正则化薄板样条函数拟合地层界面
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- 英文论文题名：Regularization Thin-plate Spline Function Fitting Stratum Interface
- 论文作者：王宝龙 ; 李青元 ; 贾会玲 ; 董前林
- 年：2016
- 作者机构：辽宁工程技术大学测绘与地理科学学院;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;中国矿业大学(北京)地球科学与测绘工程学院;
- 论文关键词：地层界面 ; 薄板样条函数 ; 正则化 ; 等边三角形网
- 英文论文关键词：Stratum Interface ; Thin-plate Spline Function(TPS) ; Regularization ; Equilateral Triangle Mesh
- 会议召开时间：2016-10-21
- 会议录名称：第十五届全国数学地质与地学信息学术研讨会论文集
- 英文会议录名称：Proceedings of the 15th National Workshop on Mathematical Geosciences and Geoinformatics
- 语种：中文
- 分类号：TE142;P628
- 学会代码：ZSYD
- 会议名称：第十五届全国数学地质与地学信息学术研讨会
- 会议地点：中国湖南长沙
- 主办单位：中国地质学会数学地质与地学信息专业委员会、中南大学、湖南省国土资源厅、湖南省地质学会
- 学会名称：中国地质学会数学地质与地学信息专业委员会
- 页数：6
- 文件大小：1105k
- 原文格式：D
- 会议级别：全国
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,提出用薄板样条曲面拟合构建地层界面的方法。简要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格网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。
Corresponding to the mechanical mechanism of the thin-plate spline mathematically, the geometry deformation of stratum interface follow the principle of the forced plate body bent form, a thin-plate spline function is proposed to construct stratum interface. First of all, the basic principle of the thin-plate spline is 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 regularization thin-plate spline function is proposed to solve the 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 are used to subdivide stratum interface and the value of mesh vertexes are fitted by the regularization thin-plate function. At last, the visualization and precision of the fitting stratum interface are required by adjusting the value of the regularization parameter.
Corresponding to the mechanical mechanism of the thin-plate spline mathematically, the geometry deformation of stratum interface follow the principle of the forced plate body bent form, a thin-plate spline function is proposed to construct stratum interface. First of all, the basic principle of the thin-plate spline is 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 regularization thin-plate spline function is proposed to solve the 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 are used to subdivide stratum interface and the value of mesh vertexes are fitted by the regularization thin-plate function. At last, the visualization and precision of the fitting stratum interface are required by adjusting the value of the regularization parameter.
引文
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[2]邹才能,董大忠,王玉满,等.2015.中国页岩气特征、挑战及前景(一)[J].石油勘探与开发,42(6):689-701
[3]邹才能,董大忠,王玉满,等.2016.中国页岩气特征、挑战及前景(二)[J].石油勘探与开发,43(2):1-13
[4]王仁宏,李崇君等.计算几何教程[M].北京:科学出版社,2008.
[5]TIKHONOVAN,ARSENINVY,Solutions of ill-posed problems[M].New York,USA:John Wiley and Sons,1997:200-21.