Abstract
The method of trend surface analysis was originally introduced into the earth sciences by Oldham and Sutherland (1955), Miller (1956), Krumbein (1956, 1959), Grant (1957) and Whitten (1959). These authors used the method for the analysis of gravity maps, stratigraphic maps (facies maps), isopach maps and maps representing specific attributes of sedimentary and igneous rocks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Agterberg, F. P.: 1964, ‘Methods of trend surface analysis’, Quarterly Colorado School of Mines 59 111–130.
Agterberg, F. P.: 1970, ‘Autocorrelation functions in geology’, in D. F. Merriam (ed.), Geostatistics, Plenum, New York, pp. 113–142.
Agterberg, F. P.: 1974a, Geomathematics, Elsevier, Amsterdam.
Agterberg, F. P.: 1974b, ‘Automatic contouring of geological maps to detect target areas for mineral exploration’, Journal of Mathematical Geology 6, 373–394.
Agterberg, F. P. and C. F. Chung: 1973, ‘Geomathematical prediction of sulphur in coal, new Lingian Mine area, Sydney coal field’, Canadian Mineralogy and Metallurgical Bulletin October, 85–96.
Agterberg, F. P. and C. F. Chung: 1975, ‘A computer program for polynomial trend-surface analysis’, Geological Survey of Canada Papers 75(21), 51 p.
Bain, G. W.: 1960, ‘Patterns to ores in layered rocks’, Economic Geology 55, 695–731.
Chung, C. F.: 1978, ‘Computer program for the logistic model to estimate the prob-ability of occurrence of discrete events’, Geological Survey of Canada Papers 78 (11), 23 p.
Chung, C. F.: 1979, ‘A system of interactive graphic programs for multivariate statistical analysis for geological data’, Proceedings of the 12th Symposium on Interface Computer Science and Statistics, University of Waterloo, pp. 452–456.
Chung, C. F. and F. P. Agterberg: 1980, ‘Regression models for estimating mineral resources from geological map data’, Journal of Mathematical Geology 12, 473–488.
Cliff, A. D. and J. K. Ord: 1973, Spatial Autocorrelation, Pion, London.
Coons, R. L., G. P. Woolard, and G. Hershery: 1967, ‘Structural significance and analysis of Mid-Continent Gravity High’, Bulletin of the American Association of Petroleum Geologists 51 2381–2399.
Davis, J. C.: 1973, Statistics and Data Analysis in Geology, Wiley, New York.
Delphiner, P.: 1976, ‘Linear estimation of nonstationary spatial phenomena’, in M. Guarascio, M. David, and C. Huigbregts (eds.), Advanced Geostatistics in the MiningIndustry,Reidel, Dordrecht, pp. 49–68..
De Wijs, H. J.: 1951, ‘Statistics of ore distribution’, Geol. Mijnbouw 30 365–375.
Derry, D. R.: 1960, ‘Evidence of the origin of the Blind River uranium deposits’, Economic Geology 55, 906–927.
Dobrin, M. B.: 1976, Introduction to Geophysical Prospecting 3rd ed., McGraw-Hill, New York.
Gannicott, R. A., G. A. Armbrust, and F. P. Agterberg: 1979, ‘Use of trend surface analysis to delimit hydrothermal alteration of patterns’, Canadian Mineralogy and Metallurgical Bulletin June, 82–89.
Grant, F. A.: 1957, ‘A problem in the analysis of geophysical data’, Geophysics 22, 309–344.
Harbaugh, J. W. and D. F. Merriam: 1968, Computer Applications in Stratigraphic Analysis, Wiley, New York.
Jakeman, B. L.: 1980, ‘The relation between formation structure and thickness in the Permo-Triassic succession of the Southern Coalfield, Sydney Basin, New South Wales, Australia’, Journal of Mathematical Geology 12, 185–212.
