On Backus average in modelling guided waves

Abstract

This thesis is a collection of five research papers. The first two are related to the Backus average. The second two are about guided waves. The fifth ties the two topics together. In the first paper we derive expressions for elasticity parameters of a homogeneous generally anisotropic medium that is long-wave-equivalent to a stack of thin generally anisotropic layers, and examine the mathematical underpinnings of the formulation. In the second paper we examine commutativity and noncommutativity of translational averages over a spatial variable and rotational averages over a symmetry group at a point. In general there is no commutativity but for weak anisotropy, which is common in near-surface seismology, there is approximate commutativity. In the third paper we review forward-modelling expressions for Love and quasi-Rayleigh waves and examine the sensitivity of Love and quasi-Rayleigh waves to model parameters. In the fourth paper we perform a Pareto Joint Inversion, using Particle Swarm Optimization, of synthetic dispersion curve data to obtain model parameters including densities, elasticity parameters, and layer thickness. In the fifth paper we tie together the two topics of Backus average and guided waves by examining the applicability of the Backus average in modelling of guided waves. As expected, the Backus average is applicable only for low frequencies and/or thin layers and the results become worse when there is a strong nonalternating vertical inhomogeneity with near-surface low-velocity layers.