LAUSR

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 of the von Karman autocorrelation function, used to characterize the spatial heterogeneity of small-scale variations of elastic rock parameters that cause elastic seismic wave scattering. Our theoretical findings are verified by numerical simulations. 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 autocorrelation function for regimes where seismic wavelengths are similar or much longer than the correlation length.