Geospline: Mathematical Model of 3D Complex Geological Medium

The original approach and releasing software GEOSpline for modeling of complex 3D geological structures are developed. The joint use of parametric b-splines for approximation of arbitrary distributed in space data, to build separate geophysical surface, and volume splines for approximation of continuous volume properties together with special tree-hierarchial structure for ordering of separate surfaces in the model and cutting of their intersecting parts are the original approaches of the development. The developed mathematical model for construction of 3D geological structures with faults allows to create complex geological structures by real data with their 3d visualization, to build adaptive grids for finite-difference and finite element modeling, as well as to make calculations of seismic and other fields in real geological structures. Introduction When the current structure of oil reserves is regressing (number of big reservoirs with high capacity collectors is decreasing, their geographical location is worsening) the requirements to detail and accuracy of the geological medium description increase. These requirements are determined by necessity of searching and determinating of thin and structurally complex oil and gas collectors. All of this causes necessity of creation of more accurate and detail models of the geological medium for solving of direct and invers geological and geophysical problems. The modern level of detail and accuracy of the geological medium description, what is necessary for searching and selection of prospective oil and gas horizons, requires the using of three-dimensional models of geological structures to solve both direct and inverse problems of seismic profiling. Thus, the three-dimensional geological modeling of complex structures with internal boundaries of real arbitrary distributed data for further three-dimensional visualization and calculation of geophysical fields in such structures is an actual problem.