AuthorsM. M. Noack and S. Clark
TitleAcoustic wave and eikonal equations in a transformed metric space for various types of anisotropy
AfilliationScientific Computing
Project(s)No Simula project
StatusPublished
Publication TypeJournal Article
Year of Publication2017
JournalHeliyon
Volume3
Issue3
Paginatione00260
Date PublishedJan-03-2017
PublisherElsevier
ISSN24058440
Abstract

Acoustic waves propagating in anisotropic media are important for various applications. Even though these wave phenomena do not generally occur in nature, they can be used to approximate wave motion in various physical settings. We propose a method to derive wave equations for anisotropic wave propagation by adjusting the dispersion relation according to a selected type of anisotropy and transforming it into another metric space. The proposed method allows for the derivation of acoustic wave and eikonal equations for various types of anisotropy, and generalizes anisotropy by interpreting it as a change of the metric instead of a change of velocity with direction. The presented method reduces the scope of acoustic anisotropy to a selection of a velocity or slowness surface and a tensor that describes the transformation into a new metric space. Experiments are shown for spatially dependent ellipsoidal anisotropy in homogeneous and inhomogeneous media and sandstone, which shows vertical transverse isotropy. The results demonstrate the stability and simplicity of the solution process for certain types of anisotropy and the equivalency of the solutions.

URLhttp://www.sciencedirect.com/science/article/pii/S240584401632093X
DOI10.1016/j.heliyon.2017.e00260

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