Enhanced recovery of subsurface geological structures using compressed sensing and the Ensemble Kalman filter

A Sparse Bayesian Imaging Technique for Efficient Recovery of Reservoir Channels With Time-Lapse Seismic Measurements

“…A new scheme was introduced in [28] to enhance the recovery of the subsurface ge-ological features, combining the EnKF with the Orthogonal Matching Pursuit (OMP) algorithm. The proposed Sparse Geological Structures Domain (SGSD)-EnKF algorithm transforms the EnKF estimation of the subsurface geological structures to a specifically constructed sparse domain learned over a large training set and was shown to provide significant improvement in recovering the channels over the standard EnKF.…”

“…It is important to realize that the sparse transformation step (step 2) is different from the optimization problem for dictionary learning discussed above as it only attempts to represent the signal K f t by finding the coefficients κ f t for the basis elements of the fixed dictionary Ψ computed offline using the K-SVD. The original SGSD-EnKF algorithm proposed in [28,29] uses the OMP algorithm [26] to compute the solution to this step. Despite the fact that the OMP algorithm is expected to provide improved reconstruction with increased sparsity rates (made possible with the inclusion of seismic data), the anticipated linear increase in the computational complexity necessitates the use of a more efficient algorithm that can provide comparable reconstruction quality while scaling the computational complexity much slowly.…”

“…[28,29] showed that a large set of realizations, each depicting a different subsurface geological field structure, can be used to train the K-SVD algorithm in order to generate a sparse basis to use within an EnKF history matching framework. The proposed Sparse Geological Structures Domain (SGSD)-EnKF scheme in [28,29] transforms the ensemble members representing the permeability field into the A slightly modified version of the SGSD-EnKF algorithm is presented in Algorithm 1 where we re-write the sparse transformation step (step 2) in its most general form. We also impose a constraint on the number of non-zero basis elements weights after the EnKF update.…”

“…In this paper; we extend the work of [28] and [29] to investigate the effects of time-lapse seismic data on the channel reconstruction performance, particularly focusing on overcoming the limitation on the sparsity rate as observed in [29]. We explore a Bayesian sparse reconstruction algorithm to deal with the expected increase in computational costs at higher sparsity rates with the OMP algorithm [29].…”

“…Section 2 provides a brief overview of the components of the sparse estimation framework and the improved ver-sion of the SGSD-EnKF algorithm originally proposed in [28,29]. Section 3 discusses the experimental setup coupling a two-phase subsurface flow model with an EnKF, and describes the simulation parameters.…”