Title: Three-dimensional mechanical models for the June 2000 earthquake sequence in the South Icelandic Seismic Zone

Transcription

1 Elsevier Editorial System(tm) for Earth and Planetary Science Letters Manuscript Draft Manuscript Number: Title: Three-dimensional mechanical models for the June earthquake sequence in the South Icelandic Seismic Zone Article Type: Regular Article Section/Category: Keywords: GPS; INSAR; triggering; Coulomb; viscoelastic; poroelastic; finite element method Corresponding Author: Prof. Kurt Feigl, Corresponding Author's Institution: University of Wisconsin-Madison First Author: Loïc Dubois, M.S. Order of Authors: Loïc Dubois, M.S.; Kurt Feigl; Dimitri Komatitsch, Ph.D.; Thóra Árnadóttir, Ph.D.; Freysteinn Sigmundsson, Ph.D. Manuscript Region of Origin: Abstract: We analyze a sequence of earthquakes that began in June in the South Iceland Seismic Zone (SISZ) in light of observations of crustal deformation, seismicity, and water level, focusing on the tendency for seismicity to migrate from east to west. At least five processes may be involved in transferring stress from one fault to another: () propagation of seismic waves, () changes of static stress caused by co-seismic slip, (3) inter-seismic strain accumulation, (4) fluctuations in hydrological conditions, and (5) ductile flow of subcrustal rocks. All five of these phenomena occurred in the SISZ during the post-seismic time interval following the June earthquakes. By using three-dimensional finite element models with realistic geometric and rheologic configurations to match the observations, we test hypotheses for the underlying geophysical processes. The coseismic slip distribution for the Mw 6.6 June mainshock is

2 deeper when estimated in a realistic layered configuration with varying crustal thickness than in a homogenous half-space. Processes () and () explain only the aftershocks within a minute of the mainshocks. A quasi-static approximation for modeling poroelastic effects in process (4) by changing Poisson's ratio from undrained to drained conditions does not provide an adequate fit to post-seismic deformation recorded by interferometric analysis of synthetic aperture radar images. The same approximation fails to explain the location of subsequent seismicity, including the June mainshock. Although a viscoelastic model of subcrustal ductile flow (5) can increase Coulomb failure stress by more than kpa, it does so over time scales longer than a year. Accumulating interseismic strain (3) in an elastic upper crust that thickens eastward breaks the symmetry in the lobes where co-seismic stress exceeds the Coulomb failure criterion. This process may explain the tendency of subsequent earthquakes to migrate from east to west across the South Iceland Seismic Zone within a single sequence. It does not, however, explain their timing.

3 Cover Letter Kurt Feigl Department of Geology and Geophysics University of Wisconsin-Madison 5 West Dayton Street Madison, WI 5376 USA feigl@wisc.edu Tel Fax October 3, 6 Rob van der Hilst Dear Rob, On behalf of my co-authors, I would like to submit the manuscript specified below for consideration by Earth and Planetary Science Letters. We look forward to hearing from you soon. Sincerely, Kurt Three-dimensional mechanical models for the June earthquake sequence in the South Icelandic Seismic Zone Loïc Dubois, Kurt L. Feigl, Dimitri Komatitsch, Thóra Árnadóttir, and Freysteinn Sigmundsson We analyze a sequence of earthquakes that began in June in the South Iceland Seismic Zone (SISZ) in light of observations of crustal deformation, seismicity, and water level, focusing on the tendency for seismicity to migrate from east to west. At least five processes may be involved in transferring stress from one fault to another: () propagation of seismic waves, () changes of static stress caused by co-seismic slip, (3) inter-seismic strain accumulation, (4) fluctuations in hydrological conditions, and (5) ductile flow of subcrustal rocks. All five of these phenomena occurred in the SISZ during the post-seismic time interval following the June earthquakes. By using three-dimensional finite element models with realistic geometric and rheologic configurations to match the observations, we test hypotheses for the underlying geophysical processes. The coseismic slip distribution for the Mw 6.6 June mainshock is deeper when estimated in a realistic layered configuration with varying crustal thickness than in a homogenous halfspace. Processes () and () explain only the aftershocks within a minute of the mainshocks. A quasi-static approximation for modeling poroelastic effects in process (4) by changing Poisson s ratio from undrained to drained conditions does not provide an adequate fit to post-seismic deformation recorded by interferometric analysis of synthetic aperture radar images. The same approximation fails to explain the location of subsequent seismicity, including the June mainshock. Although a viscoelastic model of subcrustal ductile flow (5) can increase Coulomb failure stress by more than kpa, it does so over time scales longer than a year. Accumulating interseismic strain (3) in an elastic upper crust that thickens eastward breaks the symmetry in the lobes where co-seismic stress exceeds the Coulomb failure criterion. This process may explain the tendency of subsequent earthquakes to migrate from east to west across the South Iceland Seismic Zone within a single sequence. It does not, however, explain their timing.

4 * Manuscript Click here to download Manuscript: DuboisFeiglKomatitschEPSL64.pdf a b c Three-dimensional mechanical models for the June earthquake sequence in the South Icelandic Seismic Zone Loïc Dubois a, Kurt L. Feigl a, *, Dimitri Komatitsch b, Thóra Árnadóttir c, and Freysteinn Sigmundsson c Dynamique Terrestre et Planétaire CNRS UMR 556, Université Paul Sabatier, Observatoire Midi-Pyrénées, 4 av. Édouard Belin, 34 Toulouse, France Laboratoire de Modélisation et d'imagerie en Géosciences CNRS UMR 5, Université de Pau et des Pays de l'adour, BP 55, 643 Pau Cedex, France Nordic Volcanological Center, Institute of Earth Sciences, University of Iceland, Reykjavik, Iceland Wednesday, October 4, 6 9 Submitted to Earth and Planetary Science Letters Number of characters = 665 Number of words = 576 Number of words in text only = 6455 Max is 65 (not abstract, captions or references) Supplementary Material? Yes Number of pages (including figures) = 6 Number of figures = 6 Number of tables = Total number of display items = 8 Max is. Number of references = 79 Max is 8. File name = DuboisFeiglKomatitschEPSL63b.doc Application name Microsoft Word 4 for Mac EndNote Version. for Mac MathType Version 5 for Mac. *Corresponding author, now at Department of Geology and Geophysics University of Wisconsin-Madison 5 West Dayton Street Madison, WI 5376 USA feigl@wisc.edu Tel Fax

5 Dubois et al. submitted TABLE OF CONTENTS Table of contents Abstract 3. Introduction 3. Data and Methods 6. Data 6. Numerical Solution using the Finite Element Method 7.3 Modeling poroelastic deformation with an elastic approximation 8.4 Viscoelastic modeling 9.5 Stress transfer 3. Results 3. Estimating the distribution of co-seismic fault slip 3. Modeling postseismic deformation with the elastic approximation for poroelastic effects 3.3 Viscoelastic model for post-seismic deformation 3.4 Stress transfer 3 4. Discussion and Conclusions 4 4. Co-seismic effects 4 4. Viscoelastic effects Poroelastic effects Migrating seismicity 6 Acknowledgments 6 Supplementary Material 7 SM. Testing against other solutions 7 SM. Estimating co-seismic slip by joint inversion of GPS and INSAR measurements 7 SM.3 Approximating complete poroelastic relaxation by an elastic solution 8 References Tables 6 Last page Page

6 Dubois et al. submitted ABSTRACT We analyze a sequence of earthquakes that began in June in the South Iceland Seismic Zone (SISZ) in light of observations of crustal deformation, seismicity, and water level, focusing on the tendency for seismicity to migrate from east to west. At least five processes may be involved in transferring stress from one fault to another: () propagation of seismic waves, () changes of static stress caused by co-seismic slip, (3) inter-seismic strain accumulation, (4) fluctuations in hydrological conditions, and (5) ductile flow of subcrustal rocks. All five of these phenomena occurred in the SISZ during the post-seismic time interval following the June earthquakes. By using three-dimensional finite element models with realistic geometric and rheologic configurations to match the observations, we test hypotheses for the underlying geophysical processes. The coseismic slip distribution for the Mw 6.6 June mainshock is deeper when estimated in a realistic layered configuration with varying crustal thickness than in a homogenous half-space. Processes () and () explain only the aftershocks within a minute of the mainshocks. A quasi-static approximation for modeling poroelastic effects in process (4) by changing Poisson s ratio from undrained to drained conditions does not provide an adequate fit to post-seismic deformation recorded by interferometric analysis of synthetic aperture radar images. The same approximation fails to explain the location of subsequent seismicity, including the June mainshock. Although a viscoelastic model of subcrustal ductile flow (5) can increase Coulomb failure stress by more than kpa, it does so over time scales longer than a year. Accumulating interseismic strain (3) in an elastic upper crust that thickens eastward breaks the symmetry in the lobes where co-seismic stress exceeds the Coulomb failure criterion. This process may explain the tendency of subsequent earthquakes to migrate from east to west across the South Iceland Seismic Zone within a single sequence. It does not, however, explain their timing INTRODUCTION The South Iceland Seismic Zone (SISZ) is aptly named. Located on the boundary between the North America and Eurasia plates, it accommodates their relative motion as earthquakes. The plate boundary follows the spreading mid-atlantic Ridge, comes ashore on the Reykjanes Peninsula, where it becomes a shear zone to reach the Western Volcanic Zone at a triple point near the Hengill volcanic center (Fig ). There, most of the present-day deformation continues across the SISZ to the Eastern Volcanic Zone. Overall, the SISZ accommodates sinistral shear along its east-to-west trend, but most of its large (M 6) earthquakes rupture as right-lateral strike slip on vertical faults striking north. These parallel faults are km long and ~5 km apart, analogous to books on a shelf []. Indeed, the SISZ deforms as a shear zone, accommodating 8.9 ±.5 mm/yr of relative plate motion [, 3] in a band less than km wide [4]. Consequently, the interseismic strain rate is ~ 6 per year. Its kinematics can be described as a locked fault zone slipping 6 to mm/yr below 8 to km depth with a dislocation in an elastic half-space [5]. If accumulated elastically over Page 3

