Inverse Dynamic Problem in a Viscoelastic Medium

This preprint addresses the inverse dynamic problem of recovering the parameters of a viscoelastic absorbing medium from the internal space-time wavefield and its derivatives. Vertical seismic profiling is considered as a practical source of such data. The recovered parameters are the elastic modulus, compressional-wave velocity, and stress relaxation time. Two local non-iterative solution methods are proposed: a two-stage solution of the inverse coefficient problem based on the wave equation, and a high-frequency asymptotic solution based on the characteristic equation. The Maxwell model and the standard linear solid model are considered. Numerical examples of forward wavefield modelling and inverse recovery of the medium parameters are presented.