In this paper, a comparison between the marching-jury backward beam equation (MJBBE) and the quasi-reversibility (QR) methods to perform hydrologic inversion and, more specifically, to reconstruct conservative contaminant plume spatial distributions is presented. The MJBBE, developed by Atmadja and Bagtzoglou <2000, 2001a>, was used to recover contaminant spatial distributions in heterogeneous porous media, while the QR method, first applied to groundwater contamination problems by Skaggs and Kabala <1995>, was modified to incorporate heterogeneity and explicitly handle the advective term of the transport equation. Spatially uncorrelated and correlated, stationary and nonstationary, heterogeneous dispersion coefficient fields were generated using the Bayesian nearest neighbor method (BNNM). Homogeneous and deterministically heterogeneous cases are also presented for comparison. In addition, contaminant plume initial data with uncertainty were also analyzed using the MJBBE and QR methods. The MJBBE is found to be robust enough to handle highly heterogeneous parameters and is able to preserve the salient features of the initial input data. On the other hand, the QR method is superior in handling cases with homogeneous parameters and with initial data that are plagued by uncertainty but it performs very poorly in cases with heterogeneous media.