Automated compilation of pseudo-lithology maps from geophysical data sets: a comparison of Gustafson-Kessel and fuzzy c-means cluster algorithms
Hendrik Paasche 1 3 Detlef Eberle 21 University of Potsdam, Institute of Earth and Environmental Sciences, Karl-Liebknecht-Str. 24, 14476 Potsdam-Golm, Germany.
2 Council for Geoscience, Geophysics Business Unit, Private Bag X112, Pretoria 0001, South Africa.
3 Corresponding author. Email: hendrik@geo.uni-potsdam.de
Exploration Geophysics 42(4) 275-285 https://doi.org/10.1071/EG11014
Submitted: 15 March 2011 Accepted: 22 September 2011 Published: 8 November 2011
Abstract
The fuzzy partitioning Gustafson-Kessel cluster algorithm is employed for rapid and objective integration of multi-parameter Earth-science related databases. We begin by evaluating the Gustafson-Kessel algorithm using the example of a synthetic study and compare the results to those obtained from the more widely employed fuzzy c-means algorithm. Since the Gustafson-Kessel algorithm goes beyond the potential of the fuzzy c-means algorithm by adapting the shape of the clusters to be detected and enabling a manual control of the cluster volume, we believe the results obtained from Gustafson-Kessel algorithm to be superior. Accordingly, a field database comprising airborne and ground-based geophysical data sets is analysed, which has previously been classified by means of the fuzzy c-means algorithm. This database is integrated using the Gustafson-Kessel algorithm thus minimising the amount of empirical data processing required before and after fuzzy c-means clustering. The resultant zonal geophysical map is more evenly clustered matching regional geology information available from the survey area. Even additional information about linear structures, e.g. as typically caused by the presence of dolerite dykes or faults, is visible in the zonal map obtained from Gustafson-Kessel cluster analysis.
Key words: cluster analysis, data integration, airborne, South Africa, Gustafson-Kessel, fuzzy c-means.
References
Anderson-Mayes, A. M., 2002, Strategies to improve information extraction from multivariate geophysical data suites: Exploration Geophysics, 33, 57–64| Strategies to improve information extraction from multivariate geophysical data suites:Crossref | GoogleScholarGoogle Scholar |
Bezdek, J. C., and Hathaway, R. J., 2002, Some notes on alternating optimization, in N. R. Pal, and M. Sugeno, eds., Advances in soft computing – AFSS 2002: Springer, 187–195.
Dietrich, P., and Tronicke, J., 2009, Integrated analysis and interpretation of crosshole P- and S-wave tomograms: a case study: Near Surface Geophysics, 7, 101–109
Dietrich, P., Fechner, T., Whittacker, J., and Teutsch, G., 1998, An integrated hydrogeophysical approach to subsurface characterization, in M. Herbert, and K. Kovar, eds., Groundwater quality: remediation and protection: IAHS Publication 250, 513–519.
Eberle, D., 1993, Geologic mapping based upon multivariate statistical analysis of airborne geophysical data: International Institute for Aerospace Survey and Earth Sciences (ITC) Journal, 1993–2, 173–178
Eberle, D. G., Daudi, E. X. F., Muiuane, E. A., and Pontavida, A. M., 2010, Mapeamento aero-geofísico de pegmatitos mineralizados na Província Pegmatítica de Alto Ligonha, no norte de Moçambique Revista Brasileira de Geociencias, 40, 527–536
Eppstein, M. J., and Dougherty, D. E., 1998, Optimal 3-D traveltime tomography: Geophysics, 63, 1053–1061
| Optimal 3-D traveltime tomography:Crossref | GoogleScholarGoogle Scholar |
Gustafson, D. E., and Kessel, W. C., 1979, Fuzzy clustering with a fuzzy covariance matrix, in M. M. Gupta, R. K. Ragade, and R. R. Yager, eds., Advances in fuzzy set theory and applications: North-Holland, 605–620.
Hathaway, R. J., and Bezdek, J. C., 2001, Fuzzy c-means clustering of incomplete data: IEEE Transactions on Systems, Man, and Cybernetics Part B, 31, 735–744
| Fuzzy c-means clustering of incomplete data:Crossref | GoogleScholarGoogle Scholar | 1:STN:280:DC%2BD1c%2Foslaruw%3D%3D&md5=8458c8932c1b79e8df5ed0dffa28dabfCAS |
Höppner, F., Klawonn, F., Kruse, R., and Runkler, T., 1999, Fuzzy cluster analysis: methods for classification, data analysis, and image recognition: Wiley.
Kaufmann, L., and Rousseeuw, P. J., 1990, Finding groups in data: an introduction to cluster analysis: Wiley.
