Attenuation of short period seismic waves due to scattering

Abstract

We point out first the inadequacy of the two widely used approaches in calculating the amplitude attenuation of seismic waves in a random medium, the formulation of mean field attenuation and that of the scattering coefficient under the single‐scattering approximation. Then we calculate the average amplitude attenuation due to scattering in an infinite random slab. We slice the random slab into layers of thickness a correlation length and use the Born approximation for each slice to calculate the scattered field. To include the effect of multiple scattering, we take the back‐halfspace integration of the scattered energy as the energy loss and do energy correction for each successive slice. Taking scalar wave approximation for seismic waves, we get a formula for average amplitude attenuation essentially valid for high frequency range (ka»1). The attenuation depends strongly on the form of correlation function of the random inhomogeneities. We derive the formulas for Gaussian, exponential and Von Kárman correlation functions. The frequency dependence of attenuation by our formulation agrees well with experiments.