7 Dubois et al. submitted a century, this strain could be released as ~ m of co-seismic slip. Fortunately, earthquakes in the SISZ do not rupture its entire -km length from east to west; the -km length of the north-south faults seems to limit their magnitude to 6.5 or 7. The seismic sequence of events began on 7 June, with a main shock of magnitude M w = 6.6 [6]. It produced co-seismic deformation that was measured geodetically by both GPS [7] and INSAR [8]. Three and a half days (8 hours) later, a second earthquake ruptured a distinct fault some 8 km to the west of the first event. Both earthquakes have strike-slip focal mechanisms on faults dipping nearly vertically [9]. Both earthquakes ruptured the ground surface in a right-lateral, en echelon pattern with an overall strike within a few degrees of North []. The slip distributions estimated from geodetic data for both earthquakes have maxima over m, centroid depths around 6 km, down-dip widths of km, and along-strike lengths of 6 8 km [7, ]. In this study, we build on previous estimates of the distribution of slip that occurred on the rupture surfaces of the two mainshocks in June from GPS measurements of displacements [7], INSAR recordings of range change [8], and a combination of both in a joint inversion []. All three of these studies assume an elastic half space with uniform values of shear modulus (or rigidity) µ and Poisson s ratio ν. Yet other work outside of Iceland suggest that this simple assumption can bias estimates of slip distribution [, 3]. For example, the aftershock hypocenters located by seismological procedures are deeper than the bottom of the fault rupture inferred from geodetic measurements in the case of the 994 Northridge earthquake in California [4]. In other words, the seismological and geodetic procedures for locating co-seismic slip will yield different estimates if they assume different elastic models. A similar discrepancy between the deepest aftershocks and the bottom of the slip distribution also appears to apply to the June sequence in the SISZ. Although the slip diminishes to less than m below 8 km depth [5], the relocated aftershock hypocenters reach down to km, with a few as deep as km [6]. The hypocentral depths estimated from seismology using a layered velocity model are 6.3 and 5. km for the June 7 and mainshocks, respectively [6]. By using layered models that account for increasing rigidity with depth, we expect deeper slip distributions [7, 8]. An accurate estimate of the slip distribution is required to test the hypothesis that the M 6 earthquakes in the SISZ rupture into the lower crust [9]. Accurate estimates of slip distribution are also important for calculating maps of earthquakes triggered by stress transfer. The latter is sensitive to the former because the threshold value of kpa (. bar) usually used to evaluate the Coulomb failure criterion is several orders of magnitude smaller than the stress drop for a typical earthquake [, ]. The earthquakes in the SISZ sequence seem to be causally related. Just after the June 7 mainshock, additional earthquakes struck the Reykanes Peninsula, as far as 8 km to the west of the June 7 epicenter. Three of these generated coseismic displacements large enough to measure by INSAR and GPS and to model with dislocation sources with moments equivalent to M w = 5.3, 5.5 and 5.9 [, 3]. These secondary earthquakes ruptured the surface, broke rocks, and coincided with a drop of several meters in the water level of Page 4

8 Dubois et al. submitted Lake Klevervatn [4]. Three of these events, at 8 s, 6 s, and 3 s after the June 7 mainshock at 5:4:4 UTC were dynamically triggered by the seismic wave train as it propagated westward [6]. A fourth event occurred 5 minutes after the June 7 mainshock at a distance of almost 8 km [6]. The June 7 earthquake appears to have triggered the June earthquake, based on the increase in static Coulomb stress calculated at the June hypocenter on a vertical, north-striking fault [5]. The migration of M 6 earthquakes from east to west across the SISZ has been observed in previous earthquake sequences in , 784, and 896 []. Another M 6 event occurred in 9 at the east end of the SISZ [6, 7]. Understanding the processes driving the seismicity from east to west is the second objective of this study. Although static Coulomb stress changes can explain the location of the triggered earthquakes, this simple theory cannot explain the time delay between the source (triggering) and receiver (triggered) events, as pointed out by Scholz [, 8] and recently reviewed by Brodsky and Prejean [9]. At least five processes may be involved in transferring stress from one fault to another: () propagation of seismic waves, () changes of static stress caused by co-seismic slip, (3) inter-seismic strain accumulation, (4) fluctuations in hydrological conditions, and (5) ductile flow of subcrustal rocks. All five of these phenomena occurred in the SISZ during the post-seismic time interval following the June earthquakes. () The dynamic stresses caused by propagation of seismic waves apparently triggered the earthquakes on the Reykanes Peninsula in the first minute following the June 7 mainshock, as described above [6]. () In the cascading seismicity hypothesis, one earthquake triggers the next in a kind of seismic domino effect. Changes in static stress could alter rate- and state-dependent friction, thus producing a finite time delay between successive earthquakes[3]. (3) In terms of moment, the main events in the June sequence released only about a quarter of the strain accumulated since 9, the date of the last major earthquake in the SISZ, assuming a constant strain rate over the intervening 88 years [4, 5]. Such interseismic strain accumulation could conceivably contribute to stress transfer. If strain accumulates at the rate of -6 /yr, it could increase stress by kpa in less than a year, assuming a Young s modulus of 5 GPa. (4) Fluctuations in hydrological conditions occurred in the weeks to months after the June 7 mainshock [3, 3]. Poroelastic effects can explain about half the post-seismic signal in an interferogram spanning June 9 through July 4 in the SISZ [3]. The same effects might also explain stress transfer in the SISZ sequence. Under this hypothesis, the co-seismic perturbation to the hydrologic pressure field also alters the stress conditions on faults near the mainshock, triggering aftershocks in areas where increasing pressure unclamps faults near failure [33, 34]. (5) Ductile flow of subcrustal rocks occurs over longer time scales of several years. For example postseismic deformation has been recorded by GPS around the June faults as late as May 4 [35]. These centimeter-sized displacements have been modeled using a viscoelastic Burger s rheology in a semi-analytic Page 5

9 Dubois et al. submitted spherical harmonic formulation [35]. Here, we use a linear Maxwell viscoelastic rheology in a Cartesian finite element formulation to investigate the effect of geometry, viscosity and other parameters on surface displacements. Although ductile flow is much too slow to explain the 86-hour time delay between the June 7 and June events, it may contribute to the time delays (~ years) between earthquake sequences in the SISZ. All these considerations motivate us to move beyond the approximation of a half-space with uniform elastic properties. In this study, we explore models with more realistic geometric and rheologic configurations. To do so, we calculate stress and displacement fields using a finite element method [e.g., 36]. In particular, we use the TECTON code, renovated by Charles Williams [37-39], as described below. This approach allows us to account for the variations in crustal thickness (Fig and Fig ) inferred from earthquake hypocenter locations, seismic tomography, and gravity modeling [4-44]. Call Fig. 89. DATA AND METHODS 9 9. Data In this study, we consider four types of data, all of which have been analyzed and described previously. 9 GPS The complete GPS data set, including the post-seismic time series, has been described elsewhere [5, 35]. The co-seismic displacement vectors are the same as used previously to estimate the distribution of slip on the faults that ruptured on June 7 and [7, ]. 96 INSAR Interferometric analysis of synthetic aperture radar images (INSAR) has recorded the crustal deformation that occurred between June and September,, as described previously [8, 5,, 3]. The data set used here is the same as analyzed by Pedersen et al. []The characteristic relaxation time of the post-seismic deformation near the June 7 fault is of the order of a month because another interferogram spanning the second post-seismic month ( August to 6 September) shows less than 5 mm of differential range change across the fault (blue curve in Figure e of Jónsson et al. [3]). About half of the post-seismic deformation observed within 5 km of the June 7 fault recorded by INSAR in the first month can be explained by poroelastic effects involving fluid flowing in the epicentral area [3]. Page 6

