Elastic Waves ― High Frequency Theory

This book is concerned with mathematical aspects of theory of high-frequency elastic waves, which is also known as the ray method. The foundations of elastodynamics are presented along with the basic theory of plane and spherical waves. The ray method is then described in considerable detail for bulk waves in isotropic and anisotropic media, and also for the Rayleigh waves on the surface of inhomogeneous anisotropic elastic solids. The aim of the book is to present a clear systematic description of the ray method, and at the same time to emphasize its mathematical beauty. Luckily, this beauty is usually not accompanied by complexity and mathematical ornateness.

Vassily M. Babich (born in 1930) is a leading Russian expert in mathematical theory of Diffraction and Wave Propagation. He is a co-author of ten monographs, including: Short-wavelength diffraction theory: asymptotic methods (with V.S.Buldyrev, Springer-Verlag 1991 and Alpha Science, 2007), Boundary—Layer Method in Diffraction Problems (with N.Y.Kirpichnikova) and Diffraction Theory: the Sommerfeld-Malyuzhinets Technique (with M.A.Lyalinov and V.E.Grikurov, Alpha Science, 2009). He is a head of the Laboratory of Mathematical Methods in Geophysics in St Petersburg Branch of the Steklov Institute of Mathematics, St Petersburg, Russia, and a part-time Professor at the Mathematical Faculty of St. Petersburg State University.

Aleksei P. Kiselev (born in 1948) authorized around 100 papers in Diffraction and Propagation of Waves. He worked in Seismic Exploration and in Mechanical Engineering in Leningrad—St.Petersburg. Now he is a leading researcher in the Babich’s Laboratory and a Part-time Professor at the Physical Faculty of St. Petersburg State University.