Three-dimensional mechanical models for the June 2000 earthquake sequence in the south Iceland seismic zone
Introduction
The south Iceland seismic zone (SISZ) is located on the boundary between the North America and Eurasia plates and it partly accommodates their relative motion as earthquakes. The plate boundary follows the spreading mid-Atlantic ridge, comes ashore on the Reykjanes peninsula (RP), where it becomes a shear zone to reach the western volcanic zone (WVZ) at a triple point near the Hengill volcanic center (Fig. 1). There, most of the present-day deformation continues across the SISZ to the eastern volcanic zone. Overall, the SISZ accommodates left-lateral shear along its east-to-west trend, but most of the large (M ~ 6) earthquakes there rupture with right-lateral strike slip on vertical faults striking north. These parallel faults are 10–20 km long and ~ 5 km apart, analogous to books on a shelf (Einarsson et al., 1981). Indeed, the SISZ deforms as a shear zone, accommodating 18.9 ± 0.5 mm/yr of relative plate motion (DeMets et al., 1990, DeMets et al., 1994) in a band less than 20 km wide (Sigmundsson et al., 1995). Consequently, the inter-seismic strain rate is ~ 10− 6 per year. The kinematics can be described as a locked fault zone slipping at a rate of 19 mm/yr below ~ 16 km depth (Árnadóttir et al., 2006). If accumulated elastically over a century, this strain could be released as ~ 2 m of co-seismic slip. Earthquakes in the SISZ do not rupture its entire 100-km length from east to west; the 20-km length of the north–south faults seems to limit their magnitude to 6.5 or 7.
The analyzed seismic sequence began on 17 June 2000, with a mainshock of magnitude Ms = 6.6 (Antonioli et al., 2006). It produced co-seismic deformation that was measured geodetically by both GPS (Árnadóttir et al., 2001) and InSAR (Pedersen et al., 2001). Three and a half days (81 h) later, a second earthquake of the same magnitude ruptured a distinct fault some 18 km to the west of the first event. Both earthquakes have strike-slip focal mechanisms on faults dipping nearly vertically (Ekström et al., 2005) and ruptured the ground surface in a right-lateral, en échelon pattern with an overall strike within a few degrees of north (Clifton and Einarsson, 2005). The hypocentral depths estimated from seismology using a layered velocity model are 6.3 and 5.1 km for the June 17 and 21 mainshocks, respectively (Árnadóttir et al., 2001). The slip distributions estimated from geodetic data for both earthquakes have maxima over 2 m, down-dip widths of 10–12 km, and along-strike lengths of 16–18 km (Árnadóttir et al., 2001, Pedersen et al., 2003). The estimated geodetic magnitudes for the June 17 and June 21 slip distributions are Mw = 6.4 and Mw = 6.5, respectively (Pedersen et al., 2003).
The earthquakes in the 2000 SISZ sequence appear to be causally related. Just after the June 17 mainshock, additional earthquakes struck the Reykjanes peninsula, as far as 80 km to the west of the June 17 epicenter. Three of these events generated co-seismic displacements that were large enough to be measured by InSAR and GPS and to be modeled as dislocation sources (i.e. discontinuity in displacement in the fault plane) with magnitudes between Mw = 5.3 and Mw = 5.8 (Pagli et al., 2003). These secondary earthquakes ruptured the surface, broke rocks, and coincided with a drop of several meters in the water level of Lake Kleifar (Clifton et al., 2003). Three aftershocks, at 8 s, 26 s, and 30 s (Fig. 1) after the June 17 mainshock at 15:40:41 UTC seem to have been dynamically triggered by the seismic wave train as it propagated westward (Antonioli et al., 2006). Two other events occurred 2 and 5 min after the June 17 mainshock at a distance of almost 4 km and 80 km towards the west, respectively (Antonioli et al., 2006). The June 17 earthquake brought the June 21 fault closer to failure, based on the increase in static Coulomb stress calculated at the June 21 hypocenter (Árnadóttir et al., 2003).
The migration of M ≥ 6 earthquakes from east to west across the SISZ has been observed in previous earthquake sequences in 1732–1734, 1784, and 1896 (Einarsson et al., 1981, Scholz, 2002). In 1896, for example, five strong earthquakes ruptured distinct sub-parallel faults over a distance of 50 km during an interval of three weeks (Einarsson et al., 1981, Scholz, 2002). The M ~ 7 event in 1912, however, does not appear to fit this pattern because it occurred to the east of the 1896 sequence (Bjarnason et al., 1993a, Bellou et al., 2005).
