverted from noisy, incomplete observations and invoke necessarily simplified approximations of Earth structure. Various statistical approaches have been implemented to evaluate the behavior of CSC models in the context of noise, variable Earth structure, or incorrect fault geometries, with one core takeaway being that inferred stress changes are least reliable close to regions of inferred fault slip in the source model where the effects of model errors are expected to be greatest [Steacy et al., 2004; Hainzl et al., 2009; Lohman & Barnhart, 2011; Zhan et al., 2011; Woessner et al., 2012; Wang et al., 2014]. Thus, the accuracy of inferred CSC is tied to the resolution of finite fault source inversions. In subduction zones, large megathrust earthquakes are typically characterized by offshore slip where near-source 2

14 observations are infrequent. Geodetic observations of co-seismic deformation primarily record co-seismic subsidence and trenchward displacement of the coast, while offshore displacements remain unconstrained by conventional geodesy. This spatial relationship results in an inverse problem with low model resolution in regions where slip occurs. This in turn leads to uncertain inferred stress changes. Here, I explore the limitations of CSC predictions derived from inversions of onshore geodetic observations for subduction zone earthquakes through a suite of synthetic tests with the intent of identifying sub-populations of off-fault aftershocks that may then be used to infer the statistical robustness of CSC predictions. I prescribe a known slip distribution and CSC distribution in a simulated subduction zone environment and generate noisy, synthetic surface displacement observations. I invert the synthetic observations to assess (1) to what degree the known CSC magnitude and sign (positive/negative) can be recovered, and (2) how the misfit between known and inferred CSC varies in the elastic volume surrounding the synthetic earthquake. Additionally, I examine the effects of data noise and choice of inversion regularization for different earthquake magnitudes and scenario data sets (i.e., dense InSAR and GPS, sparse GPS, seafloor geodetic observations). These synthetic tests demonstrate that low fault slip model resolution alone significantly limits the accuracy of inferred CSC without considering other sources of CSC uncertainty (i.e., modeling assumptions, receiver fault uncertainties). The inferred CSC often fails to recover the magnitude and, in some instances, the sign (positive or negative) of the known CSC; however, the accuracy of inferred stress changes improves beyond distances from mapped slip that are dependent on the characteristics of the earthquake of interest (e.g., signal to noise ratio). These results are used to develop a methodology for identifying off-fault aftershocks of the 2010 M w 8.8 Maule, Chile earthquake 3

15 that are suitable for statistical tests of static CSC triggering, where the explicit assumption is made that these events serve as a proxy for larger triggered events. The Maule earthquake is an excellent event for investigating earthquake triggering because it generated a large aftershock sequence with a range of faulting mechanisms that have been well studied [Hayes et al., 2013; Ryder et al., 2012; Lange et al., 2012]. I implement specific synthetic tests that approximate the targeted mainshock slip distribution while incorporating knowledge of available geodetic observations for this event. From an RMT catalog of 475 events [Hayes et al., 2013], a selection of 13 aftershocks are identified that fall in regions of high confidence as determined by the synthetic tests. CSC analyses are performed for these events using Monte Carlo error propagation techniques to constrain uncertainties. The CSC results for the slip distribution derived in this study are compared with those for published slip distributions [Tong et al., 2010; Delouis et al., 2011; Lorito et al., 2011; Vigny et al., 2011], highlighting that CSC uncertainties are large and that the results are inconsistent, particularly for the aftershocks located closest to regions of source slip. 2. METHODS I conduct a suite of synthetic tests to constrain the accuracy of CSC predictions in subduction zone environments. Specifically, I test the accuracy of CSC predictions when informed by fault slip distributions that are inverted from noisy onshore geodetic observations. I apply these tests to off-fault receiver faults (i.e., faults that are not co-planar with the megathrust/source fault) in order to establish whether stress changes can be resolved for such events with a high degree of certainty, and if so, over what length scales relative to mapped slip. The goal is, in part, to determine a distance threshold beyond which stress changes may be accurately resolved, which provides a means to (1) compare the accuracy of inferred stress 4

16 change distributions predicted by different slip distributions, and (2) to cull aftershocks from catalogs for statistical assessments of static stress change triggering. I then use these tests to explore potential static stress triggering of off-fault aftershocks associated with the 2010 M w 8.8 Maule, Chile earthquake Synthetic Tests A common approach to investigate the accuracy of source inversions (i.e., fault slip inversions) and predictions derived from source inversions (i.e., Coulomb stress change) is to generate rupture scenarios wherein researchers attempt to recover a known fault slip distribution and stress changes from a set of simulated surface displacement observations. In the synthetic test setup, I generate noisy surface displacements from two prescribed slip distributions of M w 8.0 and M w 8.5 (Figure 1). The known slip distributions consist of purely reverse (rake = 90 ), spatially uniform slip on a 20 dipping plane with dimensions and magnitude informed by earthquake scaling relationships [Wells & Coppersmith, 1991] (Figure 1). I forward predict the stress changes from the two slip distributions onto a three-dimensional grid (16 km x 16 km x 8 km) of receiver faults that have the same orientation and mechanism as the source fault. This generates a population of known stress changes that I seek to recover in addition to the known slip distributions (Figure 1). I impose a shear modulus of 40 GPa, an effective static coefficient of friction (μ! ) of 0.4, and a Poisson s ratio of The synthetic tests are constructed and inverted in a uniform elastic halfspace [Okada 1992, Meade 2007] Synthetic Models For each slip distribution, I generate three synthetic data sets that simulate common geodetic data configurations relative to a megathrust earthquake: sparse onshore GPS, dense onshore InSAR and GPS, and dense onshore InSAR/GPS observations combined with sparse 5

17 seafloor geodetic observations (Figure 2). For simplicity, I project all InSAR displacements into a vertical line-of-sight displacement vector. I add spatially correlated noise with variance of 0.15 mm to the noise-free InSAR displacements. I calculate synthetic three-component GPS data for 15 onshore stations and add random noise with variances of mm and 0.4 mm (standard deviations of 1.1 cm and 2.0 cm) to the horizontal and vertical displacements, respectively. The noise level is chosen to reflect the average reported GPS uncertainties from Tong et al. [2010] and Vigny et al. [2011] for the 2010 Maule earthquake. Lastly, I predict three-component seafloor displacements for a network of 10 synthetic seafloor instruments that simulates the existing networks of GPS-Acoustic (horizontal) and pressure sensor (vertical) instruments offshore of Japan and Cascadia [Iinuma et al., 2012; Sato et al., 2011; Ito et al., 2011; Chadwell & Spiess, 2008]. I add random noise with variances of mm and mm (standard deviations of 1.5 cm and 1.3 cm) to the horizontal and vertical displacements, which reflects idealized measurement uncertainties for seafloor geodetic instrumentation [Bürgmann & Chadwell, 2014]. By incorporating offshore data sets, I seek to characterize how offshore constraints improve the resolution of megathrust slip distributions and the accuracy of inferred stress changes Inversion Strategy I invert the synthetic noisy data sets for fault slip through a regularized least-squares inversion approach in a uniform elastic half space [e.g. Okada 1992, Meade 2007]. The surface displacements are inverted onto the same fault plane that was used to generate the noise-free displacements with the same slip direction (rake). Any variations between the known and recovered slip distributions/stress changes should thus be caused by the presence of noise and inversion regularization alone. I invert the displacements using the methodology of Barnhart & 6

