Development And Application Of The Software 3DCAVF For Curvature Analysis And 3D Visibility Of Structural Surfaces

Researchon the properties of the area adjacent one point on the curve or curved faceand themodality of the curve and curved face is the content of differential geometry. It describes theinwardness and the mathematical expression of the curved face. Translating the complicatedreliant relationship into the linear relationship, and the uneven course into the equable one are thetypical research methods of differential geometry. Differential geometry is widely applied into the mechanics and engineering technology. Butits applications are relatively scarcity in the geology. Many differential geometry concepts can beintroduced into the research of structural geology. It is helpful to establish the accuratelymathematical description of geologic body and to offer the analytic solutions of analysis.Classical differential geometry researching the local properties and geometrical inflexibility hasits abundant content. The curvature analysis is the primary content, and has significance for thequantitative research of structural geology. As a result, the applications of curvature analysis to the structural geology need to bestudied deeply and systematically. Introducing the differential geometry into the quantitativeresearch of structural geology, the accurately description of geologic body, quantitative researchand automatic computer visibility analysis will come true. Furthermore, the three-dimensionalvisibility of structures, visibility and visual expression of results are also indispensably importantcontent of the curvature analysis and shape analysis for structural geology. The research work of this thesis has obtained some certain results in the aspects of thequantitative research of structure geology, curvature analysis of structural surface, proceedingcrack predicting by use of curvature analysis, three-dimensional visibility of structures and thedesigning and development of the Software-3DCAVF for curvature analysis. (1) In the foregoing applications, the formula used to computer the curvature has omitted thefirst partial differential, and it can be valid only for simple thin plate model. The formula haslimitation in structural crack predicting and oil-gas resources researching, for instance, someimportant properties of the fractures development are easy to be ignored. This thesis has obtainedthe general formula for calculating the principal curvature and Gauss curvature. It is proved thatthe previous formula is a just special type of the general one in case of the first partial differentialis omitted. By analysis and actual applications, the general formula has catholicity, and overcomethe limitation of previous formula. The general formula is more suited to use in the crack oil-gasresources research, and can be used to the curvature calculation of the shape analysis of structuralsurfaces and other aspects.4 李志勇:构造面曲率分析及三维可视化软件 3DCAVF 开发与应用 2004.05 With the differential geometry being used as the theoretic tool, this thesis investigates themathematics theories and applied methods of curvature analysis for quantitative study ofstructure geology, and obtained the general formula for calculating the principal curvature andGauss curvature. The general formula has catholicity, and overcome the limitation of previousformula. (2) This thesis has discussed the necessary of introducing the system theories of differentialgeometry into the quantitative description and quantitative research of structural geology. Basedon the current applications of curvature analysis in the geology this thesis summarizes theapplications of curvature analysis in the forecasting of fractures, the analysis of structuraldeformations, the classification of fold, the hidden faults detection, the forecasting and studies ofdeposit and oil-gas resources, and other aspects. This thesis regards witch as the foundation,groping for the more widely applications of it i...