Abstract
Seismic imaging is an efficient tool to investigate the Earth interior. Many of the different imaging techniques currently used, including the so-called full waveform inversion (FWI), are based on limited frequency band data. Such data are not sensitive to the true earth model, but to a smooth version of it. This smooth version can be related to the true model by the homogenization technique. Homogenization for wave propagation in deterministic media with no scale separation, such as geological media, has been recently developed. With such an asymptotic theory, it is possible to compute an effective medium valid for a given frequency band such that effective waveforms and true waveforms are the same up to a controlled error. In this work we make the link between limited frequency band inversion, mainly FWI, and homogenization. We establish the relation between a true model and an FWI result model. This relation is important for a proper interpretation of FWI images. We numerically illustrate, in the 2-D case, that an FWI result is at best the homogenized version of the true model. Moreover, it appears that the homogenized FWI model is quite independent of the FWI parametrization, as long as it has enough degrees of freedom. In particular, inverting for the full elastic tensor is, in each of our tests, always a good choice. We show how the homogenization can help to understand FWI behaviour and help to improve its robustness and convergence by efficiently constraining the solution space of the inverse problem.
Highlights
Since the late sixties, seismic data have been used to investigate the Earth interior and to image its mechanical properties, for academic and industrial purposes, at scales ranging from few metres to the global Earth
Because of this intrinsic limitation, seismologists have developed seismic imaging and tomography techniques which are mainly based on reduced data, together with an appropriate approximate solution of the wave propagation modelling problem, that are quicker to solve than the full wave equation
One of the objectives of this paper is to extend the results obtained in the layered media case (Capdeville et al 2013), to higher dimension cases, which illustrates the fact that the model obtained from full waveform inversion (FWI) are, at best, an homogenized version of the true model
Summary
Seismic data have been used to investigate the Earth interior and to image its mechanical properties, for academic and industrial purposes, at scales ranging from few metres to the global Earth. The homogenized models are ‘simpler’ in the sense that they need a finite number of parameters to describe them, which is not the case for the true models This has been confirmed in a recent work, but only in the layered media case: it has been proposed that FWI can retrieve at best the homogenized medium and that this fact can be used to properly set up the inversion problem (Capdeville et al 2013). We show a series of examples illustrating the exposed ideas before discussing our results and concluding our work
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