Elastic Wave Propagation in Irregular Structures

Wave propagation problems involving irregular structures rarely have exact solutions. However, the most important features of such problems can be often obtained from appropriate approximate solutions. In Chapter 1, we consider refraction problems involving dipping layers. The Cagniard-de Hoop method for flat structures is extended to such problems to evaluate the non-geometric effects of critical reflection and tunneling. It is shown that the character of the dispersion is strongly affected by even relatively shallow angle dips. In Chapter 2, we consider teleseismic problems involving curved interfaces. An approximation theory, which we name "Glorified Optics", is developed to evaluate the effects of focusing and triplication due to the local curvature along such interfaces. Seismograms are dramatically complicated by those interference effects. The correla­tion between such complexity and the subsurface structure can be explicitly conceived through Glorified Optics. In Chapter 3, we perform an independent check on these approxima­tion theories by using finite element methods. The excellent agree­ment confirms the validity of our approximations. The concepts, methods and results presented in this thesis appear to be helpful in opening a new dimension in the fields of seismic modelling, inversion and prospecting.