On the significance of δ13C correlations in ancient sediments

A graphical analysis of the correlations between δc and εTOC was introduced by Rothman et al. (2003) to obtain estimates of the carbon isotopic composition of inputs to the oceans and the organic carbon burial fraction. Applied to Cenozoic data, the method agrees with independent estimates, but with Neoproterozoic data the method yields results that cannot be accommodated with standard models of sedimentary carbon isotope mass balance. We explore the sensitivity of the graphical correlation method and find that the variance ratio between δc and δo is an important control on the correlation of δc and ε. If the variance ratio σc/σo ≥ 1 highly correlated arrays very similar to those obtained from the data are produced from independent random variables. The Neoproterozoic data shows such variance patterns, and the regression parameters for the Neoproterozoic data are statistically indistinguishable from the randomized model at the 95% confidence interval. The projection of the data into δc–ε space cannot distinguish between signal and noise, such as post-depositional alteration, under these circumstances. There appears to be no need to invoke unusual carbon cycle dynamics to explain the Neoproterozoic δc–ε array. The Cenozoic data have σc/σo < 1 and the δc vs. ε correlation is probably geologically significant, but the analyzed sample size is too small to yield statistically significant results.