Target-Oriented Inversion of Time-Lapse Seismic Waveform Data

Full waveform inversion of time-lapse seismic data can be used as a means of estimating the reservoir changes due to the production.Since the repeated computa-tions for the monitor surveys lead to a large computational cost,time-lapse full wave-form inversion is still considered to be a challenging task.To address this problem,we present an efficient target-oriented inversion scheme for time-lapse seismic data using an integral equation formulation with Gaussian beam based Green’s function approach.The proposed time-lapse approach allows one to perform a local inversion within a small region of interest(e.g.a reservoir under production)for the monitor survey.We have verified that the T-matrix approach is indeed naturally target-oriented,which was mentioned by Jakobsen and Ursin[24]and allows one to reduce the compu-tational cost of time-lapse inversion by focusing the inversion on the target-area only.This method is based on a new version of the distorted Born iterative T-matrix inverse scattering method.The Gaussian beam and T-matrix are used in this approach to perform the wavefield computation for the time-lapse inversion in the baseline model from the survey surface to the target region.We have provided target-oriented inversion results of the synthetic time-lapse waveform data,which shows that the proposed scheme reduces the computational cost significantly.

Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media

We generalize the existing distorted Born iterative T-matrix(DBIT)method to seismic full-waveform inversion(FWI)based on the scalar wave equation,so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors.The elastodynamic wave equation for an ar-bitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type,with a 9-dimensional wave state(displacement-strain)vector.We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory.This allows for domain decomposition and novel variational estimates.The tensorial nonlinear inverse scat-tering problem is solved iteratively by using an expression for the Fŕechet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green’s functions and wave state vectors that are updated after each iteration.Since the generalized DBIT method is consistent with the Gauss-Newton method,it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects.The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method,with adaptive selection of the regularization parameter after each iteration.In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes,we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization.This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods.Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented,it may be particularly suitable for applications to seismic reservoir characterization and monitoring.However,the theory and method presented here is general.