Space (environment and geography)

Figure 2.3 Behavior of ideal zone and facies fossils through a hypothetical global stratigraphic section.

Quantitative stratigraphy can be traced back to work by Charles Lyell (1797-1875), who plotted what we would now call decay curves (analogous to the decay curves for radiogeneic isotopes) for the molluskan and mammalian faunas of the Tertiary basins of northwest Europe. He wanted to look at "evolution in reverse", tracking back in time from the present day to see how proportions of living taxa changed the farther back you went into the rock record. He found that the proportions of modern to extinct forms declined the farther back in time he went, and he used this to define divisions in the Tertiary system. For example his Older Pliocene included only 10% of mammals and 50% of mollusks living today, whereas in the Newer Pliocene the respective figures are 90% and 80%. These ratios were used as a method of correlating Tertiary strata quantitatively. In recent years, driven by hydrocarbon and mineral exploration, a range of quantitative, computer-based techniques has become available (Hammer & Harper 2005). Three - graphic correlation, seriation and ranking and scaling - are outlined here.

A rigorous, numerically-based mode of correlation was developed by Alan Shaw when he was working in the petroleum industry during the 1950s. Because hydrocarbon reservoir and source rocks occur within stratigraphic successions, it is essential that the rocks in oil and gas fields are accurately correlated; geologists can then locate key horizons on the basis of biostratigraphy (Fig. 2.4a). Graphic correlation by Shaw's method requires fossil range data from two or more measured sections. Data of the first and last occurrences of fossil species are plotted against a measured stratigraphic section; this is repeated for a second section. Usually only the more common taxa are plotted. A bivariate scattergram is then drawn with section 1 along the x-axis and section 2 along the y-axis. The first and last occurrences are then plotted as x-y coordinates - for example the x coordinate represents the first appearance of species a along section 1 and the y coordinate its first appearance in section 2. A regression line is fitted to all the first (FAD) and last (LAD) appearance coordinates; this line of stratigraphic correlation can be used for interpolation, permitting the accurate correspondence of all levels in the two sections. A composite standard section can be constructed and refined by correlating it against additional actual sections.

Biostratigraphers also use techniques established by archeologists in the late 1800s. Seriation is an ordering technique designed to analyze gradients. Usually the gradients are temporal but biogeo-graphic and environmental data have been investigated by seriation. Biostratigraphers tend to enter the ranges of organisms on range charts as sequential FADs. In simple terms seriation shuffles the original data matrix until the stratigraphically higher taxa are on the left hand side of the matrix and the stratigraphically lower taxa are on the right; any stratigraphic gradients in the data are then clearly visible (Fig. 2.4b) and can be interpreted.

Ranking and scaling (RASC) is a method of arranging a series of biostratigraphic events in order, and of estimating the stratigraphic distance between such events. The technique requires only first and last appearances measured in meters in a stratigraphic section, perhaps an exposure or oil well. Events are first ranked or ordered based on the majority of relative occurrences and then the distances between such events are calculated (Fig. 2.4c).

A dataset of Early Ordovician trilobite ranges is available at: http://www.blackwellpublishing. com/paleobiology. These data may be analyzed and manipulated using ranking and scaling, seriation and unitary associations; confidence intervals may also be calculated (see also Hammer & Harper 2005).

Continued

Figure 2.4 (a) Hypothetical and minimalist graphic correlation based on the stratigraphic distribution of the five apparent chronospecies of the Silurian brachiopod Eocoelia, in ascending order: E. hemisphaerica, E. intermedia, E. curtisi, E. sulcata and E. angelini; the first four range through the middle and upper Llandovery whereas the last is characteristic of the lower Wenlock. The ranges of these species are given from two artificial sections with the first appearances of each species plotted on both sections as x and y coordinates. The straight line fitted to the points allows a precise correlation between each part of the two sections. In this simple example all the points fit on a straight line; in practice a regression must be fitted to the scatter of data points. (b) Seriation of biostratigraphic data. The five Eocoelia species were collected from five horizons in a stratigraphic section; the data were collected and plotted randomly as a range chart. Seriation seeks to establish any structure, usually gradients, within the matrix by maximizing entries in the leading diagonal. The seriated matrix reveals the stratigraphic succession of Eocoelia species that is widely used for the correlation of Lower Silurian strata. Most seriations are based on much larger and more complex data matrices where any non-random structure, if present, is initially far from obvious.

Figure 2.4 (a) Hypothetical and minimalist graphic correlation based on the stratigraphic distribution of the five apparent chronospecies of the Silurian brachiopod Eocoelia, in ascending order: E. hemisphaerica, E. intermedia, E. curtisi, E. sulcata and E. angelini; the first four range through the middle and upper Llandovery whereas the last is characteristic of the lower Wenlock. The ranges of these species are given from two artificial sections with the first appearances of each species plotted on both sections as x and y coordinates. The straight line fitted to the points allows a precise correlation between each part of the two sections. In this simple example all the points fit on a straight line; in practice a regression must be fitted to the scatter of data points. (b) Seriation of biostratigraphic data. The five Eocoelia species were collected from five horizons in a stratigraphic section; the data were collected and plotted randomly as a range chart. Seriation seeks to establish any structure, usually gradients, within the matrix by maximizing entries in the leading diagonal. The seriated matrix reveals the stratigraphic succession of Eocoelia species that is widely used for the correlation of Lower Silurian strata. Most seriations are based on much larger and more complex data matrices where any non-random structure, if present, is initially far from obvious.

Figure 2.4 (Continued) (c) The RASC method predicts the solution most likely to occur in the next section based on previous data. Three sections (1-3) are presented and, based on a majority vote, the RASC solution is constructed; since the first two sections are similar they win over the third slightly different section. This is different to the maximum range solution that may be constructed by other methods. (c, based on Hammer & Harper 2005.)

Figure 2.4 (Continued) (c) The RASC method predicts the solution most likely to occur in the next section based on previous data. Three sections (1-3) are presented and, based on a majority vote, the RASC solution is constructed; since the first two sections are similar they win over the third slightly different section. This is different to the maximum range solution that may be constructed by other methods. (c, based on Hammer & Harper 2005.)

Quaternary

ct C

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