Full-waveform inversion constrained by adaptive sonic logging data within a Bayesian framework

The full waveform inversion (FWI) utilizes full wavefield data to invert subsurface parameters and is considered one of the most promising data-driven tools for obtaining high precision velocity models. However, the successful application of FWI in geophysical exploration remains limited, primarily due to the cycle-skipping issue caused by the absence of low-frequency data, which is one of the main reasons for FWI failures. Incorporating prior regularization constraints FWI can effectively compensate for the lacking low-frequency components and constrain the iterative updates of FWI toward the desired direction, offering a natural advantage in addressing this challenge. However, the weights of the prior information terms are still determined empirically, which introduces significant subjectivity and randomness to the inversion results. To solve this issue, we propose an adaptive method to determine the weight factor based on posterior probability distribution within the Bayesian theoretical framework. This factor adaptively adjusts during each iteration to balance the contributions of the data error term and the prior information term in FWI, which can effectively mitigate the cycle-skipping problem and alleviating the nonlinearity of the inversion process. Numerical examples from the Overthrust model and the Marmousi model show that our method not only enhance the accuracy of FWI, but also demonstrate strong noise resistance.