Multiscale seismic waveform inversion

Abstract

Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low‐frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

“…Moreover, diving waves are needed to update the low-wavenumber content of the model. This is essential at the early stages of the inversion process (Bunks et al, 1995). Unfortunately, some of the diving waves are missing from the real data.…”

The wavelet response as a multiscale characterization of scattering processes at granular interfaces

“…The determination of the position of the interfaces needs an accurate large-scale velocity model whose inversion is recognized to be a highly non-linear tomography problem [Tarantola, 1987;Jin et al, 1992]. This stage of imaging is performed with a smooth model of the distribution of the physical properties, also called the macro-model [Bunks et al, 1995;Billette and Lambaré, 1998;Lambaré et al, 2004], which represents the large-scale heterogeneities of the medium. The macro model is completed by an interface skeleton representing the support of the abrupt impedance contrasts located at the limits of the domains and producing the reflected echoes forming the data.…”

A local adaptive method for the numerical approximation in seismic wave modelling

“…For example, in a marine seismic acquisition survey, v min = 1500m/s, that is the water velocity, and the maximum signal frequency f max can be of the order of 150Hz. However, the maximum frequency used in the context of FWI to reduce the number of local minima in the objective function is of the order of 10 − 20Hz (e.g., [9,22]). Considering the function…”