Ralph J. Archuleta

3D Heterogeneous Staggered-grid Finite-difference Modeling of Seismic Motion with Volume Harmonic and Arithmetic Averaging of Elastic Moduli and Densities

We analyze the problem of a heterogeneous formulation of the equation of motion and propose a new 3D fourth-order staggered-grid finite-difference (FD) scheme for modeling seismic motion and seismic-wave propagation. We first consider a 1D problem for a welded planar interface of two half-spaces. A simple physical model of the contact of two media and mathematical considerations are shown to give an averaged medium representing the contact of two media. An exact heterogeneous formulation of the equation of motion is a basis for constructing the corresponding heterogeneous FD scheme. In a much more complicated 3D problem we analyze a planar-interface contact of two isotropic media (both with interface parallel to a coordinate plane and interface in general position in the Cartesian coordinate system) and a nonplanar-interface contact of two isotropic media. Because in the latter case 21 elastic coefficients at each point are necessary to describe the averaged medium, we consider simplified boundary conditions for which the averaged medium can be described by only two elastic coefficients. Based on the simplified approach we construct the explicit heterogeneous 3D fourth-order displacement-stress FD scheme on a staggered grid with the volume harmonic averaging of the shear modulus in grid positions of the stress-tensor components, volume harmonic averaging of the bulk modulus in grid positions of the normal stress-tensor components, and volume arithmetic averaging of density in grid positions of the displacement components. Our displacement-stress FD scheme can be easily modified into the velocity-stress or displacement-velocity-stress FD schemes. The scheme allows for an arbitrary position of the material discontinuity in the spatial grid. Numerical tests for 12 configurations in four types of models show that our scheme is more accurate than the staggered-grid schemes used so far. Numerical examples also show that differences in thickness of a soft surface or interior layer smaller than one grid spacing can cause considerable changes in seismic motion. The results thus underline the importance of having a FD scheme with sufficient sensitivity to heterogeneity of the medium. Manuscript received 21 May 2001.

Fault steps and the dynamic rupture process: 2‐D numerical simulations of a spontaneously propagating shear fracture

Fault steps may have controlled the sizes of the 1966 Parkfield, 1968 Borrego Mountain, 1979 Imperial Valley, 1979 Coyote Lake and the 1987 Superstition Hills earthquakes. This project investigates the effect of fault steps of various geometries on the dynamic rupture process. We have used a finite difference code to simulate spontaneous rupture propagation in two dimensions. We employ a slip-weakening fracture criterion as the condition for rupture propagation and examine how rupture on one plane initiates rupture on parallel fault planes. The geometry of the two parallel fault planes allows for stepover widths of 0.5 to 10.0 km and overlaps of −5 to 5 km. Our results demonstrate that the spontaneous rupture on the first fault segment continues to propagate onto the second fault segment for a range of geometries for both compressional and dilational fault steps. A major difference between the compressional and dilational cases is, that a dilational step requires a longer time delay between the rupture front reaching the end of the first fault segment and initiating rupture on the second segment. Therefore our dynamic study implies that a compressional step will be jumped quickly, whereas a dilational step will cause a time delay leading to a lower apparent rupture velocity. We also find that the rupture is capable of jumping a wider dilational step than compressional step.

Three-Dimensional Simulation of a Magnitude 7.75 Earthquake on the San Andreas Fault

Simulation of 2 minutes of long-period ground motion in the Los Angeles area with the use of a three-dimensional finite-difference method on a parallel supercomputer provides an estimate of the seismic hazard from a magnitude 7.75 earthquake along the 170-kilometer section of the San Andreas fault between Tejon Pass and San Bernardino. Maximum ground velocities are predicted to occur near the fault (2.5 meters per second) and in the Los Angeles basin (1.4 meters per second) where large amplitude surface waves prolong shaking for more than 60 seconds. Simulated spectral amplitudes for some regions within the Los Angeles basin are up to 10 times larger than those at sites outside the basin at similar distances from the San Andreas fault.

