Bivariate normal distribution fitting on discontinuity orientation clusters

A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a κ{script}² goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the κ{script}² test results of the IXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters {Mathematical expression} and {Mathematical expression}, based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method.