18 Lohman [2010], which iteratively re-discretizes the fault plane such that the areas of the individual slip patches reflect the model resolution of the inverse problem. In subduction zones, this approach yields large fault slip patches where model resolution is poor (offshore, far from observations) and smaller patches where model resolution improves (near the coast and beneath land). By imposing a model resolution constraint on the area of fault slip patches, the resulting slip distributions more accurately reflect the model resolution afforded by the available surface displacement observations. I impose minimum moment regularization and select the regularization coefficient using the j R i criterion [Barnhart & Lohman, 2010]. j R i identifies a best regularization coefficient as that which minimizes the contributions of data noise (perturbation error) and over-regularization (regularization error) to the slip distribution [Barnhart & Lohman, 2010, Nealy et al., 2017]. Lastly, I constrain uncertainties of the slip distributions through a Monte Carlo error propagation approach [Barnhart & Lohman, 2013; Barnhart et al., 2016]. I add 500 realizations of noise with the same noise covariance structure as the synthetic data to the predicted displacements of the inverted slip distributions. I then invert each of the realizations of noisy data using the same regularization and discretization as the bestfitting slip distributions. 1σ uncertainties are then extracted from the population of slip distributions. These uncertainties only reflect variations in the slip distribution that are introduced by observational noise. The synthetic slip distributions described below are the median slip distributions from these populations. Lastly, I forward predict the stress changes for the same grid of receiver faults as described above using each inverted slip model and compare the inferred CSC distributions to the known distribution. The results are compared for slip distributions derived from different data sets, choices of regularization, and slip distribution uncertainty bounds to examine how the 7

19 spatial coverage of surface displacement data, noise magnitude, and inversion regularization influence the accuracy of CSC predictions. Importantly, the scope of these synthetic tests does not capture the potential impacts of variable Earth rigidity structure, complex fault geometry or inelastic behavior. 3. SYNTHETIC TEST RESULTS 3.1 Inverted slip distributions The best-fitting slip distributions for the M w 8.0 and M w 8.5 scenario earthquakes are shown in Figure 2. As expected, the known slip distributions are more closely recovered with spatially dense observations than with sparse observations. For example, inversions of sparse GPS observations for both the M w 8.0 and M w 8.5 scenarios yield slip to the trench where no slip is imposed by the known slip distributions (Figure 2). The inclusion of seafloor geodetic observations provides increased resolution near the trench (indicated by smaller fault patches), allowing the inversions to constrain the near-trench slip deficit (Figure 2). Additionally, the along-strike and down-dip extents of the M w 8.5 scenario are better resolved than the M w 8.0 event despite the same level of noise (Figure 2). This behavior reflects the improved resolution afforded to the inversion by the increased signal-to-noise ratio of larger surface displacements generated by greater slip magnitudes. 3.2 CSC distributions The CSC distributions predicted by the known and inverted (from dense onshore observations) slip distributions for the M w 8.0 scenario are shown in Figure 3. The most noticeable misfits occur in regions that are close to slipping fault patches (Figure 3). These misfits are particularly apparent up-dip of the rupture area where inferred slip is smoothed to the trench (Figure 2-3). A second important pattern that emerges from these tests is that the 8

20 magnitude of the misfit of CSC (the difference between the known and inferred values) scales with the magnitude of the known CSC such that larger known stress changes correlate with larger errors in the inferred stress change (Figure 3, Figure S1). This pattern again highlights that the largest magnitude stress changes will occur in regions close to slipping fault patches and are consequently more sensitive to errors in the slip distribution. The improvement in correlation between the known and inferred stress changes with increased distance from the source fault supports the hypothesis that there is a distance at which short wavelength details of the slip distribution no longer influence the predicted static stress changes (Figure 4) [King et al., 1994]. When only the receiver faults greater than 20 km from the M w 8.0 source region are considered, the known and inferred stress change values approach a 1:1 relationship (Figure 4). The improved correlation suggests that the accuracy of inferred CSC distributions improves with increased distance; however, this result may only be an apparent improvement due to the scaling of misfit with stress change magnitude. Despite the smaller magnitudes of misfit for receiver faults far from the source fault, the relative error (the ratio of misfit to known stress change) of the inferred stress changes at these locations is not necessarily improved when compared with receiver faults close to the source fault. The relative error provides insight as to where inferred stress changes deviate from the known values in such a way that the known sign (i.e., positive or negative stress change) may not be recovered. I define the relationship Φ as a means to quantify the magnitude of the relative error of CSC predictions: Φ = (!"#$%%$&!"!!!"#$"!"!)!"#$"!"! (Equation 2). I focus on Φ values exceeding 0.5, which indicate significantly large CSC errors relative to the known stress changes. Figure 5 shows Φ for stress changes for the M w 8.0 scenarios in cross- 9

21 section and in map view at 20 km depth. An inspection of these maps yields two key observations. First, large Φ values trace out nodal planes of stress change (e.g., the X pattern in map view; Figure 5, Figure S2), which are regions where the stress change transitions between positive and negative values (Figure 3). In these locations, the stress change predictions are highly sensitive to any perturbations to the input slip distribution and consistently yield large relative errors (i.e., Φ > 1). As previously noted by Woessner et al. [2012], the locations of stress change nodal planes should be taken into consideration when assessing CSC results for a given source-receiver pair. For the purposes of these synthetic tests, I omit all receiver faults with a known CSC in the interval -0.1 to 0.1 bars, which are assumed to reflect receiver faults that fall within stress change nodal planes. Second, large (>0.5) Φ values dominate the near field (<1 rupture length) of the source slip distribution where receiver faults are in close proximity to mapped slip (Figure 5). The saturation of large Φ values for the onshore data sets is diminished when seafloor constraints are added (Figure 5; Figure S2). Interestingly, the increased density of onshore observations afforded by synthetic InSAR observations yields little improvement over the CSC predictions derived from (Figure 5; Figure S2). These results, which are consistent for the M w 8.0 and M w 8.5 scenarios, suggest that the accuracy of CSC predictions is more dependent on the proximity of observations to the source fault, rather than the density of geodetic observations. For each scenario, the distribution of Φ values in cross-section shows that the relative errors are small near the coast (X = 100 km). In contrast, the up-dip regions of the rupture and outer trench rise exhibit large Φ values, indicating lower accuracy of CSC predictions that is consistent with the resolution of the fault slip distributions (Figure 2; Figure 5). 10

