Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion

Seismic waveform inversion is a highly challenging task. Nonlinearity, nonuniqueness, and robustness issues tend to make the problem computationally intractable. We have developed a simple regularized Gauss-Newton-type algorithm for the inversion of seismic data that addresses several of these issues. The salient features of our algorithm include an efficient approach to sensitivity computation, a strategy for band-limiting the Jacobian matrix, and a novel approach to computing regularization weight that is iteration adaptive. In this paper, we first review various forward modeling and differential seismogram computation algorithms and then evaluate different strategies for choosing the regularization weight. Under the assumption of locally 1D earth models, we design an efficient algorithm by rearranging recursion formula in the reflection matrix approach to compute plane wave seismograms and the Frechet derivative matrix as a by-product of forward modeling. We then demonstrate that in a gradient-descent-type optimization scheme, regularization is critical for obtaining stable and geologically realistic solutions. Although, in most applications, the regularization weight (relative importance between data and model misfit) is chosen in an ad-hoc manner; the robustness in model estimation and computational stability improve significantly by allowing adaptivity in the choice of the regularization weight in each iterative step. We evaluate performances of several methods, namely, an L-curve approach, generalized cross-validation technique, and methods based on a discrepancy principle with application to field ocean-bottom-cable data, and we propose a new hybrid approach in computing iteration adaptive regularization weight for prestack inversion.