Horizontal and Vertical Regularity of Elastic Wave Geometry
Joonas Ilmavirta, Pieti Kirkkopelto, Antti Kykk\"anen
TL;DR
This paper explores the mathematical properties of anisotropic stiffness tensors in elastic materials to enable Finsler-geometric methods for solving inverse imaging problems with elastic waves.
Contribution
It characterizes the analytic and algebraic conditions on stiffness tensor fields necessary for applying Finsler geometry to elastic wave inverse problems.
Findings
Identifies conditions for Finsler-geometric applicability
Provides a framework for analyzing elastic wave inverse problems
Enhances understanding of anisotropic elastic properties
Abstract
The elastic properties of a material are encoded in a stiffness tensor field and the propagation of elastic waves is modeled by the elastic wave equation. We characterize analytic and algebraic properties a general anisotropic stiffness tensor field has to satisfy in order for Finsler-geometric methods to be applicable in studying inverse problems related to imaging with elastic waves.
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Taxonomy
TopicsNumerical methods in inverse problems · Microwave Imaging and Scattering Analysis · Thermoelastic and Magnetoelastic Phenomena