22 3.3 CSC Accuracy-Distance Thresholds Next, I attempt to define a critical distance (D c ) from the source fault beyond which I assume that CSC predictions can be reliably resolved (magnitude and sign) with a regularized slip inversion. The distance to mapped slip (or distance from the source fault) is defined as the distance from the center of a given receiver fault to the center of the nearest slipping fault patch. I consider the distance distributions for receiver faults with large relative errors (Φ > 0.5) and define D c as the distance from the source fault that accounts for 95% of these receiver faults (i.e., the cumulative probability of receiver faults with Φ > 0.5 as a function of distance, P(D < D c ) = 0.95; Figure 6A-B). To validate this approach, I bin the distribution of Φ values for all receiver faults into discrete distance increments from mapped slip (see Figure S3). This method yields D c estimates that are compatible with the results of our initial approach, which suggests that these estimates are representative of the accuracy of the inferred CSC distributions. Though D c does not capture all complexity leading to spatially variable CSC errors (e.g., asymmetric misfit across the source fault, variations along strike), it provides a reasonable means to compare results for different input slip distributions and to establish a culling criterion for aftershock catalogs. Figure 6A-B shows the distance distributions of receiver faults that exhibit large relative errors (Φ > 0.5) for each of the M w 8.0 scenarios. The density of these receiver faults is greatest at short distances from the source fault and diminishes as a function of distance from mapped slip (Figure 6A). The CSC distribution constrained by seafloor observations yields the smallest D c estimate (~55 km), while the stress change distributions informed by onshore geodetic observations yield similar D c estimates in excess of 100 km (Figure 6B-C). The M w 8.5 scenarios yield similar results for each data set, though with increased magnitude the D c values do not increase substantially. The D c estimates for the CSC distributions informed by onshore 11

23 observations actually decrease with increased earthquake magnitude (Figure 6C). Conversely, the D c estimate for the seafloor data set increases, but only slightly. These variations of D c with earthquake magnitude is likely due to the improved signal-to-noise ratio of observations for the larger earthquake, which manifests as higher resolution fault slip distributions and therefore, more accurate inferred stress change distributions [e.g., Barnhart & Lohman, 2010]. The impacts of data noise and inversion regularization on D c estimates are shown in Figure 6D for the dense onshore data set scenarios (InSAR and GPS) for each earthquake magnitude. The associated slip distributions are shown in Figures S4-5. In each case, the regularization dependent D c values do not vary a great deal from the preferred slip distribution. For the M w 8.0 scenario, the 1σ uncertainty slip distributions yield a much wider range of D c estimates compared to those determined for regularization dependent slip distributions. The M w 8.5 scenario reflects the opposite relationship. These relationships demonstrate that observational noise contributes less to CSC uncertainties with increasing earthquake magnitude. 4. MAULE EARTHQUAKE 4.1 Data & Modeling Here, I apply the techniques described above to a well-documented subduction zone earthquake. The 2010 February 27 M w 8.8 Maule earthquake ruptured ~500 km of the Chilean subduction zone and generated a damaging tsunami that propagated throughout the Pacific basin. The earthquake was followed by a rich aftershock sequence comprised of a variety of faulting mechanisms in spanning the slab interface and interior, upper plate, and outer trench rise [e.g., Delouis et al., 2010; Lay et al., 2010; Moreno et al., 2010; Tong et al., 2010; Farias et al., 2011; Kiser & Ishii, 2011; Lorito et al., 2011; Luttrell et al., 2011; Pollitz et al., 2011; Vargas et al., 2011; Vigny et al., 2011; Agurto et al., 2012; Koper et al., 2012; Lange et al., 2012; Moreno et 12

24 al., 2012; Rietbrock et al., 2012; Ryder et al., 2012; Wang et al., 2012; Bedford et al., 2013; Hayes et al., 2013; Lin et al., 2013; Scott et al., 2014; Yue et al., 2014]. The aftershock catalog used here consists of 475 regional moment tensor (RMT) solutions of aftershocks with highprecision, calibrated relocations [Hayes et al., 2013] (Figure 7). The aftershocks have average horizontal uncertainties of 2.8 km and depth uncertainties of 3.5 km. The reported uncertainties for strike and dip are 20 and 25 [Hayes et al., 2013]. These events and their reported uncertainties are used to define the population of receiver faults for CSC analysis, which entails the explicit yet oversimplified assumption that the static co-seismic stress change is the only perturbation acting on these events. The broad crustal deformation pattern associated with this earthquake was welldocumented through InSAR observations and both continuous and campaign GPS observations [e.g., Tong et al., 2010; Vigny et al., 2011] (Figure 7). I obtained ascending and descending SAR imagery from the JAXA L-band ALOS-PALSAR sensor and processed co-seismic interferograms using the JPL/Caltech ISCE software package [Rosen et al., 2012; Table 1]. Topographic effects were removed from each interferogram using the Shuttle Radar Topography Mission 30 m DEM [Farr et al., 2007]. The interferograms were filtered using the Goldstein filtering algorithm [Goldstein & Werner, 1998] and unwrapped using the branch cut algorithm from Goldstein et al. [1988]. Any noticeable unwrapping errors were manually corrected where the correct phase ambiguity could be identified; otherwise, unwrapping errors were deleted from the dataset. I used the methodology of Lohman & Simons [2005] to downsample the interferograms and estimate the data covariance. Additional downsampled InSAR data from ScanSAR descending path 422 were obtained from Tong et al. [2010] (Table 1). I estimated the covariance of the ScanSAR displacements by assuming the presence of spatially-correlated noise 13

