Rapid integration of large airborne geophysical data suites using a fuzzy partitioning cluster algorithm: a tool for geological mapping and mineral exploration targeting

Hendrik Paasche; Detlef G. Eberle

doi:10.1071/EG08028

RESEARCH ARTICLE

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Rapid integration of large airborne geophysical data suites using a fuzzy partitioning cluster algorithm: a tool for geological mapping and mineral exploration targeting

Hendrik Paasche ¹ ³ Detlef G. Eberle ² ³

+ Author Affiliations

- Author Affiliations

¹ University of Potsdam, Institute of Geosciences, Karl-Liebknecht-Str. 24, D-14476 Potsdam, Germany.

² Geophysics BU, Council for Geoscience, Private Bag X112, Pretoria 0001, South Africa.

³ Corresponding authors. Email: hendrik@geo.uni-potsdam.de; deberle@geoscience.org.za

Exploration Geophysics 40(3) 277-287 https://doi.org/10.1071/EG08028
Submitted: 17 December 2008 Accepted: 4 June 2009 Published: 21 September 2009

Abstract

Unsupervised classification techniques, such as cluster algorithms, are routinely used for structural exploration and integration of multiple frequency bands of remotely sensed spectral datasets. However, up to now, very few attempts have been made towards using unsupervised classification techniques for rapid, automated, and objective information extraction from large airborne geophysical data suites. We employ fuzzy c-means (FCM) cluster analysis for the rapid and largely automated integration of complementary geophysical datasets comprising airborne radiometric and magnetic as well as ground-based gravity data, covering a survey area of approximately 5000 km² located 100 km east-south-east of Johannesburg, South Africa, along the south-eastern limb of the Bushveld layered mafic intrusion complex. After preparatory data processing and normalisation, the three datasets are subjected to FCM cluster analysis, resulting in the generation of a zoned integrated geophysical map delineating distinct subsurface units based on the information the three input datasets carry. The fuzzy concept of the cluster algorithm employed also provides information about the significance of the identified zonation. According to the nature of the input datasets, the integrated zoned map carries information from near-surface depositions as well as rocks underneath the sediment cover. To establish a sound geological association of these zones we refer the zoned geophysical map to all available geological information, demonstrating that the zoned geophysical map as obtained from FCM cluster analysis outlines geological units that are related to Bushveld-type, other Proterozoic- and Karoo-aged rocks.

Key words: airborne geophysics, cluster analysis, geological mapping, multivariate statistics, South Africa.

Acknowledgments

The authors thankfully acknowledge the preparedness of the Council for Geoscience to make available the complementary data suite and supplementary geological information for this study. This research work has been partly supported by the International Bureau of the German Federal Ministry of Education and Research (BMBF; grant SUA08/015), the South African National Research Foundation (NRF; UID 69441) and the German Research Foundation (DFG; grant PA1643/1-1).

References

Ahn, C. W., Baumgardner, M. F., and Biehl, L. L., 1999, Delineation of soil variability using geostatistics and fuzzy clustering analyses of hyperspectral data: Soil Science Society of America Journal 63, 142–150.
| CAS | Bezdek J. C. , 1981, Pattern recognition with fuzzy objective function algorithms: Plenum Press.

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.

Bragato, G., 2004, Fuzzy continuous classification and spatial interpolation in conventional soil survey for soil mapping of the lower Piave plain: Geoderma 118, 1–16.
| Crossref | GoogleScholarGoogle Scholar | Buchanan P. C. , 2006, The Rooiberg Group, in M. R. Johnson, C. R. Anhaeusser, and R. J. Thomas, eds, The geology of South Africa: Geological Society of South Africa, Johannesburg, 283–289.

Cole P. , 2004, South-eastern Bushveld airborne magnetic survey: Open file report no. 2004–0103, Council for Geoscience, Pretoria.

Cole J. , and Maré L. P. , 2004, A geophysical investigation of the regional potential field data over the south-eastern limb of the Bushveld Complex: Open file report no. 2004–0101, Council for Geoscience, Pretoria.

Council for Geoscience, 1986, Geological Map 2628 (East Rand), 1 : 250 000 Geological Series, Pretoria.

de Bruin, S., and Stein, A., 1998, Soil-landscape modelling using fuzzy c-means clustering of attribute data derived from digital elevation model (DEM): Geoderma 83, 17–33.
| Crossref | GoogleScholarGoogle Scholar | Durrheim R. J. , 1987, The interpretation of the 2628 (East Rand) aeromagnetic map: Open file report no. 1987–0101, Council for Geoscience, Pretoria.

Eberle D. , 1993, Geologic mapping based upon multivariate statistical analysis of airborne geophysical data: International Institute for Aerospace Survey and Earth Sciences (ITC) Journal Special issue, 173–178.

Eberle D. G. , Cole J. , Häuserer M. , and Stettler E. H. , 2005, Combined stochastic and deterministic modelling as an innovative approach to jointly interpret multi-method airborne geophysical data sets: Extended abstract, 9th SAGA Biennial Conference and Exhibition, Cape Town.

Eberle D. G. , Nyabeze P. K. , and Legotle L. R. , 2008, Geophysical ground truth control of airborne magnetic and gamma-ray anomalies in the Dwarsberge, map reference 2426: [Council for Geoscience, Pretoria.] Series number: 2000-0130. p. 51.

