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This paper presents a new joint inversion approach to shape-based inverseproblems. Given two sets of data from distinct physical models, the mainobjective is to obtain a unified characterization of inclusions within thespatial domain of the physical properties to be reconstructed. Although ourproposed method generally applies to many types of inversion problems, the mainmotivation here is to characterize subsurface contaminant source-zones byprocessing down gradient hydrological data and cross-gradient electricalresistance tomography (ERT) observations. Inspired by Newton's method formulti-objective optimization, we present an iterative inversion scheme thatsuggests taking descent steps that can simultaneously reduce both data-modelmisfit terms. Such an approach, however, requires solving a non-smooth convexproblem at every iteration, which is computationally expensive for apixel-based inversion over the whole domain. Instead, we employ a parametriclevel set (PaLS) technique that substantially reduces the number of underlyingparameters, making the inversion computationally tractable. The performance ofthe technique is examined and discussed through the reconstruction of sourcezone architectures that are representative of dense non-aqueous phase liquid(DNAPL) contaminant release in a statistically homogenous sandy aquifer. Inthese examples, the geometric configuration of the DNAPL mass is consideredalong with additional information about its spatial variability within thecontaminated zone, such as the identification of low and high saturationregions. Comparison of the reconstructions with the true DNAPL architectureshighlights the superior performance of the model-based technique and jointinversion scheme.

A Geometric Approach to Joint Inversion with Applications to Contaminant Source Zone Characterization