Born Approximation for Wave Scattering in Inhomogeneous Media

Abstract

As shown by well-log data introduced in Chapter 2, the earth’s lithosphere can be characterized as a randomly inhomogeneous elastic medium using an autocorrelation function (ACF). Characteristics of seismograms discussed in Chapter 2 support the view of treating wave propagation in the earth with a scattering approach. The phenomenological approaches discussed in Chapter 3 provide reasonable models of some features of the observed seismograms. We will now present the mathematical basis for the study of wave propagation and/or scattering in inhomogeneous media based on the first-order perturbation method known as the Born approximation. We will begin with the scalar wave equation and investigate the Born approximation for a plane wave incident on a localized inhomogeneity. Then we will present the concepts of an ensemble of random media and the stochastic average. Finally, we will study scattering of elastic vector waves in inhomogeneous elastic media.