10 Dubois et al. submitted Water level in wells and boreholes Fluctuations in hydrological conditions have been observed in periodic measurements of pressure and water level in wells and boreholes around the SISZ [3, 3]. The polarity of these changes can be well described by the two mainshock focal mechanisms [3, 3]. In the post-seismic interval, however, the wells recover over time scales varying from hours to weeks, indicating large variations in the rock-mechanical properties over distances as short as a few kilometers Earthquake locations and focal mechanisms The earthquakes recorded by the SIL seismological network [9, 45] operated by the Icelandic Meteorological Office have been relocated using multiplet algorithms [46-48] to establish a catalog of focal mechanisms and locations with a precision better than km in all three dimensions [6, 49, 5] as part of the PREPARED project [5] Numerical Solution using the Finite Element Method TECTON is a software package that implements a finite element formulation based on three-dimensional hexahedral elements [37-39]. We have tested TECTON for accuracy by comparing its results to semi-analytic solutions, as described in the doctoral thesis of the first author [5] and in the Supplemental Material. We use the word configuration to describe the combination of the geometry of the mesh (topology) and distribution of mechanical properties (rheology) within it. These configurations appear in Fig, Fig, Table, and Table Mesh We have developed two meshes specifically for this problem to reproduce the main interfaces in our problem: upper/lower crust, mantle/crust, as well as the fault rupture surfaces for the June 7 and June mainshocks. The boundary conditions on the bottom and four sides are fixed while the top surface is free. The region under study is 8 km by km by km (blue box in Fig ). To avoid edge effects, we extend the meshes to 3 km by 3 km by km. The elastic solution achieves numerical convergence with 7 nodes, but we use 4 nodes to handle the time-dependence in the viscoelastic case [5]. The fault slip is described as relative, horizontal displacements at 69 split nodes [38]. The simplest configuration is a homogeneous half-space labeled HOM. The mesh for HOM includes horizontal layers with constant thickness. The same mesh defines the geometry of the heterogeneous HET configuration. A different mesh, used in the TOM and ISL configurations, allows lateral variations in crustal thickness, and thus gradients in rheologic properties, as sketched in Fig B. Page 7

11 Dubois et al. submitted Rheology After defining the meshes, we now define the rheology for each configuration. All the rheologic configurations obey an elastic constitutive relation (Hooke s law), with stress linearly proportional to strain. For each element in the mesh, we specify the Poisson s ratio ν and a shear modulus µ, as summarized in Fig and Table. In the HOM and TOM configurations, we assume ν =.8 and µ = 3 GPa throughout the half-space []. In the layered HET and ISL configurations, Poisson s ratio varies from ν =.8 in the upper crust to ν =.5 in the lower crust, and then to ν =.3 in the mantle, in accordance with previous studies of Iceland [4, 53, 54]. The thickness of these layers is constant in the HET configuration, with the base of the upper crust set to H u = 5 km depth and the base of the lower crust set to H c = 3 km depth. In the ISL configuration, the upper and lower crustal layers vary in thickness, as sketched in Fig B and Fig C. These two crustal layers both thicken and dip toward the east (Fig ) as evident in previous three-dimensional studies [4, 4, 43, 44, 54]. Given the density, we then use the P-wave and S-wave velocities [5] to calculate ν and µ (under undrained conditions) for each element (Fig ). The shear modulus is set to µ = 3 GPa in the HOM and TOM configurations. In the HET and ISL configurations, it varies from µ = 3 GPa in the upper crust to µ = 6 GPa in the mantle. The HOF and HEF configurations add weak fault zones to the HOM and HET configurations, respectively. In the elements located within a few kilometers of the faults, the HOF and HET configurations include values as low as µ = 3 GPa, i.e. four times smaller than in the surrounding crustal rocks [55]. Such low values can be justified by previous coseismic studies that have assumed values as low as µ = GPa [56] and as high as µ = 5 GPa [57]. Following Cocco and Rice [55, 58], we assume that the bulk modulus has the same value in the damage zone as in the surrounding rock. Hence we set Poisson s ratio as high as ν =.43 within the weak fault zones in the HEF and HOF configurations. A thorough sensitivity analysis suggests that the co-seismic displacement field at the surface is most sensitive to the value of the shear modulus (rigidity) µ [5]. For this parameter, a perturbation of percent can increase the misfit to coseismic displacements measured by GPS and INSAR by as much as 5 percent. The shape of the displacement field is also fairly sensitive to the geometric location of the fault, particularly its depth. The displacement field, however, is relatively insensitive to the geometry of the subcrustal layers. Similarly, the absolute value of Poisson s ratio makes little difference. A displacement field calculated with ν =.5 is extremely similar to one with ν =.8, in agreement with a previous study of the June earthquakes []. To describe the post-seismic time interval, we introduce viscosity in the lower crust below a depth of H u, and in the upper mantle, below a depth of H c Modeling poroelastic deformation with an elastic approximation Page 8

12 Dubois et al. submitted To explain the post-seismic interferogram (Fig 5), Jónsson et al. invoke poroelastic effects in the first month following the June 7 mainshock [3]. To describe the observed signal, they employ a modeling approach involving changes in Poisson s ratio ν. This quasi-static approximation, originally introduced by Rice and Cleary [59] and described in the Supplementary Material, uses only two elastic coefficients to solve a problem in a two-phase, poroelastic medium that requires at least two more coefficients to describe completely. This quasi-static model assumes a change in elastic properties, specifically Poisson s ratio, from undrained to drained conditions, as for several other earthquakes in different tectonic settings [6, 6]. The validity of the assumptions underlying this simple, static and elastic approximation to what is actually a complex, timedependent, poroelastic problem [6] will enter into our discussion below. Using all these assumptions, this single-parameter description approximates the complete post-seismic displacement fields generated by poroelastic rebound as the difference between two co-seismic fields calculated with different values of Poisson s ratio. Consequently, only the change in Poisson s ratio Δν = ν undrained ν drained controls the shape of the displacement field. The previous study of the SISZ sequence [3] makes strong assumptions about the spatial distribution of the Poisson s ratio change Δν. As a first approximation, it uses a half-space formulation to calculate the Green s functions G such that Δν =.4 everywhere [63]. As a second approximation, it develops a different formulation with horizontal layers, such that the drainage occurs only in the uppermost.5 km of the crust, where Δν =.8. Making a third approximation is one of the goals of this study. Here we allow the Poisson s ratio change Δν to vary horizontally as well as vertically. Indeed, the finite element method can calculate the elastic Green s function G from an arbitrary geometric distribution of change in Poisson s ratio Δν. In the Supplementary Material, we conclude that Δν=.4 is a reasonable average value for the change in Poisson s ratio. We note, however, that this parameter trades off with the thickness of the drainage layer. Accordingly, we experiment with different values and geometric configurations, as listed in Table. To summarize, we consider three categories of poroelastic configurations, depending on spatial distribution of Δν. In the first category, Δν is uniform (INV, FOR and FOR). In the second category Δν is a function of depth only (FOR3, TRY, TRY, TRY3, INV, and INV3). In the third category, Δν varies with depth and horizontal position (INV4). Call Fig Viscoelastic modeling To describe post-seismic deformation, we introduce a linear Maxwell viscoelastic rheology in the lower crust and upper mantle layers of the geometric configurations described above. Varying the viscosity in a series of forward models, we seek the value that minimizes the misfit to the horizontal components of the Page 9

13 Dubois et al. submitted displacement field measured by GPS in the post-seismic interval from the time of the earthquakes through May 4 [5, 35] Stress transfer Using the slip distributions estimated as described above, we calculate the Coulomb stress on faults in the SISZ using the same notation and values as Árnadóttir et al. [5] Call Fig 3 35!" C =!" t + µ f (!" n # B 3!" kk ) () where B =.5 is Skempton s coefficient, µ f =.75 is the effective coefficient of friction on the fault, Δσ t is the increase in shear stress projected onto the fault plane (taken positive in the sense of the slip vector), Δσ n is the increase in normal stress (taken positive in tension), and σ kk is the trace of the stress tensor. To evaluate the Coulomb failure criterion, we project the stress tensor onto the horizontal strike slip vector on a north-striking vertical receiver fault that typifies the SISZ focal mechanisms [5]. The result is a scalar Coulomb stress Δσ C. At a given location, if the value of Δσ C exceeds a critical (threshold) value Δσ (critical) C, then we conclude that the stressing process favors the occurrence of earthquakes there. If, in fact, an aftershock occurs at the given location, then we count it as a triggered event. In this study, we assume a threshold value of Δσ (critical) C = kpa, equivalent to the stress induced by a column of water m high RESULTS Estimating the distribution of co-seismic fault slip Using the method described in the Supplementary material, we estimate the distribution of co-seismic slip for the two mainshocks in a joint inversion of the GPS and INSAR measurements. The shape and depth of the slip distribution depend on the geometric and rheologic configurations used in the calculation. 3 Homogenous configurations Using the homogeneous geometric configuration (HOM), we estimate the distribution of co-seismic slip on the June 7 and June fault planes. It is essentially similar to that estimated using the dislocation formulation [5], further validating our finite-element approach. The largest differences are in the upper-most part of the fault, where the dislocation and finite-element methods parameterize the slip differently, as described above. The uncertainty in the slip estimates reaches m near the surface, particularly in the section of the June 7 fault south of the hypocenter. This result may reflect discrepancies between the INSAR and GPS measurements for points near the fault. Elsewhere on both faults, however, the standard deviation of the slip is less than.5 m. Most of the slip is shallow, above 6 km depth. The slip decays to less than.5 m below 9 km Page

