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Full‐waveform inversion for reverse vertical seismic profiling data based on a variant of the optimal transport theory

Full‐waveform inversion has become a useful tool to construct the details of the geological structure. However, due to the strong nonlinearity of the inverse problem and inaccuracy of the initial model, full‐waveform inversion often faces severe cycle‐skipping problems and thus may exhibit poor inversion results. The optimal transport‐based full‐waveform inversion can mitigate the cycle‐skipping problem. For that, transformations of oscillatory seismic data to distributions need to satisfy positive and mass conservation conditions. In this work, we introduce a new data normalization method based on the Sigmoid function. The convexity of the objective function is improved compared to the traditional L2 norm by setting appropriate parameters. Combined with the adaptive quadratic Wasserstein distance, our approach presents strong adaptability to a poor initial model and can reduce cycle skipping. Numerical examples are provided to validate the method in a reverse vertical seismic profiling geometry, and the inverted models obtained by different normalization methods are also compared.