A new gradient regularization algorithm for source term inversion in 1D solute transportation with final observations

In this paper, a new gradient regularization algorithm is introduced and applied to solve an inverse problem of determining source terms in one-dimensional advection–dispersion equation with final observations. By functional approximations, the algorithm is reduced to find an optimal perturbation for a given source parameter involving computations of gradient vectors. In the case of using accurate data, the optimal perturbation can be directly worked out by the least square method; in the case of with random noisy data, regularization strategy may be useful to the realization of the algorithm. As compared with ordinary gradient regularization algorithm, the new gradient regularization algorithm gives a possible approach to the precise choices of optimal regularization parameters. Several numerical simulations under different conditions are carried out showing that the algorithm is feasible and efficient. Furthermore, the algorithm is successfully applied to solve a real life example of determining an average magnitude of groundwater pollution sources.