14 Dubois et al. submitted depth for the June 7 fault and km depth for the June fault. The centroid depths are 3.7 and 3.8 km, respectively. Some of the aftershock hypocenters are located outside the high-slip areas: between 8 and km depth in the June 7 fault plane and between easting coordinates -8 and -6 km in the June fault plane Layered configurations The upper two panels of Fig 3 show the slip distribution estimated using the HET configuration. The difference between the HET and HOM configurations appears in Fig 4. The slip extends slightly deeper in HET than in HOM. The centroid is.3 km deeper for the June 7 fault and.5 km deeper for the June fault. For the June fault, there is over m more slip at km depth in HET than in HOM. The increase in slip concentrates around the hypocenter relocated at 5. km depth from seismology using a layered velocity model [6]. This difference is statistically significant with over 95 percent confidence because it is more than two times larger than the standard deviation of the HET estimate (Fig 4). The surface slip is also significantly larger in the HET configuration than in the HOM estimate. The slip distributions using the ISL configuration are essentially the same as those found with HET [5] Configurations with fault damage zones The HOF configuration adds a weak damage zone around the mainshock faults to the HOM configuration. The slip estimated in HOF concentrates in the upper crust, significantly increasing the maximum slip value around the June hypocenter at 5 km depth (Fig 4). The slip is significantly shallower in HOF than in HOM. Of all the configurations, HOF shows the steepest slip gradient and thus the highest residual stress. The aftershock locations seem to correlate with these areas of high slip gradient, particularly for the southern edge of the June rupture. The aftershocks also concentrate at the edges of the slip distribution where the slip estimates become smaller than their typical 5-cm uncertainties. Adding a damage zone to the HET configuration to specify the HEF configuration also changes the slip distribution. The HEF result has significantly more slip in the uppermost mesh elements and around the hypocenters in both fault planes than does the HET result Modeling postseismic deformation with the elastic approximation for poroelastic effects Fluids flowing in the fractured and fissured rock around the June 7 fault seem to be the most likely explanation for the observed time delays: 86 hours between the two mainshocks and the month-long postseismic signature observed in the interferogram (Fig 5). To explore this possibility, we consider poroelastic effects by extending the work of Jónsson et al. [3] with a series of model calculations summarized in Table. To begin, we reproduce their results by using the homogeneous geometric configuration HOM and a Poisson s ratio contrast Δν =.4. This model calculation (FOR) has a variance reduction of δσ = 39 percent for the Page

15 Dubois et al. submitted observed one-month interferogram with respect to a null model. Another such calculation, FOR, concentrates the drainage in the uppermost km of crust, similar to the layered model of Jónsson et al. [3]. It increases the Poisson s contrast to Δν =.6 to achieve a variance reduction of 48 percent. Both FOR and FOR appear to fit the data well in a profile across strike (A-A in Fig 5c), in agreement with the black and green dashed curves, respectively, in Figure of Jónsson et al. [3]. In map view and a profile parallel to strike (B-B in Fig 5b), however, the deformation calculated with the finite element approach exhibits small features near the fault that are not present in the dislocation calculation [3]. We interpret these features as a consequence of the increased surface slip allowed in the finite element formulation. Another attempt, FOR3, using Δν =.6 in the HET configuration, yields a slightly different result (δσ = 4 percent), highlighting the importance of layering in poroelastic models. We also estimate the Poisson s ratio change Δν in a trial-and-error procedure. The TRY configuration fits the data (δσ = 44 percent) as well as any other solution we could find by assigning a high value of Δν=. to the shallow layer between and km. The TRY configuration achieves the same reduction with lower values of Δν. The TRY3 solution is equivalent to FOR3 (Table ). Next, we allow horizontal variations in the Poisson s contrast Δν in an attempt to reproduce the diminished southwest lobe of the post-seismic fringe pattern. This set of geometric configurations includes a damage zone extending -3 km around the fault. The damage zone can be further subdivided into four quadrants in two layers, adding as many as eight free parameters that we estimate using a non-negative least squares method [64]. One such attempt, the INV solution with only one free parameter, seems reasonable because it resembles FOR in Δν and δσ. The INV solution with two free parameters and INV3 solution with five free parameters, resemble TRY and TRY respectively (Table ). An extreme attempt with 8 free parameters, INV4, achieves a variance reduction of δσ = 65 percent by forcing the Poisson s ratio contrast to the physically unreasonable value of Δν =.44 in the southwest quadrant of the damage zone between and 5 km depth Viscoelastic model for post-seismic deformation Of the parameters in the viscoelastic model, viscosity has the most influence on the post-seismic displacement field, based on a sensitivity study that varies each parameter individually [5]. By optimizing the fit to the horizontal components of the GPS measurements, we estimate the viscosities in the lower crust and upper mantle, albeit with large uncertainties. For the lower crust, we find the 95 percent confidence interval for viscosity to fall between and EPa.s during the first post-seismic year, and 9 9 EPa.s for the interval from July to May 4. ( exapascal-second = 8 Pa.s). The different geometric configurations HOM, HET and ISL yield similar results. For the upper mantle, the best-fitting viscosity is 3 EPa.s for the early postseismic interval and the ISL configuration. The other configurations yield lower viscosity estimates with wider confidence intervals, suggesting that using a realistic geometry is particularly important when continuous GPS Page

16 Dubois et al. submitted observations are sparse. For the upper mantle, a viscosity of EPa.s, irrespective of geometric configuration, fits the -4 data. These values are compatible with a previous study that used a different modeling approach to describe the same post-seismic observations [35] Stress transfer earthquakes. Next, we evaluate the consequences of various sources of stress in terms of their ability to trigger June 7 and co-seismic stress Does the June 7 mainshock increase the Coulomb stress on a north-striking, vertical strike-slip fault at the June hypocenter? Yes, the increase is to 5 kpa, in the three layered configurations (HEF, HET and ISL), confirming the result of a previous study [5] that assumes a homogeneous half-space equivalent to our HOM configuration. In all three cases, the stress increase calculated at the June hypocenter exceeds the conventional threshold of kpa. In map view, the area where earthquakes are favored, within the contour of kpa, is somewhat smaller when calculated with the layered HET configuration than with the uniform HOM configuration (Fig 6a). Do the two mainshocks increase the Coulomb stress at the location of the aftershocks? Yes, about half the aftershocks are located within the -kpa threshold contour. Thus we conclude that only half the earthquakes after the June 7 mainshock, including the June mainshock, can be explained by the co-seismic stress produced by the June 7 mainshock under the Coulomb failure criterion. In other words, only half the seismicity is triggered by increases in static stress. The other half must be triggered by some other, presumably dynamic, process, as considered in the following paragraphs Domino effect of cascading aftershocks We generalize the Coulomb stress calculation to include all the earthquakes between June 7 and December 3 for which reliable focal mechanisms have been estimated, except the June mainshock. This calculation determines the time-dependent changes in the Coulomb stress field on vertical, north-striking strikeslip faults. (To save calculation time, we use the layered configuration HET and the EDGRN/EDCMP implementation to calculate the Green s functions [65]). Fig 6c shows the changes in Coulomb stress at 4 km depth. This stress increase occurs within less than minutes of the June 7 mainshock and remains roughly constant until the end of. At the June hypocenter, however, the increase is only 5 kpa. The primary contributor to the static stress increase is a magnitude 5 aftershock that occurred some 3 seconds after the June 7 mainshock at 5:4:5 midway between the two mainshock faults [6, 49]. Accounting for this large event enlarges the area of increased Coulomb stress on the June fault plane. Page 3

17 Dubois et al. submitted Modeling stress transfer with the elastic approximation for poroelastic effects The elastic approximation for modeling poroelastic effects explains the location of only the aftershocks nearest to the mainshock faults. For example, even the extreme HET configuration with the INV4 Δν values does not increase the Coulomb failure stress on the June fault (Fig 6b) Viscoelastic processes Viscoelastic processes are also capable of triggering seismicity. After four years of post-seismic relaxation, the Coulomb failure stress at 4 km depth exceeds the threshold of kpa over most of the SISZ (Fig 6d). The threshold contour for the ISL configuration is less symmetric than the one for the HET configuration, highlighting the importance of a realistic geometric configuration in stress calculations Interseismic strain accumulation Stress also builds up during the interseismic phase of the earthquake cycle as elastic strain accumulates between large earthquakes. If the interseismic strain rate is constant in time and uniform in space, but the rigid upper crust thickens from west to east, then the stress rate field will exhibit a gradient. At a given depth, say 5 km (on the upper/lower crust boundary near the June mainshock hypocenter), the rigidity increases westward because the stiffer lower crust is shallower there. Consequently, stress will be higher on the west side of a fault than on the east side, thereby explaining the tendency of seismicity to migrate from east to west across the SISZ. To quantify this purely geometric effect, we run a simple finite element model to mimic the constant interseismic strain rate. This elastic interseismic model applies the far-field boundary conditions as 9 cm of displacement at N o on the east and west faces of the mesh to mimic years of plate motion. Since the strain depends on the dimension of the mesh, we cannot calibrate the absolute stress values. To isolate the stress contributed by the geometric variation in crustal thickness, we run this model twice, once in the HET geometric configuration with horizontal layers, and then again in the ISL configuration with the crust thickening toward the east. After projecting the resultant stresses onto North-striking vertical strike-slip faults, we subtract the two fields to obtain the geometric contribution to the change in Coulomb stress Δσ C. This stress field exhibits a strong gradient. It is 4 kpa higher on the June fault than on the June 7 fault (Fig 6e). Combined with the co-seismic stress imposed by the June 7 mainshock alone, this geometric interseismic effect produces a stress field that is distinctly asymmetric (Fig 6f). Its threshold contour ( kpa) includes more of the aftershocks located between 3 and 5 km depth than for the other models DISCUSSION AND CONCLUSIONS Co-seismic effects Page 4

