Waves in inhomogeneous media

In this thesis we study wave propagation in inhomogeneous media. Examples of the classical (massless) waves we consider are acoustic waves (sound) and electromagnetic waves (light, for example). Interaction with inhomogeneities embedded in a reference medium alter the propagation direction, velocity and amplitude of waves. We describe the properties of these (multiple) scattering processes to answer some questions in the field of waves in complex media, both on a fundamental level and from the point of view of applications. In the introductory chapter we motivate our research by discussing two applications for which studying wave propagation in inhomogeneous media is essential, namely seismic exploration to image the earth's subsurface, and diffuse optical tomography (DOT) with near infrared (NIR) light for medical imaging purposes. Chapter 2 discusses propagation of monochromatic waves in one-, two- and three-dimensional (3D) inhomogeneous media. Here, the complex medium is an acoustic reference medium with many embedded, similar, spherical scatterers with a finite radius smaller than the wavelength. In chapter 3 we study boundary conditions between large scattering objects when wave energy propagation is primarily diffuse. These boundary conditions are applied to a diffuse imaging problem in chapter 4. The fifth and final chapter of this thesis deals with a numerical method, the recursive Green function technique, to solve the classical wave equation in disordered 2D media. We use this method to study the arrival time and amplitudes of head waves from rough interfaces