Robust elastic nonlinear waveform inversion: Application to real data

Abstract

International audienceNonlinear elastic waveform inversion has advanced to the point where it is now possible to invert real multiple‐shot seismic data. The iterative gradient algorithm that we employ can readily accommodate robust minimization criteria which tend to handle many types of seismic noise (noise bursts, missing traces, etc.) better than the commonly used least‐squares minimization criteria. Although there are many robust criteria from which to choose, we have tested only a few. In particular, the Cauchy criterion and the hyperbolic secant criterion perform very well in both noise‐free and noise‐added inversions of numerical data. Although the real data set, which we invert using the sech criterion, is marine (pressure sources and receivers) and is very much dominated by unconverted P waves, we can, for the most part, resolve the short wavelengths of both P impedance and S impedance. The long wavelengths of velocity (the background) are assumed known. Because we are deriving nearly all impedance information from unconverted P waves in this inversion, data acquisition geometry must have sufficient multiplicity in subsurface coverage and a sufficient range of offsets, just as in amplitude‐versus‐offset (AVO) inversion. However, AVO analysis is implicitly contained in elastic waveform inversion algorithms as part of the elastic wave equation upon which the algorithms are based. Because the real‐data inversion is so large—over 230,000 unknowns (340,000 when density is included) and over 600,000 data values—most statistical analyses of parameter resolution are not feasible. We qualitatively verify the resolution of our results by inverting a numerical data set which has the same acquisition geometry and corresponding long wavelengths of velocity as the real data, but has semirandom perturbations in the short wavelengths of P and S impedance

Simulation-enhanced fracture detection: research and demonstration in U.S. basins

“…However, to obtain the gradient of the data misfit function, it is not necessary to compute the Jacobian explicitly. The adjoint state method requires only several forward computations to generate the gradient (Tarantola 1984;Mora 1987, Crase et al 1990, Pratt et al 1998). …”

“…Mora (1987) applied this method to elastic problems in time domain and Pratt et al (1998) to acoustic problems in frequency domain. Despite its low demand of computations, this inversion scheme suffered from recovering background velocity information (Gauthier et al 1986;Mora 1987;Crase et al 1990;Hicks and Pratt 2001).…”

An Imaging Technique for Subsurface Faults Using Teleseismic-Wave Records. SH Case.

“…Our imaging algorithm is similar to that of Gauthier et al (1986), exploited for acoustic or elastic waveform inversion of reflection data (e .g., Crase et al, 1990;Sun and McMechan , 1991), which is based on the simplest gradient method , i.e., the steepest descent method (Tarantola , 1984). Waveform inversion is an inherently nonlinear problem that is approximated locally at each iteration by a linear problem.…”

The roles of the spatial regularization in seismic deconvolution

“…Generally, the robust inversion (e.g. Crase et al 1990;Yuan et al 2015) is a choice to deal with the undersampled data set or low quality migration data set to obtain an acceptable inversion result. In this paper, we illustrate that the spatial regularization can help recovering the reflectivity of the missing and/or poor-quality traces by slightly rewriting Eq.…”