An Application of the Geostatistical Approach to the Inverse Problem in Two‐Dimensional Groundwater Modeling

Abstract

The geostatistical approach to the estimation of transmissivity from head and transmissivity measurements is developed for two‐dimensional steady flow. The field of the logarithm of transmissivity (log‐transmissivity) is represented as a zero‐order intrinsic random field; its spatial structure is described in this application through a two‐term covariance function that is linear in the parameters θ 1 and θ 2 . Linearization of the discretized flow equations allows the construction of the joint covariance matrix of the head and log transmissivity measurements as a linear function of θ 1 and θ 2 . In this particular application the coefficient matrices are calculated numerically in a noniterative fashion. Maximum likelihood estimation is employed to estimate θ 1 and θ 2 as well as additional parameters from measurements. Linear estimation theory (cokriging) then yields point or block‐averaged estimates of transmissivity. The approach is first applied to a test case with favorable results. It is shown that the application of the methodology gives good estimates of transmissivities. It is also shown that when the transmissivities are used in a numerical model they reproduce the head measurements quite well. Results from the application of the methodology to the Jordan aquifer in Iowa are also presented.