Sedimentation rates, observation span, and the problem of spurious correlation

Abstract

Plots of sedimentation rates vs. time span of observation are routinely used to demonstrate that sedimentation rates decrease if one averages over longer time spans. However, these plots are suspect because they plot a variable, time, against its inverse. It has been shown that even random numbers may yield correlation coefficients of 0.7 or higher under these circumstances. We have circumvented this problem by splitting observed sedimentation rates into time classes and performing regression on the primary variables, thickness and time, separately in each class. An alternative is weighted regression that corrects for the effect of spurious correlation. Regression on the primary variables has been performed on real data from siliciclastic and carbonate rocks. Data were sorted into time classes of 10 −1–10 2 yr, 10 2–10 5 yr, and 10 5–10 8 yr. Sedimentation rates decrease systematically as the time windows increase. The experiment indicates that the decrease of sedimentation rates with increase of time is not simply an effect of the mathematical transformation. It is a physical phenomenon, probably related to the fact that sedimentation is an episodic process and that the sediment record is riddled with hiatuses on all scales.