25 with a length scale of 10 km and a variance of 0.4 mm. Three-dimensional static co-seismic displacements from continuous and campaign GPS were obtained from Vigny et al. [2011] and Tong et al. [2010] (Figure 7A). Due to the long spatial wavelength of the co-seismic deformation pattern that spans multiple InSAR orbital paths, I adjusted the interferograms to a common reference frame using the GPS observations. I identified the nearest pixel in each resampled interferogram to each GPS station and projected the GPS displacement into the satellite line of sight (LOS). I then inverted for an offset between the GPS and InSAR displacements and removed this offset from the downsampled interferograms. I inverted the onshore surface displacements using the same methodology described for the generalized synthetic tests. I imposed a planar fault geometry informed by the Slab1.0 subduction zone geometry model [Hayes et al., 2012] and allowed rake to vary freely between , forcing dextral reverse slip. To define a preferred slip distribution and 1σ uncertainties, I implement a Monte Carlo approach in which 500 independent realizations of noise are added to the InSAR and GPS displacements (spatially-correlated and random noise, respectively) predicted by the best-fitting model and reiterate the inversions using the same fault model discretization and regularization coefficient (Figure 7B) [Barnhart & Lohman, 2013]. The preferred model and 1σ uncertainties are defined as the median, 16 th, and 84 th percentile slip distributions from the population of models (Figure S6). The preferred slip distribution agrees well with previously published models for this event [e.g., Tong et al., 2010; Delouis et al., 2011; Lorito et al., 2011; Vigny et al., 2011; Hayes et al., 2013]. It is important to note that significant post-seismic deformation is likely mapped into the inversions. Several interferograms were formed with SAR acquisitions that include up to three months of post-seismic deformation when the contributions of frictional afterslip to interferograms of this and similar earthquakes is 14

26 greatest [Vigny et al., 2011; Lin et al., 2013; Bedford et al., 2013; Barnhart et al., 2016; Klein et al., 2016] (Table 1). The contributions of un-modeled afterslip may in part explain the spatially coherent residuals that are apparent in some interferograms (Figure S7-S8). 4.2 Synthetic Tests The generalized synthetic tests described previously showed that the location and signalto-noise ratio of the available surface displacements data for a megathrust earthquake place limitations on the length scales (relative to mapped slip) over which co-seismic stress changes can be confidently inferred. Therefore, rigorous statistical tests of static stress triggering require a selection of off-fault aftershocks at great enough distances from mapped slip for accurate predictions of co-seismic stress changes. I implement synthetic tests that simulate the Maule earthquake utilizing the workflow described previously to estimate D c to identify off-fault aftershocks that are suitable for CSC analysis. I prescribe a known slip distribution on the same fault geometry used for the Maule fault slip inversions (Figure 8) and impose a rake of 108 in agreement with the reported focal plane solution [USGS NEIC, The synthetic slip distribution consists of a uniform rupture that approximates the magnitude (M w 8.8) and spatial extent of slip of the Maule earthquake (Figure 8). I predict synthetic noisy data using the locations, look vectors, and noise covariance structure of the observations used to model the Maule earthquake slip distribution (Figure 8). I then predict a known CSC distribution for a three-dimensional grid (16 km x 16 km x 8 km) of receiver faults with the same orientation as the source model with a fixed rake vector (strike: 17, dip: 15, rake: 108 ). I also predict CSC distributions for receiver faults with normal (strike = 342, dip = 60, rake = -90 ) and strike-slip (strike = 72, dip = 90, rake = 0 ) mechanisms as well as randomly generated orientations and mechanisms to ensure that the results are not dependent on a specific receiver fault orientation 15

27 and mechanism. Lastly, I invert the synthetic data to recover the known slip distribution and forward predict the CSC distributions using the derived slip distribution. The inverted slip distribution does an excellent job of recovering the spatial distribution and magnitude of slip of the known slip model (Figure 8). Each CSC distribution (random, reverse, normal, strike-slip) predicted by this slip distribution yields a similar number of receiver faults with large relative errors (Φ > 0.5), though the randomly generated receiver faults yield the smoothest cumulative distribution functions of distance to mapped slip (Figure S9). This is interpreted to be a result of a more even sampling of receiver faults with large relative errors as a function of distance without a strong dependence on the locations at which CSC predictions are made (i.e., lesser dependence on the proximity to nodal planes). I focus on the CSC distribution for randomly generated receiver faults since I expect the results to be most representative of the accuracy of inferred CSC predictions for the aftershocks of the Maule earthquake. The estimated D c value for this CSC distribution is 50 km (Figure S9). Of the 475 aftershocks in the RMT catalog from Hayes et al. [2013], I identify only 13 aftershocks are that occurred greater than this distance, which I select for further analysis (Figure 7B). The majority of these aftershocks occurred in the upper plate; however, four of these aftershocks are classified as interface (occurring on the megathrust) events [Hayes et al., 2013] (Table 2). These events are still included since they occurred far from the Maule rupture area (Figure 7B). 4.3 Coulomb Stress Change Analysis Given this selection of aftershocks, I seek to identify which of these events are consistent with static stress triggering (i.e., positive stress changes). Due to the nodal plane ambiguity for values of μ greater than 0, I predict the CSC for each RMT nodal plane [Ma et al., 2005; Toda et al., 2011]. I predict the CSC using an assumed effective coefficient of friction of 0.4; however, I 16

28 also test a range of values from Small offset faults are often assumed to have higher coefficients of friction (μ > 0.4) that agree with laboratory measurements, while megathrust faults are typically characterized by lower coefficients of friction [Parsons et al., 1999; Hardebeck 2015]. I utilize a Monte Carlo approach in which 500 iterations of the CSC predictions are performed for each receiver fault nodal plane, randomly perturbing the receiver fault geometries and locations using the reported RMT uncertainties [Hayes et al., 2013]. Slip distribution uncertainties are not considered due to the negligible differences between the median and +1σ uncertainty models (Figure S6). This approach yields a population of CSC predictions that are consistent within the uncertainty of each CSC parameter. Final CSC values and uncertainty are reported as the median, 16 th (-1σ), and 84 th (+1σ) percentiles of the populations of CSC values. These calculations are repeated for several published slip distributions derived from inversions of geodetic observations to investigate the consistency between CSC predictions from different slip distributions [Tong et al., 2010; Delouis et al., 2010; Vigny et al., 2011; Lorito et al., 2011] (Figure S10). The final CSC values predicted by each slip distribution are shown in Table 2. The stress changes predicted for these aftershocks highlight several important results. First, CSC uncertainties frequently exceed the magnitude of inferred stress change, which supports the conclusions of previous studies that CSC uncertainty estimates are typically large (Table 2) [e.g., Wang et al., 2014, Woessner et al., 2012]. Receiver fault uncertainties propagate large variations into the CSC predictions, even for receiver faults at distances from mapped slip where CSC predictions are expected to be accurate (Figure 9). Approximately half of the culled aftershocks yield uncertainty ranges that range from positive to negative stress change. Strike and dip uncertainties induce the largest variations in CSC values, while location uncertainties play a 17

