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Abstract

Since at least forty years, mathematicians and geophysics have studied seismic waveform inversion. Its computational cost and its ill-posedness (i.e. the presence of local minima and the non-uniqueness of the solutions) make its use difficult with real-sized problems. Nevertheless, with the improvements in data quality and in acquisition and the increase in computer power, several real data examples have been reported. In the literature, waveform inversion has been formulated either in the data domain or in the model domain. In this presentation, I shall discuss the data-domain formulation, where we minimize the misfit between the observed data and the computed data that are direct solutions of the wave equation. I shall consider three main applications. In the first group of applications, waveform inversion is solved with a global optimization and a simple 1D forward modeling. The objective is, generally, to derive some petrophysical parameters from the seismic reflection traces. In the second group of applications, waveform inversion is solved with a local optimization assuming a known background velocity, the objective is to retrieve reflectivity or impedance maps from reflection data. In the third group of applications, waveform inversion is solved with a local optimization and a multiscale approach. The goal is to estimate the background velocity mainly from low-frequency and long-offset data. While reviewing these waveform inversion applications, I shall discuss the challenges we are still facing. The focus of the presentation will be the applications of waveform inversion for macroscopic (background velocity) model building.

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/content/papers/10.3997/2214-4609.20149892
2012-07-04
2024-03-28
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