Abstract
A primary concern of geologists is the relative ordering of events in Earth history. On a regional basis, spatial relationships of separate or overlapping rock bodies are used for accomplishing this goal. For correlation over large distances between regions or when the rate of change of geological processes is being considered, it is necessary to use the numerical time scale which is mainly based on radiometric dates of variable. precision. Existing statistical models for estimating the ages of chronostratigraphic boundaries and the corresponding error bars are reviewed. An alternative approach based on the method of maximum likelihood is presented. Computer simulation experiments are described to compare estimates obtained by different methods from small samples of age determinations. A spline-fitting technique can be used to combine estimates for successive stage boundaries with one another. The Jurassic time scale is used to exemplify this statistical approach.
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References
Armstrong, R. L., 1978, Pre-Cenozoic Phanerozoic time scale, in Cohee, G. V., Glaessner, M. G., and Hedberg, H. D., eds., Contributions to the geologic time scale: Am. Assoc. Petroleum Geologists, Studies in Geology No. 6, p. 73-91.
Cox, A. V., and Dalrymple, G. B., 1967, Statistical analysis of geomagnetic reversal data and the precision of potassium-argon dating: Jour. Geophysical Research, v. 72, no. 10, p. 2603–2614.
Courant, R., and Hilbert, D., 1953, Methods of mathematical physics, vol. 1: Wiley-Inter science, New York, 561 p.
Cramer, H., 1946, Mathematical methods of statistics: Princeton Univ. Press, Princeton, New Jersey, 575 p.
Gyji, R. A., and McDowell, F. W., 1970, Potassium argon ages of glauconites from a biochronologically dated Upper Jurassic sequence of northern Switzerland: Eclogae Geol. Helvetiae, v. 63, no. 1, p. 11–118.
Hallam, A., 1975, Jurassic environments: Cambridge Univ. Press, Cambridge, 269 p.
Harland, W. B., 1983, More time scales: Geol. Magazine, v. 120, no. 4, p. 393–400.
Harland, W. B., Cox, A. V., Llewellyn, P. G., Pickton, C. A. G., Smith, A. G., and Walters, R., 1982, A geologic time scale: Cambridge Univ. Press, Cambridge, 131 p.
Kendall, M. G., and Stuart, A., 1961, The advanced theory of statistics, vol. 2: Hafner, New York, 676 p.
Kent, D. V., and Gradstein, F. M., in press, A Jurassic to Recent chronology, in Tucholke, B. E., and Vogt, P. R., eds., The geology of North America: Geol. Soc. America.
Odin, G. S., ed., 1982, Numerical dating in stratigraphy, parts I and II: Wiley-Interscience, Chichester, 1040 p.
Rao, C. R., 1973, Linear statistical inference and its applications: John Wiley & Sons, New York, 625 p.
Reinsch, C. H., 1967, Smoothing by spline functions: Numerische Mathematik, v. 10, p. 177–183.
Reinsch, C. H., 1971, Smoothing by spline functions. II: Numerische Mathematik, v. 16, p. 451–454.
Schoenberg, I. J., 1967, On spline functions, in Shisha, O., ed., Inequalities: Academic Press, New York, p. 255–291.
Watson, G. S., 1984, Smoothing and interpolation by kriging and with splines: Jour. Math. Geology, v. 16, no. 6, p. 601–615.
Wegman, E. J., and Wright, I. W., 1983, Splines in statistics: Jour. Am. Statist. Assoc., v. 78, no. 382, p. 351–365.
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© 1988 Plenum Press, New York
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Agterberg, F.P. (1988). Quality of Time Scales — a Statistical Appraisal. In: Merriam, D.F. (eds) Current Trends in Geomathematics. Computer Applications in the Earth Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7044-4_5
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DOI: https://doi.org/10.1007/978-1-4684-7044-4_5
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