Geomorphic origins of statistical regularity in the geologic record

Time and topography are represented in strata in distorted, or "filtered," form because the depositional record is incomplete and the autogenic dynamics of geomorphic processes that create it are known to be partially stochastic. Two measurable characteristics of the stratigraphic record show statistical regularity over a range of environments: 1) The Layer Thickness Inventory was developed as an unbiased measure of layering in lithologic logs. The "fractal nature" of the stratigraphic record as inferred from the LTI leads to the conclusion that geophysical series have negative long range negative dependence with depth. 2) The Sadler Effect, in which calculated average linear deposition rate is a decreasing power-law function of measurement interval, is known to arise when the distribution of hiatus lengths in the record are also power-law. These power-laws arise when earth surface fluctuations have negative long range negative dependence. Long range negative dependence refers to a series with long term switching between high and low values and is described by a correlation function that decays very slowly (as a power law). Why should such long range correlation exist in surface fluctuations? Recent work that generalizes the Edwards-Wilkinson equation for surface growth reveals that the time series of elevation at a point on an evolving surface will exhibit the long-range dependence described above as a result of spatial correlations with the rest of the system. This may inform models for landscape evolution and has implications for detection and identification of cycles in the stratigraphic record.