Simulation of fine-scale electrical conductivity fields using resolution-limited tomograms and area-to-point kriging

Abstract

SUMMARY Deterministic geophysical inversion approaches yield tomographic images with strong imprints of the regularization terms required to solve otherwise ill-posed inverse problems. While such tomograms enable an adequate assessment of the larger-scale features of the probed subsurface, the finer-scale details tend to be unresolved. Yet, representing these fine-scale structural details is generally desirable and for some applications even mandatory. To address this problem, we have developed a two-step methodology based on area-to-point kriging to generate fine-scale multi-Gaussian realizations from smooth tomographic images. Specifically, we use a co-kriging system in which the smooth, low-resolution tomogram is related to the fine-scale heterogeneity through a linear mapping operation. This mapping is based on the model resolution and the posterior covariance matrices computed using a linearization around the final tomographic model. This, in turn, allows us for analytical computations of covariance and cross-covariance models. The methodology is tested on a heterogeneous synthetic 2-D distribution of electrical conductivity that is probed with a surface-based electrical resistivity tomography (ERT) survey. The results demonstrate the ability of this technique to reproduce a known geostatistical model characterizing the fine-scale structure, while simultaneously preserving the large-scale structures identified by the smoothness-constrained tomographic inversion. Small discrepancies between the geophysical forward responses of the realizations and the reference synthetic data are attributed to the underlying linearization. Overall, the method provides an effective and fast alternative to more comprehensive, but computationally more expensive approaches, such as, for example, Markov chain Monte Carlo techniques. Moreover, the proposed method can be used to generate fine-scale multivariate Gaussian realizations from virtually any smoothness-constrained inversion results given the corresponding resolution and posterior covariance matrices.