Nonparametric estimation of age–depth models from sedimentological and stratigraphic information

Abstract. Age–depth models are fundamental tools used in all geohistorical disciplines. They assign stratigraphic positions to ages (e.g., in drill cores or outcrops), which is necessary to estimate rates of past environmental change and establish timing of events in sedimentary sequences. Methods to estimate age–depth models commonly use parametric assumptions on the uncertainties of ages of tie points. The distribution of time between tie points is estimated using the same assumptions on the formation of the stratigraphic record, regardless of the depositional environment or timescale studied, although depositional environments are known to differ systematically in their sedimentary dynamics. Integration of all empirical data or expert knowledge (e.g., from sedimentary structures such as erosional surfaces or from basin models) from multiple disciplines remains a challenge for age–depth model inference. Many information sources that can potentially provide geochronologic information remain unused or underused. Here, we present two nonparametric methods to estimate age–depth models from complex sedimentological and stratigraphic data. The methods are complementary as they use different sources of information (sedimentation rates and observed tracer values), 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 methods, we construct age–depth models for the Late Devonian Steinbruch Schmidt section in Germany and use them to estimate the timing of the Frasnian–Famennian boundary and the duration of the Upper Kellwasser event. use measurements of extra-terrestrial 3He from Integrated Ocean Drilling Program (IODP) site 1266 (Walvis Ridge) to construct age–depth models for the Paleocene–Eocene Thermal Maximum (PETM). The first case study suggests that the Upper Kellwasser event lasted 92 kyr (IQR: 84 to 97 kyr) and places the Frasnian–Famennian boundary at 371.834 ± 0.101 Ma (2σ), whereas the second case study provides a duration of 85 to 100 kyr for the PETM recovery interval. 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 in both available data and expert knowledge.