The solid Earth's medium is heterogeneous over a wide range of scales. Seismological observations, including envelope broadening with increasing distance from an earthquake source and the excitation of long-lasting coda waves, provide a means of investigating velocity inhomogeneities in the crust. These phenomena have been studied primarily using radiative transfer theory with random medium modelling. This book presents the mathematical foundations of scalar- and vector-wave scattering in random media, using the Born or Eikonal approximation, which are useful for understanding random inhomogeneity spectra and the scattering characteristics of the solid Earth. A step-by-step Monte Carlo simulation procedure is presented for synthesizing the propagation of energy density for impulsive radiation from a source in random media. Simulation results are then verified by comparison with analytical solutions and finite-difference simulations. Presenting the latest seismological observations and analysis techniques, this is a useful reference for graduate students and researchers in geophysics and physics.