The monotonicity method for the inverse elastic scattering on unbounded domains

TL;DR

This paper introduces a monotonicity-based method for solving inverse elastic scattering problems involving inhomogeneous objects in unbounded domains, enabling the characterization of material support from far field data.

Contribution

It develops a novel monotonicity relation for the far field operator and extends the monotonicity method to elastic scattering with inhomogeneous media.

Findings

Monotonicity relation for the far field operator established.

Method characterizes support of inhomogeneities in elastic parameters.

Extension of the monotonicity method to unbounded elastic scattering domains.

Abstract

We discuss a time-harmonic inverse scattering problem for the Navier equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity relation for the far field operator that maps superpositions of incident plane waves to the far field patterns of the corresponding scattered waves. Combining the monotonicity relation with the method of localized potentials, we extend the so called monotonicity method to characterize the support of inhomogeneities in the Lam\'{e} parameters and the density in terms of the far field operator.