Universality and Information Loss in the Stratigraphic Record

Sandy Hardian Susanto Herho , Dasapta Erwin Irawan, Rubiyanto Kapid

Sedimentary rocks are the main archive of Earth history, yet most of the time they span is not represented by rock. Material deposited at any moment survives only if the depositional surface never later erodes below it, so the stratigraphic column keeps only the lowest levels that a fluctuating surface will reach in the future. We treat this rule as a filter on a randomly evolving surface and connect it to the statistical physics of records and first passage. The fraction of time that is preserved depends on a single ratio between the resolution of observation and a crossover time set by net accumulation and surface roughness. At fine resolution this dependence is universal, the same for erosion by many small events or by rare catastrophic ones, provided successive events are independent. The Sadler effect, the decline of apparent accumulation rate with measurement interval, is governed by the persistence of the surface and changes form only when erosion has memory. With net accumulation, the age of a column as a function of height advances in independent jumps, which yields the complete statistics of hiatuses and shows that the longest gap produced by ordinary fluctuations grows only slowly with the length of the record. The same description predicts that an astronomical cycle appears in depth broadened, shifted toward longer apparent periods, and coherent over a limited number of repetitions. These results provide null models for unconformities and quantitative limits on the timing information that sedimentary sequences retain.