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Comparing directional line sets using non-parametric statistics: a new approach for geoenvironmental applications

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Abstract

The need to compare the distributions of directions of the discontinuities present in rock masses prompted the development of a new surrogate measure for non-parametric statistical tests. This is used to quantify the degree of matching between polymodal azimuth direction distributions determined from remotely sensed data for different areas and also between these and field measurements. The approach is based on an application of the Kolmogorov–Smirnov (K–S) goodness-of-fit test. However, in this application the main interest is to accept the null hypothesis (instead of rejecting it) so that there is a risk of committing a Type II statistical error when it is false, particularly if sample sizes are too small. Therefore, a method that employs a set of empirical criteria for calibrating the statistical decision was devised. The statistic used (D ratio) provides a measure of the degree of reliability about the decision on whether or not to accept or reject the hypothesis. The methodology is tested and implemented using existing geological data and a tectonic model valid over a limited region, within which two study areas were taken for these developments. The results obtained indicate reasonable improvement of the performance of K–S tests for inferential purposes when empirical reliability criteria are used. This was acknowledged by increased matching between occurring and inferred discontinuities (tectonic structures) and reduction in rates of errors. Other applications envisaged include different data sources such as climate and soil data.

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Acknowledgements

The authors would like to thank: Steve M. Wise (Department of Geography, University of Sheffield) for critical reading and thoughtful suggestions; Dr. Roseli A. Leandro (ESALQ, University of São Paulo) and Dr. Maria I. Vitorino (UFMA, Federal University at Maranhão) for the encouragement and help with statistical problem solving; the Brazilian National Council for Scientific and Technological Development—CNPq (grant no. 201029/97-9) and the United Kingdom Foreign Commonwealth Office, Chevening Programme (grant no. SPA2261-9818) for co-sponsoring this research; and to the anonymous reviewers.

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Authors and Affiliations

  1. Geological Institute, São Paulo State Secretariat of Environment, Av. Miguel Stefano nr. 3900, CEP, 04301-903, São Paulo, Brazil

    P. C. Fernandes da Silva

  2. Department of Civil and Structural Engineering, University of Sheffield, Mappin Street, S1 3JD, Sheffield, UK

    J. C. Cripps

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  1. P. C. Fernandes da Silva
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  2. J. C. Cripps
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Correspondence to P. C. Fernandes da Silva.

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Fernandes da Silva, P.C., Cripps, J.C. Comparing directional line sets using non-parametric statistics: a new approach for geoenvironmental applications. Stoch Environ Res Risk Assess 22, 231–246 (2008). https://doi.org/10.1007/s00477-007-0110-9

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