Evidence for a Supershear Transient during the 2002 Denali Fault Earthquake

Elastodynamic considerations suggest that the acceleration of ruptures to supershear velocities is accompanied by the release of Rayleigh waves along the fault from the stress breakdown zone. These waves generate a secondary slip pulse trailing the rupture front, but manifest almost entirely in ground motion perpendicular to the fault in the near-source region. We construct a spontaneously propagating rupture model exhibiting these features and use it to explain ground motions recorded during the 2002 Denali fault earthquake at pump station 10, located 3 km from the fault. We show that the initial pulses on both the fault normal and fault parallel components are due to the supershear stress release on the fault, whereas the later- arriving fault normal pulses result from the trailing subshear slip pulse on the fault. Online material: MPEG movies of rupture history and ground motion.

The Three-Dimensional Dynamics of Dipping Faults

Recent two-dimensional dynamic simulations of dip-slip faulting (Niel- sen, 1998; Oglesby et al., 1998, 2000; Shi et al., 1998) have shown that the asym- metric geometry of dip-slip faults that intersect the free surface can have large effects on the dynamics of earthquake rupture. The nonvertical dip angle of such faults leads to larger motion on the footwall than the hanging wall, as well as much larger motion from thrust/reverse faults than from normal faults with the same geometry and stress magnitudes. In the present work we perform full three-dimensional simulations of thrust/reverse, normal, and strike-slip faults, and show that the same effects exist in three dimensions. Strike-slip fault motion is either in between or lower than the motion of both dip-slip faults. Additional three-dimensional effects include strong rake rotation at the free surface. The results confirm the findings of the previous studies and further elucidate the dynamic effects of the free surface on fault rupture, slip, and ground motion. They are also borne out by early analyses of the 1999 Chi- Chi (Taiwan) thrust earthquake, which displayed higher motion on the hanging wall than on the footwall, and a strong oblique component of motion at the surface.

Prediction of Broadband Ground-Motion Time Histories: Hybrid Low/High- Frequency Method with Correlated Random Source Parameters

We present a new method for calculating broadband time histories of ground motion based on a hybrid low-frequency/high-frequency approach with correlated source parameters. Using a finite-difference method we calculate low- frequency synthetics (< ∼1 Hz) in a 3D velocity structure. We also compute broadband synthetics in a 1D velocity model using a frequency-wavenumber method. The low frequencies from the 3D calculation are combined with the high frequencies from the 1D calculation by using matched filtering at a crossover frequency of 1 Hz. The source description, common to both the 1D and 3D synthetics, is based on correlated random distributions for the slip amplitude, rupture velocity, and rise time on the fault. This source description allows for the specification of source parameters independent of any a priori inversion results. In our broadband modeling we include correlation between slip amplitude, rupture velocity, and rise time, as suggested by dynamic fault modeling. The method of using correlated random source parameters is flexible and can be easily modified to adjust to our changing understanding of earthquake ruptures. A realistic attenuation model is common to both the 3D and 1D calculations that form the low- and high-frequency components of the broadband synthetics. The value of Q is a function of the local shear-wave velocity. To produce more accurate high-frequency amplitudes and durations, the 1D synthetics are corrected with a randomized, frequency-dependent radiation pattern. The 1D synthetics are further corrected for local site and nonlinear soil effects by using a 1D nonlinear propagation code and generic velocity structure appropriate for the site’s National Earthquake Hazards Reduction Program (nehrp) site classification. The entire procedure is validated by comparison with the 1994 Northridge, California, strong ground motion data set. The bias and error found here for response spectral acceleration are similar to the best results that have been published by others for the Northridge rupture.

Kinematic Inversion of the 2004 M 6.0 Parkfield Earthquake Including an Approximation to Site Effects

The 2004 M 6.0 Parkfield earthquake yielded one of the largest amounts of near-source strong ground motion seismic data ever. We invert strong-motion seismograms to obtain a model for the space-time distribution of coseismic slip on the fault. To reduce noise in the inversion, we take into account local amplifications that affect each station by using records of the 1983 M 6.5 Coalinga earthquake. Site amplification correlates well with large peak ground velocities registered during the 2004 Parkfield mainshock. The inversion for a kinematic rupture model yields a nonunique solution; we therefore analyze various rupture models that explain the data equally well. Our preferred rupture model identifies a primary zone of high slip surrounding the hypocenter, where the maximum slip is 57 cm. A secondary slip area, over which contours are not well resolved, is located northwest of the hypo- center. The rupture speed is highly heterogeneous. We infer an average rupture ve- locity of 2.8 km/sec close to the hypocenter, and of 3.3 km/sec in the secondary region of large slip to the northwest of the hypocenter. By correlation of our rupture model with both microseismicity and velocity structure, we identify six patches on the fault plane that behave in seismically distinct ways. Online material: Kinematic rupture model parameters.

