Application of Statistical Package Programs in Geology, Especially Referring to the Factor Analysis on the Composition of Sandstones

Abstract

The utilization of the package program is introduced with an example of the factor analysis on the geologic data, intending to popularize the computer application in geology.
There are 'enormous amount of data and informations in geology as in other fields of science, and we cannot make good use of them without a help of the high capacity computer. However, special knowledges, experiences, time and labors are required for programming. The program package or package program has been developed for researchers to use the computer more easily and promptly.
We have made efforts to prepare the package program for geologic use (GEOPAK). However, it cannot be completed in a short time, and we would like to introduce some package programs for analyzing geologic problems. There are two popular package programs in the world, the one is the BMD (Biomedical Computer Programs) and the other is the SPSS (Statistical Package for the Social Sciences). The former is famous in the world, for its high computational ability and variety of programs, and has been introduced to almost all the institutes it the United States. The latter has an excellent data file system organically combined with many subprograms for various statistical analyses, and may be called a package program in the strict sense. The both programs have already been introduced into several computer centers in Japan and can be utilized by many scientists.
To show the high usefulness of the package program some basic examples of the SPSS processings are explained at first, that is, set-up of control cards, calculation of descriptive statistics, preparation of histogram and scattergram. Then an example of multivariated analysis by using the SPSS is presented, for the multivariated analysis is one of the most important techniques of the computer application to science. Many attempts to apply the technique to geologic problems have been done showing its usefulness in various branches of geology. However, it is not easy to make up a program in each case. Under such circumstances, the SPSS has made it possible to apply the technique with very simple procedures. Besides the ordinal cards of the SPSS only a few control cards of natural language are needed for the computation.
As an example a factor analysis is presented on the compositional data of sandstones of the Cretaceous Goshonoura and Himenoura Groups in Kyushu, West Japan. The purpose of the factor analysis is to clarify the structure of the data, and as the result some data structures different from those generally accepted have been clarified. For example, the amount of quartz, generally treated as a simple component of informations concerned with the composition of sandstones, has revealed to include two components. It must, therefore, be divided into two types, i.e. metamorphic quartz and igneous quartz. Some factors extracted from the data of the major compositions may be related to some ones extracted from those of the heavy minerals, i.e. the second factor of the former is equivalent to the second factor of the latter, the third factor of the former is opposite to the fourth factor of the latter. The result supports the general triangle diagram in the heavy mineral analysis whose end embers are zircon, garnet and tourmarine.
Although much more examinations should be done before the data structure is clearly defined, such an examination may give us many informations on the data structure and, furthermore, many : suggestions on the collecting technique of the data. The readiness of such a complicated calculation as the factor analysis by using the SPSS helps us check a data structure before collecting and/or interpreting geological data.
Some technical informations and references to use these package programs in the computer centers in Japan are also added for the beginners.