Reweighted variational full-waveform inversions

Starting from an initial model and predefined priors, a distributions of model parameters via optimization using a Bayesian theorem. Thus, VFWI is useful in estimating uncertainties in full-waveform inversions (FWIs). However, the resolution of the inverted models from VFWIs is usually not as good as those from conventional FWIs. We decompose the loss function in a VFWI into two terms: the complexity cost and the data misfit. The data variance, which balances these two terms, is expected to decrease during an iterative optimization to gradually put higher weight on the data misfit. We develop and compare two reweighting schemes in VFWI that can produce high-resolution velocity models and the associated uncertainties. Inversions are performed efficiently in a deep-learning framework to take advantage of automatic differentiation. Tests using synthetic data and blind data indicate that reweighted VFWIs are less sensitive to initial models and can generate inversion results that have higher resolution than those from conventional FWIs.