Hysteretic and Dilatant Behavior of Cohesionless Soils and Their Effects on Nonlinear Site Response: Field Data Observations and Modeling

In this study we present evidence that nonlinearity can be directly observed in acceleration time histories such as those recorded at the Wildlife Refuge and Kushiro Port downhole arrays from the 1987 Superstition Hills, California, and the 1993 Kushiro-Oki, Japan, earthquakes, respectively. These accelerograms and others compiled in this study present a characteristic waveform composed of intermittent high-frequency peaks riding on a low-frequency carrier. In addition, soil amplification of the surface records is strongly observed compared to their downhole counterpart; this is contrary to the expected amplification reduction produced by the nonlinear soil behavior. Laboratory studies show that the physical mechanism that produces such phenomena is the dilatant nature of cohesionless soils, which introduces the partial recovery of the shear strength under cyclic loads. This recovery translates into the ability to produce large deformations followed by large and spiky shear stresses. The spikes observed in the acceleration records are directly related to these periods of dilatancy and generation of pore pressure. These results are significant in strong-motion seismology because these spikes produce large if not the largest acceleration. They are site related, not source related. Using the in situ observations from the Kushiro Port downhole array, we have modeled the 1993 Kushiro-Oki earthquake. The synthetic accelerograms show the development of intermittent behavior—high frequency peaks—as observed in the recorded acceleration time histories. Shear modulus degradation due to pore pressure produces large strains in the soil with large amplification in the low-frequency band of the ground motion. We also modeled data from the 1987 Superstition Hills earthquake recorded at the Wildlife Refuge station. The results show the importance of better soil characterization when pore pressure may develop and the effects of dilatancy in the understanding of nonlinear site response.

Constraining earthquake source inversions with GPS data: 1. Resolution-based removal of artifacts

[1] We present a resolution analysis of an inversion of GPS data from the 2004 Mw 6.0 Parkfield earthquake. This earthquake was recorded at thirteen 1-Hz GPS receivers, which provides for a truly coseismic data set that can be used to infer the static slip field. We find that the resolution of our inverted slip model is poor at depth and near the edges of the modeled fault plane that are far from GPS receivers. The spatial heterogeneity of the model resolution in the static field inversion leads to artifacts in poorly resolved areas of the fault plane. These artifacts look qualitatively similar to asperities commonly seen in the final slip models of earthquake source inversions, but in this inversion they are caused by a surplus of free parameters. The location of the artifacts depends on the station geometry and the assumed velocity structure. We demonstrate that a nonuniform gridding of model parameters on the fault can remove these artifacts from the inversion. We generate a nonuniform grid with a grid spacing that matches the local resolution length on the fault and show that it outperforms uniform grids, which either generate spurious structure in poorly resolved regions or lose recoverable information in well-resolved areas of the fault. In a synthetic test, the nonuniform grid correctly averages slip in poorly resolved areas of the fault while recovering small-scale structure near the surface. Finally, we present an inversion of the Parkfield GPS data set on the nonuniform grid and analyze the errors in the final model.

The 2004 Mw6.0 Parkfield, California, earthquake: Inversion of near-source ground motion using multiple data sets

On 28 September 2004, the M(w)6.0 Parkfield earthquake became the most densely recorded earthquake for near-source ground-motion. To infer the kinematic nature of this event we invert the strong-motion data. The non-linear global inversion yields slip amplitude, slip rake, average rupture velocity, and rise time over the fault. By using subsets of the data, we study the dependence of the kinematic solutions on data input. The inversions reveal that the slip amplitude was less than 0.65 m and outline two major areas of slip; one that laterally surrounds the hypocenter, preferentially extending to its SE; the other 10 to 20 km NW of the hypocenter, at a depth between 2 and 8 km. The slip amplitude we obtain for each point on the fault varies less than 0.15 m depending on data set used; the rake angle variability is less than 40 degrees.