In this study, our first objective is to evaluate the influence of geometric and rheologic lithospheric heterogeneities on the inter-, co-, and post-seismic deformation and stress fields in the SISZ. To explain the co-seismic deformation, we build on previous estimates of the distribution of slip that occurred on the rupture surfaces of the two mainshocks in June 2000 from GPS measurements of displacements (Árnadóttir et al., 2001), InSAR recordings of range change (the component of displacement along the line of sight from the ground to the satellite) analyzed by Pedersen et al. (2001), and a combination of both in a joint inversion (Pedersen et al., 2003). 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 previous studies outside of Iceland suggest that assuming homogeneity can bias estimates of slip distribution (Cattin et al., 1999, Masterlark, 2003, Cianetti et al., 2005). For example, the aftershock hypocenters located by seismological methods are deeper than the bottom of the fault rupture inferred from geodetic measurements in the case of the 1994 Northridge earthquake in California (Hudnut et al., 1996). 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 2000 sequence in the SISZ. Although the slip diminishes to less than 1 m below 8 km depth (Pedersen et al., 2003), the relocated aftershock hypocenters reach down to 10 km, with a few as deep as 12 km (Hjaltadottir et al., 2005). Furthermore, the estimated slip distribution is sensitive to the material properties and fault geometry, especially the shear modulus (rigidity) μ in the upper crust (Dubois, 2006). By using layered models that account for increasing rigidity with depth, we expect deeper slip distributions (Cattin et al., 1999, Hearn and Bürgmann, 2005). Furthermore, an accurate estimate of the slip distribution is required to test the hypothesis that M 6 earthquakes in the SISZ rupture into the lower crust (Stefansson et al., 1993). Accurate estimates of slip distribution are also important for calculating maps of induced stress changes and assessing seismic hazard. Accordingly, we evaluate the effects of geometric and rheologic lithospheric heterogeneities in the inter- and post-seismic time intervals, especially in terms of stress changes. All of our stress calculations in a particular model are consistent with the slip distribution estimated with the same model. This strategy, suggested by Masterlark et al. (2001), avoids biasing the results.
Our second objective is to understand why seismicity appears to migrate from east to west across the SISZ. As on the North Anatolian fault in Turkey, it appears that one earthquake can trigger the next one (Barka, 1996, Stein et al., 1997, Hubert-Ferrari et al., 2000, Parsons et al., 2000). Unlike Turkey, where successive earthquakes rupture different segments of the same contiguous fault, the sequences in Iceland involve distinct parallel faults, separated by roughly one (~ 10 km) fault dimension. 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, 1990, Scholz, 2002 and recently reviewed by Brodsky and Prejean (2005). At least six processes may be involved in transferring stress from one fault to another: (1) propagation of seismic waves, (2) changes in the static stress field caused by major co-seismic slip, (3) seismicity “cascading” in an aftershock sequence, (4) fluctuations in hydrological conditions, (5) flow of ductile rocks, and (6) inter-seismic strain accumulation. All six of these phenomena occurred in the SISZ before, during, and after the June 2000 events.
- 1.
The dynamic stress changes caused by propagation of seismic waves apparently triggered the earthquakes on the Reykjanes peninsula in the first minute following the June 17 mainshock (Antonioli et al., 2006). Although this process is beyond the scope of our study, introducing the geometric and rheologic heterogeneities considered here into seismological models would presumably improve the accuracy of the synthetic seismograms (e.g., Komatitsch et al., 2004).
- 2.
During an earthquake, the co-seismic slip on the fault plane permanently alters the stress field in the surrounding rock. By resolving the stress tensor onto a fault plane with a specified orientation, one can evaluate whether it is more or less likely to fail in a future earthquake based on the Coulomb failure stress changes. This calculation has been performed previously using a homogeneous half-space for the June 17 and 21 events in the SISZ (Árnadóttir et al., 2003), as well as for many other earthquake sequences, especially in strike-slip settings such as California (e.g., King et al., 1994, Stein, 1999).
- 3.
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 (e.g.,Toda et al., 2005). Here, we evaluate if the aftershock seismicity in the June 2000 sequence changed the stress field enough to modify the assessment of seismic hazard (e.g., Helmstetter et al., 2005).
- 4.
Fluctuations in hydrological conditions occurred in the weeks to months after the June 17 mainshock (Björnsson et al., 2001, Jónsson et al., 2003). Poro-elastic effects can explain about half the post-seismic signal in an interferogram spanning June 19 through July 24 in the SISZ (Jónsson et al., 2003). The same effects might also explain stress transfer in the 2000 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 and shear stress respectively unclamps and leads faults near failure (Nur and Booker, 1972, Noir et al., 1997).
- 5.
Viscous flow in ductile rocks occurs in the months to years after an earthquake. For example, post-seismic deformation has been recorded by GPS around the June 2000 faults as late as May 2004 (Árnadóttir et al., 2005). These centimeter-sized displacements have been modeled using a visco-elastic Burger's rheology in a semi-analytical spherical-harmonic formulation by Árnadóttir et al. (2005). Here, we use a linear Maxwell visco-elastic rheology in a Cartesian finite-element formulation to investigate the effect of geometry and other rheologic parameters on stress changes due to viscous relaxation. Although ductile flow is much too slow to explain the 86-hour time delay between the June 17 and June 21 events, it may contribute to the time delays (~ 100 years) between earthquake sequences in the SISZ.
