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

Abstract

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-Newtontype 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 Fréchet 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 oceanbottom-cable data, and we propose a new hybrid approach in computing iteration adaptive regularization weight for prestack inversion.

Full waveform seismic inversion using a distributed system of computers

“…Once the noise estimate of the data is known, an a posteriori optimal α can be obtained in every iterative step using (17). Sen and Roy [12] evaluated various schemes based on L-curve, generalized cross validation and the discrepancy principle for computing iteration adaptive regularization weights in seismic waveform inversion applications and concluded that Engl's approach is the most efficient when an initial estimate of noise can be made.…”

“…Such a technique enhances the efficiency of generation of the sensitivity matrix. Here we employed an approach developed in [12] that is more efficient than the approach considered in [11], in which we avoid two steps of upward and downward propagation and simply evaluate new seismograms by reusing pre-computed reflectivity matrices from either upward or downward propagation alone. In a forward problem computation, we compute all four reflection/transmission coefficient matrices for each layer in a top-down fashion and use the recursive equations (4) to compute the above matrices for composite media.…”

FDTD3C—A FORTRAN program to model multi-component seismic waves for vertically heterogeneous attenuative media

“…For many cases in exploration seismology (e.g., amplitude variation with offset (AVO)) and earthquake seismology (e.g., receiver function analysis) estimating seismic plane-wave response of onedimensional (1D) earth models provides adequate information for further processing and analysis (e.g., Kormendi and Dietrich, 1991;Martinez and McMechan, 1991;Sen and Roy, 2003;Ji and Singh, 2005). Additionally, in any large-scale seismic modelling and inversion using a realistic structure model, even a single iteration requires significant computational resources.…”

Adaptive reconstruction method of impedance model with absolute and relative constraints

“…The edge-preserving regularization used by Charbonnier et al (1997) and Zhang et al (2007) got good effect in preserving the discontinuity of the images and the geological model, respectively. Moreover, Sen and Roy (2003) and Zhang et al (2007) adaptively adjusted regularization parameters by the maximum likelihood method (ML) in inversion procedure in order to improve inversion result and convergence speed. But their methods cannot obtain satisfying results in faults because of large impedance gradients at faults.…”