29 smaller, less important role (Figure 9). Horizontal location and depth uncertainties likely play such a small role for the selected aftershocks due to the large distances from the source fault plane. Conversely, location uncertainty alone was enough to invert the sign of inferred stress changes for some near-field aftershocks of the Maule earthquake as demonstrated by Hayes et al. [2013]. Second, the agreement between the predicted CSC for different published slip distributions varies with distance from mapped slip (Figure 10). At distances greater than ~100 km, each slip distribution predicts similar CSC values, replicating the CSC sign and approximate magnitude predicted by the other models (Table 2, Figure 10). Conversely, at distances less than ~100 km from the source fault, the CSC predictions are more inconsistent which suggests that variability in the details of each slip distribution produces significantly different CSC values (Figure 10). This inability to reproduce CSC predictions with different published slip models indicates an important limitation of stress change modeling. 5. DISCUSSION 5.1 Synthetic Tests- Accuracy of CSC Predictions The goal of the generalized synthetic tests was to address the accuracy of CSC predictions given a regularized slip distribution derived from noisy geodetic observations with an incomplete spatial footprint. These tests show that without seafloor geodetic observations in subduction zones, inferred slip distributions for megathrust earthquakes exhibit low model resolution, which in turn reduces the accuracy of inferred stress changes. Though numerous studies have addressed the uncertainty (i.e., the precision) of CSC predictions due to various model parameters (e.g., friction, slip distribution uncertainty, fault geometry), few address how closely stress change predictions reflect the true stress perturbations (i.e., the accuracy) due to a 18

30 lack of knowledge of the true co-seismic slip distribution [Steacy et al., 2004; Lohman & Barnhart, 2011; Zhan et al., 2012; Woessner et al., 2012; Wang et al., 2014, Mildon et al., 2016]. Though the tests presented in this study only consider the effects of the spatial coverage and density of geodetic observations, observational noise, and inversion regularization, they show that there are baseline restrictions on the distances relative to mapped slip over which CSC can be accurately inferred. These restrictions are conservative estimates of CSC errors because only simple slip distributions, fixed receiver fault properties, and homogeneous mechanical assumptions are considered. In contrast, real earthquakes such as the Maule earthquake introduce considerably more complex slip distributions (Figure 7) and fault geometries [Hayes et al., 2012; Hayes et al., 2013]. In addition, InSAR observations of the Maule earthquake contain signals generated by both co- and post-seismic deformation due to the limited temporal resolution of InSAR observations. Importantly, the 6 day repeat intervals of the current European Space Agency Sentinel-1 SAR mission has enabled the acquisition of independent observations of coand post-seismic signals for recent and future earthquakes [e.g., Barnhart et al., 2016]. The results of the synthetic tests also highlight that it is very difficult to recover the true stress change magnitude (i.e., the known magnitude) for a given receiver fault. The inferred stress changes often do not replicate the magnitude and sometimes even the sign of known stress changes. This issue is prevalent for receiver faults with small magnitude stress changes that occur in close proximity to nodal planes or in the far field of the source fault (beyond the influence of significant stress perturbations). Therefore, identifying receiver faults that are consistent with resolvable positive or negative stress changes appears to be more instructive than emphasizing the actual magnitude of stress change which can be biased by uncertain parameters (e.g., receiver fault geometry) or assumptions (e.g., effective coefficient of friction; Figure 9). 19

31 While various studies have attempted to resolve a static stress triggering threshold, the results of this study suggest that CSC predictions are too sensitive to confidently distinguish between positive and negative stress changes at small magnitudes (< 1 bar) [e.g., Reasenberg & Simpson, 1992; King et al., 1994; Ziv & Rubin, 2000]. Although larger magnitude earthquakes induce stress changes over broader areas, the D c values estimated for such events do not increase a great deal compared with smaller earthquakes. In the synthetic tests, the improved signal to noise ratio for the M w 8.5 synthetic example resulted in more accurate stress change distributions than the M w 8.0 scenario. This suggests that observational noise introduces a significant contribution to uncertainty in inferred slip distributions and CSC predictions and plays a larger role for smaller magnitude earthquakes. For each magnitude, the addition of dense InSAR observations to sparse onshore GPS observations yields little improvement to the accuracy of inferred stress changes. The addition of sparse seafloor observations to onshore observations yields increased model resolution of slip distributions nearest the trench and improved CSC predictions. These observations suggest that the proximity of geodetic observations to the source fault is more important than the density of the observations with respect to the accuracy of CSC predictions. Other factors such as the megathrust dip, distance from the trench to coast, and depth distribution of co-seismic slip will control the proximity of onshore observations to the source fault and therefore the accuracy of CSC predictions. Synthetic tests such as those implemented in this study can be used to assess how well resolved stress change predictions are for a specific earthquake, similar to checkerboard resolution tests for fault slip inversions [e.g., Tong et al., 2010]. These tests can be specifically crafted to evaluate the accuracy of stress changes for an earthquake of interest 20

32 provided knowledge of the available data sets and the characteristics (magnitude and spatial extent) of the co-seismic slip distribution. 5.2 Maule CSC- Uncertainties and Interpretations Using synthetic tests to simulate the Maule earthquake, I found that only 13 aftershocks from the RMT catalog of Hayes et al. [2013] occurred far enough from mapped slip (50 km) to be deemed suitable for CSC analysis (Figure 7B). This small sample size alone highlights a key result that the majority of aftershocks, which occur on or near the source fault, happen in regions where CSC predictions are unreliable. The reported CSC uncertainties frequently exceed the magnitude of inferred stress change, a result that is consistent with the findings of previous studies [e.g., Wang et al., 2014]. These uncertainties reflect the propagation of receiver fault uncertainties, which highlights the importance of robustly constraining these parameters for precise estimates of CSC. Figure 11 shows the CSC and uncertainties predicted for these aftershocks considering different receiver fault uncertainty ranges. When the receiver fault strike and dip uncertainties are cut in half or removed, the resulting CSC uncertainty bounds are much smaller, making it easier to unambiguously discern which events are positively or negatively stressed. Due to the small sample size (n = 13) tested in this study, the large CSC uncertainties, and inconsistencies among the stress changes predicted by different slip distributions, it is difficult to make any meaningful interpretations regarding static stress changes and aftershock triggering. The poor agreement between the CSC predictions for various published slip distributions for nearly half of the aftershocks illustrates the fact that different fault slip modeling approaches and assumptions (e.g., fault geometry, rigidity structure) can introduce significant variations into the inferred slip distributions and subsequent stress change predictions (Figure 21

