Geologic interpretation of 3D anisotropic resistivity models from conventional marine controlled-source electromagnetic (CSEM) data inversion faces difficulties in low-resistivity contrast sediments and structurally complex environments that typify the new frontiers for hydrocarbon exploration. Currently, the typically reconstructed horizontal resistivity and vertical resistivity models often have conflicting depth structures that are difficult to explain in terms of subsurface geology, and the resulting resistivities may not be close to the true formation resistivities required for estimating reservoir parameters. We have investigated the concept that an objective geologically oriented or structurally tailored inversion can be achieved by requiring that the cross-product of the gradient of horizontal resistivity and the gradient of the vertical resistivity is equal to zero at significant geologic boundaries. We incorporate this boundary-shape criterion in our 3D inverse problem formulations, implemented within nonlinear model-space and conjugate-gradient contexts, for cases in which a priori calibration data from wells and/or seismically derived subsurface boundaries are available and for cases in which these are lacking. The resulting fit-for-purpose solutions serve to better analyze the peculiarity of a given data set. We applied these algorithms to synthetic and field CSEM data sets representing a fold-thrust environment with low-resistivity and low-contrast sediments. The resulting and models from cross-gradient joint inversion of synthetic data of appropriate frequency bandwidth without a priori information are structurally similar and consistent with the test models, whereas those from the inversions of band-limited field data are consistent with the available seismic and resistivity well-log data. This particular approach will thus be useful for lithologic correlation in frontier regions with limited a priori information using broadband CSEM data. For these band-limited field data, we found that the anisotropic bulk resistivities of the low-contrast sediments are better determined by incorporating a priori calibration data from triaxial resistivity logs and seismic horizons.