Computationally Efficient Regularized Inversion for Highly Parameterized MODFLOW Models

Though popular in the geophysical modeling community, specification of spatially distributed parameters at a scale commensurate with prevailing geological heterogeneity has not been possible in common groundwater modeling practice. The principal reasons for this are (1) the high computational burden of obtaining derivatives necessary for parameter estimation, (2) the memory required to store the derivative and coefficient matrices generated in classical Levenberg-Marquardt methods, and (3) lack of experience within the groundwater modeling community with regularized inversion. The development of adjoint state derivatives calculation within MODFLOW-2000 removed the first of these roadblocks. Efficient compression of the sensitivity matrix (Jacobian) within the inversion code PEST dramatically reduces memory requirements while increasing solution speed. An independent regularization model allows for the specification of arbitrarily complex linear and non-linear regularization schemes. These developments have enabled investigation of the role of various regularization schemes within systems comprising many hundreds to thousands of parameters. Some example regularization schemes are presented for use in different model calibration settings. The methods presented complement zone and pilot-point based parameterization schemes for complex 2and 3-dimensional groundwater systems, due to the ability to accommodate the estimation of a large number of parameters in a numerically stable and geologically realistic manner.