正则化薄板样条函数拟合地层界面  

Fitting stratum interface through regularized thin-plate spline function

作　　者：王宝龙[1] 李青元[2] 贾会玲[3] 董前林[3] 魏竹斌 李青[1] 

机构地区：[1]辽宁工程技术大学测绘与地理科学学院,辽宁阜新123000 [2]中国测绘科学研究院地理信息工程国家测绘地理信息局重点实验室,北京100830 [3]中国矿业大学(北京)地球科学与测绘工程学院,北京100083

出　　处：《煤田地质与勘探》2017年第5期23-27,32,共6页Coal Geology & Exploration

基　　金：国家自然科学基金项目(41272367)~~

摘　　要：地层界面几何形态形成的力学机理与数学上广泛应用的薄板样条形成的力学机理十分相似,都遵循板状体受力弯曲变形的力学机理。通过分析讨论曲面拟合的常用方法,以及这些方法对于稀疏不均匀离散地层界面的采样数据应用中的不足,提出用薄板样条曲面拟合构建地层界面的方法。介绍了薄板样条函数的基本原理,并引入正则化方法来解决因原始采样点分布不均匀而导致曲面拟合中发生"过冲"现象(在数据贫乏区域,产生陡坡的现象)以及原始采样点存在噪声的问题。最后以某页岩气勘探区水平钻井数据为例,用具有最优几何形态的等边三角形网格加密数据点的方式构建地层界面,采用正则化的薄板样条函数确定这些加密点,通过调节正则化参数的值,使拟合的地质界面在可视化效果和精度上都能满足要求。The mechanical mechanism of formation of stratum interface geometry is very similar to that of thin-plate spline widely used mathematically,both follow the mechanical mechanism of bending deformation of stressed plate.This paper introduced the common methods of surface fitting and their deficiencies of fitting the sparse and discrete original sampling points,then a thin-plate spline function was proposed to construct stratum interface.First of all,the basic principle of the thin-plate spline was presented briefly.In some cases,fitting surface overshoots due to original sampling points are distributed unevenly in the study area and at the same time the original data are also noisy,a regularized thin-plate spline function was proposed to solve two problems.Taking the horizontal drilling data in an shale gas field for example,in order to construct stratum interface,the equilateral triangle mesh with optimal geometry was used to subdivide stratum interface and the value of mesh vertexes was fitted by the regularized thin-plate function.At last,the value of the regularization parameter was adjusted to make the visualization and precision of the fitting stratum interface meet the requirements.

关 键 词：地层界面 薄板样条函数 正则化 等边三角形网 

分 类 号：P208[天文地球—地图制图学与地理信息工程]