skip to main content

Title: Earthquake Stress Drop for a Circular Crack in an Anisotropic Medium
ABSTRACT The circular-crack model has been widely used in seismology to infer earthquake stress drop. A common assumption is that the background medium is isotropic, although many earthquakes occur in geologically anisotropic settings. In this article, we study the effect of anisotropy on stress drop for a circular crack model and present explicit formalism in both static and kinematic cases. In the static case, we obtain the relationship between stress drop and slip for a circular crack model in an arbitrarily anisotropic medium. Special attention is given to the transversely isotropic (TI) medium. The static formalism is useful in understanding stress drop, but not all quantities are observables. Therefore, we resort to the kinematic case, from which we can infer stress drop using recorded far-field body waves. In the kinematic case, we assume that the crack ruptures circularly and reaches the final displacement determined by the static solutions. The far-field waveforms show that the corner frequency will change with different anisotropic parameters. Finally, we calculate the stress drops for cracks in isotropic and anisotropic media using the far-field waveforms. We find that in an isotropic medium, only shear stress acting on the crack surface contributes to shear slip. However, in a TI medium, if the anisotropy symmetry axis is not perpendicular or parallel to the crack surface, a normal stress (normal to the crack surface) can produce a shear slip. In calculating stress drop for an earthquake in an anisotropic medium using far-field body waves, a large error may be introduced if we ignore the possible anisotropy in the inversion. For a TI medium with about 18% anisotropy, the misfit of inferred stress drop could be up to 41%. Considering the anisotropic information, we can further improve the accuracy of stress-drop inversion.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Bulletin of the Seismological Society of America
Page Range / eLocation ID:
297 to 311
Medium: X
Sponsoring Org:
National Science Foundation
More Like this

    Accurate synthetic seismic wavefields can now be computed in 3-D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because high-amplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography.

    This can be addressed by redefining the cost-function and computing the cross-correlation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3-D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility of designing a weighting scheme to bring out the contribution of overtones and body waves. It also makes it possible to balance the contributions of frequently sampled paths versus rarely sampled ones, as in more conventional tomography.

    Here we present the results of proof of concept testing of such an approach for a synthetic 3-component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3-D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked time-series, starting from a 1-D model, using source stacked waveforms and station-pair cross-correlations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of cross-talk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function.

    The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and trade-offs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on single-event wavefield computations.

    more » « less
  2. Abstract

    Mature faults with large cumulative slip often separate rocks with dissimilar elastic properties and show asymmetric damage distribution. Elastic contrast across such bimaterial faults can significantly modify various aspects of earthquake rupture dynamics, including normal stress variations, rupture propagation direction, distribution of ground motions, and evolution of off‐fault damage. Thus, analyzing elastic contrasts of bimaterial faults is important for understanding earthquake physics and related hazard potential. The effect of elastic contrast between isotropic materials on rupture dynamics is relatively well studied. However, most fault rocks are elastically anisotropic, and little is known about how the anisotropy affects rupture dynamics. We examine microstructures of the Sandhill Corner shear zone, which separates quartzofeldspathic rock and micaceous schist with wider and narrower damage zones, respectively. This shear zone is part of the Norumbega fault system, a Paleozoic, large‐displacement, seismogenic, strike‐slip fault system exhumed from middle crustal depths. We calculate elastic properties and seismic wave speeds of elastically anisotropic rocks from each unit having different proportions of mica grains aligned sub‐parallel to the fault. Our findings show that the horizontally polarized shear wave propagating parallel to the bimaterial fault (with fault‐normal particle motion) is the slowest owing to the fault‐normal compliance and therefore may be important in determining the elastic contrast that affects rupture dynamics in anisotropic media. Following results from subshear rupture propagation models in isotropic media, our results are consistent with ruptures preferentially propagated in the slip direction of the schist, which has the slower horizontal shear wave and larger fault‐normal compliance.

