The book presents a consistent treatment of the seismic ray method, applicable to high-frequency seismic body waves propagating in complex 3-D laterally varying isotropic or anisotropic layered and block structures. The seismic ray method is based on the asymptotic high-frequency solution of the elastodynamic equation. For finite frequencies, the ray method is not exact, but it is only approximate. Its accuracy, however, is sufficient to solve many 3-D wave propagation problems of practical interest in seismology and seismic exploration, which can hardly be treated by any other means. Moreover, the computed rays may be used as a framework for the application of various more sophisticated methods.

In the seismic ray method, the high-frequency wavefield in a complex structure can be expanded into contributions, which propagate along rays and are called elementary waves. Individual elementary waves correspond, for example, to direct P and S waves, reflected waves, various multiply reflected/transmitted waves, and converted waves. A big advantage of the ray method is that the elementary waves may be handled independently. In the book, equations controlling the rays, travel times, amplitudes, Green functions, seismograms, and particle ground motions of the elementary waves are derived, and the relevant numerical algorithms are developed and discussed.

In general, the theoretical treatment in the book starts with a relatively simple problem in which the main ideas of the solution are easier to explain. Only then are the more complex problems dealt with. That is one of the reasons why pressure waves in fluid models are also discussed. All the derivations for pressure waves in fluid media are simple, clear, and comprehensible.