Translating tomographic ambiguity into the probabilistic inference of hydrologic and engineering target parameters

Abstract

Geophysical tomography allows for spatially continuous imaging of physical parameters. In many hydrological or engineering exploration tasks, other parameters than those imaged by geophysical tomography are of higher interest, but they cannot be measured continuously in space. We have developed a methodology linking multiple tomograms imaging different physical parameters with a sparsely measured target parameter striving to achieve probabilistic, spatially continuous predictions of the target parameter distribution. Building on a fully nonlinear tomographic model reconstruction searching the solution space globally, we translate the tomographic model reconstruction ambiguity into the prediction of the target parameter. In doing so, we structurally integrate physically different tomograms achieved by individual inversion by transforming them into fuzzy sets. In a postinversion analysis, systems of linear equations are then set up and solved linking the fuzzy sets and sparse information about the target parameter, e.g., measured in boreholes. The method is fully data driven and does not require knowledge or assumptions about the expected relations between the tomographically imaged physical parameters and the target parameter. It is applicable to 2D and 3D tomographic data. Practically, the parameter interrelations can be of any complexity, including nonuniqueness. We evaluate the methodology using a synthetic database allowing for maximal control of the achieved predictions. We exemplarily predict 2D probabilistic models of porosity based on sparse porosity logging data and sets of equivalently plausible radar and seismic-velocity tomograms.