Assessing the probability of training image-based geological scenarios using geophysical data

In multiple-point statistics (MPS), the construction of training im-ages (TIs) is one of the most critical steps. Reliable geological studies may not always be available to depict with certainty what geological patterns or heterogeneity are present. In this context, geophysical techniques may provide additional information to reduce the possible large uncertainty in the understanding of prior geological scenarios. \\To overcome this problem, we developed a methodology to verify the consistency of geophysical data with independently-built TIs representing different plausible geological scenarios. If a TI is deemed consistent with the field geophysical survey, then in a sec-ond step we calculate a likelihood probability for each consistent TI. Our methodology starts by creating subsurface models with each TI. From these models we create synthetic geophysical data and from this synthetic data, synthetic inverted models. These models are now compared with a single inverted model obtained from the field sur-vey, allowing for our definition of what is {``}consistent{''}. To that ex-tent, we calculate the Euclidean distance between any two inverted models as well as field data and visualize the results in a 2D or 3D space using multidimensional scaling (MDS). With this technique, it is possible to verify if field cases fall in the distribution represented by synthetic cases, and thus are consistent with them. In a second step, we present a cluster analysis on the MDS-map to highlight which parameters are the most sensitive for the construction of TI. Based on this analysis, a probability of each geological scenario is computed through kernel smoothing of the densities in reduced pro-jected metric space. \\This approach was tested using electrical resistivity tomography as geophysical data to analyze TI scenarios for the Meuse alluvial aqui-fer (Belgium), where the lack of reliable sedimentological data lead to the definition of a multitude of geological scenarios, hence TIs