Link Between Full Waveform Inversion Models and Homogenized Effective Elastic Properties and Sources
Abstract
In the seismic imaging context, retrieving spatial scales smaller than the minimum wavelength leads to difficulties by introducing strong linearity in the inverse problem. This is the case for example for velocity discontinuities or point source locations: inverting explicitly for these quantities makes the inverse problem more difficult than just inverting for smooth quantities. This difficulty can be waved by acknowledging that elastic or acoustic waves with a minimum wavelength do not see the true fine-scale medium and sources, but an effective version of them. Inverting for these smooth effective or equivalent quantities makes the seismic inverse problem simpler to formulate and to implement. Nevertheless, if such an effective inversion is performed, it is important to know the link between a fine-scale model and its effective version. In this work we claim that, if the fine scales are known, these effective quantities can be computed with homogenization techniques, opening to the down-scaling of tomographic images. We show examples, in a 2-D elastic setting, based on a Gauss-Newton full waveform inversion where the full elastic tensor and density are inverted. Based on these examples, we numerically show that a full waveform inversion recovers, at best, the effective version of the underlying true model and sources. We discuss the consequences for the inversion strategy and interpretation of the inverted results.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.S34A..06C
- Keywords:
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- 0545 Modeling;
- COMPUTATIONAL GEOPHYSICS;
- 7260 Theory;
- SEISMOLOGY;
- 7270 Tomography;
- SEISMOLOGY;
- 7290 Computational seismology;
- SEISMOLOGY