### Wykorzystanie metod analizy skupień w interpretacji pionowych sondowań elektrooporowych (PSE)

#### Abstract

THE USE OF CLUSTER ANALYSIS METHODS IN INTERPRETATION OF ELECTRIC RESISTANCE PROFILLING

Summary

The quantitative interpretation is the basic method in analysis of results of vertical electric resistance profilling. However, this requires interpretation of each curve separately which becomes laborious and time-consuming task when the number of curves is large. This procedure may be facilitated by using a technique of preliminary processing of measurement data by clustering curves into groups of curves similar in character. The interpretation of curves put into such groups is less time-consuming, easier and more reliable. Moreover, such groups when shown in a map tend to reflect geological-tectonic structure of an area. The hitherto used techniques involve compilation of maps of curve types (4, 7) and the use of calculations of similarity of curves ("association parameters" - Habberjam, 2, 3, and Landa and Mazac, 5).

The author proposes the use of statistic method - hierarchical analysis of clusters (Davis, 1), widely used in natural sciences. The method involves calculations of similarity measures for individual measurements and groups of measurements. In the present case, its final product is a dendrogram with hierarchical structure, well showing similarities and correlations between individual curves of electric resistance profilling. Correlation coefficient (formula 2), cosinus of angle (formula 3) and Euclid distance (formula 4) were here used as similarity measures, and the modes of weighted means and single joining - in clustering measurements into groups (Fig. 1).

A set of 142 curves of electric resistance profilling, obtained for 10 profiles in the vicinities of Braszowice in the Lower Silesia (Peroń, 6), was used for testing the above method. Correlation maps were drawn with reference to subdivision of the profillings in accordance to relevant dendrograms (Figs. 2a, b, c) and results of computer calculations. Maps and dendrograms calculated for individual measures markedly differ from one another whereas those calculated for the same similarity measure are practically identical, despite of differences in the mode of clustering. That is why only maps and dendrograms obtained for single joining are shown here (Fig. 2).

Visual assessment of correlation maps and dendrograms and their comparison with geological map (Fig. 3) make it possible to state that the best results are obtained using Euclid distance as similarity measure. The results are the best both in the case of subdivision of electric resistance profilling curves within a dendrogram and comparison of correlation maps with the geological once.

Summary

The quantitative interpretation is the basic method in analysis of results of vertical electric resistance profilling. However, this requires interpretation of each curve separately which becomes laborious and time-consuming task when the number of curves is large. This procedure may be facilitated by using a technique of preliminary processing of measurement data by clustering curves into groups of curves similar in character. The interpretation of curves put into such groups is less time-consuming, easier and more reliable. Moreover, such groups when shown in a map tend to reflect geological-tectonic structure of an area. The hitherto used techniques involve compilation of maps of curve types (4, 7) and the use of calculations of similarity of curves ("association parameters" - Habberjam, 2, 3, and Landa and Mazac, 5).

The author proposes the use of statistic method - hierarchical analysis of clusters (Davis, 1), widely used in natural sciences. The method involves calculations of similarity measures for individual measurements and groups of measurements. In the present case, its final product is a dendrogram with hierarchical structure, well showing similarities and correlations between individual curves of electric resistance profilling. Correlation coefficient (formula 2), cosinus of angle (formula 3) and Euclid distance (formula 4) were here used as similarity measures, and the modes of weighted means and single joining - in clustering measurements into groups (Fig. 1).

A set of 142 curves of electric resistance profilling, obtained for 10 profiles in the vicinities of Braszowice in the Lower Silesia (Peroń, 6), was used for testing the above method. Correlation maps were drawn with reference to subdivision of the profillings in accordance to relevant dendrograms (Figs. 2a, b, c) and results of computer calculations. Maps and dendrograms calculated for individual measures markedly differ from one another whereas those calculated for the same similarity measure are practically identical, despite of differences in the mode of clustering. That is why only maps and dendrograms obtained for single joining are shown here (Fig. 2).

Visual assessment of correlation maps and dendrograms and their comparison with geological map (Fig. 3) make it possible to state that the best results are obtained using Euclid distance as similarity measure. The results are the best both in the case of subdivision of electric resistance profilling curves within a dendrogram and comparison of correlation maps with the geological once.