一种适用于泛克里金趋势函数的优化方法  

An Optimization Method for Universal Kriging Trend Function

作　　者：杨金璇 潘懋[1,2] 刘钰洋 雷征东[3] 吴耕宇[1,2] YANG Jinxuan;PAN Mao;LIU Yuyang;LEI Zhengdong;WU Gengyu(School of Earth and Space Sciences of Peking University,Beijing 100871;Institute of Oil and Gas of Peking University,Beijing 100871;Research Institute of Petroleum Exploration&Development,Beijing 100083)

机构地区：[1]北京大学地球与空间科学学院造山带与地壳演化教育部重点实验室,北京100871 [2]北京大学石油与天然气研究中心,北京100871 [3]中国石油勘探开发研究院,北京100083

出　　处：《计算机与数字工程》2020年第2期271-276,共6页Computer & Digital Engineering

基　　金：国家科技重大专项(编号:2017ZX05013002-002)资助。

摘　　要：由于地质参数空间分布特征存在自相关和互相关的特性,未知点属性值可通过特定方法内插得到。泛克里金插值方法正是结合数据的相关特性,计算未知点属性值的算法。泛克里金方法使用前提是样品点满足正态分布,但正态分布不能代表样品点的地质属性在研究区内具有一定的变化规律,即不能保证趋势函数的有效性。因此,在样品点满足正态分布的前提下,对趋势函数的精度进行研究是必要的。论文提出,在插值过程中,应用多元线性回归拟合样品点在研究区域内的变化趋势,对趋势函数应用残差分析方法,剔除奇异点,可以达到对趋势函数的优化。在实例应用中,运用论文方法对孔隙度数据进行插值,结果与未使用残差分析的泛克里金插值结果相比较,论文方法插值效果更好。Due to the autocorrelation and cross-correlation properties of the spatial distribution characteristics of geological parameters,the properties of unknown points can be interpolated by specific methods. Universal Kriging(UK)method is an algorithm that combines the relevant characteristics of data to calculate the characteristics of unknown points. The use of UK method is that the sample points satisfy the normal distribution,but the normal distribution does not mean that the geological properties of the sample points have a certain variation law in the study area,that is,the validity of the trend function cannot be guaranteed. Therefore,it is necessary to study the accuracy of the trend function on the premise that the sample point satisfies the normal distribution. In the UK interpolation process,a multiple linear regression method is applied to fit the variation trend of the sample points in the study area.The residual analysis method is applied to the trend function,and the error points are eliminated to achieve the precision optimization of the trend function. In the example application,the porosity data is interpolated by the method of this paper,and the results are proved to be better than the results of the UK without residual analysis.

关 键 词：泛克里金 残差分析 奇异点 

分 类 号：O174[理学—数学]