Full waveform inversion of shot gathers in terms of poro-elastic parameters
Résumé
We have developed a full waveform iterative inversion procedure for determining the porosity, permeability, interstitial fluid properties and mechanical parameters of stratified porous media. The inverse problem is solved by using a generalized least-squares formalism. The proposed method achieves computational efficiency through semi-analytical, semi-numerical solutions for calculating the reference and perturbation wave fields from Biot's theory. When this algorithm is applied to noise-free synthetic data, it is found that the inversion of a single parameter as a function of depth generally yields satisfactory results. However, simultaneous or sequential multi-parameter inversions underline, as expected, the inter-dependence between parameters having different physical dimensionality. The strong correlations that may exist between parameters of different types remain a major issue in multiparameter estimation, but viable solutions may be found when some a priori knowledge of the porous medium is available. For instance, the seismic data can be inverted for the saturation rate by knowing the properties of the interstitial fluid. Nevertheless, the approach proposed here militates in favor of a combination of different methods to solve the challenging task of estimating poro-elastic parameters from seismic data.
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