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Probabilistic model constraints for full-waveform inversion
Aquino de Aragao, Odette C.
Aquino de Aragao, Odette C.
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2021
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Abstract
A reliable understanding of the Earth's subsurface is one of the main goals of Geophysics. In seismic exploration, for example, an accurate subsurface image is needed for characterization of hydrocarbon reservoirs. Seismic images could be constructed using elastic or anelastic models using techniques like full-waveform inversion (FWI) that represents the state-of-the-art in subsurface model building. FWI operates by minimizing the difference between observed seismic data and data simulated using models subjected to a wave equation. When the FWI objective function is purely based on this data misfit, the inversion could become highly non-linear and ill-posed, which may prevent convergence towards the true subsurface model. For multiparameter FWI, such as elastic or viscoelastic, artifacts due to the interparameter crosstalk and unphysical models that do not represent feasible geological units could arise rendering FWI useless.
In this thesis, I propose to include in the FWI objective function a petrophysical penalty term formulated in a probabilistic framework to constrain elastic and viscoelastic subsurface models. I use petrophysical information, such as that provided by well logs, to build probability density functions (PDFs), representing the model parameter space, and formulate the penalty function such that the update models have to be consistent with this petrophysical distribution. I show that this probabilistic penalty term can be used in different FWI configurations: isotropic or anisotropic models, elastic or anelastic properties, single or multiple distributions representing different lithological units or spatial trends of petrophysical parameters. I validate the proposed method with complex and realistic numerical examples that show that the petrophysical penalty term reduces the ill-posedness and non-linearity nature of FWI, while mitigating the interparameter crosstalk artifacts and ensuring that the inverted models represent feasible geological units. The ability to directly use observed petrophysical information without assuming potentially inaccurate relationships among the inverted parameters paves the way to define a high-standard for recovering reliable high-resolution subsurface models that simultaneously honor both seismic and petrophysical data. This technique avoids unfeasible model updates in areas where seismic data do not constrain sufficiently the subsurface properties. A similar formulation prevents the inversion from producing models that violate conditions that cause numerical dispersion and instability in wavefield modeling.
The techniques I propose in this thesis have a general character and could be used for a variety of inversion problems supported by multiple geophysical measurements. These technologies can thus inspire new geophysical application that aim to characterize multiple subsurface parameters, while exploiting prior petrophysical information in a consistent and easy to implement numerical optimization framework.
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