Influence of the regularization weighting matrix on parameter estimates

Abstract

Optimization techniques are often used in parameter estimation. An objective function can be formed with a measurement term and regularization term. The measurement term is formed from the weighted sum of squares of the difference between head measurements and their computed values. The regularization term is formed by the weighted sum of squares of departures from the original parameter estimates. Most often, a diagonal regularization weighting matrix is used. A diagonal matrix corresponds to an assumption of no spatial correlation between the errors in the original parameter estimates, but the errors will most often be correlated. Consequently, non-diagonal weighting matrices should be used. Numerical experiments have been performed to test the influence of non-diagonal regularization weighting matrices on parameter estimates. It is demonstrated that using the correct structure for the weighting matrix can improve transmissivity estimates. The transmissivity fields computed from the non-diagonal weighting matrices are closer in statistical structure and more accurate than those computed with diagonal weighting matrices, and the connectivity of the extreme values is more accurately imaged. The use of non-diagonal weighting matrices can improve the computed flow field, and therefore, the accuracy of transport simulations. The results indicate that using the correct weighting can improve transmissivity estimates more effectively than adding many new observation points.