Kim B. Olsen

Stress-Breakdown Time and Slip-Weakening Distance Inferred from Slip-Velocity Functions on Earthquake Faults

We estimate the critical slip-weakening distance on earthquake faults by using a new approach, which is independent of the estimate of fracture energy or radiated seismic energy. The approach is to find a physically based relation between the breakdown time of shear stress Tb, the time of peak slip-velocity Tpv, and the slip-weakening distance Dc, from the time histories of shear stress, slip, and slip velocity at each point on the fault, which can be obtained from dynamic rupture calculations using a simple slip-weakening friction law. Numerical calculations are carried out for a dynamic shear crack propagating either spontaneously or at a fixed rupture velocity on a vertical fault located in a 3D half-space and a more realistic horizontally layered structure, with finite-difference schemes. The results show that Tpv is well correlated with Tb for faults even with a heterogeneous stress-drop dis- tribution, except at locations near strong barriers and the fault edges. We also inves- tigate this relation for different types of slip-weakening behavior. We have applied the method to two recent, strike-slip earthquakes in western Japan, the 2000 Tottori and the 1995 Kobe events. We integrated the slip-velocity functions on the vertical fault obtained from kinematic waveform inversion of strong- motion and teleseismic records from the arrival time of rupture Tr to the time of the peak-slip velocity Tpv, and we then corrected the slip obtained at Tpv for the errors expected from the dynamic calculations. It was found that the slip-weakening dis- tance D c estimated in the frequency window between 0.05 and 0.5 Hz ranges between 40 and 90 cm on the two earthquake faults. However, if we consider the limited frequency resolution of the observed waveforms, probable time errors in the slip- velocity functions obtained from kinematic inversion, and the uncertainty of the slip- weakening behavior, the above estimates may be those located between the minimum resolvable limit and the upper bound of their real values. The estimated Dc values do not necessarily seem to indicate larger values in the shallower part and smaller values in the deeper part of the fault, but rather a spatially heterogeneous distribution that appears to be dependent on the local maximum slip. This possible dependence might be interpreted by the frictional properties of the fault such as the degree of roughness or the thickness of gouge layers, in addition to stress heterogeneities.

Fréchet Kernels for Imaging Regional Earth Structure Based on Three-Dimensional Reference Models

High-resolution images of three-dimensional (3D) seismicstructuresare not only of scientific interest, but also of practical importance in predicting strong ground motion after large earthquakes. Given the source and station distributions, resolutions in current regional seismic tomography studies have been limited by two types of simplifying practices: the adoption of high-frequency approximations such as the ray theory and the use of one-dimensional (1D) reference (starting) models. We have developed a new approach to compute accurate finite-frequency 3D Frechet (sensitivity) kernels of observed travel time and amplitude anomalies relative to 3D reference models. In our approach, we use a fourth-order staggered-grid finite- difference method to model the seismic-wave propagation in 3D media, and the reciprocity property of the Greens tensor to reduce the number of numerical simu- lations. This approach accounts for the perturbations in compressional- and shear- wave speeds in the same way, leading to a capability of inverting for the shear-wave speed directly from seismic data. The algorithm is readily parallelized to allow for realistic regional high-resolution 3D tomography inversions. We have implemented the algorithm for the Southern California Earthquake Center (SCEC) Community Velocity Model, SCEC CVM 3.0, a complex 3D model for Southern California in- cluding a number of sedimentary basins. By enabling the inversion of 3D structural perturbations to 3D reference models, our approach provides a practical means of iteratively solving the nonlinear regional tomography problems.

ShakeOut-D: Ground motion estimates using an ensemble of large earthquakes on the southern San Andreas fault with spontaneous rupture propagation

[1]xa0We simulate ground motion in southern California from an ensemble of 7 spontaneous rupture models of large (Mw7.8) northwest-propagating earthquakes on the southern San Andreas fault (ShakeOut-D). Compared to long-period spectral accelerations from the Next Generation Attenuation (NGA) empirical relations, ShakeOut-D predicts similar average rock-site values (i.e., within roughly their epistemic uncertainty), but significantly larger values in Los Angeles and Ventura basins due to wave-guide focusing effects. The ShakeOut-D ground motion predictions differ from those of a kinematically parameterized, geometrically similar, scenario rupture: (1) the kinematic rock-site predictions depart significantly from the common distance-attenuation trend of the NGA and ShakeOut-D results and (2) ShakeOut-D predictions of long-period spectral acceleration within the basins of the greater Los Angeles area are lower by factors of 2–3 than the corresponding kinematic predictions. We attribute these differences to a less coherent wavefield excited by the complex rupture paths of the ShakeOut-D sources.

