Surface Waves in Dissipative Media: Forward and Inverse Modelling

Abstract

Scope of this chapter is to review the theory of surface wave propagation in linear, one-constituent, vertically inhomogeneous, dissipative continua. Subjects of discussion will include both forward and inverse modelling. Although the basic theory will be applicable to both Love and Rayleigh waves, most of the attention will be dedicated to Rayleigh waves due to their major relevance in the applications. After reviewing standard results of the theory of surface wave propagation in elastic and weakly dissipative media (including solution of the Lamb’s problem) using the formalism of variational calculus, the full theory of Rayleigh wave propagation is developed for arbitrarily dissipative linear viscoelastic materials. Emphasis is placed on illustrating a technique for the solution of the Rayleigh eigenproblem based on the application of Cauchy’s theorem of complex variable theory. The last section of the chapter is dedicated to illustrate the inverse problem associated with surface wave motion and its properties. The previous results obtained for the solution of the coupled forward problem are used to develop an algorithm for the joint inversion of Rayleigh dispersion and attenuation curves to determine the transversal phase velocity and quality factor of viscoelastic, layered systems. Application of the inversion algorithm is shown through examples using synthetic and real surface wave data.