Full waveform inversion constrained to well log velocity data and seismic data using random mixing

Full Waveform Inversion (FWI) is a state-of-the-art technique for reconstructing high-resolution subsurface velocity models. However, conventional deterministic FWI is highly sensitive to the initial model and does not provide uncertainty quantification, while Bayesian FWI, although capable of addressing uncertainty, often incurs substantial computational cost. To bridge the gap between these two frameworks, previous work introduced a stochastic approach known as Random Mixing (RM). The method generates a collection of velocity models that are all reproduced given observational data and are conditional on a known geostatistical characterization in the form of a spatial correlation and marginal distribution. In this study, we extend the RM method for FWI by incorporating well-log information alongside seismic wavefield data. Vertical velocity profiles obtained from well logs are used to estimate the required geostatistical parameters, and the generated velocity realizations are constrained to honor the well-log measurements. We demonstrate the effectiveness of this approach using two test cases, including one with a simulated anisotropic layered velocity structure. The tests show that data provided by well logs allow for estimating geostatistical parameters with an accuracy sufficient for successful RM FWI and that restriction to velocity realizations conditional on well log data reduces uncertainty in the RM inversion results. The results validate the effectiveness of RM under both linear and non-linear constraints.