Federico Galster

Discrete Biochronological Time Scales

The study of the Jacksonian and Vicksburgian of the Paleogene in western Alabama and eastern Mississippi was published in the early 1960s by Deboo (Alabama Geol Surv Bull 80:1–84, 1965). The goal of Deboo was two-fold: first, he intended to solve some problems posed by correlating the lithologic units classically used in this region (Fig. 5.1) and second, he wanted to use new biochronologic arguments to determine more precisely the boundary between the Jacksonian and Vicksburgian local stages.

Interval Graphs and Stratigraphic Contradictions

We have already seen above that a discrete biochronological range chart strictly corresponds to the maximal clique matrix associated to an interval graph. The literature contains several characterizations of such graphs.

Transgressive-Regressive Cycles and Benthic Foraminifera

The study of the Jacksonian and Vicksburgian of the Paleogene in western Alabama and eastern Mississippi was published in the early 1960s by Deboo (Alabama Geol Surv Bull 80:1–84, 1965). The goal of Deboo was two-fold: first, he intended to solve some problems posed by correlating the lithologic units classically used in this region (Fig. 5.1) and second, he wanted to use new biochronologic arguments to determine more precisely the boundary between the Jacksonian and Vicksburgian local stages.

The UA Method and the UAgraph Program

The logical steps of the UA method described below are strictly followed by the UAgraph program of Hammer and Guex. For that reason each step of the method will be illustrated by an example of application of that program.

Calibrating Biochronological Zones with Geochronology

One fundamental problem in geology is to calibrate precisely the Phanerozoic geological stages based on fossils with accurate geochronological data. To proceed to such a calibration we need essentially to use marine time diagnostic fossils like Graptolites, Trilobites, Ammonites or planctonic Foraminifera associated with coeval volcanic ashes or lava flows containing radiogenic minerals like zircons for U-Pb dating or K-feldspars for Ar–Ar dating. Ideal situations are where marine basins are closely associated with volcanic arcs such as the Mesozoic basins of the Pacific cordilleras in South and North America. Such basins usually provide marine organisms associated with ash beds (tephras) containing zircons or other silicates which can easily be dated with routine radiochronologic methods.

Statistical Pseudo-improvements of the UA Method

In a recent Lethaia paper, Monnet et al. (Lethaia. doi:10.1111/j.1502-3931.2010.00256.1-21, 2011) propose a series of refinements intended to ameliorate the performances of the Unitary Association Method (UAM) and of the UAgraph program. Monnet et al. (loc.cit) main criticisms will quickly be reevaluated in the present chapter.

Lower Jurassic Radiolarian Biochronology and Evolutionary Rates

In 2006 Gorican et al. published a comprehensive monograph on the systematics of Early Jurassic polycystine radiolarians which served as a coherent taxonomic base to establish a global radiolarian zonation for three stages that were poorly known before: the Pliensbachian, Toarcian, and Aalenian.

Problems of Datums Diachronism and Comparison Between UAgraph and the Program Conop

A very challenging quantitative biochronological problem integrating comprehensive diatom biostratigraphy, magnetostratigraphy, and tephrostratigraphy from 32 Neogene sections around the Southern Ocean and Antarctic continental margin has been recently studied by Cody et al. (Palaeogeogr Palaeoclimatol Palaeoecol 260:92–121, 2008). A new method, known as Constrained Optimization (Conop), which can be viewed as a multidimensional version of graphic correlation, is applied to that complex database. In this chapter we will review some discussions of a paper by Galster et al. (Palaeogeogr Palaeoclimatol Palaeoecol 285:237–247, 2010) concerning Conop and focus our analysis on the large scale correlations based on Cody’s data and the implication of the diachronism of “datums” in the quantitative treatment of biostratigraphic data.