Model for Basin Effects on Long-Period Response Spectra in Southern California

We propose a model for the effect of sedimentary basin depth on long-period response spectra. The model is based on the analysis of 3-D numerical simulations (finite element and finite difference) of long-period (2–10 s) ground motions for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin region. We find depth to the 1.5 km/s S-wave velocity isosurface to be a suitable predictor variable, and also present alternative versions of the model based on depths to the 1.0 and 2.5 km/s isosurfaces. The resulting mean basin-depth effect is period dependent, and both smoother (as a function of period and depth) and higher in amplitude than predictions from local 1-D models. The main requirement for the use of the results in construction of attenuation relationships is determining the extent to which the basin effect, as defined and quantified in this study, is already accounted for implicitly in existing attenuation relationships, through (1) departures of the average “rock” site from our idealized reference model, and (2) correlation of basin depth with other predictor variables (such as Vs30).

TeraShake2: Spontaneous Rupture Simulations of Mw 7.7 Earthquakes on the Southern San Andreas Fault

Abstract Previous numerical simulations (TeraShake1) of large ( M w 7.7) southern San Andreas fault earthquakes predicted localized areas of strong amplification in the Los Angeles area associated with directivity and wave-guide effects from northwestward-propagating rupture scenarios. The TeraShake1 source was derived from inversions of the 2002 M w 7.9 Denali, Alaska, earthquake. That source was relatively smooth in its slip distribution and rupture characteristics, owing both to resolution limits of the inversions and simplifications imposed by the kinematic parameterization. New simulations (TeraShake2), with a more complex source derived from spontaneous rupture modeling with small-scale stress-drop heterogeneity, predict a similar spatial pattern of peak ground velocity (PGV), but with the PGV extremes decreased by factors of 2–3 relative to TeraShake1. The TeraShake2 source excites a less coherent wave field, with reduced along-strike directivity accompanied by streaks of elevated ground motion extending away from the fault trace. The source complexity entails abrupt changes in the direction and speed of rupture correlated to changes in slip-velocity amplitude and waveform, features that might prove challenging to capture in a purely kinematic parameterization. Despite the reduced PGV extremes, northwest-rupturing TeraShake2 simulations still predict entrainment by basin structure of a strong directivity pulse, with PGVs in Los Angeles and San Gabriel basins that are much higher than predicted by empirical methods. Significant areas of those basins have predicted PGV above the 2% probability of exceedance (POE) level relative to current attenuation relationships (even when the latter includes a site term to account for local sediment depth), and wave-guide focusing produces localized areas with PGV at roughly 0.1%–0.2% POE (about a factor of 4.5 above the median). In contrast, at rock sites in the 0–100-km distance range, the median TeraShake2 PGVs are in very close agreement with the median empirical prediction, and extremes nowhere reach the 2% POE level. The rock-site agreement lends credibility to some of our source-modeling assumptions, including overall stress-drop level and the manner in which we assigned dynamic parameters to represent the mechanical weakness of near-surface material. Future efforts should focus on validating and refining these findings, assessing their probabilities of occurrence relative to alternative rupture scenarios for the southern San Andreas fault, and incorporating them into seismic hazard estimation for southern California.

Hybrid Broadband Ground-Motion Simulations: Combining Long-Period Deterministic Synthetics with High-Frequency Multiple S-to-S Backscattering

We present a new approach for computing broadband (0–10 Hz) synthetic seismograms by combining high-frequency (HF) scattering with low-frequency (LF) deterministic seismograms, considering finite-fault earthquake rupture models embedded in 3D earth structure. Site-specific HF-scattering Green’s functions for a heterogeneous medium with uniformly distributed random isotropic scatterers are convolved with a source-time function that characterizes the temporal evolution of the rupture process. These scatterograms are then reconciled with the LF-deterministic waveforms using a frequency-domain optimization to match both amplitude and phase spectra around the target intersection frequency. The scattering parameters of the medium, scattering attenuation ηs, intrinsic attenuation ηi, and site-kappa, as well as frequency-dependent attenuation, determine waveform and spectral character of the HF-synthetics and thus affect the hybrid broadband seismograms. Applying our methodology to the 1994 Northridge earthquake and validating against near-field recordings at 24 sites, we find that our technique provides realistic broadband waveforms and consistently reproduces LF ground-motion intensities for two independent source descriptions. The least biased results, compared to recorded strong-motion data, are obtained after applying a frequency-dependent site-amplification factor to the broadband simulations. This innovative hybrid ground-motion simulation approach, applicable to any arbitrarily complex earthquake source model, is well suited for seismic hazard analysis and ground-motion estimation.