Lanne, E., 1986, Statistical multivariate analysis of airborne geophysical data on the SE border of the central Lapland Greenstone Complex: Geophysical Prospecting, 34, 1111–1128
| Statistical multivariate analysis of airborne geophysical data on the SE border of the central Lapland Greenstone Complex:Crossref | GoogleScholarGoogle Scholar |
Linder, S., Paasche, H., Tronicke, J., Niederleithinger, E., and Vienken, T., 2010, Zonal cooperative inversion of P-wave, S-wave and georadar traveltime data sets: Journal of Applied Geophysics, 72, 254–262
| Zonal cooperative inversion of P-wave, S-wave and georadar traveltime data sets:Crossref | GoogleScholarGoogle Scholar |
Mahalanobis, P. C., 1936, On the generalised distance in statistics: Proceedings of the National Institute of Science of India, 12, 49–55
Miller, D. J., Nelson, C. A., Cannon, M. B., and Cannon, K. P., 2009, Comparison of fuzzy clustering methods and their applications to geophysics data: Applied Computational Intelligence and Soft Computing, ,
| Comparison of fuzzy clustering methods and their applications to geophysics data:Crossref | GoogleScholarGoogle Scholar |
Paasche, H., and Eberle, D. G., 2009, Rapid integration of large airborne geophysical data suites using a fuzzy partitioning cluster algorithm: a tool for geological mapping and mineral exploration targeting: Exploration Geophysics, 40, 277–287
| Rapid integration of large airborne geophysical data suites using a fuzzy partitioning cluster algorithm: a tool for geological mapping and mineral exploration targeting:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXhtFCktb%2FJ&md5=78a0c70e12e5cd7b2fd928e2ea1704a2CAS |
Paasche, H., and Tronicke, J., 2007, Cooperative inversion of 2D geophysical data sets: A zonal approach based on fuzzy c-means cluster analysis: Geophysics, 72, A35–A39
| Cooperative inversion of 2D geophysical data sets: A zonal approach based on fuzzy c-means cluster analysis:Crossref | GoogleScholarGoogle Scholar |
Paasche, H., Tronicke, J., Holliger, K., Green, A. G., and Maurer, H., 2006, Integration of diverse physical-property models: Subsurface zonation and parameter estimation based on fuzzy c-means cluster analyses: Geophysics, 71, H33–H44
| Integration of diverse physical-property models: Subsurface zonation and parameter estimation based on fuzzy c-means cluster analyses:Crossref | GoogleScholarGoogle Scholar |
Paasche, H., Wendrich, A., Tronicke, J., and Trela, C., 2008, Detecting voids in masonry by cooperatively inverting P-wave and georadar traveltimes: Journal of Geophysics and Engineering, 5, 256–267
| Detecting voids in masonry by cooperatively inverting P-wave and georadar traveltimes:Crossref | GoogleScholarGoogle Scholar |
Pirkle, F. L., Howell, J. A., Wecksung, G. W., Duran, B. S., and Stablein, N. K., 1984, An example of cluster analysis applied to a large geologic data set: aerial radiometric data from Copper Mountain, Wyoming: Mathematical Geology, 16, 479–498
| An example of cluster analysis applied to a large geologic data set: aerial radiometric data from Copper Mountain, Wyoming:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL2cXkvFCkt7s%3D&md5=96b67a6fa645b8fde26ee2b5d772cffeCAS |
Späth, H., 1985, Cluster dissection and analysis: Horwood.
Tronicke, J., Paasche, H., Holliger, K., and Green, A. G., 2002, Combining crosshole georadar velocity and attenuation tomography for site characterization, in S. Koppenjan, and H. Lee, eds., Proceedings of the 9th International Conference on Ground Penetrating Radar: SPIE 4758, 170–175.
Tronicke, J., Holliger, K., Barrash, W., and Knoll, M. D., 2004, Multivariate analysis of crosshole georadar velocity and attenuation tomograms for aquifer zonation: Water Resources Research, 40, W01519
| Multivariate analysis of crosshole georadar velocity and attenuation tomograms for aquifer zonation:Crossref | GoogleScholarGoogle Scholar |
Ugalde, H., and Morris, W. A., 2010, Cluster analysis of Euler deconvolution solutions: new filtering techniques and geologic strike determination: Geophysics, 75, L61–L70
| Cluster analysis of Euler deconvolution solutions: new filtering techniques and geologic strike determination:Crossref | GoogleScholarGoogle Scholar |
Van Leekwijck, W., and Kerre, E. E., 1999, Defuzzification: criteria and classification: Fuzzy Sets and Systems, 108, 159–178
| Defuzzification: criteria and classification:Crossref | GoogleScholarGoogle Scholar |