18 Dubois et al. submitted The slip distributions are significantly deeper in realistic three-dimensional geometric configurations than in the conventional uniform half-space configuration. The slip diminishes to negligible values less than 5 cm below km depth, supporting the notion that large earthquakes in the SISZ can penetrate into the lower crust [9]. The layered HET configuration is well suited for calculating coseismic deformation and stress. The coseismic stress increase generated by the June 7 mainshock can explain the location of the June mainshock, confirming a previous study [5]. The domino effect of cascading aftershocks following the June 7 aftershock also increases the stress on the (future) location of the June mainshock. Since static stress migrates at the speed of an elastic wave, standard Coulomb calculations based on the June 7 mainshock or its aftershocks cannot explain the 86-hour time delay between the two mainshocks Viscoelastic effects The simple Maxwell viscoelastic model can explain the postseismic deformation between June and May 4 with viscosities of the order of ~ EPa.s for both the lower crust and the upper mantle. Although the uncertainties are large (an order of magnitude at 68 percent confidence), the acceptable ranges are slightly higher and narrower using realistic geometric configurations. For the first year, the GPS measurements of postseismic displacements can be fit with a lower viscosity, of the order of ~ EPa.s, albeit with large uncertainties. We conclude that the available data provide only weak constraints on subcrustal viscosity, partly because the poroelastic and viscoelastic effects have similar amplitude Poroelastic effects None of the poroelastic models fit the geodetic data very well, despite drastic increases in the complexity of the models. It seems that the elastic approximation described in the Supplementary Material is insufficient to describe the post-seismic observations in this case. Even with drastic increases in the number of free parameters, this approach achieves only modest reductions in variance. Nor does it account for the location of many aftershocks. The explanation for this shortcoming probably involves time-dependent effects. The elastic approximation described above is valid only after a very long time has elapsed and the fluid flow field has returned to equilibrium (drained) conditions. The elastic approximation does not reproduce the map view of the post-seismic interferogram very well, particularly in the fringe lobe southwest of the June 7 rupture. There, the half-space model with Δν =.4 everywhere predicts about two times more uplift than is observed. To explain this discrepancy, Jónsson et al. [3] suggest that the poroelastic rebound was faster in this area than elsewhere. Indeed, if the hydrological state had returned to drained conditions in the two days following the June 7 mainshock, then the poroelastic signal would not appear in the interferogram beginning June 9. The water level Page 5

19 Dubois et al. submitted in the well at Hallstun (HR-9), just south of the June 7 rupture, lends some support to this interpretation. It recovers faster than other wells, suggesting locally high permeability (and thus a large change in Poisson s ratio Δν) in this area. Yet our attempts to account for such a local heterogeneity do not fit the observed fringe pattern much better than the uniform half-space model. We infer that time dependence, rather than spatial heterogeneity, is contributing to the misfit. We conclude that the conditions for the static elastic approximation to be a valid are not fulfilled. A complete time-dependent treatment, however, would require describing the material parameters with more parameters to account for permeability, porosity, etc. [6, 66, 67] Migrating seismicity We have found that a combination of co-seismic and accumulated interseismic stress can explain the tendency of seismicity to migrate from east to west across the SISZ during a single sequence of earthquakes. This new result indicates that realistic geometry, including crustal thickening, is important for modeling interseismic processes. This mechanism does not, however, explain the 86-hour delay observed between the June 7 and June mainshocks. The interseismic process is quite slow, increasing Coulomb failure stress at a given point by only ~ Pa per day. To explain the delay, we imagine a two-step process like the coupled poroelastic effect that Scholz suggested to explain two successive earthquakes in the Imperial Valley, California [68]. In the first step, the source shock instantaneously changes the pressure of pore fluids in the rock around the receiver fault. In the second (slower) step, the hydrological flow field gradually returns to equilibrium, increasing the pore pressure, unclamping the receiver fault and triggering the second earthquake. Other examples of this two-step unclogging process have been invoked in California [9, 69, 7], Oregon [7], and elsewhere [7, 73]. Over longer time scales, in the ~ year intervals between sequences of earthquakes in the SISZ (e.g., 9 to ), inter- and post-seismic processes seem the most plausible explanation. Indeed, we have shown that a linear viscoelastic rheology can increase the Coulomb failure stress by kpa at distances longer than km in only 4 years, as to be expected from the characteristic Maxwell time of to years approximated by the ratio of a viscosity to EPa.s to a rigidity of 3 GPa. Longer time scales presumably involve more complicated rheologies ACKNOWLEDGMENTS We thank Charles Williams for generously providing the source code for his revised version of TECTON, as well as Frank Roth and his colleagues for the EDGRN/EDCMP and PSGRN/PSCMP codes. We also thank Eric Hetland, Tim Masterlark, Rikke Pedersen, Kristin Vogfjord, Fred Pollitz, Sandra Richwalski, Pall Einarsson and Herb Wang for helpful discussions. Grimur Bjornsson kindly explained the well data graciously provided by Iceland Geosurvey and Reykjavik Energy. Kristin Vogfjord and Ragnar Stefansson Page 6

20 Dubois et al. submitted provided the relocated earthquake catalog estimated by the Icelandic Meteorological Office as part of the PREPARED project. This work was financed by EU projects RETINA, PREPARED and FORESIGHT as well as French national programs GDR STRAINSAR and ANR HYDRO-SEISMO. 5 SUPPLEMENTARY MATERIAL SM. Testing against other solutions To evaluate the accuracy of our finite-element modeling procedure, we compare its predictions to a standard analytic solution for a rectangular dislocation buried in an elastic half-space, as formulated by Okada [74] and implemented in the RNGCHN code [75]. Using the coseismic slip distribution estimated in a uniform half space [5], we calculate the displacement field at the surface by both methods. The average difference is less than mm in all three components, thus validating our finite-element approach [5]. To increase our confidence in the geometrically complex ISL configuration, we test its mesh in the TOM configuration. Like HOM, the TOM configuration has a uniform rheology: Poisson s ratio ν =.8 and shear modulus µ = 3 GPa throughout the half-space. Like ISL, the TOM configuration uses a mesh that accounts for dipping layers with variable thickness. The co-seismic surface displacement fields calculated using the HOM and TOM configurations differ by less than mm for all three components. For the post-seismic viscoelastic models, we compare the surface displacement fields calculated using two different methods. The first is our finite-element approach using the TECTON software, as described above. The second is a semi-analytic Green s function approach using the PSGRN/PSCMP software [76]. The average difference in surface displacement is less than 3 mm for all three components after complete relaxation [5] SM. Estimating co-seismic slip by joint inversion of GPS and INSAR measurements To estimate the distribution of slip on the June 7 and June fault planes, we use the same data set and inversion algorithm as Pedersen et al. [5]. In this study, we allow more realistic geometric and rheologic configurations by using the three-dimensional finite-element formulation to calculate the elastic Green s functions, i.e. the partial derivatives of the measurable quantities (displacements) with respect to the model parameters (slip values in discrete fault patches). This difference in approach entails a difference in the fault parameterization. The dislocation formulation specifies the slip as a constant value inside each rectangular rupture patch on the fault plane. The parameterization in the finite-element approach assigns a slip value to each split node. In other words, the slip distribution is discontinuous in the dislocation formulation, but continuous (piece-wise planar) in the finite-element formulation. As a result, the latter leads to smoother slip distributions and smaller stress concentrations than the former. The finite element formulation also allows non- Page 7

21 Dubois et al. submitted zero slip at the uppermost node located at the air-rock interface, thus avoiding a singularity in the case of an earthquake with surface rupture. Another technical improvement involves choosing the appropriate amount of smoothing to optimize the trade-off between fitting the data and finding a reasonable slip distribution. Here we choose the value of the smoothing parameter that minimizes the sum of the absolute values of the slip parameters [67]. To evaluate the uncertainty of the slip estimates, we use a bootstrap algorithm [77]. Accordingly, we resample N b = times the data vector randomly according to its (diagonal) covariance. For each realization of the data vector, we solve the inverse problem to estimate a population of the estimates ˆm for the model parameters m. Then the vector of the standard deviations of the model parameter estimates is 557!(m) = N b # [( ˆm i " E( ˆm) ] i= Nb " () 558 where the E operator denotes the expected value SM.3 Approximating complete poroelastic relaxation by an elastic solution Just after the co-seismic rupture, at time t + q, undrained conditions apply because the fluid in a representative elementary volume has not yet reached equilibrium with an external boundary [6]. Presumably, the same undrained conditions also apply during the brief time interval when a seismic wave propagates through a representative elementary volume. According to previous studies [3, 6, 78], the Poisson s ratio under undrained conditions is!(t + q ) =! undrained!.3 (3) At a much later time t, the fluids have reached equilibrium with an external boundary, deformation is controlled by the solid matrix alone, and the rocks can be considered drained. Under these conditions, Poisson s ratio is [3, 6, 78]!(t " ) =! drained!.7 (4) The differential post-seismic displacement accumulated in the interval of time between t + q and t is thus w = u(t! ) " u(t + q ) = $ G #=#drained " G & % #=#undrained ' (u (5) where G is the Green s function relating co-seismic slip Δu on the fault plane to displacement u at the free surface. We assume the geometric configuration and the slip Δu to be identical in both terms. Furthermore, we assume that the rigidity µ is the same under drained and undrained conditions [55, 58, 6]. Page 8

