Simultaneous inversion for dispersion coefficients and space-dependent source magnitude in 2D solute transportation

This paper deals with an inverse problem of simultaneously determining the dispersion coefficients and the space-dependent source magnitude in 2D advection dispersion equation with finite observations at the final time. The forward problem is solved by using the alternating direction implicit (ADI) finite difference scheme, and then the optimal perturbation algorithm with the regularization parameter chosen by a Sigmoid-type function is introduced to solve the simultaneous inversion problem numerically. Numerical inversions are presented, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating that the optimal perturbation algorithm with the Sigmoid-type regularization parameter is efficient for the simultaneous inversion problem in 2D solute transportation. Key–Words: 2D advection dispersion equation, simultaneous inversion, optimal perturbation algorithm, regularization parameter, numerical simulation