Nonlinear reverse‐time inversion of elastic offset vertical seismic profile data

Abstract

An iterative nonlinear inversion algorithm for two‐dimensional elastic media gives estimates of P-velocity and S-velocity distributions from synthetic offset vertical seismic profiles. The algorithm is a hybrid of inversion and principles borrowed from reverse‐time migration. Gradients of the misfit function are dynamically determined by crosscorrelations of the computed incident wave fields with the scattered compressional and shear wave fields. Model perturbations are defined in the steepest descent direction. In order to optimize the sensitivity of the inversion to both compressional and shear velocity distributions, two data collection experiments are required, one with a compressional wave source and the other with a shear wave source. Inversion iterations alternate between the compressional and shear source data sets. In test examples, the new algorithm converges successfully to the correct solution when the starting model’s compressional and shear velocities deviated by as much as 20 percent from the correct solution.