摘要 设有 k 个母体 G1,G2,…,Gk,Fi 为来自母体 Gi 的随机变量,Pi 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-1B 的度量达到极大,则认为这种归属达到最优,于是可用 W-1B 的特征方程的根来度量 W-1B。其所有根的和可以 tr(W-1B)表示,tr(W-1B)表示 W-1B 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。
Abstract:Assuming that there are k parent populations (G,G2,…,Gk) and that Fi whose probability density is Pi, is a random variable from the parent population Gi we can derive both the covariance matrix W in parent population and the covariance matrix B between parent populations 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-1B, 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.