A contraction theorem for the one-dimensional seismic inverse problem on a viscoelastic medium

Abstract

This paper concerns itself with an analytic proof of the solvability of the one-dimensional seismic inverse problem on a viscoelastic medium. This problem uses techniques similar to that of the attenuating system, but encounters additional difficulties due to the presence of the memory variable. The proof is based on showing that an integral equation for the impedance is a contraction mapping using energy methods.