Solving an Inverse Dynamic Seismic Problem by Multicomponent Elastic Full Waveform Inversion

Abstract

A numerical method for solving an inverse problem of the theory of seismic wave propagation, relying on the modified least square method, is proposed, substantiated, and implemented. The proposed modification is based on the decomposition of the velocity model of the geological medium into the subspaces of smoothly changing propagators and sharply changing reflectors. The modified functional exhibits strong nonlinearity relative to the macro-velocity component, since the operator M, which transforms the time reflector to the space reflector, depends on it significantly. However, the low dimensions of the subspace of the macro-velocity models make it possible to use quite effective minimizing methods successfully.