22 Dubois et al. submitted In the following, we attempt to determine reasonable values for Δν. Under drained conditions, the value of Poisson s ratio is [6] 577! drained = 3! " # B(+! undrained ) 3 " # B( +! undrained ) (6) where we set the Biot-Willis parameter α =.8 and the Skempton s coefficient B =.5 to find ν drained =.5. Under undrained conditions, the value of Poisson s ratio can be calculated from the ratio of P-wave to S- wave velocities Vp/Vs estimated from seismological studies 58 # &! undrained = % ( % " ( % # V p & ( $ % ' ( " $ % ' ( V s (7) In and around the SISZ, the V p /V s ratio is typically between.7 and.85, as measured by seismic tomography [4, 79]. Bjarnason et al. [54] suggest a value of.9 for the undrained value for Poisson s ratio in the SISZ. Page 9

23 Dubois et al. submitted REFERENCES [] P. Einarsson, S. Bjornsson, G. Foulger, R. Stefansson, T. Skaftadóttir, Seismicity pattern in the south Iceland seismic zone, in: D. Simpson, P. Richards, (Eds), Earthquake Prediction, an International Review. M. Ewing Ser. 4, American Geophysical Union, Washington, D.C., 98, pp [] C. DeMets, R.G. Gordon, D.F. Argus, S. Stein, Current plate motions, Geophys. J. Int. (99) [3] C. DeMets, R.G. Gordon, D.F. Argus, S. Stein, Effect of the recent revisions to the geomagnetic reversal time scale on estimates of current plate motions, Geophys. Res. Lett. (994) [4] F. Sigmundsson, P. Einarsson, R. Bilham, E. Sturkell, Rift-transform kinematics in south Iceland: deformation from Global Positioning System measurements, 986 to 99, J. Geophys. Res. (995) [5] T. Árnadóttir, W. Jiang, K.L. Feigl, H. Geirsson, E. Sturkell, Kinematic models of plate boundary deformation in southwest Iceland derived from GPS observations, J. Geophys. Res. (6) B74. [6] A. Antonioli, M.E. Belardinelli, A. Bizzarri, K.S. Vogfjord, Evidence of instantaneous dynamic triggering during the seismic sequence of year in south Iceland, J. Geophys. Res. (Solid Earth) (6) 33. [7] T. Árnadóttir, S. Hreinsdottir, G. Gudmunsson, P. Einarsson, M. Heinert, C. Völksen, Crustal deformation measured by GPS in the South Iceland Seismic Zone due to two large earthquakes in June, Geophys. Res. Lett. 8 () [8] R. Pedersen, F. Sigmundsson, K.L. Feigl, T. Árnadóttir, Coseismic interferograms of two MS=6.6 earthquakes in the South Iceland Seismic Zone, June, Geophys. Res. Lett. 8 () [9] G. Ekström, A. Dziewonski, N. Maternovskaya, M. Nettles, Centroid-Moment Tensor Project, 5. [] A. Clifton, P. Einarsson, Styles of surface rupture accompanying the June 7 and, earthquakes in the South Iceland seismic zone, Tectonophysics 396 (5) [] R. Pedersen, S. Jónsson, T. Árnadóttir, F. Sigmundsson, K.L. Feigl, Fault slip distribution of two June Mw 6.5 earthquakes in South Iceland estimated from joint inversion of InSAR and GPS measurements, Earth and Planetary Science Letters 3 (3) [] T. Masterlark, C. DeMets, H.F. Wang, O. Sánchez, J. Stock, Homogeneous vs heterogeneous subduction zone models: Coseismic and postseismic deformation, Geophys. Res. Lett. 8 () [3] S. Cianetti, C. Giunchi, M. Cocco, Three-dimensional finite element modeling of stress interaction: An application to Landers and Hector Mine fault systems, J. Geophys. Res. (Solid Earth) (5). [4] K.W. Hudnut, Z. Shen, M. Murray, S. McClusky, R. King, T. Herring, B. Hager, Y. Feng, P. Fang, A. Donnellan, Y. Bock, Co-seismic displacements of the 994 Northridge, California, earthquake, Bulletin of the Seismological Society of America 86 (996) [5] R. Pedersen, S. Jónsson, T. Árnadóttir, F. Sigmundsson, K.L. Feigl, Fault slip distribution derived from joint inversion of InSAR and GPS measurements of two June Mw 6.5 earthquakes in South Iceland, Earth Plan. Sci. Lett. 3 (3) [6] S. Hjaltadottir, K.S. Vogfjord, R. Slunga, Mapping subsurface faults in southwest Iceland using relatively located microearthquakes, EGU General assembly, Geophysical Research Abstracts 7, European Geoscience Union, Vienna, 5, p [7] R. Cattin, P. Briole, H. Lyon-Caen, P. Bernard, P. Pinettes, Effects of superficial layers on coseismic displacements for a dip-slip fault and geophysical implications, Geophys. J. Int. 37 (999) [8] E.H. Hearn, R. Burgmann, The effect of elastic layering on inversions of GPS data for coseismic slip and resulting stress changes: Strike-slip earthquakes Bull. Seismol. Soc. Am. 95 (5) [9] R. Stefansson, R. Bodvarsson, R. Slunga, P. Einarsson, S. Jakobsdottir, H. Bungum, S. Gregersen, J. Havskov, J. Hjelme, H. Korhonen, Earthquake prediction research in the South Iceland seismic zone and the SIL Project, Bulletin of the Seismological Society of America 83 (993) [] S. Steacy, D. Marsan, S.S. Nalbant, J. McCloskey, Sensitivity of static stress calculations to the earthquake slip distribution, J. Geophys. Res. 9 (4) doi:.9/jb365. [] C.H. Scholz, The mechanics of earthquakes and faulting, Cambridge University Press, Cambridge, U.K. ; New York,, 47 pp. [] C. Pagli, R. Pedersen, F. Sigmundsson, K.L. Feigl, Triggered fault slip on June 7, on the Reykjanes Peninsula, SW-Iceland captured by radar interferometry, Geophys. Res. Lett. 3 (3) 6-. [3] T. Árnadóttir, H. Geirsson, P. Einarsson, Coseismic stress changes and crustal deformation on the Reykjanes Peninsula due to triggered earthquakes on 7 June, J. Geophys. Res. (Solid Earth) 9 (4) 937. [4] A.E. Clifton, C. Pagli, J.F. Jonsdottir, K. Eythorsdottir, K. Vogfjord, Surface effects of triggered fault slip on Reykjanes Peninsula, SW Iceland, Tectonophysics 369 (3) Page

