Multiscale seismic waveform inversion

TLDR

Iterative seismic inversion struggles with complex models such as Marmousi because the objective function contains numerous local minima at all scales, preventing convergence to the global minimum. The multigrid approach mitigates this by decomposing the problem into long‑scale components with fewer, more separated minima, and applying it to a subsampled, low‑frequency Marmousi dataset. Using multigrid, iterative inversion achieves closer proximity to the global minimum, improves performance, and substantially reduces computational cost, facilitating future 3‑D extensions.

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.