Theory of Elastic Wave Propagation and its Application to Scattering Problems

Elastic wave propagation applies to a wide variety of fields, including seismology, non-destructive testing, energy resource exploration, and site characterization. New applications for elastic waves are still being discovered. Theory of Elastic Wave Propagation and its Application to Scattering Problems starts from the standpoint of continuum mechanics, explaining stress and strain tensors in terms of mathematics and physics, and showing the derivation of equations for elastic wave motions, to give readers a stronger foundation. It emphasizes the importance of Green?s function for applications of the elastic wave equation to practical engineering problems and covers elastic wave propagation in a half-space, in addition to the spectral representation of Green?s function. Finally, the MUSIC algorithm is used to address inverse scattering problems.

• Offers comprehensive coverage of fundamental concepts through to contemporary applications of elastic wave propagation
• Bridges the gap between theoretical principles and practical engineering solutions

The book?s website provides the author?s software for analyzing elastic wave propagations, along with detailed answers to the problems presented, to suit graduate students across engineering and applied mathematics.

1. Introduction. 2. Basic properties of solution for elastic wave equation and representation theorem. 3. Elastic wave propagation in 3D elastic half-space. 4. Analysis of scattering problems by means of Green's functions. Appendix A. Tensor algebra for continuum mechanics. Appendix B. Fourier transform, Fourier-Hankel transform, and Dirac delta function. Appendix C. Green's function in the wavenumber domain. Appendix D. Comparison of Green's function obtained using various computational methods. Appendix E. Music algorithm for detecting location of point-like scatters. Answers. References.

Terumi Touhei is a Professor at the Tokyo University of Science, with extensive experience of teaching graduate students.