An interactive display of results obtained from the inversion of logging data is produced by obtaining and inverting the logging data using a Monte-Carlo inversion. An interactive plot having a percentile scale plotted against a location parameter is produced and a particular percentile is selected using the interactive plot. A cross-section plot for the particular percentile using the results of the Monte-Carlo inversion is produced. The particular percentile can be a curve representing a best-fit solution or a polyline representing selected solutions. Background color/shading can be displayed on the interactive plot to indicate user-defined constraints have been applied. Uncertain features can be plotted on a corresponding cross-section display using fading. Clusters of solutions that are substantially equally likely, given the measurements at a particular drill location, can be identified and plotted. A cross-section constructed from the layered models belonging to a particular cluster can be overlaid on another cross-section.