最大迹判别分析及其在识别油气异常中的应用

Maximum-trace discriminate analysis and its application to identifying oil-gas indication

设有 k 个母体 G_1,G_2,…,G_k,F_i 为来自母体 G_i 的随机变量,P_i 为其概率密度,根据多元统计分析理论,可以求出母体内的协方差阵 W 和各母体间的协方差阵 B。当样本归属于不同的母体空间时,则会引起 W 和 B 的变化。若某一种归属能使 W^(-1)B 的度量达到极大,则认为这种归属达到最优,于是可用 W^(-1)B 的特征方程的根来度量 W^(-1)B。其所有根的和可以 tr(W^(-1)B)表示,tr(W^(-1)B)表示 W^(-1)B 的迹。利用最大迹的判别分析方法可以识别油气异常。文中给出判别准则及具体计算方法,并以一个试验区为例,选取构造、层厚度、层振幅、层频率和层速度等五个参数变量组成五元变量,进行方差分析、均值检验和评判,说明这种方法具有识别油气的能力。

Assuming that there are k parent populations(G_1,G_2,…,G_k)and that F_i,whose probability density is P_i,is a random variable from the parent population G_i,we can derive both the covariance matrix W in parent population and the covariance matrix B between parent popula- tions in the light of multivariate statistical analysis theory.W and B vary when samples belong in different parent-population spaces.If a belongingness makes W^(-1)B maximum,we consider the belongingness as optimum one,and then use the root of characteristic equation of W^(-1)B to measure W^(-1)B.The sum of all roots can be expressed as tr(W^(-1)B), which expresses the trace of W^(-1)B.Oil and gas indications can be identified using the maximum-trace discriminate analysis.Both the discrimination criterion and the computation method are given here.We made variance analysis,average examination and discrimination of five variables relating to a given formation,which are structure,thickness, reflection amplitude,reflection frequency and interval velocity.It has been proved that this method is applicable for identifying oil and gas.