And the geophysicist replied: “Which model do you want?”

Abstract

Marine controlled-source electromagnetic (CSEM) and magnetotelluric (MT) soundings were carried out between 1997 and 2003 over the Gemini prospect in the Gulf of Mexico during early development of marine instrumentation. The resulting data sets provide a good test bed for examining the effect of the data type and misfit choice on regularized inversion solutions. We inverted the data sets individually and jointly for isotropic and anisotropic resistivity at a variety of data misfits. We found that multifrequency CSEM inversions vastly improved structural resolution over single-frequency inversions, suggesting that variation in skin depth added significant information. Joint MT and CSEM inversion appeared to improve resolution over MT-only inversions at depths considerably deeper than the CSEM data can resolve, probably by constraining shallow structure in the parts of the model to which the MT data were sensitive. The addition of model anisotropy improved data fit, but introduced an arbitrary scaling between the regularization penalty on model roughness and the penalty on anisotropy. A small relative penalty on anisotropy produced two independent models for horizontal and vertical resistivity, whereas a large penalty reproduced the isotropic models. Intermediate penalties produced pleasing models, but there was no objective criterion to choose one particular model. Inverted models also depend significantly on the choice of target data misfit, but the optimum misfit is difficult to determine even with well-estimated errors. So-called L-curves do not provide an objective choice of misfit because they are both heuristic and depend on the choice of data that is plotted. Various measures of structure in data residuals were tested in an attempt to guide the misfit choice, with some success, but this too was somewhat heuristic. Ultimately, of the 100 or so inversions that were run, no single model could be considered “preferred,” but together they provided a good understanding of the information contained in the data.