LIMITATIONS ON STRATIGRAPHIC ANALYSES DUE TO INCOMPLETE AGE CONTROL AND THEIR RELEVANCE TO SEDIMENTARY PALEOMAGNETISM

Abstract

A major limitation in the analysis of physical quantities measured from a stratigraphic core is incomplete knowledge of the depth to age relationship for the core. Records derived from diverse locations are often compared or combined to construct records that represent a global signal. Time series analysis of individual or combined records is commonly employed to seek quasi-periodic components or characterize the timescales of relevant physical processes. Assumptions that are frequently made in the approximation of depth to age relationships can have a dramatic and harmful effect on the spectral content of records from stratigraphic cores. A common procedure for estimating ages in a set of samples from a stratigraphic core is to assign, based on complementary data, the ages at a number of depths (tie points) and then assume a uniform accumulation rate between the tie points. Imprecisely dated or misidentified tie points and naturally varying accumulation rates give rise to discrepancies between the inferred and the actual ages of a sample. We develop a statistical model for age uncertainties in stratigraphic cores that treats the true, but in practice unknown, ages of core samples as random variables. For inaccuracies in the ages of tie points, we draw the error from a zero-mean normal distribution. For a variable accumulation rate, we require the actual ages of a sequence of samples to be monotonically increasing and the age errors to have the form of a Brownian bridge. That is, the errors are zero at the tie points. The actual ages are modeled by integrating a piecewise constant, randomly varying accumulation rate. In each case, our analysis yields closed form expressions for the expected value and variance of resulting errors in age at any depth in the core. By Monte Carlo simulation with plausible parameters, we find that age errors across a paleomagnetic record due to misdated tie points are likely of the same order as the tie point discrepancies. Those due to accumulation rate variations can be as large as 30 kyr, but are probably less than 10 kyr. We provide a method by which error estimates like these can be made for similar stratigraphic dating problems and apply our statistical model to an idealized marine sedimentary paleomagnetic record. Both types of errors severely degrade the spectral content of the inferred record. We quantify these effects using realistic tie point ages, their uncertainties and depositional parameters.