33 10). In addition, the time independent nature of static co-seismic stress changes makes it difficult to rule out the stress changes contributions due to post-seismic deformation sources such as frictional afterslip [Vigny et al., 2011; Bedford et al., 2013; Lin et al., 2013], viscoelastic relaxation [Freed & Lin, 2001], or poroelastic rebound [Hughes et al., 2010] when considering aftershocks that occur weeks to months after the mainshock. The inferred critical distance (D c ) from the synthetic tests of the Maule earthquake suggests that there are regions where CSC analyses can be applied with a high degree of confidence. For instance, in the Maule region, the Andean volcanic arc is suitably far away from slipping portions of the megathrust for investigations of earthquake-volcano stress interactions (Figure 7B). Pritchard et al. [2013] investigated the changes in normal stress at volcanic centers in the Andean southern volcanic zone that experienced subsidence following the Maule earthquake. Furthermore, in continental regions subjected to elevated seismic hazard due to aftershock seismicity, stress change predictions can be used to infer where co-seismic stress changes are more likely to trigger aftershocks. Given some constraints on the accuracy of stress change predictions (i.e., D c estimates), stress changes can be predicted in regions of high confidence for optimally-oriented receiver faults or for receiver faults that are consistent with the regional structures. 5.3 Strategies to improve the accuracy of CSC predictions The limitations of CSC predictions presented in this study can be mitigated, in part, by several strategies aimed at improving data coverage and better constraining receiver fault parameters. The addition of seafloor geodetic and seismological instrumentation to major subduction zones can provide crucial constraints on offshore slip and aftershock seismicity that is otherwise poorly resolved by onshore observations alone. Seafloor geodetic observations have 22

34 been shown to help identify large slip magnitudes near the trench for the 2011 M w 9.0 Tohoku- Oki, Japan earthquake, which were underestimated by up to 20 m by onshore GPS alone [Sato et al., 2011; Iinuma et al., 2012]. These additions can increase the accuracy of CSC predictions particularly in regions such as the outer rise and offshore accretionary wedge where aftershock seismicity is common following a megathrust earthquake. There are several approaches that may be effective in providing robust constraints (or eliminating the need) for receiver faults parameters. First, Coulomb stress change may be resolved onto a mapped fault plane with a known slip direction. This approach is most useful in well-monitored regions where fault orientations are well known, with constraints on the changes in fault orientation with depth and position along strike. In subduction zones, this may be applicable to faults in the continental forearc, whereas marine splay faults in the accretionary prism require costly imaging techniques, which are not often available. Another approach is to predict the CSC for optimally-oriented receiver faults [e.g., King et al., 1994]. This approach eliminates the need for precise receiver fault orientations, though this method may fail to reconcile aftershock mechanisms with the optimally-oriented fault orientations. Lastly, for those aftershocks that produce a detectable geodetic signature, InSAR and GPS observations can be used to constrain the causative fault plane geometry and mechanism [e.g., Lohman & Barnhart, 2011; Ryder et al., 2012; Ruiz et al., 2013; Scott et al., 2014]. Ryder et al. [2012] investigated static stress triggering of the Pichilemu aftershocks of the Maule earthquake using InSAR and GPS to determine the fault geometry that produced these large ~M7 events. These events were not tested in this study due to the close proximity to the source fault (< 30 km). Despite the utility of this approach, it is rare to find a large selection of aftershocks with independent geodetic constraints that are detectable with geodetic techniques. Furthermore, for large events 23

35 like the Maule earthquake, geodetic observations of aftershock deformation can be masked by broad post-seismic deformation patterns due to afterslip and viscoelastic relaxation. 6. CONCLUSION In this study, I demonstrate the importance of the observation distribution relative to the fault slip distribution and observation quality (signal-to-noise ratio) with respect to evaluating the accuracy of co-seismic stress change predictions. The addition of InSAR observations to onshore GPS observations in a subduction zone environment does not substantially improve the accuracy of CSC calculations despite apparent improvements in the model resolution of the fault slip distribution. Alternatively, the addition of sparse and noisy offshore observations immediately above the earthquake source region allows for a substantial improvement in the accuracy of inferred stress changes (Figures 5-6). This implies that improving the proximity of observations to the earthquake source is of greater importance than increasing observation density for the purposes of inferring crustal stress changes. The small differences between stress change accuracy inferred from onshore GPS and onshore GPS plus InSAR alone are important for island arc settings such as Japan, Sumatra, or the Aleutian arc where InSAR observations of large megathrust earthquakes are often useless. In these places, GPS networks alone provide a reasonable observation source from which to infer stress changes; though, accuracy would be improved with the addition of offshore geodetic observations. Despite the considerable aftershock sequence triggered by the 2010 M w 8.8 Maule earthquake, I find that stress changes can be confidently resolved for only 13 aftershocks that occurred at distances greater than 50 km from inferred co-seismic slip. The CSC predictions for these aftershocks yield large uncertainties that commonly approach the stress change magnitude due to uncertain receiver fault parameters (i.e., strike, dip, location). Furthermore, the stress 24

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42 FIGURES 31

43 Figure 1: Synthetic test setup. The known slip distribution (A) and the predicted noise free surface displacement observations (B) are shown in map view for a synthetic M w 8.5 earthquake. The observations consist of dense onshore InSAR data, sparse onshore GPS (white), and sparse seafloor geodetic data (black). The known slip distribution consists of a uniform rupture prescribed onto a fault plane with a dip of 20 [Wells & Coppersmith, 1991]. The known CSC predicted for receiver faults with the same orientation and faulting mechanism as the source fault are plotted in map view at 20 km depth (C) and in cross-section (D). Regions of red and blue correspond to positive and negative stress changes while green corresponds to ~0 stress change which highlights the nodal planes of stress change and regions of negligible stress change. The white line indicates the extent of the known rupture area in cross-section. 32

44 Figure 2: Synthetic observations and inverted slip distributions for synthetic M w 8.0 and M w 8.5 earthquakes. Synthetic InSAR observations are plotted onshore (X > 100 km) with horizontal GPS displacements shown in black and seafloor displacements shown in gray and blue for a simulated subduction zone environment. The bold red line indicates the trench and the dashed black line highlights the extent of the known rupture area. In each case, the dominant onshore InSAR signal is subsidence, while offshore uplift and trenchward displacements are constrained by sparse seafloor observations. The derived slip distributions are shown for inversions of dense onshore observations (InSAR and sparse GPS), sparse GPS, and dense onshore observations coupled with sparse seafloor observations (right). The white lines trace out the known rupture area and the color bars saturate at the known slip magnitude. The slip distributions reflect improved resolution (smaller fault patches) when observations with increased spatial density and coverage are used. The inversions do not recover the slip deficit near the trench and smooth slip up-dip of the known rupture area without seafloor constraints. 33

45 Figure 3: CSC maps predicted by slip distributions informed by dense onshore (InSAR & GPS) observations for a synthetic M w 8.0 earthquake. The stress changes are predicted for receiver faults with the same orientation and mechanism as the source fault. The known and inferred stress changes are shown in map view at 20 km depth (top) and in cross-section (bottom) with the associated misfits (known CSC inferred CSC). The color bar saturates at +5 bars for visualization and the known rupture area is outlined in white in all plots. CSC misfit scales with the magnitude of known stress change, and exhibits the largest errors close to the source fault. 34

