Morphological approach to volume calculation of complex 3D geological objects

This paper presents a new approach capable of volume calculation of 3D reconstructed geological objects. The method is based on a well-known concept that states the volume of an object can be computed as the limit of the sum of the area of infinite number of sections, which cut the 3Dobject. Since shortage of input data about the geological objects usually exists, Mathematical Morphology and polynomial interpolation are employed to generate a set of intermediate sections between the set of initial sections. A Mathematical Morphology tool is applied to compute the area of the two of sets initial and generated 2D sections. Regularities together with Delaunay Triangulation are employed to perform 3D reconstruction. A formula is developed on purpose of volume calculation of the reconstructed objects. A set of ten theoretical, electrical resistivity cross-sections were generated and used to perform an experiment to show the capability of our approach to estimate the volume of complex 3D geological object in case of sparse 2D sections. The volume determined using the morphological approach presented in this paper show good correlation with the volume of the original input object. Advantages and disadvantages of our volume calculation approach are discussed in the conclusion of this paper. Keywords: electrical resistivity, sparse 2D sections, geological objects, smooth 3D visualization and volume calculation.