[1] We have developed a robust 2D joint inversion scheme incorporating the new concept of cross-gradients of electrical resistivity and seismic velocity as constraints so as to investigate more precisely the resistivity-velocity relationships in complex near-surface environments. The results of joint inversion of dc resistivity and seismic traveltime data from collocated experiments suggest that one can distinguish between different types or facies of unconsolidated and consolidated materials, refining a previously proposed resistivity-velocity interrelationship derived from separate inversions of the respective data sets. A consistent interpretive structural model can be obtained from the joint inversion models.

[1] It is now common practice to perform collocated DC resistivity and seismic refraction surveys that complement each other in the search for more accurate characterization of the subsurface. Although conventional separate DC resistivity and seismic models can be diagnostic, we posit that better results can be derived from jointly estimated models. We make the assumption that both methods must be sensing the same underlying geology and have developed an innovative resistivity-velocity cross-gradients relationship to evaluate the structural features common to both methods. The cross-gradients function is incorporated as a constraint in a nonlinear least squares problem formulation, which is solved using the Lagrange multiplier method. The resultant iterative two-dimensional (2-D) joint inversion scheme is successfully applied to synthetic data (serving as validation tests here) and to field data from collocated DC resistivity and seismic refraction profiling experiments and also compared to conventional separate inversion results. The joint inversion results are shown to be superior to those from separate 2-D inversions of the respective data sets, since our algorithm leads to resistivity and velocity models with remarkable structural agreement.

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We extend the cross-gradient methodology for joint inversion to three-dimensional environments and introduce a solution procedure based on a statistical formulation and equality constraints for structural similarity resemblance. We apply the proposed solution to the joint 3D inversion of gravity and magnetic data and gauge the advantages of this new formulation on test and field-data experiments. Combining singular-value decomposition (SVD) and other conventional regularizing constraints, we determine 3D distributions of the density and magnetization with enhanced structural similarity. The algorithm reduces some misleading features of the models, which are introduced commonly by conventional separate inversions of gravity and magnetic data, and facilitates an integrated interpretation of the models.