Elastic wavefield inversion and the adjoint operation for the elastic wave equation.

Seismic data is nonlinearly related to the elastic parameters, elastic moduli and density so the analytic solution to the inverse problem of finding the earth parameters corresponding to seismic data is very difficult. In principle, the solution may be located numerically using some kind of Monte Carlo technique but this is infeasible on todays computers due to the nontrivial computer time required to solve the elastic forward problem. Therefore, a more restrictive but cheaper method such as the nonlinear least squares must be used. Crucial to any nonlinear inversion scheme based on least squares iterations is the adjoint operator. This is used to define the gradient direction on the least squares functional surface which is in turn used to evaluate the perturbations in the elastic parameters at each iteration. -from Author