Posterior sampling for random noise attenuation via score-based generative models

Random noise attenuation is an ill-posed inverse problem with multiple solutions, especially in complicated field noise situations. We develop a method to sample stochastic solutions from the posterior distribution of seismic data for a given noisy input. Posterior sampling can be performed by Langevin dynamics with a conditional score function, which can be described as a trained score network (in score-based generative models) plus an analytical expression related to the noise distribution. Each solution from the posterior distribution is reasonable and of high quality. The numerous solutions we obtain may contain underground structural information of interest. We also achieve interactive posterior sampling by automatically estimating a noise level or manually setting it according to the noise level map of the field noise. Experiments on synthetic and field data verify the superiority of our posterior sampling approach.