Causality-constrained model-independent joint migration inversion

Instead of attempting to retrieve model parameters (velocity and density in the acoustic situation), Model-Independent Joint Migration Inversion tries to obtain operators, reflection and augmented transmission, the sum of transmission and wavenumber perturbation operators. However, one does not know whether the retrieved operators are correct or not without first modeling them. Thus, we model those operators for a simple model with vertical and horizontal dips only. The modeled results show that all the lateral heterogeneity is contained in the augmented transmission operator, while the reflection operator contains none of the lateral heterogeneity— only the vertical one. We then compute the critical ingredients of the inversion process, the gradients of the misfit functional. The gradients exhibit overall resemblance to those ideal operators, but less resemblance was exhibited by the augmented transmission operators and their ideal counterparts. While the resulting gradients seem promising, most of the remaining challenge would be in producing effective regularization of the augmented transmission operator.


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