Stochastic deamplification of spatially varying seismic motions

Abstract

The spatial and temporal characteristics exhibited by earthquake ground motions at points below the soil surface have important implications for both deeply embedded structures and for spatially extended constructed facilities. In most cases, the characteristics of the seismic motion are known only at the surface, since it is there where most (but not all) of the historical earthquake records have been obtained. While downhole arrays can provide valuable additional information on motion statistics below the surface, it is both possible and desirable to supplement the available database with predictive computational models. With this goal in mind, this paper presents an analytical model to estimate the statistical properties of seismic motions at any point in the ground on the basis of the statistical properties obtained from records on the surface. The emphasis is on the particular cases of stationary SH-waves propagating in a multi-layered soil, and of stationary P-waves propagating in a half-space. The stochastic deconvolution model considered here is based on a formulation with matrices of spectral density functions. Together with the existing formulation based on cross-correlation matrices proposed earlier by Kausel and Pais (J. Engng Mech. Div., ASCE 113 (2) (1998) 266–277), this stochastic deconvolution technique will be referred to as the Complete Stochastic Deamplification Approach (CSDA). The results obtained show that the reduction in the intensity of shaking with embedment is more pronounced when SH-waves propagate in a stratified soil than when they propagate in a homogeneous half-space. Also, it is found that incident P-waves exhibit greater coherency than incident SH-waves, an indication that it is important to distinguish between such wave types when developing coherence models from array data.