Incidence angles maximizing the Goos-Haenchen shift in seismic data analysis

TL;DR

This paper derives formulas for the Goos-Haenchen shift in seismic reflections, compares optical and seismic models, and identifies incidence angles that maximize lateral displacement at interfaces.

Contribution

It provides closed-form expressions for the Goos-Haenchen phase in seismic data and analyzes the conditions for maximum lateral displacement at interfaces.

Findings

Formulas for the Goos-Haenchen phase in seismic reflections.

Comparison between Zoeppritz equations and optical calculations.

Identification of incidence angles maximizing lateral displacement.

Abstract

In the solid/liquid and liquid/solid scenarios, for the cases in which the P and S reflected waves are represented by complex amplitudes, we give the closed formulas for the Goos-Haenchen phase from which we can then determine the lateral displacements. We compare the results of the analysis done by using the Zoeppritz equations with the calculations which appear in Optics. We also discuss under which circumstances the plane wave analysis is valid and what happens for critical incidence where divergences appear. For the liquid/solid interface, the incidence angles maximizing the lateral displacement are given as solutions of a polynomial equation.