Estimating the error of age interpolation in sedimentary rocks

Abstract

Magnetostratigraphic data can provide information on rates of sediment accumulation within a single sedimentation system over time spans from 104 to 106 yr. The short-term rate of sediment deposition varies with time; the apparent average rate over any longer interval also depends on the relative durations of periods of deposition, stasis (non-deposition), and erosion. While the average rate can be used to infer the time of occurrence of an event from its stratigraphical position, the inferred age has an uncertainty deriving from the variability in rate of sediment accumulation over all shorter timescales. We analyse here variability in sediment accumulation rates provided by the magnetostratigraphy of Miocene, Siwalik sediments from Pakistan. For long periods (>106 yr), sediment accumulation is approximately linear through time. Over short intervals (104–105yr), however, there is considerable variability. To provide an error term for an absolute age interpolated between boundaries of polarity units, we use a resampling technique similar to the statistician's ‘bootstrapping’. We illustrate this approach by estimating a standard error for the interpolated age of a biostratigraphical datum: the first appearance of hipparionine equids in the Siwalik sequence near the town of Khaur. The first appearance of “Hipparion” in the Khaur sequence is 9.22±0.09 Myr.