46 Figure 4: Correlation between known and inferred stress changes. Each plot shows the inferred CSC plotted versus the known CSC for all receiver faults beyond the designated distance from mapped slip. The dashed black line represents the linear fit between the known and inferred stress changes, while the red dotted line indicates a slope of one (i.e., perfect agreement). When receiver faults in close proximity to the source fault are omitted, the relationship between known and inferred stress change drastically improves. This improvement is most distinct when the receiver faults within 20 km of the source fault are omitted, then the correlation gradually improves as the inferred and known stress changes approach a one to one relationship. 35

47 Figure 5: Φ distributions for stress changes predicted for each M w 8.0 scenario. Maps are shown for receiver faults in map view at 20 km depth (top) and in cross-section (bottom). These maps indicate the relative error of CSC predictions made for receiver faults with the same orientation and mechanism as the source fault (strike = 0, dip = 20, rake = 90). The extent of the known rupture area is traced in white. Φ saturates at 0.5 along stress change nodal planes (i.e., the X pattern in map view) and in the near field of the source fault. Φ exceeds 0.5 over larger areas beyond the trench (X < 0 km), likely due to the poor slip model resolution near the trench. In contrast, CSC predictions exhibit improved accuracy near the coast (X > 100 km). 36

48 Figure 6: Critical distance (D c ) methods and results. (A) Probability density function of distance to mapped slip for receiver faults with large relative errors (Φ > 0.5) for all data sets for the synthetic M w 8.0 scenario. (B) Cumulative distribution function of distance to mapped slip for receiver faults with Φ values exceeding 0.5. D c is defined as the distance at which the cumulative probability is 0.95 (dashed black line). (C) D c values determined for each data set for the M w 8.0 and M w 8.5 scenarios. The addition of seafloor constraints yields considerably smaller D c estimates than the onshore data sets. The addition on dense InSAR observations to sparse onshore GPS does not yield any notable improvements. The D c estimates for the M w 8.5 scenarios improve upon the M w 8.0 results, which is likely due to the improved signal to noise ratio for the larger earthquake. (D) D c estimates for slip distributions derived from different choices of regularization and for 1σ uncertainties. D c estimates exhibit the largest ranges for the 1σ uncertainty slip distributions while regularization-dependent results do not vary a great deal. The effects of noise are greater for the M w 8.0 than the M w 8.5 scenario due to the smaller signal to noise ratio. 37

49 Figure 7: Observations and inferred co-seismic slip distribution of the 2010 M w 8.8 Maule earthquake. (A) Geodetic observations and relocated aftershocks of the Maule earthquake. Ascending interferograms derived from observations from the ALOS-PALSAR sensor are shown with the reported three-component static co-seismic GPS displacements from Tong et al. [2010] and Vigny et al. [2011]. Relocated aftershock regional moment tensor (RMT) solutions from Hayes et al. [2013] are plotted in blue. The mainshock epicenter is indicated by the gray focal mechanism [USGS NEIC, (B) Preferred slip distribution of the 27 February 2010 Maule earthquake derived in this study. Inferred co-seismic slip is concentrated at two local maxima to the North and South of the reported epicenter, which is indicated by the black focal mechanism [USGS NEIC]. Black arrows indicate the rake vector for each fault patch. Green moment tensors denote the aftershocks from the catalog from Hayes et al. [2013] selected for CSC analysis in this study. Red triangles indicate the locations of volcanoes in the Andean arc. 38

50 Figure 8: Maule earthquake synthetic test set up and inverted slip distribution. The synthetic slip distribution and noisy data predicted using the locations, look vectors, and noise structure of the real observations are shown in map view (left). Line of sight displacements for the downsampled descending interferograms are shown as colored circles. Black and blue arrows indicate onshore horizontal and vertical GPS displacements. The slip distribution derived from inversions of the synthetic data (right) agrees well with the known slip distribution. The white dashed lines indicate the extent of the known slip distribution. The color bar saturates at the known slip magnitude. 39

51 Figure 9: CSC sensitivities to model parameters. (A-D). The population of CSC predictions for each RMT nodal plane are plotted versus the perturbed strike, dip, depth, and horizontal position for a selected aftershock. (E) Sensitivity of CSC predictions to the effective coefficient of friction. The median CSC value for the populations of stress change predictions reflects a scaling relationship between inferred CSC and coefficient of friction (µ ). (F) The distributions of CSC predictions for each nodal plane (µ = 0.4). The populations of CSC predictions yield skewed distributions that are most sensitive to strike and dip perturbations (A-B) and less dependent on location uncertainties (C-D). Bold and dashed lines indicate the median CSC and 1σ uncertainties for each nodal plane. 40

52 Figure 10: Correlation between the inferred stress changes predicted by several published slip distributions and the slip distribution derived in this study. The plotted values are colored by distance to the nearest fault patch of the slip distribution from this study for all RMTs at distances greater than 20 km from mapped slip. The dashed black line indicates a slope of one (i.e., perfect agreement). There is notable scatter among the CSC values predicted by each slip distribution that improves as distance is increased (warmer colors). 41

53 6 5 Final CSC-This Study Nodal Plane 1 Nodal Plane 2 CSC- Half Strike/Dip Uncertainty Nodal Plane 1 Nodal Plane 2 CSC- Location Uncertainty Only Nodal Plane 1 Nodal Plane CSC (bars) A Distance to nearest fault patch (km) Distance to nearest fault patch (km) B Distance to nearest fault patch (km) C Figure 11: CSC predictions and uncertainties for different RMT uncertainty magnitudes. (A) Reported CSC values and uncertainties predicted by the slip distribution derived in this study including full receiver fault uncertainties reported by Hayes et al. [2013]. Receiver fault uncertainties are propagated into the CSC analysis through Monte Carlo error propagation techniques. (B) CSC predictions and uncertainties for halved strike and dip uncertainties. When smaller strike and dip uncertainties are considered, the CSC uncertainty ranges are notably smaller for several aftershocks. (C) CSC predictions and uncertainties when only location (horizontal and depth) uncertainties are considered. The exclusion of strike and dip uncertainties significantly minimizes the CSC uncertainties, which makes it much easier to resolve positive and negative stress changes. 42

