Flexible Coupling in Joint Inversions: A Bayesian Structure Decoupling Algorithm
Résumé
When different geophysical observables are sensitive to the same volume, it is possible to invert them simultaneously to jointly constrain different physical properties. The question addressed in this study is to determine which structures (e.g., interfaces) are common to different properties and which ones are separated. We present an algorithm for resolving the level of spatial coupling between physical properties and to enable both common and separate structures in the same model. The new approach, called structure decoupling (SD) algorithm, is based on a Bayesian trans-dimensional adaptive parameterization, where models can display the full spectra of spatial coupling between physical properties, from fully coupled models, that is, where identical model geometries are imposed across all inverted properties, to completely decoupled models, where an independent parameterization is used for each property. We apply the algorithm to three 1-D geophysical inverse problems, using both synthetic and field data. For the synthetic cases, we compare the SD algorithm to standard Markov chain Monte Carlo and reversible-jump Markov chain Monte Carlo approaches that use either fully coupled or fully decoupled parameterizations. In case of coupled structures, the SD algorithm does not behave differently from methods that assume common interfaces. In case of decoupled structures, the SD approach is demonstrated to correctly retrieve the portion of profiles where the physical properties do not share the same structure. The application of the new algorithm to field data demonstrates its ability to decouple structures where a common stratification is not supported by the data. Plain Language Summary One of the present-day challenges for geodata analysis consists in the joint inversion of an incredible number of data, where both number of observations and the number of observables are exponentially increasing. This trend in geophysics research is definitely positive and could lead to a considerable increase in our knowledge of the Earth's interior, if the correct tools are applied for making inferences out of the data. Unfortunately, our old tools for geodata analysis show all their weakness when faced to this new challenge, especially where subjective choices force models associated to different physical properties to be similar and to show the same spatial structures. Here we present the next evolution of Monte Carlo sampling applied to joint inversion of two or more geo-observables. Monte Carlo sampling of solutions to joint inverse problem is used to infer spatial correlation between different physical properties, where supported by data, or, at the contrary, to point out Earth's volumes where such properties are varying following different structures.
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