Approximate sensitivity coefficients for integrating hydraulic head data into geological models

Abstract

It is straightforward to obtain an approximation of the matrix of sensitivity coefficients of hydraulic head response at a set of calibration data locations to the values of permeability at each model cell. The approximate system of sensitivities consists of an indicator matrix of zeros and ones flagging locations of significant parameter sensitivity, with the appropriate sign. A rules-based approach for determining the required parameter sensitivity information is based upon: (1) delineation of flowpaths through the calibration head data, (2) transformation of the permeability field into a binary categorical variable in order to define relatively high-transmissivity and low-permeability geobodies, and (3) identification of geobody connections to source or sink terms. A comparison with traditionally-computed exact sensitivity coefficients demonstrates the completeness of the approximate system of coefficients and that their use in iterative model calibration codes is feasible. The merit of this study is not only in demonstrating a relatively simple assessment of permeability sensitivity to hydraulic head, but also to provide a general understanding of these sensitivity coefficients. Visualizing the Jacobian matrix reveals the physically-intuitive criteria that govern the structure of the sensitivity coefficients and precisely identifies which criteria affect the sensitivity of the hydraulic head response to the permeability field.