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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 …