Abstract
We derive a theoretical parameter for three seismic scattering regimes where seismic wavelengths are either much shorter, similar, or much longer than the correlation length of small-scale Earth heterogeneities. We focus our analysis on the power spectral density (PSD) of the von Karman autocorrelation function (ACF), used to characterize the spatial heterogeneity of small-scale variations of elastic rock parameters that cause elastic seismicwave scattering. Our analysis is based on the assumption that the PSD of the medium heterogeneities at the corresponding wavenumber is related to the wavefield scattering. Our theoretical findings are verified by numerical simulations. The seismic scattering effects in our simulations are assessed by examining attenuation of peak ground acceleration. We discover (1) that seismic scattering is proportional to the standard deviation of velocity variations in all three regimes, (2) that scattering is inversely proportional to the correlation length for the regime where seismic wavelengths are shorter than correlation length, but directly proportional to the correlation length in the other two regimes, and (3) that scattering effects are weak due to heterogeneities characterized by a gentle decay of the von Karman ACF for regimes where seismic wavelengths are similar or much longer than the correlation length.