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Abstract:
We present the application of the gradient‐based total least squares (TLS) method to the local estimation of parameters for flow and transport in porous media. The concept is based on the evaluation of partial derivatives of spatially and temporally resolved data using TLS as a maximum likelihood estimator. While ordinary inverse modeling approaches are often complicated by the spatially varying properties of porous media, the present approach can directly localize the estimation to an arbitrary range in space and time. The estimation of the local parameters can be achieved without requiring any explicit solution of the respective transport equation. First the basic ideas and the formalism of TLS are introduced with a simple example of a straight line fit. Then the ideas of the gradient‐based approach and its application to the parameter estimation for a large class of dynamic processes are presented. We further discuss relevant computational issues such as the calculation of the derivatives, choice of the local neighborhood and the determination of a measure of confidence. The performance of the method is then exemplified by the estimation of local velocities and dispersion coefficients from numerical solutions of the convection‐dispersion equation.
