Joint two‐dimensional DC resistivity and seismic travel time inversion with cross‐gradients constraints

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.