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Waves in layered media. Transl. from the 2nd Russian ed. by Robert T. Beyer. (English) Zbl 0558.73018

Applied Mathematics and Mechanics, 16. New York - London etc.: Academic Press (Harcourt Brace Jovanovich, Publishers) XIII, 503 p. (1980).
[For the 1st Russian ed. 1957 see Zbl 0112.434; the 2nd Russian ed. was published in 1973.] The main theorem of this book is the development and analysis of solutions (formal). This is done somewhat at the expense of thorough expositions of the underlying physics. The prospective reader should have a good background in Fourier integrals, complex variables (including an extended treatment of multivalued functions), special functions (to the level of Weber cylindrical function and Airy functions), WKB approximations and steepest descent methods.
In addition to the usual offerings, the book has some novel features. There is an excellent discussion on the reflection of beams of finite width. The treatment of rays in media whose properties vary in one direction is quite exhaustive and includes all the complications that can occur near caustics and turning points. Media that vary in two spatial directions are also covered.
Most of the waves are taken to have a harmonic time dependence, but some transients are also investigated. In this connection it is surprising that no mention is made of the Cagniard-de Hoop method, a technique which has been widely used in the last few decades.
The book is flawed by numerous, mostly minor, misprints. Though the reviewer would not use it as a course text (in view of the background that would be required of the students), he recommends it as an excellent addition to a research library on wave propagation.

MSC:

74J99 Waves in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids