The amplitude and duration of strong ground motions from hypothesized Mw = 8 subduction zone thrust earthquakes in the Puget Sound-Portland region were estimated using a semi-empirical method. The simulation procedure assumes the rupture surface may be represented by a grid of fault elements. Finite difference wave simulation in a detailed 2-D velocity structure identifies direct S and the Moho postcritical reflection as the primary components of the S wave field at horizontal distances of 0 to 150 km. Green's functions containing these two arrivals are computed with generalized ray theory in an equivalent 1-D structure for each source element-receiver propagation path. Scattering and attenuation structure are empirically modeled by the use of corrected accelerograms from Mw ∼ 7 Michoacán, Mexico, and Valparaíso, Chile, aftershocks for the fault element source functions. Different site conditions are empirically included in the simulation procedure by using empirical source functions recorded on rock and soil sites. Spatial variations in slip on the fault (asperities) are introduced by weighting the fault elements. The technique has been validated for large subduction zone earthquakes by modeling acceleration time histories and response spectra from the 1985 Michoacán (Mw = 8.0) and Valparaíso (Mw = 8.0) main shocks (Somerville et al., 1991).

Fault models for the Puget Sound and Portland regions and seismic velocity structure models have been adapted from published regional studies. Uncertainty in the location of the asperities on the fault surface results in a large degree of uncertainty in the simulated ground motions at a given site. If distance is defined as the distance to the closest asperity, then the variability in the ground motions is reduced, indicating that this uncertainty can be lessened by constraining the depth of the asperity. The ground motion estimates are relatively insensitive to the difference in fault dip between the Puget Sound and Portland fault models. The attenuation of peak acceleration with distance r from the fault asperity for a Mw = 8 subduction earthquake is given by
where s is a site term equal to 0 for rock and 1 for soil. When distance r is the distance to the fault plane, the attenuation relation is

Formal estimates of uncertainty in the calculated ground motions have been obtained by estimating both parametric uncertainty (from the range of source models of hypothesized Cascadia subduction earthquakes) and modeling and random uncertainty (from the misfit between recorded and simulated ground motions of the 1985 Michoacán and Valparaíso earthquakes). For periods less than 1 sec, the estimated response spectral velocities on soil sites in the Seattle-Olympia region are about twice those recorded during the 1949 Olympia and 1965 Seattle Wadati-Benioff zone earthquakes, and the durations of strong motion on rock sites are significantly longer (45 to 60 sec versus 10 to 15 sec).

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