Hybrid Broadband Ground-Motion Simulations: Combining Long-Period Deterministic Synthetics with High-Frequency Multiple S-to-S BackscatteringHybrid Broadband Ground-Motion Simulations: Combining Deterministic Synthetics with Backscattering

Abstract We present a new approach for computing broadband (0–10xa0Hz) synthetic seismograms by combining high-frequency (HF) scattering with low-frequency (LF) deterministic seismograms, considering finite-fault earthquake rupture models embedded in 3D earth structure. Site-specific HF-scattering Green’s functions for a heterogeneous medium with uniformly distributed random isotropic scatterers are convolved with a source-time function that characterizes the temporal evolution of the rupture process. These scatterograms are then reconciled with the LF-deterministic waveforms using a frequency-domain optimization to match both amplitude and phase spectra around the target intersection frequency. The scattering parameters of the medium, scattering attenuation η s , intrinsic attenuation η i , and site-kappa, as well as frequency-dependent attenuation, determine waveform and spectral character of the HF-synthetics and thus affect the hybrid broadband seismograms. Applying our methodology to the 1994 Northridge earthquake and validating against near-field recordings at 24 sites, we find that our technique provides realistic broadband waveforms and consistently reproduces LF ground-motion intensities for two independent source descriptions. The least biased results, compared to recorded strong-motion data, are obtained after applying a frequency-dependent site-amplification factor to the broadband simulations. This innovative hybrid ground-motion simulation approach, applicable to any arbitrarily complex earthquake source model, is well suited for seismic hazard analysis and ground-motion estimation.

Estimation of the Critical Slip-Weakening Distance: Theoretical Background

It has been shown that a trade-off exists between estimates of the break- down strength drop and the critical slip-weakening distance (e.g., Guatteri and Spu- dich, 2000). For this reason, only the fracture energy, proportional to these two parameters, may be estimated from waveform modeling. However, Mikumo et al. (2003) proposed a new technique to estimate the slip-weakening distance of earth- quakes, separate from the fracture energy. For this method to be valid, the peak slip- velocity time must be close to the stress breakdown time. Here we explain the theo- retical background of this assumption and clarify the limitations of this technique using numerical simulations based on the boundary integral equation method. The theoretical analysis using the boundary integral equation and some numerical tests indicates that a rather smooth rupture process and relatively sharp change in stress at the stress breakdown time in the slip-weakening curve ensure the validity of the method.

Nonlinear dynamic rupture inversion of the 2000 Western Tottori, Japan, earthquake

[1]xa0We have developed a systematic nonlinear inversion method for estimating rupture propagation and the underlying dynamic parameters for large historical earthquakes. The rupture modeling is carried out using a three-dimensional finite-difference method, and the inversion is implemented by a neighbourhood algorithm, minimizing the misfit between computed and observed near-fault seismograms. We test the method by estimating the stress drop within 32 regions on the causative fault for the 2000 magnitude 6.6 Western Tottori, Japan, earthquake. While the dynamic models show both similarities and differences with the conventional kinematic models, our method provides an ensemble of physically-correct models with plausible rupture propagation for the earthquake.

Expected seismic shaking in Los Angeles reduced by San Andreas fault zone plasticity

Computer simulations of large (M ≥ 7.8) earthquakes rupturing the southern San Andreas Fault from SE to NW (e.g., ShakeOut, widely used for earthquake drills) have predicted strong long-period ground motions in the densely populated Los Angeles Basin due to channeling of waves through a series of interconnected sedimentary basins. Recently, the importance of this waveguide amplification effect for seismic shaking in the Los Angeles Basin has also been confirmed from observations of the ambient seismic field. By simulating the ShakeOut earthquake scenario (based on a kinematic source description) for a medium governed by Drucker-Prager plasticity, we show that nonlinear material behavior could reduce the earlier predictions of large long-period ground motions in the Los Angeles Basin by up to 70% as compared to viscoelastic solutions. These reductions are primarily due to yielding near the fault, although yielding may also occur in the shallow low-velocity deposits of the Los Angeles Basin if cohesions are close to zero. Fault zone plasticity remains important even for conservative values of cohesions, suggesting that current simulations assuming a linear response of rocks are overpredicting ground motions during future large earthquakes on the southern San Andreas Fault.