Autocorrelation can also be used to measure the degree of similarity among porosity values measured at different locations. Cross correlation and autocorrelation are important to the analysis of repeated patterns observed in time and space, such as depth-related data recorded from geological stratigraphic sequences. Multiple correlation and partial correlation are useful when studying relationships involving more than two variables. Correlation based on the ranks (numerical ordering) of measurements of two variables is an important alternative for simple linear correlation when the number of samples is small and/or the joint distribution of the two variables is not simple. Many useful types of correlation other than simple linear correlation exist. = corresponding sample (arithmetic) means.
= corresponding ith observation of the second variable.= ith observation of the first variable.Where the summation is made over the n sample values available and where The sample value of r, which can range from -1 to +1, is computed using the following formula: The correlation coefficient (also called the Pearson correlation coefficient), r, is a dimensionless numerical index of the strength of that relationship. The term correlation most often refers to the linear association between two quantities or variables, that is, the tendency for one variable, x, to increase or decrease as the other, y, increases or decreases, in a straight-line trend or relationship. The investigation of permeability- porosity relationships is a typical example of the use of correlation in geology. The regression line is determined so as to minimize the sum of squared deviations:Ĭorrelation analysis, and its cousin, regression analysis, are well-known statistical approaches used in the study of relationships among multiple physical properties. Note the negative slope corresponding to a negative correlation.
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