Scale And Frequency Dependence Of Reflection And Transmission Coefficients

Abstract

Well-logs show that heterogeneities occur at many different spatial scales. In this paper, we want to characterize how waves are affected by these heterogeneities, and we study how reflection and transmission coefficients depend on temporal frequency and spatial scale. We use wavelet transformations to filter certain spatial scales from the velocity logs. The scale-filtered logs serve as input for a numerical layer-stack model to calculate reflection and transmission coefficients as functions of frequency and scale. We find that transmission coefficients are largely independent of frequency or scale. They depend mostly on average slowness. Contrarily, reflection coefficients are extremely sensitive to the perturbations of the slownesses, even at low frequencies.