Improved geologic surface approximation using a multiquadric method with additional constraints  

作　　者：SONG Xianfeng RUI Xiaoping JU Yiwen YANG Yongguo 

机构地区：[1]Laboratory of Computing Geodynamics, Graduate University of Chinese Academy of Sciences, Beijing 100049, China [2]School of Resource and Geoscience, China University of Mining & Technology, Xuzhou 221116, China

出　　处：《Mining Science and Technology》2010年第4期600-606,共7页矿业科学技术（英文版）

基　　金：provided by the National Science and Technology Major Project of China (Nos.2009ZX05039-004 and 2009ZX 05039-002);the National Natural Science Foundation of China (Nos.40771167 and 70621001)

摘　　要：Geologic surface approximation is profoundly affected by the presence, density and location of scattered geologic input data. Many studies have recognized the importance of utilizing varied sources of information when reconstructing a surface. This paper presents an improved geologic surface approximation method using a multiquadric function and borehole data. Additional information, i.e., inequality elevation and dip-strikes data extracted from outcrops or mining faces, is introduced in the form of physical constraints that control local changes in the estimated surface. Commonly accepted hypothesis states that geologic surfaces can be approximated to any desired degree of exactness by the summation of regular, mathematically defined, surfaces: in particular displaced quadric forms. The coefficients of the multiquadric functions are traditionally found by a least squares method. The addition of physical constraints in this work makes such an approach into a non-deterministic polynomial time problem. Hence we propose an objective function that represents the quality of the estimated surface and that includes the additional constraints by incorporation of a penalty function. Maximizing the smoothness of the estimated surface and its fitness to the additional constraints then allows the coefficients of the multiquadric function to be obtained by iterative methods. This method was implemented and demonstrated using data collected from the 81'st coal mining area of the Huaibei Coal Group.Geologic surface approximation is profoundly affected by the presence, density and location of scattered geologic input data. Many studies have recognized the importance of utilizing varied sources of information when reconstructing a surface. This paper presents an improved geologic surface approximation method using a multiquadric function and borehole data. Additional information, i.e., inequality elevation and dip-strikes data extracted from outcrops or mining faces, is introduced in the form of physical constraints that control local changes in the estimated surface. Commonly accepted hypothesis states that geologic surfaces can be approximated to any desired degree of exactness by the summation of regular, mathematically defined, surfaces： in particular displaced quadric forms. The coefficients of the multiquadric functions are traditionally found by a least squares method. The addition of physical constraints in this work makes such an approach into a non-deterministic polynomial time problem. Hence we propose an objective function that represents the quality of the estimated surface and that includes the additional constraints by incorporation of a penalty function. Maximizing the smoothness of the estimated surface and its fitness to the additional constraints then allows the coefficients of the multiquadric function to be obtained by iterative methods. This method was implemented and demonstrated using data collected from the 81 ＇st coal mining area of the Huaibei Coal Group.

关 键 词：geologic surface spatial interpolation multiquadric function exterior penalty function physical constraints 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] P618.130.2[自动化与计算机技术—计算机科学与技术]