Wave propagation in anisotropic media applied to imaging

This article is the second and last of a series. It aims to present didactically the development of numerical formulations for wave propagation problems and their application to the imaging of structures using seismic data, specifically in simple anisotropic media. Hence, it is developed equations in which the medium is treated as elastic, which suffers deformations when subjected to stresses, returning to its equilibrium configuration when these cease to exist. Both isotropic and anisotropic materials are treated, and the “acoustic” equations for the case of media with vertical transverse symetric, showing that these equations reduces to acoustic wave equation as anisotropic parameters are null. Simple numerical solutions of the anisotropic equations are discused, as well as their application to the problem of mapping geological structures, characterized by discontinuity of physical properties. A synthetic example is implemented and discussed in detail, demonstrating that correct anisotropy treatment substantially improves the final image.

Keywords
Waves; elastic media; anisotropy; finite-diference method; imaging