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Heterogeneity of hydrogeological parameters is typically great and is characterized by multiple spatial scales. Because conventional (wellbore) characterization approaches reflect very localized conditions, they often can not provide characterization data at the scale upon which conceptual models are based and at which remediation work occurs. Geophysical data, collected from the ground surface or between wellbores, hold promise for rapid, minimally-invasive, and vastly improved characterization and monitoring of the shallow subsurface. We have developed several estimation methodologies for use with geophysical data, which permit systematic fusion of multiple sources of information and incorporation of complex petrophysical models. As illustrated by the following links, we have used these methods with high-resolution geophysical data to estimate hydrogeological parameters such as hydraulic conductivity, geochemical heterogeneity, lithology, and moisture movement over time in the subsurface.