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Alternative misfit functions in Full Waveform Inversion : From synthetic to field data

Abstract : Full-waveform inversion is a seismic imaging method known to yield high-resolution results that go towards directly interpretable reconstructed models. Unfortunately, it suffers from a flaw: the need for accurate initial models to converge toward meaningful reconstruction of subsurface parameters. This limitation is due to the non-convexity of the least-squares distance conventionally used as the distance measurement function, which translates into the cycle-skipping issue that has been documented since the introduction of full-waveform inversion itself.Thus, finding solutions to improve full-waveform inversion robustness to cycle-skipping has been the subject of a large number of studies. From all the propositions made to improve this method, one of the most documented is replacing the classical least-squares norm with alternative misfit functions.We first propose a review of multiple propositions of alternative misfit functions, coming either from the literature or from ideas I have explored during my years of research. We explain which principles these methods are based on and illustrate how they are designed to better handle kinematic mismatch than the least-squares misfit function. A set of carefully designed synthetic benchmarking tests is then introduced to assess the behavior of a selection of alternative misfit functions containing two optimal transport-based misfit functions, a wiener filter based, an instantaneous enveloped based, and finally, a normalized integration based misfit function. On these several canonical synthetic tests, each formulation is pushed to its limits, allowing us to establish the pros and cons of each formulation.This work can also be seen as an attempt to promote a more systematic cross-comparison of alternative misfit functions on fair benchmarking setups, as we observed that alternative misfit functions are often proposed on carefully designed synthetic setups that maximize their benefits. This is, to us, at the origin of the discrepancy observed between the number of propositions made in the literature and actual case studies performed with them on field data.Finally, after selecting what is to us the most promising candidates - a graph-space optimal transport-based misfit function - we compare it to the least-squares distance in a case study based on the three-dimensional ocean bottom cable data from the Valhall field. The motivation behind the use of this data set comes from the wide variety of studies already performed with it. This allows us to work in a relatively controlled environment. The comparison is first performed starting from a reflection traveltime tomography initial model used in previous studies. Then, a second comparison is performed starting from a crude, linearly varying in-depth one-dimensional initial velocity model. This last setup illustrates the robustness to cycle-skipping obtained through a change of the misfit function inside the full-waveform inversion formalism. The encouraging and meaningful results obtained from this case study demonstrate that cycle-skipping robustness of full-waveform inversion can be drastically improved using the proposed graph-space optimal transport-based misfit function.
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Submitted on : Wednesday, July 21, 2021 - 11:03:12 AM
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Arnaud Pladys. Alternative misfit functions in Full Waveform Inversion : From synthetic to field data. Earth Sciences. Université Grenoble Alpes [2020-..], 2021. English. ⟨NNT : 2021GRALU016⟩. ⟨tel-03293646⟩

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