CONTINUOUS-TIME STOCHASTIC-ANALYSIS OF GROUNDWATER-FLOW IN HETEROGENEOUS AQUIFERS

The problem of depth-averaged groundwater flow in heterogeneous aquife rs is looked at from a stochastic point of view. The Galerkin finite e lement version of the linearized stochastic equation governing the flo w is solved analytically in time using an eigenvalue-eigenvector techn ique. The stochastic solution, which is valid for small variance of aq uifer log transmissivity, relates spatial and temporal variabilities o f aquifer head to aquifer heterogeneity, stochastic recharge, and rand om initial head. The computational effort requires the evaluation of i ntegrals of matrices whose elements are linear functions of the nodal mean heads. The solutions are obtained for the exact (i.e., continuous ) and quasi-steady approximation of the mean head. Aquifer-head tempor al covariances are evaluated using standard matrix operations once the storage matrix is inverted and the associated generalized eigenvalue problem is solved. Implication of the level of spatial discretization on the performance of the solution is examined, and the influence of a quifer heterogeneity on spatial and temporal variances of hydraulic he ads is investigated in the presence of a semipervious boundary.