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Quantitative Stratigraphy, Splining and Geologic Time Scales

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Geomathematics: Theoretical Foundations, Applications and Future Developments

Part of the book series: Quantitative Geology and Geostatistics ((QGAG,volume 18))

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Abstract

Quantitative stratigraphy uses logical and mathematical tools to help define the stratigraphic framework of the Earth’s crust. Biostratigraphy uses observations on fossil taxa. Biostratigraphic events commonly used for this purpose are the observed first and last occurrence (abbreviated to FO and LO) of each fossil taxon considered. Co-occurrences of fossil taxa in the biostratigraphic record can be used as well. Methods for the integration and long-distance correlation of observed biostratigraphic events include the RASC method for RAnking and SCaling. The main difference between RASC and other methods of regional biostratigraphic correlation is that RASC estimates the relative positions of average fossil events instead of maximal time-stratigraphic ranges, although maximal ranges also can be obtained by using RASC. Different methods of quantitative stratigraphy are briefly reviewed in this chapter. Initially, ranking is illustrated by application to a simple, artificial dataset. Scaling is explained as a refinement of ranking. Implications of techniques of sampling stratigraphic sections are discussed. RASC probable positions with error bars can be determined in different sections for CASC correlation over long distances. This process makes use of spline-curve fitting (splining). For method comparison, several datasets published by others are re-analyzed, not only to establish regional biostratigraphic standards but also to perform correlations between stratigraphic sections. These datasets include FOs and LOs of Eocene nannofossils in wells drilled in California and trilobites from the Cambrian Riley Formation in central Texas. Large-scale RASC/CASC applications involving many thousands of observations include results for well data from the Cenozoic North Sea basin, northwestern Atlantic margin and the Cretaceous seaway between Norway and Greenland. Paleoceanographic interpretations of RASC biozonations supplemented by analysis of variance to study diachronism and correlations between wells are exemplified as well.

The international numerical geologic time scales have been and continue to be partially based on spline-curves fitted to relate age determinations on rock samples to their positions in the relative geologic time scale that is based on classifications of rock units that can be correlated worldwide. Methods of time scale construction are discussed at the end of this chapter.

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  1. Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC), Ottawa, ON, Canada

    Frits Agterberg

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Agterberg, F. (2014). Quantitative Stratigraphy, Splining and Geologic Time Scales. In: Geomathematics: Theoretical Foundations, Applications and Future Developments. Quantitative Geology and Geostatistics, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-06874-9_9

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