24 Dubois et al. submitted [5] T. Árnadóttir, R. Pedersen, S. Jónsson, G. Gudmundsson, Coulomb stress changes in the South Iceland Seismic Zone due to two large earthquakes in June, Geophys. Res. Lett. 3 (3) doi:.9/gl6495. [6] M. Bellou, F. Bergerat, J. Angelier, C. Homberg, Geometry and segmentation mechanisms of the surface traces associated with the 9 Selsund Earthquake, Southern Iceland, Tectonophysics 44 (5) [7] I.T. Bjarnason, P. Cowie, M.H. Anders, L. Seeber, C.H. Scholz, The 9 Iceland earthquake rupture: Growth and development of a nascent transform system, Bulletin of the Seismological Society of America 83 (993) [8] C.H. Scholz, The mechanics of earthquakes and faulting, Cambridge University Press, Cambridge [England] ; New York, 99, 439 pp. [9] E.E. Brodsky, S.G. Prejean, New constraints on mechanisms of remotely triggered seismicity at Long Valley Caldera, J. Geophys. Res. (Solid Earth) (5) 43. [3] S. Toda, R.S. Stein, K. Richards-Dinger, S.B. Bozkurt, Forecasting the evolution of seismicity in southern California: Animations built on earthquake stress transfer, J. Geophys. Res. (Solid Earth) (5). [3] G. Bjornsson, O.G. Flovenz, K. Semundsson, E.M. Einarsson, Pressure changes in Icelandic geothermal reservoirs associated with two large earthquakes in June, Twenty-sixth workshop on geothermal reservoir engineering SGP-TR-68, Stanford University,. [3] S. Jónsson, P. Segall, R. Pedersen, G. Bjornsson, Post-earthquake ground movements correlated to pore-pressure transients, Nature 44 (3) [33] A. Nur, J.R. Booker, Aftershocks caused by pore fluid flow?, Science 75 (97) [34] J. Noir, E. Jacques, S. Bekri, P.M. Adler, P. Tapponnier, G.C.P. King, Fluid flow triggered migration of events in the 989 Dobi earthquake sequence of central Afar Geophys. Res. Lett. 4 (997) [35] T. Árnadóttir, S. Jónsson, F. Pollitz, W. Jiang, K.L. Feigl, E. Sturkell, H. Geirsson, Post-seismic deformation following the June earthquake sequence in the south Icelandic seismic zone, J. Geophys. Res (5) B38. [36] G. Dhatt, G. Touzot, The finite element method displayed, Wiley, Chichester [West Sussex] ; New York, 984, 59 pp. [37] N.F. Stevens, G. Wadge, C.A. Williams, J.G. Morley, J.P. Muller, J.B. Murray, M. Upton, Surface movements of emplaced lava flows measured by synthetic aperture radar interferometry, J. Geophys. Res., B, Solid Earth and Planets 6 (),93-,33. [38] H.J. Melosh, A. Raefsky, A simple and efficient method for introducing faults into finite element computations, Bulletin of the Seismological Society of America 7 (98) [39] C.A. Williams, R.M. Richardson, A rheologically layered three-dimensional model of the San Andreas fault in central and southern California, J. Geophys. Res. 96 (99) 6,597-56,56,63. [4] A. Tryggvason, S.T. Rognvaldsson, O. Flovenz, Three-dimensional imaging of the P- and S- wave velocity structure and earthquake locations beneath Southwest Iceland, Geophys. J. Int. 5 () [4] R.M. Allen, G. Nolet, W.J. Morgan, K. Vogfjörd, B.H. Bergsson, P. Erlendsson, G.R. Foulger, S. Jakobsdóttir, B.R. Julian, M. Pritchard, S. Ragnarsson, R. Stefánsson, Imaging the mantle beneath Iceland using integrated seismological techniques, J. Geophys. Res. (Solid Earth) 7l (). [4] R.M. Allen, J. Tromp, Resolution of regional seismic models: Squeezing the Iceland anomaly, Geophysical Journal International 6 (5) [43] F.A. Darbyshire, R.S. White, K.F. Priestley, Structure of the crust and uppermost mantle of Iceland from combined seismic and gravity study, Earth Planet. Sci. Lett. 8 () [44] M.K. Kaban, O.G. Flovenz, G. Palmason, Nature of the crust-mantle transition zone and the thermal state of the upper mantle beneath Iceland from gravity modelling, Geophys. J. Int. 49 () [45] R. Bövarsson, S.T. Rögnvaldsson, R. Slunga, E. Kjartansson, The SIL data acquisition system-at present and beyond year, Physics of the Earth and Planetary Interiors 3 (999) 89-. [46] R. Slunga, S.T. Rognvaldsson, R. Bodvarsson, Absolute and relative locations of similar events with application to microearthquakes in southern Iceland, Geophysical Journal International 3 (995) [47] S.T. Rognvaldsson, R. Slunga, Single and joint fault plane solutions for microearthquakes in South Iceland, Tectonophysics 37 (994) [48] R. Slunga, Microearthquake Analysis at Local Seismic Networks in Iceland and Sweden and Earthquake Precursors, Lecture Notes in Earth Sciences (3) [49] K. Vogfjord, Triggered Seismicity after the June 7, Mw=6.5 Earthquake in the South Iceland Seismic Zone: The first five minutes, EGS - AGU - EUG Joint Assembly, Abstracts from the meeting held in Nice, France, 6 - April 3, abstract #5 (3) 5. [5] K. Vogfjord, R. Slunga, Rupture in the South Iceland Seismic Zone forced by magmatic intrusion in the Hengill area, EGS - AGU - EUG Joint Assembly, Abstracts from the meeting held in Nice, France, 6 - April 3, abstract #9685 (3) Page

25 Dubois et al. submitted [5] R. Stefansson, PREPARED final report, Icelandic Meterological Office, Reykjavik 6. [5] L. Dubois, Mechanical study of the June earthquake sequence with 3D finite element models: rheologic and geometric effects (in French), Ph.D. thesis, Université Paul Sabatier, Toulouse III, France, 6. [53] R.M. Allen, G. Nolet, W.J. Morgan, K. Vogfjörd, M. Nettles, G. Ekström, B.H. Bergsson, P. Erlendsson, G.R. Foulger, S. Jakobsdóttir, B.R. Julian, M. Pritchard, S. Ragnarsson, R. Stefánsson, Plume-driven plumbing and crustal formation in Iceland, J. Geophys. Res. (Solid Earth) 7h (). [54] I.T. Bjarnason, W. Menke, O. Flóvenz, D. Caress, Tomographic image of the mid-atlantic plate boundary in southwestern Iceland, J. Geophys. Res. 98 (993) [55] M. Cocco, J.R. Rice, Pore pressure and poroelasticity effects in Coulomb stress analysis of earthquake interactions, J. Geophys. Res. 7 () ESE - to -7. [56] G. Dal Moro, M. Zadro, Remarkable tilt-strain anomalies preceding two seismic events in Friuli (NE Italy): their interpretation as precursors, Earth Planet. Sci. Lett. 7 (999) 9-9. [57] S.E. Barrientos, S.N. Ward, The 96 Chile earthquake: inversion for slip distribution from surface deformation, Geophys. J. Int. 3 (99) [58] M. Cocco, J.R. Rice, Corrections to "Pore pressure and poroelasticity effects in Coulomb stress analysis of earthquake interactions" 3. [59] J.R. Rice, M.P. Cleary, Some basic stress-diffusion solutions for fluid-saturated elastic porous media with compressible constituents, Reviews of Geophysics and Space Physics 4 (976) 7-4. [6] G. Peltzer, P. Rosen, F. Rogez, K. Hudnut, Poroelastic rebound along the Landers 99 earthquake surface rupture, J. Geophys. Res. 3 (998) [6] Y. Fialko, Evidence of fluid-filled upper crust from observations of postseismic deformation due to the 99 Mw 7.3 Landers earthquake, J. Geophys. Res. (Solid Earth) 9 (4) 84. [6] H.F. Wang, Theory of poroelasticity with applications to geomechanics and hydrology, Princeton University Press,. [63] P. Segall, Induced stresses due to fluid extraction from axisymmetric reservoirs, Pure and Applied Geophysics 39 (99) [64] C.L. Lawson, R.J. Hanson, Solving least squares problems, Prentice-Hall, 974. [65] R. Wang, F. Martin, F. Roth, Computation of deformation induced by earthquakes in a multi-layered crust - FORTRAN programs EDGRN/EDCMP, Comp. Geosci. 9 (3) [66] E.F. Kaaschieter, A.J.H. Frijns, Sqeezing a sponge: a three-dimensional solution in poroelasticity, Computational Geosciences 7 (3) [67] T. Masterlark, Finite element model predictions of static deformation from dislocation sources in a subduction zone: Sensitivities to homogeneous, isotropic, Poisson-solid, and half-space assumptions, J. Geophys. Res. 8 (3) /JB96. [68] K.W. Hudnut, L. Seeber, J. Pacheco, Cross-Fault Triggering in the November 987 Superstition Hills Earthquake Sequence, Southern-California, Geophys. Res. Let. 6 (989) 99-. [69] T. Masterlark, H.F. Wang, Poroelastic coupling between the 99 Landers and Big Bear Earthquakes, Geophys. Res. Lett. 7 () [7] T. Masterlark, H.F. Wang, Transient stress-coupling between the 99 Landers and 999 Hector Mine, California, earthquakes, Bull. Seism. Soc. Amer. 9 () [7] E.E. Brodsky, E. Roeloffs, D. Woodcock, I. Gall, M. Manga, A mechanism for sustained groundwater pressure changes induced by distant earthquakes, J. Geophys. Res. (Solid Earth) 8h (3). [7] D.P. Hill, P.A. Reasenberg, A. Michael, W.J. Arabaz, G. Beroza, D. Brumbaugh, J.N. Brune, R. Castro, S. Davis, D. depolo, W.L. Ellsworth, J. Gomberg, S. Harmsen, L. House, S.M. Jackson, M.J.S. Johnston, L. Jones, R. Keller, S. Malone, L. Munguia, S. Nava, J.C. Pechmann, A. Sanford, R.W. Simpson, R.B. Smith, M. Stark, M. Stickney, A. Vidal, S. Walter, V. Wong, J. Zollweg, Seismicity remotely triggered by the magnitude 7.3 Landers, California earthquake, Science 6 (993) [73] S.G. Prejean, D.P. Hill, E.E. Brodsky, S.E. Hough, M.J.S. Johnston, S.D. Malone, D.H. Oppenheimer, A.M. Pitt, K.B. Richards-Dinger, Remotely triggered seismicity on the United States west coast following the M (sub w) 7.9 Denali Fault earthquake, Bulletin of the Seismological Society of America 94 (4) [74] Y. Okada, Surface deformation to shear and tensile faults in a half-space, Bull. Seism. Soc. Am. 75 (985) [75] K.L. Feigl, E. Dupré, RNGCHN: a program to calculate displacement components from dislocations in an elastic half-space with applications for modeling geodetic measurements of crustal deformation, Computers and Geosciences 5 (999) [76] R. Wang, Mart, F.L. 'in, F. Roth, PSGRN/PSCMP - a new code for calculating co-postseismic deformations and geopotential changes based on the viscoelastic-gravitational dislocation theory, Elsevier Science (5). Page