54 TABLES 43

55 Master Date Slave Date Path Frames B (m) Ascending 5/27/07 3/4/ /3/10 3/21/ /15/08 4/7/ /22/10 3/9/ /8/10 5/11/ /25/10 5/28/ /22/08 3/14/ /13/10 3/31/ /15/10 3/2/ Descending 1/26/10 3/13/ /10/08 3/1/ sw3* /14/10 3/1/ sw4* Table 1: ALOS-PALSAR acquisitions spanning the 27 February 2010 M w 8.8 Maule earthquake. *Obtained from Tong et al. [2010] 44

56 Lon Aftershock Locations Depth Lat (km) Distance (km) Tectonic Indicator This Study Delouis et al., 2011 Lorito et al., 2011 Tong et al., 2010 Vigny et al., 2011 Coulomb Stress Change NP1 NP2 NP1 NP2 NP1 NP2 NP1 NP2 NP1 NP L L L I L U L U L I L I I Table 2: Final Coulomb stress change predictions for the 13 aftershocks selected from the RMT catalog from Hayes et al. [2013]. Predicted CSC values are reported for each RMT nodal plane (NP1 and NP2) for the slip distribution derived in this study and several published slip distributions. All positive stress changes are indicated by bold text and values that exhibit resolvable stress change sign (consistent sign within uncertainty) are highlighted in gray. The tectonic indicator specifies the tectonic environment inferred by Hayes et al. [2013] based on the minimum rotation angle of the moment tensor relative to the local subduction zone geometry. Aftershocks are categorized as interface (I), upper plate (U), or lower plate (L) events. 45

57 APPENDIX- SUPPLEMENTAL FIGURES This supplemental appendix contains additional information and figures regarding the generalized synthetic tests, Maule earthquake modeling and synthetic tests, and aftershock culling approaches. The generalized synthetic tests results for the synthetic M w 8.5 earthquake are shown to supplement the M w 8.0 results shown in the main text (Figure S1-S2). Our alternative approach to estimate a critical distance (D c ) for accurate Coulomb stress change (CSC) predictions is illustrated in Figure S3. Figures S4-S5 show the slip distributions inverted for synthetic M w 8.0 and M w 8.5 subduction zone earthquakes highlighting the impacts of observation noise and inversion regularization. Figures S6-S8 show the final slip distributions and uncertainties for the Maule earthquake along with the GPS and InSAR observations and model residuals. Figure S9 summarizes the D c estimates for different receiver fault geometries for the Maule earthquake synthetic tests used to define a culling criterion for aftershocks. Lastly, Figure S10 shows each fault slip distribution of the Maule earthquake used for Coulomb stress change analysis of off-fault aftershocks. 46

58 Figure S1: CSC maps predicted by slip distributions informed by dense onshore (InSAR & GPS) observations for a synthetic M w 8.5 earthquake. The stress changes are predicted for receiver faults with the same orientation and mechanism as the source fault. The known and inferred stress changes are shown in map view at 20 km depth (top) and in cross-section (bottom) with the associated misfits (known CSC inferred CSC). The color bar saturates at +5 bars for visualization and the known rupture area is outlined in white in all plots. 47

59 Figure S2: Φ distributions for stress changes predicted for each M w 8.5 scenario. Maps are shown for receiver faults in map view at 20 km depth (top) and in cross-section (bottom). These maps indicate the relative error of CSC predictions made for receiver faults with the same orientation and mechanism as the source fault (strike = 0, dip = 20, rake = 90). The extent of the known rupture area is traced in white. Φ saturates at 0.5 along stress change nodal planes (i.e., the X pattern in map view) and in the near field of the source fault. 48

60 Figure S3: Alternative method for estimating critical distance (D c ). In discrete distance ranges (bin widths of 10, 15, and 20 km are tests) I calculate Φ for all receiver faults and determine the 2σ Φ value from the distribution. D c is estimated as the approximate distance at which the 2σ Φ value is less than 0.5 (where 95% of the receiver faults reflect Φ < 0.5). The plots are shown for all data sets of the M w 8.0 scenario. The D c estimates for each data set closely replicate the values determined using the initial approach (Figure 6). 49

61 Figure S4: Slip distribution results for the M w 8.0 synthetic example. The slip distributions are shown for inversions of onshore (InSAR and GPS) observations for different regularization coefficients (top) and uncertainty ranges due to noise from Monte Carlo tests (bottom). Each set of slip distributions is plotted on the same color scale. The uncertainty ranges due to noise are large due to the relatively low signal to noise ratio of onshore geodetic observations of a M w 8.0 subduction zone earthquake. 50

62 Figure S5: Slip distribution results for the M w 8.5 synthetic example. The slip distributions are shown for inversions of onshore (InSAR and GPS) observations for different regularization coefficients (top) and uncertainty ranges due to noise from Monte Carlo tests (bottom). Each set of slip distributions is plotted on the same color scale. The uncertainty ranges due to noise and slip distributions derived from different choices of regularization coefficients yield notably smaller variations than for the M w 8.0 scenario. 51

63 Figure S6: Monte Carlo results for slip distributions of the Maule Earthquake. The + 1σ uncertainties represent the uncertainty bounds due to noise. The median slip distribution is the final reported model. Each slip distribution is plotted on the same color scale, highlighting the negligible differences between the median model and uncertainty bounds. 52

64 Figure S7: Horizontal and vertical GPS data and model residuals. Static GPS displacements from Tong et al. [2010] and Vigny et al. [2011] are plotted with the predicted displacements from the slip distribution derived in this study (left). The residuals (data synthetic) are largest in the south (~37 S) near the Arauco peninsula. 53

65 Figure S8: Downsampled ascending (top) and descending (bottom) InSAR observations and data predicted by the slip distribution of the Maule earthquake derived in this study. The model predicted data agrees well with the true data despite regions of coherent residuals. Ascending p114 yields coherent residuals of up to 1 m, which may be due to post-seismic deformation or the sparse GPS observations used for InSAR corrections. 54

66 Figure S9: Critical distance (D c ) estimates for different receiver fault geometries/mechanisms. The cumulative distribution functions of distance to mapped slip for receiver faults with large relative errors (Φ>0.5) are shown for CSC distributions for random, reverse, normal, and strike-slip receiver faults (left). Randomly generated receiver faults yield the smoothest cumulative distribution functions and the smallest D c estimate (50 km). The other receiver fault geometries yield rougher cumulative distribution functions, which are interpreted to be due to strong dependencies of CSC errors on location. The reverse, strike-slip, and normal receiver fault distributions yield larger D c estimates (53-75 km). 55

67 Figure S10: Maximum Coulomb stress changes predicted by different slip distributions for the aftershocks tested in this study. All slip distributions are derived from fault slip inversions that incorporate geodetic observations. All models are plotted on the same axes and fit to the same color scale. The white line indicates the position of the trench. The aftershocks tested in this study are plotted as circles and colored according to the maximum CSC predicted for the two fault plane solutions. 56