Project

Backus averaging and surface waves in transversely isotropic layered media.

Goal: I'm working on a Ph.D. doing forward modelling and joint inversion of Love and quasi-Rayleigh (like Rayleigh only in layered media) waves, initially for isotropic media but eventually for layered transversely isotropic media, including the case where one of the layers is a Backus averaged equivalent medium of a series of thin isotropic or transversely isotropic layers.

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David Dalton
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We examine the sensitivity of the Love and the quasi-Rayleigh waves to model parameters. Both waves are guided waves that propagate in the same model of an elastic layer above an elastic halfspace. We study their dispersion curves without any simplifying assumptions, beyond the standard approach of elasticity theory in isotropic media. We examine the sensitivity of both waves to elasticity parameters, frequency and layer thickness, for varying frequency and different modes. In the case of Love waves, we derive and plot the absolute value of a dimensionless sensitivity coefficient in terms of partial derivatives, and perform an analysis to find the optimum frequency for determining the layer thickness. For a coherency of the background information, we briefly review the Love-wave dispersion relation and provide details of the less common derivation of the quasi-Rayleigh relation in an appendix. We compare that derivation to past results in the literature, finding certain discrepancies among them.
Dalton and Slawinski (2016) show that, in general, the Backus (1962) average and the Gazis et al. (1963) average do not commute. Herein, we examine the extent of this noncommutativity. We illustrate numerically that the extent of noncommutativity is a function of the strength of anisotropy. The averages nearly commute in the case of weak anisotropy.
David Dalton
added a project goal
I'm working on a Ph.D. doing forward modelling and joint inversion of Love and quasi-Rayleigh (like Rayleigh only in layered media) waves, initially for isotropic media but eventually for layered transversely isotropic media, including the case where one of the layers is a Backus averaged equivalent medium of a series of thin isotropic or transversely isotropic layers.