以高斯理论为基础计算弯曲钻孔节点空间坐标  

THE CALCULATION OF THE SPATIAL VALUES FOR NODES OF THE CURVE ON THE CROOKED BOREHOLE BY GAUSS NUMERICAL DIFFERENTIATION

作　　者：朱学立[1] 燕长海[1] 胡安国[2] 李荣成[2] 

机构地区：[1]河南省地质调查院,河南郑州450007 [2]河南省科学院数学研究所,河南郑州450053

出　　处：《物探化探计算技术》2007年第6期545-549,共5页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：国家863项目(2002AA134010)

摘　　要：为了拟合出更加接近钻孔实际的曲线,结合钻孔测斜实际,以严密的高斯理论为基础,给出了以钻孔天顶角和倾角为参数的弯曲钻孔的参数方程。并在此基础上,推出了钻孔曲线各点的计算公式,更准确地描述了钻孔的实际情况,为后续工作剖面图的绘制和储量计算提供了基础。这里使用高斯和折线法作为一个实例,对比计算了赤土店铅锌矿区ZK13002钻孔。计算结果表明:在钻孔曲线形状、累计弧长、插值点特征等多个方面的高斯法都优于折线法,而因算法的改变引起的工作量又是很小的。In order to draft the correct curve approximating to the real hole, authors have collected many data of the measured points on the crooked borehole,and taken the zenith angle and dip angle of the borehole as parameters to establish the calculation equation of the spatial values of the points in the hole based on the Gauss numerical differentiation theory.The correct hole positions calculated can provide convenience for the later work,such as making the geological section and calculating the reserves.Taking the drill ZK13002 in a lead-zinc ore deposit as an example,the calculations are made through two methods: the traditional polygonal line and Gauss numerical differentiation, respectively. The results show that the mathematic method is superior to the traditional one according to the calculation and description to the shape of the hole curve,the total length of the arc and the characters of the interpolates with adding minor workload.

关 键 词：高斯理论 钻孔节点 空间坐标 计算 

分 类 号：O241[理学—计算数学]