NONLINEAR TWO-DIMENSIONAL ELASTIC INVERSION OF MULTIOFFSET SEISMIC DATA.

The treatment of multioffset seismic data as an acoustic wave field is becoming increasingly disturbing to many geophysicists. The problems of using the conventional acoustic wave equation approach can be eliminated via an elastic approach. In this paper, equations are derived to perform an inversion for P-wave velocity, S-wave velocity, and density as well as the P-wave impedance, S-wave impedance, and density. The inversion is based on nonlinear least squares and proceeds by iteratively updating the earth parameters until a good fit is achieved between the observed data and the modeled data corresponding to these earth parameters. The iterations are based on the preconditioned conjugate gradient algorithm. The fundamental requirement of such a least-squares algorithm is the gradient direction which tells how to update the model parameters. The gradient direction can be derived directly from the wave equation and it may be computed by several wave propagations. Although in principle any scheme could be chosen to perform the wave propagations, the elastic finite-difference method is used because it directly simulates the elastic wave equation and can handle complex, and thus realistic, distributions of elastic parameters.