Multivariate Statistical Analysis In Formation Evaluation
Authors: Hempkins W. Brent 
Published: December 2007

Hempkins, W. Brent, Standard Oil Company of California

Multivariate techniques are powerful tools for aid in formation evaluation. Some uses of multiple regression, cluster, discriminant, and principle components analyses are given. Case history examples are presented to show how a particular problem was solved with each of these statistical techniques. Examples include problems from California, Colorado, and Gulf Coast fields with data from oil chemistry, conventional well log suites, and nuclear magnetic resonance data. The problems involve reef lithology determination, correlation of producing zones, an pore distribution characterization. pore distribution characterization

Introduction

Statistical approaches to analyses of data have been present since the beginning of the collection of data. These were of course simplistic and largely involved counting traits of objects. In the geological field, we can recognize formal approaches since about 1830. The very recognition of the fact that there are differences between groups of objects forms the basis of such statistical analysis. However, there is a great difference between this recognition of differences and an attempt to formulate probabilistic statements as to the significance of the observed differences.

In formation evaluation, which I consider only another facet of the geological sciences, we have been reluctant to accept the more complex and sometimes more powerful techniques that multivariate statistical analysis offers. It has been stated before by others that there is a difference between multivariate and multivariable analyses. Most workers describe multivariate analysis as the study of more than two variables at a time. Multiple regression is on e such example from two or more variables. Regression is really a multivariable analysis.

Multivariate techniques often take advantage of the redundancy (collinearity) between variables; a multivariable analysis does not necessarily utilize this trait. Thus, one may have many variables present in an analysis but may not use these in a multivariate sense.

For the sake of simplicity, I will treat multiple regression, i.e. the prediction of one variable from two or more variables a multivariate analysis. There are many other techniques such as cluster, discriminant and factor analysis which are definitely multivariate. I surveyed the first 4 years of the Transactions of the Society of Professional Well Log Analysts to see how often multivariate techniques were presented. In the period 1960–1964, there was only 7 papers presented. In the period 1960–1964, there was only 7 papers that involved fitting of a straight line to bivariate data. I was very generous in giving credit for statistical treatment of this data as there were no statistical criteria reported.

As computers and software became more readily available, the use of statistical approaches increased. In the period 1971–1973, I found the number of regression analyses reported was 15. Two of these reported some statistic relating to the goodness of the fitted regression line. None were adequate statistical tests of significances.

In 1976 alone there were 8 simple regression papers, one multiple regression and one on discriminant papers, one multiple regression and one on discriminant analysis.

For the transactions of the SPE from 1940 to 1969 and for JPT 1959 to 1969 there were 12 papers which mentioned a statistical term in the title.

This certainly is not an accurate reporting of the literature, for I personally know of many other papers on formation evaluation which have used multivariate papers on formation evaluation which have used multivariate approaches. They are, however, all within the last 10 years and are few and far between.