Method For Representing The Geological Body Heterogeneous Property Field Using The Quadratic Generalized Tri-prism Volume Function Model

3D geological modeling is an effective tool for subsurface space informationization,it should accurately represent geometric structure boundary and property field of geobject,which provides an important reference for geological industry production.Traditionally,most researches have focused on the geometric modeling of the complex geological body,but the heterogeneous geological property field is rarely studied,such as the sedimentary strata property field with geological interface constrain.However,the spatial distribution of property fields in numerical simulation and calculation has a great deal of practical significance and economic value than 3D visualization.Directly using geostatistical interpolations in voxel models is the common method in GIS field,but the precision is depended on the voxel size,so voxel models require a huge amount of data with high accuracy.In addition,stratified geological body has many complex geometric constrains,like fault,fold and missing strata,and spatial interpolation method needs combine the geological geometric structure constrain,it could represent the spatial distribution of property field correctly.However,Engineers previously lacked appropriate methods designed to represent heterogeneous property fields,it both takes into account the special situation of the geological body and meets the precision requirements.To address the problem,a method was proposed in this paper,quadratic general tri-prism volume function model(QGTPVF),it is a type of the volume function model.The volume function model is based on the 3D geometric voxel model and extended to the four dimensions space to express the geological property change.It is defined as a piece function to describe a parameterized geological property field space and created by fitting property function of voxel.The fitting subdomain of QGTPVF is the generalized tri-prism(GTP)voxel,the precision reaches to quadratic mathematic function,and it is designed for the borehole sample data and sedimentary strata structure.So the QGTPVF could combine the stratiform geometric structure constrain,including geological interface,fault and boundaries,and GTP could distinguish bedding and cross-bedding direction,so the QGTPVF has better geological interpretation.A property field of sedimentary strata could be fitted according to the stratum separately,a stratum property field consists of the single QGTPVF,a voxel's property change is expressed with a continuous volume function,then the property field function could be obtained by smooth adjustment among adjacent QGTPVF in a continuous unit,and the property change rate also could be adjusted when possible,this is the essence of the QGTPVF.Like the spline function interpolation,the volume function fitting focuses on the local simulation but global,and the local error could not spread to global,this is different to the geostatistical spatial interpolation method.In addition,this paper mainly study the methodology of fitting the stratified geologic body's QGTPVF,but the detailed geological context and complex geological geometric modeling method are unconcerned.This paper discussed the essential characteristic of the stratiform geological body,including geological property sample data,voxel geometric model method and spatial interpolation method.The basic definition of volume function model is introduced in detailed,it includes mathematical meaning and geometric meaning;the type of volume function are linear or quadratic tetrahedron and GTP;and the general process of fitting property field by volume function,it is similar with the building mechanism of the spline surface and B-spline volume.QGTPVF fitting theory is the research focus of this paper,the model definition is given firstly,and it is different between voxel model and B-Rep method.The barycentric coordinate theory and quadratic GTP element are introduced to fit a single QGTPVF,and an iterative average method is proposed to adjust adjacent QGTPVF of bedding direction smoothly.If the change rate of bedding and cross-bedding is different,method for adjusting cross-bedding change rate is also given in this paper.In order to apply this method in geological engineering,the general process framework of building geological property model is given in this paper,and the solution of the crucial issues are also studied,the preprocess method of fault and missing stratum is used for building complex stratiform geological property model,the method of determining bedding directional GTP number is also discussed in context of dense sample data.In addition,QGTPVF could be converted to tetrahedron voxel and 3D grid model,and the QGTPVF could be used to.numerical analysis and computing directly.The feasibility study of this method is proved by a coal-bed gas application,and the precision is also verified by a cross-validation method of kriging and Inverse Distance Weighted(IDW)interpolation.The reason for causing error and parameter correction method are also discussed.Finally,the application scope and advantages of the QGTPVF method are concluded,it is the important guideline for practice geological application.