Visualization of subsurface data using three-dimensional cartograms

Abstract

A three-dimensional cartogram is a thematic 3D map on which the volume of each region is linearly proportional to an extensive property enclosed within. This work formulated a 3D cartogram using a linear diffusion process. The 3D cartogram algorithm may be applied to a uniform Cartesian grid such that the distribution of the property of interest, such as the hydrocarbon pore volume in each cell, is equalized throughout the transformed domain. The spatial distortion of the grid cells serves as the qualitative indicator of this property, and the color may be used to visualize the spatial distribution of another property, such as permeability. Such a 3D cartogram on which a second property is mapped is a two-variable 3D cartogram.