Damped least-squares inversion of confined aquifer pumping data based on singular value decomposition

An iterative method for calculating the transmissivity and storage coefficient from pumping test data for a confined aquifer is presented. The method optimizes the fit between the measured and the theoretical data (computed using the Theis equation) in the leastsquare sense. Unlike the existing schemes, this method employs the Levenberg-Marquardt method and the singular value decomposition technique resulting in a stable and rapidly convergent data inversion algorithm. The inverse procedure is initialized by an automatically created starting model derived using a novel technique that operates on the timederivative of the drawdown curve. An important feature of the algorithm is that all the computations are done in logarithmic space which effectively linearizes the pmblem. The proposed method has several advantages over the conventional iterative inversion algorithms because of the linearizing parameterizations at both the forward and inverse stages of the problem. Detailed derivations of the basic equations are provided to guide the potential users as well as applications to field data to demonstrate the usefulness of the proposed algorithm.