The completeness of a stratigraphical section is the fraction of time intervals of some specified length (t) that have left a record. A record is left when some sediment is deposited during the interval and is not subsequently eroded. A complete section contains no hiatuses longer than t. The completeness of a section varies with t and its accumulation rate varies with the length of the time span over which it is measured. Plots of measured accumulation rate against time span are an empirical means of estimating completeness. Simple theoretical models help extrapolate meagre data and identify bias.
Completeness at time scale t can depend upon three general properties of the accumulation history: the age of the section, the long term net accumulation rate (drift) and the unsteadiness of the sedimentation rate. The way unsteadiness is measured depends upon the kinds of fluctuations that can be recognized in the accumulation rate. To describe random fluctuations a standard deviation of rates is sufficient. One dimensional Brownian motion is a model of random fluctuations that explains many aspects of stratigraphical completeness. Regular periodic fluctuations in accumulation rate may be described in terms of wavelength and amplitude. Completeness is an increasing function of t, drift and, in the periodic case, the wavelength of fluctuations; it decreases with increasing standard deviation of accumulation rate and the amplitude of periodic fluctuations. The completeness and thickness of stratigraphical sections are weakly positively associated.