The solid-fluid transmission problem

TL;DR

This paper analyzes the transmission problem at the interface between an elastic solid and a fluid, constructing a microlocal parametrix to describe wave interactions, and demonstrates how to recover physical wave speeds from boundary data.

Contribution

It introduces a microlocal analysis framework for the solid-fluid interface, including wave reflection, transmission, mode conversion, and surface wave formation, with a method to recover wave speeds from measurements.

Findings

Constructed a parametrix describing reflected and transmitted waves.

Proved well-posedness of the coupled solid-fluid system.

Showed how to recover wave speeds from boundary measurements.

Abstract

We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid, and pressure and velocity in the fluid, coupled by suitable transmission conditions at the interface. We show well posedness for the coupled system and study the problem microlocally, constructing a parametrix for it using geometric optics. This construction describes the reflected and transmitted waves, including mode converted ones, related to incoming waves from either side. We also study formation of surface Scholte waves. Finally, we prove that under suitable assumptions, we can recover the s- and the p-speeds, as well as the speed of the liquid, from boundary measurements.