Seismic waveform inversion in the frequency domain, Part 2: Fault delineation in sediments using crosshole data

Abstract

A crosshole experiment was carried out in a layered sedimentary environment in which a normal fault is known to cut through the section. Initial traveltime inversions produced stable but low-resolution images from which the fault could be only vaguely inferred. To image the fault, wavefield inversion was used to produce a velocity model consistent with the detailed phase and amplitude of the data at a number of frequencies. Our wavefield inversion scheme uses a classical, descent-type algorithm for decreasing the data misfit by iteratively computing the gradient of this misfit by repeated forward and backward propagations. Our propagator is a full-wave equation, frequency-domain, acoustic, finite-difference method. The use of the frequencyspace domain yields computational advantages for multisource data and allows an easy incorporation of viscous effects.By running wavefield inversion on the field data, a quantitative velocity image was produced that yielded

Crosshole seismic tomography with cross-firing geometry

“…This frequency grouping strategy is for mitigating the effect of data noise, which is not necessarily white in the frequency domain (Pratt and Shipp, 1999;Wang and Rao, 2006). Simultaneously using neighboring frequencies from the same spatial imaging position in the inversion effectively increases the number of equations without changing the number of unknown model parameters; this means the inverse problem being much better determined.…”

“…In anisotropic waveform tomography, if the anisotropy parameter can be assumed to be a constant only in the background, it may be preset as a constant shrink factor in the whole investigation area during the numerical calculation (Pratt and Shipp, 1999). In this paper, however, a 2D anisotropic model is explicitly defined in seismic simulation with an anisotropic wave equation, instead of a simple shrinking factor working on finite-differencing grids.…”

Using a Poroelastic Theory to Reconstruct Subsurface Properties: Numerical Investigation

“…Gauthier et al, 1986;Pratt et al, 1998) or 3D structures (for instance, Ben-Hadj- Ali et al, 2008;Sirgue et al, 2008). Applications to real data are even more recent (Hicks & Pratt, 2001;Operto et al, 2006;Pratt & Shipp, 1999). The elastic case is more challenging, as the coupling between P and S waves leads to ill-conditioned problems.…”

Wave-equation-based travel-time seismic tomography – Part 1: Method

“…It also made the conceptual wave-equation-based seismic inversion methods such as the one presented by Tarantola (1984) feasible in realistic applications Fichtner and Trampert, 2011;Zhu et al, 2012). To our best knowledge, adjoint tomography (Tromp et al, 2005;Fichtner et al, 2006), scattering integral methods (L. Chen et al, 2007b), and full waveform inversion (FWI) in the frequency domain (Pratt and Shipp, 1999;Operto et al, 2006) are among the most popular tomographic techniques based upon solving full wave equations. FWI in the frequency domain has been mainly used in exploration problems (e.g., Virieux and Operto, 2009;Lee et al, 2010).…”