Koch, Jr., G. S. and R. F. Link: 1971, Statistical Analysis of Geological Data, Vol. 2, Wiley, New York.
Krumbein, W. C.: 1956, ‘Regional and local components in facies maps’, Bulletin of the American Association of Petroleum Geologists 40, 2163–2194.
Krumbein, W. C.: 1959, ‘Trend-surface analysis of contour type maps with irregular control-point spacing’, Journal of Geophysical Research 64, 823–834.
Krumbein, W. C. and F. A. Graybill: 1965, An Introduction to Statistical Models in Geology, McGraw-Hill, New York.
Lee, Y. W.: 1960, Statistical Theory of Communication, Wiley, New York.
MacGregor, I. D. and C. H. Smith: 1963, ‘The use of chrome spinels in petrographic studies of ultramafic intrusions’, Canadian Mineralogist 7, 403–412.
Matheron, G.: 1956, Les variables régionalisées et leur estimation, Masson, Paris. Matheron, G.: 1967, ‘Kriging or polynomial interpolation procedures?’, Transactions of the Canadian Institute of Mineralogy and Metallurgy 70, 240–244.
Miller, R. L.: 1956, ‘Trend surfaces: Their application to analysis and description of environments of sedimentation’, Journal of Geology 64, 425–446.
Oldham, C. H. G. and D. B. Sutherland: 1955, ‘Orthogonal polynomials: Their use in estimating the regional effect’, Geophysics 20, 295–306.
Parzen, E.: 1967, ‘Time series analysis for models of signal plus white noise’, in Spectral Analysis of Time Series, Wiley, New York.
Ripley, B. D.: 1981, Spatial Statistics, Wiley, New York.
Robertson, J. A.: 1966, ‘The relationship of mineralization to stratigraphy in the Blind
River area, Ontario’, Geological Association of Canada Special Paper 3, 121–136.
Robinson, J. E. and D. F. Merriam: 1980, ‘Recognition of subtle features in geological maps’, in A. D. Miall (ed.), Facts and Principles of World Petroleum Occurrence
Canadian Society of Petroleum Geologists Mem. 6, pp. 269–282.
Schwarzacher, W.: 1980, ‘Models for the theory of stratigraphic correlation’, Journal of Mathematical Geology 12, 213–234.
Stanton, R. L.: 1972, Ore Petrology, McGraw-Hill, New York.
Tukey, J. W.: 1970, ‘Some further inputs’, in D. F. Merriam (ed.), Geostatistics, Plenum, New York, pp. 163–174.
Vistelius, A. B. and V. J. Hurst: 1964, ‘Phosphorus in granitic rocks of North America’, Geological Society of America Bulletin 75, 1055–1092.
Watson, G. S.: 1971, Trend-surface analysis’, Journal of Mathematical Geology 3, 215–226.
Whitten, E. H. T.: 1959, ‘Composite trends in a granite: Modal variation and ghost stratigraphy in part of the Donegal Granite, Eire’, Journal of Geophysical Research 64, 835–848.
Whitten, E. H. T.: 1970, ‘Orthogonal polynomial trend surfaces for irregularly spaced data’, Journal of Mathematical Geology 2, 141–152.
Wrigley, N.: 1976, Introduction to the Use of Logistic Models in Geography, Concepts and Techniques in Modern Geography No. 10, Geo Abstracts, Norwich.
Wrigley, N.: 1977, Probability Surface Mapping: An Introduction with Examples and FORTRAN Programmes, Concepts and Techniques in Modern Geography No. 16, Geo Abstracts, Norwich.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Agterberg, F.P. (1984). Trend Surface Analysis. In: Gaile, G.L., Willmott, C.J. (eds) Spatial Statistics and Models. Theory and Decision Library, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3048-8_8
Download citation
DOI: https://doi.org/10.1007/978-94-017-3048-8_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8385-2
Online ISBN: 978-94-017-3048-8
eBook Packages: Springer Book Archive