A Brief Overview of Interpolating Time

Developing age models for stratigraphic sections requires integrating information from across a wide range of geoscience disciplines, including radioisotope geochronology, astrochronology, biostratigraphy, magnetostratigraphy, and others. Combining these disparate data into cohesive models of age often proves challenging, as each field follows its own procedures for estimating geologic age, chronostratigraphic correlation, and how best to propagate uncertainty. When limited to individual stratigraphic sections, where position can reasonably be represented as depth or height, age-depth modeling is a tractable problem with a variety of frequentist and Bayesian statistical methods commonly used to translate stratigraphic position into numerical time. However, even in these cases, as the types of age information grow more complex, how to choose the statistical model most amenable to the available data is not always clear. Furthermore, not all algorithms can easily assimilate all types of geochronological or chronostratigraphic data. Broadly, algorithms for age-depth modeling can be placed into two categories, those based on classical frequentist statistics and, more recently, Bayesian methods; Each with their own strengths and weaknesses. Frequentist methods (e.g., linear regression, splines, polynomials) are underlain by mathematics with centuries of history. They can be easily reproduced using a wide variety of free software and are not computational intensive, allowing models to be fit to data in a matter of seconds. However, within the context of stratigraphic age-depth modeling, frequentist statistics have several drawbacks. They can be inflexible and may not accurately capture the complexities of the rock record. Moreover, they often underestimate uncertainties and can violate fundamental geologic principles. Over the past c. 15 years, Bayesian methods have been developed to address many of these shortcomings. A critical improvement is the incorporation of prior information into age-depth model construction. Bayesian age-depth models can be made to absolutely respect fundamental geologic principles, such as superposition, using the relative ordering of events to reduce model uncertainties. Furthermore, since most Bayesian models use a sedimentation model to “interpolate” numerical time between geochronological tie-points, they can be conditioned to have sedimentation rates similar to those expected for the lithology of a given stratigraphic section. This flexibility and power comes at a cost however. Most Bayesian models are computationally intensive and may take minutes to hours to fit a given section. There are several challenges to translating existing models from single stratigraphic sections to Geologic Time Scales (regional or global). For example, when tens or even hundreds of individual sections are composited into a chronostratigraphic scale, information about sediment characteristics is lost, making it difficult to specify appropriate prior distributions for accumulation “rate”. Likewise, handling the uncertainties that arise from the construction of the chronostratigraphic scaling becomes substantially more important. Despite these challenges, Bayesian methods are clearly the way forward for GTS construction, offering a flexible framework that can grow and change for the next and future iterations of the Geologic Time Scale.