Multiple realizations: Model variance and data uncertainty

Geophysicists typically produce a single model, without addressing the issue of model variability. By adding random noise to the model regularization goal, multiple equiprobable models can be generated that honor some a priori estimate of the model’s second-order statistics. By adding random noise to the data, colored by the data’s covariance, equi-probable models can be generated that give an estimate of model uncertainty resulting from data uncertainity. The methodology is applied to a simple velocity inversion problem with encouraging results.