Nonliner inversion of seismic reflection data in a laterally invariant medium

Abstract Interpretation of seismic waveforms can be expressed as an optimization problem based on a nonlinear least-squares criterion to find the model which best explains the data. An initial model is corrected iteratively using a gradient method (conjugate gradient). At each iteration, computation of the direction of the model perturbation requires the forward propagation of the actual sources and the reverse-time propagation of the residuals (misfit between the data and the synthetics); the two wave fields thus obtained are then correlated. An extra forwardpropagation is required to compute the amplitude of the perturbation along the conjugate-gradient direction. Thenumber of propagations to be simulated numerically in each iteration equals three times the number of shots. Since a 2-D finite-difference code is employed to solve forwardand backward-propagation problems. the method is general and can handle arbitrary 2-D source-receiver configurations and lateral heterogeneities. Using conventionalvelocity analysis to derive an initial velocity model, the method is implemented on a real marine data set. Thedata set which has been selected corresponds approximately to a horizontally stratified medium. Consequently, a single-shot gather has been used for inversion. In spite of some simplifying assumptions used for wave-field propagation (acoustic approximation, point source), and using synthetics generated by a nearby sonic log to calibrate amplitudes, our final synthetics match the input data very well and the inversion result has clear similarities to the log.