11R61. Seismic Ray Theory. - V Cerveny (Charles Univ, Praha, Czech Republic). Cambridge UP, Cambridge, UK. 2001. 713 pp. ISBN 0-521-36671-2. $95.00.

Reviewed by JG Berryman (Geophys and Global Security Div, LLNL, 7000 East Ave, Mail Stop L-200, Livermore CA 94550).

Vlastislav Cerveny has been a leader in the area of seismic ray theory for about 40 years. He has received various international awards for his work and has co-authored two previous books on aspects of the same topic. The present book appears to be designed to serve as a fairly comprehensive reference book on ray theory, with the main applications being elastodynamics and seismology. In the Introduction, the author clarifies what will and will not be covered in the text. The book aims to cover high-frequency asymptotic methods, and in particular, the emphasis is almost entirely on the zeroth-order terms in the well-known high-frequency expansion. Other approaches, such as variational methods and computational methods that give direct numerical solutions of the elastodynamic equations, are specifically excluded from consideration.

One distinction which is commonly made between the kinematic and the dynamic parts of the seismic ray method is made here early on and is used to organize the material discussed. The kinematics of ray theory consists of finding the seismic ray paths, wavefronts, and the corresponding traveltimes. The dynamics of ray theory consists of finding the amplitudes of the displacements along the ray paths, and also of computing in some cases synthetic seismograms and even ground motion diagrams associated with the rays. Some of these computations can be elementary in media composed of homogeneous layers of elastic material, but the book seeks to describe and solve the harder problems of 3D heterogeneous elastic media. In such media, it is generally difficult to separate compressional and shear modes in a simple way, and it is, at least in part, this complication that drives many of the choices made about what to present in the book.

Following the brief introductory chapter, the book is organized into five topics, with a single chapter devoted to each topic. These topics are 1) the equations of elastodynamics, 2) seismic rays and traveltimes, 3) dynamic ray tracing and paraxial ray methods, 4) ray amplitudes, and 5) ray-based synthetic seismograms. Two chapters are thus devoted to kinematics and three to dynamics. The book ends with a short appendix on Fourier transforms.

The level of exposition—starting in Chapter 2 and remaining quite consistent throughout—makes extensive use of matrix and tensor notation. This level is appropriate for mathematically well-prepared undergraduates and graduate students in engineering, applied mathematics, physics, and seismology. For use as an advanced textbook in a graduate-level course, it would probably require supplementation with handouts of some of the most recent work that is not covered in depth here.

To get a feeling for how the book might be used, this reviewer looked for various topics, some standard and some more recent, in the subject index and also directly in the text. This reviewer found Zoppritz equations discussed briefly, but no mention of Haskell matrices. Caustics, weak elastic anisotropy, random media, and parabolic equations are all briefly mentioned, while a more extensive discussion of Gaussian beams is presented. Eikonal equations solvers based on finite difference approximations are mentioned, as are fast marching methods, but the connection between fast marching and level set methods is not discussed. Of these two topics, neither fast marching nor level sets is listed in the subject index.

As might be expected, the strongest contributions of the book are in areas of the author’s own research publications. These topics include perturbation methods for traveltimes, synthetic body wave seismograms, Gaussian beams, and ray tracing methods for laterally varying layered media. For his own research, this reviewer thought the long section (5.4) on ray amplitudes in elastic anisotropic structures seemed especially comprehensive and should provide a valuable resource in future work.

This reviewer recommends that libraries covering wave propagation of all types, and especially those related to seismic waves and geophysical imaging, should have a copy of Seismic Ray Theory available for their patrons. Students and individual researchers doing computations involving seismic waves will probably also want to have a personal copy for frequent use, both because of the exposition in those sections where details are stressed and because of the many pointers to the literature where expansion can be found on issues raised, but not discussed at length in the text. There is also an extensive bibliography (having more than 800 references) to the literature. This bibliography is not truly comprehensive, but presumably no single book could be comprehensive in covering a topic as broad and heavily studied as this one. The present reference listing will nevertheless be very useful to many researchers.