    more » « less
  3. The recent 2019 Ridgecrest earthquake sequence in Southern California jostled the seismological community by revealing a complex and cascading foreshock series that culminated in a M7.1 mainshock. But the central Garlock fault, despite being located immediately south of this sequence, did not coseismically fail. Instead, the Garlock fault underwent post-seismic creep and exhibited a sizeable earthquake swarm. The dynamic details of the rupture process during the mainshock is largely unknown, as is the amount of stress needed to bring the Garlock fault to failure. We present an integrated view of how stresses changed on the Garlock fault during and after the mainshock using a combination of tools including kinematic slip inversion, Coulomb stress change, and dynamic rupture modeling. We show that positive Coulomb stress changes cannot easily explain observed aftershock patterns on the Garlock fault, but are consistent with where creep was documented on the central Garlock fault section. Our dynamic model is able to reproduce the main slip asperities and kinematically estimated rupture speeds (≤ 2 km/s) during the mainshock, and suggests the temporal changes in normal and shear stress on the Garlock fault were greatest near the end of rupture. The largest static and dynamic stress changes on the Garlock fault we observe from our models coincide with the creeping region, suggesting that positive stress perturbations could have caused this during or after the mainshock rupture. This analysis of near-field stress change evolution gives insight into how the Ridgecrest sequence influenced the local stress field of the northernmost Eastern California Shear Zone. 
    more » « less
  4. null (Ed.)
    Two types of surface wave anisotropy are observed regularly by seismologists but are only rarely interpreted jointly: apparent radial anisotropy, which is the difference in propagation speed between horizontally and vertically polarized waves inferred from Love and Rayleigh waves, and apparent azimuthal anisotropy, which is the directional dependence of surface wave speeds (usually Rayleigh waves). We show that a new data set of Love and Rayleigh wave isotropic phase speeds and Rayleigh wave azimuthal anisotropy observed within and surrounding eastern Tibet can be explained simultaneously by modeling the crust as a depth-dependent tilted hexagonally symmetric (THS) medium. We specify the THS medium with depth-dependent hexagonally symmetric elastic tensors tilted and rotated through dip and strike angles and estimate these quantities using a Bayesian Monte Carlo inversion to produce a 3-D model of the crust and uppermost mantle on a 0.5° × 0.5° spatial grid. In the interior of eastern Tibet and in the Yunnan-Guizhou plateau, we infer a steeply dipping THS upper crustal medium overlying a shallowly dipping THS medium in the middle-to-lower crust. Such vertical stratification of anisotropy may reflect a brittle to ductile transition in which shallow fractures and faults control upper crustal anisotropy and the crystal-preferred orientation of anisotropic (perhaps micaceous) minerals governs the anisotropy of the deeper crust. In contrast, near the periphery of the Tibetan Plateau the anisotropic medium is steeply dipping throughout the entire crust, which may be caused by the reorientation of the symmetry axes of deeper crustal anisotropic minerals as crustal flows are rotated near the borders of Tibet. 
    more » « less
  5. null (Ed.)
    SUMMARY Earthquake ruptures are generally considered to be cracks that propagate as fracture or frictional slip on pre-existing faults. Crack models have been used to describe the spatial distribution of fault offset and the associated static stress changes along a fault, and have implications for friction evolution and the underlying physics of rupture processes. However, field measurements that could help refine idealized crack models are rare. Here, we describe large-scale laboratory earthquake experiments, where all rupture processes were contained within a 3-m long saw-cut granite fault, and we propose an analytical crack model that fits our measurements. Similar to natural earthquakes, laboratory measurements show coseismic slip that gradually tapers near the rupture tips. Measured stress changes show roughly constant stress drop in the centre of the ruptured region, a maximum stress increase near the rupture tips and a smooth transition in between, in a region we describe as the earthquake arrest zone. The proposed model generalizes the widely used elliptical crack model by adding gradually tapered slip at the ends of the rupture. Different from the cohesive zone described by fracture mechanics, we propose that the transition in stress changes and the corresponding linear taper observed in the earthquake arrest zone are the result of rupture termination conditions primarily controlled by the initial stress distribution. It is the heterogeneous initial stress distribution that controls the arrest of laboratory earthquakes, and the features of static stress changes. We also performed dynamic rupture simulations that confirm how arrest conditions can affect slip taper and static stress changes. If applicable to larger natural earthquakes, this distinction between an earthquake arrest zone (that depends on stress conditions) and a cohesive zone (that depends primarily on strength evolution) has important implications for how seismic observations of earthquake fracture energy should be interpreted. 
    more » « less