Bayesian-based Full Waveform Inversion

Full waveform inversion methods evaluate the properties of subsurface media by minimizing the misfit between synthetic and observed data. However, these methods omit measurement errors and physical assumptions in modeling, resulting in several problems in practical applications. In particular, full waveform inversion methods are very sensitive to erroneous observations (outliers) that violate the Gauss–Markov theorem. Herein, we propose a method for addressing spurious observations or outliers. Specifically, we remove outliers by inverting the synthetic data using the local convexity of the Gaussian distribution. To achieve this, we apply a waveform-like noise model based on a specific covariance matrix definition. Finally, we build an inversion problem based on the updated data, which is consistent with the wavefield reconstruction inversion method. Overall, we report an alternative optimization inversion problem for data containing outliers. The proposed method is robust because it uses uncertainties. This method enables accurate inversion, even when based on noisy models or a wrong wavelet.