The Importance of the Spatial Variability of Geotechnical Properties for Numerical Models of Downhole Seismic Arrays

Ground motion models at downhole seismic arrays are often inaccurate at frequencies where the upgoing wave interferes with the downgoing wave. At these frequencies, the interference of the waves creates spectral holes in the theoretical amplifications that are often not observed in the empirical transfer function (ETF). We illustrate this behavior by comparing estimates of the ETF to the plane SH-wave theoretical transfer function (TTF) within a laterally constant medium at two KiK-Net stations. One example site, where the 1D plane SH-wave formulation poorly predicts the ETF, shows that modeling the seismic properties as spatially correlated random fields can dramatically improve the fit of the TTF to the ETF. The improved fit results from the seismic scattering produced by the heterogeneities of the random field, thus diminishing the destructive interference between the upgoing and downgoing waves. The scale of fluctuation, or range parameter, of the random field controls the wavelengths of the scattered waves, and thus the frequencies where the scattering will influence the TTF.