- 6.
In terms of moment, the main events in the June 2000 sequence released only about a quarter of the strain accumulated since 1912, the date of the last major earthquake in the SISZ, assuming a constant strain rate over the intervening 88 years (Sigmundsson et al., 1995, Pedersen et al., 2003). Such inter-seismic strain accumulation could conceivably increase the stress in the SISZ and drive faults there closer to failure. Assuming that the crust thickens from west to east, we describe the elastic properties at a given depth as stiffer in the west than in the east. As a result, a uniform strain field that is imposed as far-field boundary conditions will lead to an asymmetric stress field that has higher stresses in the west than in the east. Furthermore, if the crust is considered as a thin plate, there will be an accumulation of stress in the thinnest (western) part. The resulting stress gradient could be steep enough to cause earthquakes to occur preferentially in the west.
All these considerations motivate us to move beyond the approximation of a half-space with uniform elastic properties used in previous co-seismic studies and beyond the horizontal layering approximation used in the visco-elastic models. In this study, we explore models with rheologic and geometric heterogeneities, such as dipping layers with variable thickness and/or a weak fault damage zone around the mainshock faults. To do so, we calculate stress and displacement fields using a finite-element method (e.g., Dhatt and Touzot, 1984). We use the TECTON code, renovated by Williams and Richardson (1991), as described below. This approach allows us to account for the variations in material properties (density, shear modulus, and Poisson's ratio) and their geometric configuration inferred from earthquake hypocenter locations (Stefánsson et al., 1993), seismic tomography (Bjarnason et al., 1993b, Darbyshire et al., 1998, Allen et al., 2002, Tryggvason et al., 2002), and gravity modeling (Menke, 1999, Darbyshire et al., 2000, Kaban et al., 2002).
Section snippets
Data
In this study, we consider different types of data: interferometric analysis of synthetic aperture radar images (InSAR), displacement vectors from GPS stations, location, focal mechanisms, and magnitude of the events in the June 2000 sequence.
The crustal deformation that occurred between June and September 2000 was recorded by the ERS-2 satellite in descending passes, with incidence angles varying from 19° to 27°. The acquired images have been described previously (Pedersen et al., 2001,
Model
In order to account for vertical and horizontal gradients of the elastic parameters and fault damage zones (weaker zones centered on the faults) in the co-seismic inversion, we define five configurations of an elastic lithospheric model: (1) a homogeneous configuration which is an elastic homogeneous medium, (2) a configuration which includes horizontal layers and a depth-dependent gradient in rigidity, (3) a configuration similar to the previous one (2) but in which the layers have variable
Finite-element method (FEM)
To calculate the surface displacements due to slip in the fault plane, we use TECTON (Williams and Richardson, 1991), a software package that implements a finite-element formulation based on three-dimensional hexahedral elements. A revised version of this package, now called PyLith/LithoMop, is maintained by the Computational Infrastructure for Geodynamics (CIG, 2008). We have created two meshes (Fig. 5) to account for the primary interfaces in our problem: upper/lower crust, mantle/crust, as
Co-seismic joint inversion
The results of the inversions in all the configurations fit the data as well as those in Pedersen et al. (2003) (Fig. 6). The “Iceland” configuration has the best fit but its RMS misfit is not significantly better than for the other configurations. Fig. 2c and d shows the interferometric residuals and Fig. 2e and f shows maps with the modeled displacements and the GPS measurements. Although these maps have been calculated using the configuration with horizontal layers, the other configurations
Surface slip and poro-elastic relaxation
The co-seismic inversions in the layered configurations show more slip in the uppermost 2 km of the crust than those in the homogeneous half-space configurations (Fig. 9a and b). If we follow Jónsson et al. (2003) in assuming that poro-elastic stresses have completely relaxed within a month or two of the mainshock, we can use a single, ubiquitous value for the change in Poisson's ratio. This “completely relaxed” approximation has been described in Section 4.3. Fig. 12 shows the range change due
Conclusions and perspectives
We have analyzed the sensitivity of three quantities (co-seismic slip distribution, viscosity estimates, and stress change fields) to the structural heterogeneities which vary in space within the SISZ and evolve with time during the earthquake cycle for the sequence of earthquakes that occurred in June 2000. We have reached the following conclusions:
- 1)
Structural heterogeneities play an important role. In inversions of measurements of co-seismic deformation, the slip distributions are
Note added in proof:
On May 29, 2008, another earthquake occurred in the SISZ. According to the U.S. Geological Survey, the magnitude is Mw = 6.2 and the centroid is located at N64.037, W21.092, on the west edge of the SISZ.
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, Kristín Vogfjörd, Fred Pollitz, Sandra Richwalski, Páll Einarsson and Herb Wang for helpful discussions. Grimur Björnsson kindly explained the well data graciously provided by Iceland Geosurvey and Reykjavik Energy. Kristín Vogfjörd and Ragnar
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