Nonparametric estimation of age-depth relationships from sedimentological and stratigraphic information

Age-depth models are fundamental tools used in all disciplines that rely on geohistorical records. They assign ages to stratigraphic positions (e.g., in outcrops or drill cores), which is necessary to estimate rates of past environmental change and establish timing of events in the Earth’s history.

Methods to estimate age-depth models commonly use simplified parametric assumptions on the uncertainties of ages of tie points, e.g., that they follow a normal distribution. The distribution of time between tie points is estimated using simplistic assumptions on the formation of the stratigraphic record, for example that sediment accumulation follows a Poisson process. As a result, these methods cannot incorporate evidence from complex empirical data or expert knowledge (e.g., from sedimentary structures such as erosional surfaces or from basin models) into their estimates, leaving important sources of information un- or underused.

Here, we present two non-parametric methods to estimate age-depth relationships from complex sedimentological and stratigraphic data. The methods are implemented in the admtools package for R Software and allow the user to specify any error model and distribution of uncertainties. As use cases of the package, we

• construct age-depth models for Devonian strata in the La Thure section, Belgium, using sedimentation rates constrained by cyclostratigraphic methods.
• use measurements of extra-terrestrial ³He from ODP site 690 (Maud Rise, Weddell Sea) to construct age-depth models for the Paleocene–Eocene thermal maximum.
• examine how temporally variable ²¹⁰Pb fluxes in lacustrine environments affect estimates of sedimentation rates and age-depth models.

These examples show how information from a variety of sedimentological and stratigraphic sources can be combined to estimate age-depth relationships that accurately reflect uncertainties of both available data and expert knowledge.