Fridgen, J. J., Kitchen, N. R., Sudduth, K. A., Drummond, S. T., Wiebold, W. J., and Fraisse, C. W., 2004, Management Zone Analyst (MZA): Software for subfield management zone delineation: Agronomy Journal 96, 100–108.
Holliger K. , Tronicke J. , Paasche H. , and Dafflon B. , 2008, Quantitative integration of hydrogeophysical and hydrological data: Geostatistical approaches, in C. J. G. Darnault, ed., Overexploitation and contamination of shared groundwater resources: Springer, 67–82.

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.

Knab, M., Appel, E., and Hoffmann, V., 2001, Separation of the anthropogenic portion of heavy metal contents along a highway by means of magnetic susceptibility and fuzzy c-means cluster analysis: European Journal of Environmental and Engineering Geophysics 6, 125–140.
Paasche H. , Günther T. , Tronicke J. , Green A. G. , Maurer H. , and Holliger K. , 2007, Integrating multi-scale geophysical data for the 3D characterization of an alluvial aquifer: Istanbul, Turkey: 13th European Conference on Environmental and Engineering Geophysics (EAGE Near Surface Geophysics), Expanded Abstracts, 5 p.

Peschel, G., 1973, Zur quantitativen komplexen Interpretation gravimetrischer und magnetischer Profile: Zeitschrift für Angewandte Geologie 19, 287–292.
Runkler T. A. , and Glesner M. , 1994, Defuzzification and ranking in the context of membership value semantics, rule modality, and measurement theory: Proceedings of the 1st European Congress on Intelligent Techniques and Soft Computing (EUFIT 94), ELITE Foundation, Expanded Abstracts, 1206–1210.

Shi H. , Shen Y. , and Liu Z. , 2003, Hyperspectral bands reduction based on rough sets and fuzzy c-means clustering: Proceedings of the 20th IEEE Instrumentation and Measurement Technology Conference, Vol. 2, 1053–1056.

Siehl A. , 1984, Mehrdimensionale statistische Verfahren, in F. Bender, ed., Angewandte Geowissenschaften Bd. II: Methoden der angewandten Geophysik und mathematischen Verfahren in den Geowissenschaften: Enke, 709–741.

Stettler R. H. , Du Plessis J. G. , Venter C. P. , Potgieter T. D. , Share F. G. , and Hattingh E. , 2000, Regional gravity survey of the 2628 (East Rand) 1: 250 000 sheet: Unpublished report 2000–0049, Council for Geoscience, Pretoria.

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.
| Crossref | GoogleScholarGoogle Scholar |

Urbat, M., Dekkers, M. J., and Krumsiek, K., 2000, Discharge of hydrothermal fluids through sediment at the Escanaba Trough, Gorda Rich (ODP Leg 169); assessing the effects on the rock magnetic signal: Earth and Planetary Science Letters 176, 481–494.
| Crossref | GoogleScholarGoogle Scholar | CAS |

Van Leekwijck, W., and Kerre, E. E., 1999, Defuzzification: criteria and classification: Fuzzy Sets and Systems 108, 159–178.
| Crossref | GoogleScholarGoogle Scholar |

Xie, X. L., and Beni, G., 1991, A validity measure for fuzzy clustering: IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 841–847.
| Crossref | GoogleScholarGoogle Scholar |

Appendix

Fuzzy c-means (FCM) is a partitioning cluster algorithm grouping n data points in a t-dimensional space into a specified number of c subsets or clusters by iteratively minimizing the objective function

where u_ij denotes the degree of membership of data point d_j to cluster i defined by its centre v_i. Memberships are constrained to be positive and to satisfy

The weighting exponent f, also referred to as the ‘fuzzification parameter’ (e.g. Güler and Thyne, 2004; Fridgen et al., 2004) controls the degree of fuzziness in the resulting memberships and must be selected from the interval 1 < f < ∞. As f approaches unity, FCM cluster analysis approximates the crisp k-means cluster algorithm; increasing f results in increased fuzziness of the memberships. For most databases to be clustered a selection of f between 1.5 and 2 is regarded as suitable choice (e.g. Hathaway and Bezdek, 2001). The Euclidian distance between the j-th data point and the i-th cluster centre is calculated in a t-dimensional space

where the locations of data points d_j and cluster centres v_i are defined by t attributes.

After providing the initial parameters (number of clusters c, fuzzification parameter f, and an initial guess of u_{1..c, 1..n} or v_{1..c, 1..t}), J is minimised with respect to u_ij and v_i by iterative alternating optimisation (Bezdek and Hathaway, 2002). One iteration consists of updating the membership values u_ij

and the cluster centres v_i

The order depends on whether initial memberships or centre locations are given. The algorithm terminates after a predefined number of iterations or if the improvement of J falls below a given threshold.

Suitability of the chosen c can be statistically evaluated by repeating cluster analysis for different c and calculating the Xie-Beni-index (XBI) (Xie and Beni, 1991)

with z = 1…c and z ≠ i.

A crisp clustering result assigning each d_j uniquely to one of the c clusters can be obtained by defuzzification of the fuzzy membership information. Here, we use the rather simple core selection defuzzification (e.g. Van Leekwijck and Kerre, 1999) and obtain a n-element vector h containing the cluster numbers the n data point are assigned to by

with h_j ∈ {1…c}.