Stochastic Modeling of California Ground Motions

Abstract

Ground-motion relations are developed for California using a stochastic simulation method that exploits the equivalence between finite-fault models and a two-corner point-source model of the earthquake spectrum. First, stochastic simulations are generated for finite-fault ruptures, in order to define the average shape and amplitude level of the radiated spectrum at near-source distances as a function of earthquake size. The length and width of the fault plane are defined based on the moment magnitude of the earthquake and modeled with an array of subfaults. The radiation from each subfault is modeled as a Brune point source using the stochastic model approach; the subfault spectrum has a single-corner frequency. An earthquake rupture initiates at a randomly chosen subfault (hypocenter), and propagates in all directions along the fault plane. A subfault is triggered when rupture propagation reaches its center. Simulations are generated for an observation point by summing the subfault time series, appropriately lagged in time. Fourier spectra are computed for records simulated at many azimuths, placed at equidistant observation points around the fault. The mean Fourier spectrum for each magnitude, at a reference nearsource distance, is used to define the shape and amplitude levels of an equivalent point-source spectrum that mimics the salient finite-fault effects. The functional form for the equivalent point-source spectrum contains two corner frequencies.Stochastic point-source simulations, using the derived two-corner source spectrum, are then performed to predict peak-ground-motion parameters and response spectra for a wide range of magnitudes and distances, for generic California sites. The stochastic ground-motion relations, given in the Appendix for rock and soil sites, are in good agreement with the empirical strong-motion database for California; the average ratio of observed to simulated amplitudes is near unity over all frequencies from 0.2 to 12 Hz. The stochastic relations agree well with empirical regression equations (e.g., Abrahamson and Silva, 1997;Sadigh et al., 1997) in the magnitude-distance ranges well represented by the data, but are better constrained at large distances, due to the use of attenuation parameters based on regional seismographic data. The stochastic ground-motion relations provide a sound basis for estimation of ground motions for earthquakes of magnitude 4 through 8, at distances from 1 to 200 km.

Simulation of Ground Motion Using the Stochastic Method

“…corner frequencies f a and f b appearing in the factors and the seismic moment, as shown in Table 3 (which also contains the scaling for the ATKINSON and SILVA (2000) model for California; a number of illustrations later in the paper use their model). The constant C in equation (5) is given by…”

“…Although it is true that nearand intermediate-field terms are lacking, in most applications the frequencies are high enough that the far-field terms dominate, even if the site is near the fault. Furthermore, the effects of a finite-fault averaged over a number of sites distributed around the fault (to average over radiation pattern and directivity effects) can be captured in several ways: 1) using the closest distance to faulting (as is done in empirically derived ground-motion prediction equations) as the source-to-site distance; 2) using a two-corner source spectrum (ATKINSON and SILVA, 2000); 3) allowing the geometrical spreading to be magnitude dependent . In addition, it should be possible to extend the method to account for specific fault-station geometries in a simple way, perhaps combining the simple computation of envelopes of acceleration (MIDORIKAWA and KOBAYASHI, 1978;COCCO and BOATWRIGHT, 1993) with statistical descriptions of the source (e.g., LOMNITZ-ADLER and LUND, 1992;HERRERO and BERNARD, 1994;JOYNER, 1995;BERNARD et al, 1996;HISADA, 2000).…”

Modelling Earthquake Ground Motions by Stochastic Method

“…Similarly, the inferred ratio of ground shaking between the mid-continental region of Central and Eastern North America and that of Mexican Gulf (of younger geological formations) has been found to be 1.5 -1.6 based on the stochastic model of Toro et al (1997). The inferred ratio between Western North American and Central and Eastern North America has been found to be in between 1.3 -1.8 based on the stochastic model of Atkinson and Silva (2000). These inferred ratios are all in broad agreement with the values of the  V and  D factors that have been recommended by CAM.…”

“…For example, the original Brune source model has been replaced by the empirical source model of Atkinson (1993) which was developed from seismogram data recorded in Central and Eastern North America to represent conditions of intraplate earthquakes. A similar model was subsequently developed by Atkinson & Silva (2000) which was developed from data recorded in Western North America to represent conditions of interplate earthquakes. A model to account for the complex spread of energy in space taking into account the wave-guide phenomenon and the dissipation of energy along the wave travel path has also been developed (Atkinson & Boore, 1995).…”

Seismic Reliability Assessment of Rocking Behaviour Under Near-Fault Excitations

“…Both the radiation spectrum and the duration of the ground motion depend on M w and R e . The particular parameters used herein are taken from the Atkinson and Silva [24] study.…”