26 Dubois et al. submitted [77] B. Efron, R. Tibshirani, Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statistical Science (986) [78] G. Peltzer, P. Rosen, F. Rogez, K. Hudnut, Postseismic rebound in fault step-overs caused by pore fluid flow, Science 73 (996) -4. [79] A.D. Miller, B.R. Julian, G.R. Foulger, Three-dimensional seismic structure and moment tensors of non-double couple earthquakes at Hengill-Grensdalur volcanic complex, Iceland, Geophys. J. Int. 33 (998) [8] P. Einarsson, and K. Sæmundsson, Earthquake epicenters and volcanic systems in Iceland, in: T.I. Sigfusson, (Ed), Festschrift for Th. Sigurgeirsson, Menningarsjodur, Reykjavık, 987. Page 3

27 Dubois et al. submitted Captions Fig. Map showing (above) the main tectonic features of the study area from Árnadóttir et al. [3]. The Reykjanes Peninsula (RP), the Hengill triple junction (He), the Western Volcanic Zone (WVZ), the South Iceland Seismic Zone (SISZ), and the Eastern Volcanic Zone (EVZ) are indicated. The light shaded areas are individual fissure swarms with associated central volcanoes. Mapped surface faults of Holocene age are shown with black lines [8]. The epicenter locations of earthquakes on June 7, are shown with black stars. The 7 June main shock is labeled J7. The Reykjanes Peninsula events are 6 s afterwards on the Hvalhnúkur fault (H), 3 s afterwards near Lake Kleifarvatn (K), and 5 minutes afterwards at Núpshlídarháls (N) as located by geodesy [3] and timed by seismology [6]. Location of the June main shock is shown with a white star labeled J. The location of Reykjavik, the capital of Iceland, is noted. Inset shows a simplified map of the plate boundary across Iceland, with the location of the main part of the figure indicated by the black rectangle. The black arrows show the relative motion between the North America and Eurasian plates from NUVEL-A [, 3]. Block diagram (below) showing thickening of the crust from east to west across the SISZ as inferred from the literature [43, 44]. The dimensions of the mesh are 3 x 3 x km (whole box). Color code shows Iceland (gray), the SISZ (blue rectangle), water (blue), upper crust (green), lower crust (orange), the upper mantle (red), fault traces (red) for the June 7 (east) and June (west) faults, and the reference point (gray dot) at the center of the modeled June fault trace (63.99 o N,.7 o W) for the local easting and northing coordinate system Fig. Geometric configuration of rheologic parameters. A) Cross section showing, as a function of depth, the following rheologic parameters: density ρ (thick dashed line), rigidity µ (thick solid line), and Poisson s ratio ν (thin solid line). The thicknesses of the rheologic layers depend on the depths H u and H c to the bases of the upper and lower crust, respectively. The configurations are composed of: a uniform half space (HOM and TOM), horizontal layers with constant thickness (HET), dipping layers with variable thickness (ISL), a half-space with a damage zone (HOF), and horizontal layers with a damage zone (HEF). (B) Thickness of the upper crust H u as parameterized in the TOM and ISL configurations. Contour interval is km. (C) Depth to the interface between lower crust and upper mantle H c in the TOM and ISL configuration. Contour interval is 5 km. Solid lines represent traces of modeled faults for June 7 (east) and June (west). Dot indicates the reference point of the local cartographic coordinate system, centered on the June epicenter Fig 3. View of fault planes showing the slip distribution estimated for the June 7 main shock (left column) and June main shock (right column) in the horizontally-layered HET configuration (upper row). White stars indicate the hypocenters of the mainshocks. Black dots indicate aftershocks within km of each fault and 4 hours of the June 7 and June mainshocks, respectively, as relocated by the Icelandic Meteorological Office, Page 4

28 Dubois et al. submitted as described in the section on data and methods. The lower panels show the -σ uncertainty of the slip estimates for the June 7 (left) and June (right) events Fig 4. View of fault planes of the June 7 main shock (left column) and June main shock (right column) showing the differences in estimated slip distribution for the HET configuration with respect to HOM (top row), HOF with respect to HOM (middle row), and HEF with respect to HET (bottom row). The black lines denote the significance ratio, defined as the slip estimate divided by its -σ uncertainty. The contour where this ratio equals thus includes the area where the differences are statistically significant at the level of 95% confidence. For each panel, the white circle indicates the centroid of the first slip distribution in the pair, while the black circle indicates the centroid of the second, e.g., white circle is the HET centroid in the first row Fig 5. Poroelastic models for a postseismic interferogram, showing range change (the component of displacement along the line of sight from the ground to satellite) in map view as observed (a) and calculated from the FOR configuration (d). Solid black lines outline the co-seismic portion of the fault plane that ruptured during the June 7 mainshock. Dashed lines indicate locations of profiles. Panel (b) shows negative range change as a function of distance along east-west profile A-A as observed (points), and calculated from various configurations: FOR3 (black line), TRY (green line), INV (blue line), and INV4 (red lines). Panel (c) shows negative range change as a function of distance along north-south profile B-B with the same plotting conventions. All range changes pertain to the first month of the post-seismic interval, from June 9 to July 4. Negative range change corresponds to uplift; positive range change corresponds to subsidence Fig 6. Change in Coulomb failure stress Δσ C as a result of four candidate processes for stress transfer. The contours outline the areas where the change in Coulomb failure stress Δσ C resolved on north-striking vertical faults at 4 km depth exceeds the conventional threshold value of Δσ (critical) C = kpa. The sources of stress include: (A) the co-seismic stresses generated by the June 7 mainshock calculated using configurations HOM (black line) and HET (blue line); (B) poroelastic effects calculated using the elastic approximation and two different configurations for the change in Poisson s ratio Δν: INV (green line) and INV4 (blue line); (C) the domino effect of cascading aftershocks, (D) viscoelastic processes accumulated in mid 4 calculated from the HET (blue line) and ISL (green line) configurations (E) geometric contribution to years of interseismic strain accumulation obtained by subtracting the interseismic stress field calculated using the HOM geometric configuration from that obtained with the ISL configuration; (F) combination of the co-seismic and the geometric contribution to interseismic stress integrated over years, calculated as the sum of the HET field (A) and panel (E). Red lines indicate faults for the June 7 (east) and June (west) mainshocks. Dots in panels (A, B, C, E, F) indicate the epicenters of earthquakes between June 7 and, [6, 49]. Page 5

29 Dubois et al. submitted TABLES 88 Table. Geometric and rheologic parameters for configurations used to estimate distributions of co-seismic slip Table. Parameter values for poroelastic modeling of post-seismic deformation and the variance reduction. In the FOR and TRY series, the parameter values are input to forward calculations. In the INV series, the parameters are estimated from the data shown in Fig LAST PAGE Page 6

30 Figure Click here to download Figure: Fig=A.pdf R WVZ RP N K H He J J7 SISZ EVZ km Up East North km 3 km 3 km Fig. Dubois et al.

31 Figure Click here to download Figure: Fig=B.pdf A) Surface - H u / 5 - x H u / 5-3 x H u / 5-4 x H u / 5 HOM & TOM HET & ISL HOF (damaged zone) HEF (damaged zone) } }} Upper crust - H u - ( H c + H u ) Lower crust - H c Mantle Density ρ ( kg/m 3 ) Rigidity µ ( GPa ) Poisson's ratio ν drained Poisson's ratio ν undrained B) Thickness of the upper crust (km) C) Thickness of the whole crust (km) Northing (km) Northing (km) Easting (km) Easting (km)

32 Figure 3 Click here to download Figure: Fig3=C.pdf 7 June June Depth (km) Right-lateral strike slip (m) Depth (km) σ uncertainty (m) south along-strike coordinate (km) north south along-strike coordinate (km) north

33 south along-strike coordinate (km) north south along-strike coordinate (km) north Slip difference (m) Depth (km) 7 June June H E T - H O M Depth (km) Depth (km) H O F - H O M H E F - H E T Figure 4 Click here to download Figure: Fig4=F.pdf

34 Figure 5 Click here to download Figure: Fig5=J.pdf Down range change (cm) Up a) Unwrapped interferogram B 5 A A' b) 5 Profile B-B OBS FOR3 TRY INV INV4 Northing (km) 5 Northing (km) 5 B' Easting (km) Down range change (cm) Up c) -3 Profile A-A d) FOR configuration Down range change (cm) Up Northing (km) Easting (km) Easting (km)

35 Figure 6 Click here to download Figure: Fig6=P.pdf 4 A) B) HOM HET INV INV4 Northing (km) Northing (km) 4 4 Coseismic (June 7) Full poro-elastic (June 7) C) HET 4 D) HET ISL 4 Seismicity (from June 7 to June ) 4 Visco-elastic (June 7 & June ) σ C (kpa) σ C (kpa) E) 4 F) Northing (km) 4 Inter-seismic (ISL - HET) 4 Co-seismic (June 7) + Inter-seismic (ISL-HET) Easting (km) Easting (km)