Incorporating PROPACK into PEST to Estimate the Model Resolution Matrix for Large Groundwater Flow Models

Regularized inversion of groundwater flow models can be used to delineate geological heterogeneities using subspace methods like the singular value decomposition (SVD). To characterize heterogeneity, thousands of system parameters and, with appropriate regularization, thousands of observations may be necessary. The SVD method is not practical because it requires significant memory space and is time consuming. In previous work, we demonstrated the LSQR can be used to estimate the many unknown parameters in large groundwater flow inverse problems. However, in doing so, a resolution analysis is needed to characterize the reliability of the resulting model parameters. We adopted an approach developed for large seismic tomography problems and incorporate the PROPACK package into PEST, a model independent parameter estimation program. PROPACK estimates singular values and vectors for large sparse matrices efficiently and accurately based on the Lanczos bidiagonalization, the core of LSQR, with partial reorthogonalization. Unlike other LSQR-based resolution approaches, this PROPACK-based approach calculates the full resolution matrix. We estimate the model resolution matrix for a synthetic approximation based on a regional MODFLOW model of the Trout Lake Basin, Wisconsin, and compare it with results from the more commonly used SVD approach.