Generation of three dimensional fractal subsurface structure by Voronoi Tessellation and computation of gravity response of such fractal structure

Abstract

The invention is an entirely new application of domain characterization generated by Voronoi tessellation, which is very close to realistic geology and computation of gravity response of such domain, which has three dimensional fractal basin structure, and is favorable for oil exploration. In this work the interfaces or tessellating domains are represented by a set of parameters, which are referred as Voronoi centers. These parameters can be perturbed by any amount without getting into representational problems as faced by the conventional techniques. To accomplish such representation Voronoi tessellation is used, which in two dimensional space consists of enclosing every Voronoi center by a Voronoi polygon such that the common edge of adjacent polygons is perpendicular bisector to the line joining the Voronoi centers on both the sides of that edge. In this invention instead of using conventional Euclidian distances, the notion of Voronoi tessellation is generalized by using Lp distances, where p can hold any real value so that Voronoi domains are not necessarily polygonal. Desired fractal subsurface is generated using this approach that is quite close to the natural settings than the conventional planer or polygonal representation. Next, the gravity response due to this fractal subsurface structure has been computed. The new invention has a significant advantage over the conventional methods especially in geophysical inversion where initial model parameters are updated in each iteration, which can be done more easily and efficiently by Voronoi tessellation merely by changing Voronoi centers.

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