Random Field Models of Spatially Varying Ground Motions

The spatial variation of ground motion should be carefully considered in the seismic design of buried lifeline facilities, such as pipeline systems and underground tunnels. It may also have significant influence on the seismic response of long-span bridges and widely spread tanks.

Stochastic ground motion models are established and calibrated here from strong motion array data at four sites in Shizuoka Prefecture, Japan. These adopt a stationary Gaussian random field model of each event's ground displacement in time and space. These models are used to estimate maximum relative displacements, using conventional Poisson models of temporal and spatial extremes.

Two simple variants of standard spectral models are introduced here to reduce data collection and processing needs. The first model chooses a coherence function that varies with separation length but is independent of frequency. This model can be further simplified by assuming an essentially infinite wave propagation velocity; this leads to a second model with time-space separable correlation function. In this second model, the coherence function can be alternatively viewed and estimated as the spatial correlation between simultaneous ground motions. Good agreement is found with observed relative displacements, both root mean square values and maximum values.

Finally, while the predicted relative displacements follow the observed trend with separation distance, the data show somewhat more scatter than the stochastic models imply. This scatter arises in the RMS values as well as maximum displacements, suggesting the basic limitation lies not in the Poisson model of extremes but rather in the stationary Gaussian spectral model. More general nonstationary models, both in time and space, may prove more accurate. Formulation and calibration of such models will become increasingly practical as the quantity of dense array data increases. Differences among various models may also be more evident in predicting dynamic response of large structures; such applications may be sensitive to the precise frequency spectra of relative displacements as well as their RMS values.