Combining asymptotic linearized inversion and full waveform inversion

Abstract

A method for combining the asymptotic operator designed by Beylkin (Born migration operator) for the solution of linearized inverse problems with full waveform inversion is presented. This operator is used to modify the standard L2 norm that measures the distance between synthetic and observed data. The modified misfit function measures the discrepancy of the synthetic and observed data after they have been migrated using the Beylkin operator. The gradient of this new misfit function is equal to the cross-correlation of the single scattering data with migrated/demigrated residuals. The modified misfit function possesses a Hessian operator that tends asymptotically towards the identity operator. The trade-offs between discrete parameters are thus reduced in this inversion scheme. Results on 2-D synthetic case studies demonstrate the fast convergence of this inversion method in a migration regime. From an accurate estimation of the initial velocity, three and five iterations only are required to generate high-resolution P-wave velocity estimation models on the Marmousi 2 and synthetic Valhall case studies.