Scattering Control for the Wave Equation with Unknown Wave Speed

TL;DR

This paper introduces an iterative control method for the wave equation that effectively removes wave history up to a certain depth without knowing the wave speed, aiding seismic and ultrasound imaging by eliminating reflections.

Contribution

It presents a novel iterative control procedure that operates without prior knowledge of the wave speed to erase wave history in the medium.

Findings

Successfully erases wave history up to a specified depth

Operates without prior knowledge of wave speed

Applicable to seismic and ultrasound imaging

Abstract

Consider the acoustic wave equation with unknown, not necessarily smooth, wave speed $c$. We propose and study an iterative control procedure that erases the history of a wave field up to a given depth in a medium, without any knowledge of $c$. In the context of seismic or ultrasound imaging, this can be viewed as removing multiple reflections from normal-directed wavefronts.