Calibration of channelized subsurface flow models using nested sampling and soft probabilities

A new method for calibration of channelized subsurface flow models is presented. The proposed method relies on the nested sampling algorithm and on adaptive construction of soft probability maps. Nested sampling (NS) is a Bayesian sampling algorithm for estimating the Bayesian evidence and obtaining samples from the posterior distribution of the unknown fields. NS utilizes a set of samples (active set) that evolves to high-likelihood regions. The sample evolution process is achieved by iteratively replacing the sample with the lowest likelihood within the active set by a new sample from the prior but with higher likelihood value (constrained sampling). For channelized models, drawing samples from the prior model based on a training image and only accepting the samples satisfying the likelihood constraint is computationally inefficient due to low acceptance rates. We develop an efficient constrained sampling step utilizing soft probability maps in addition to the training image (using the Tau model) to obtain samples from the prior satisfying the likelihood constraint. The soft probability map is constructed by averaging the samples within the active set and is shown to significantly increase the acceptance rate of the nested sampling algorithm. The proposed algorithm is applied for calibration of several channelized subsurface flow models. In addition, the NS algorithm is applied for prior model selection of a channelized model with different training images obtained by changing the orientation angles of a reference training image. The results show that selecting the prior model based on the data mismatch can be misleading. This highlights the need to evaluate the Bayesian evidence (estimated by the nested sampling algorithm) as a more reliable prior model selection statistics, especially when the amount of calibration data is limited.