Rates of geological processes

Rates are widely used to characterize processes in the geological sciences, and the ratios that rates represent deserve more careful attention. The numerator is a measure of change or difference, and the denominator is generally a corresponding interval of time. Temporal scaling is the quantitative relationship of differences and rates to their associated time intervals. These relationships are proportional and appropriately studied on log-arithmic axes. Here log-difference-interval (LDI) and log-rate-interval (LRI) graphs are analyzed for nine empirical case studies involving creep on the San Andreas Fault, anthropogenic carbon emissions, glacial advance and retreat, sediment accumulation, tectonic uplift and exhumation, river incision, beryllium-10 dating of outcrop and basin erosion, climate-related temperature change, and species-level extinction. Two studies, fault creep and carbon emissions, are directional in the sense that each has observed differences changing in proportion to their associated time intervals; calculated rates are consequently independent of their denominators. The remaining studies are random or stationary in having differences that are independent to some degree from their associated intervals, and rates that are consequently dependent on their denominators. Rates dependent on denominators are common in geological studies because observed changes or differences are often constrained to a relatively narrow range compared to the much longer spans of time over which geological rates are calculated. When LDI or LRI temporal scaling shows change to fit a random or stationary model, meaning rates are dependent on their denominators, then any comparison of the rates involved must be restricted to, or projected to, some common denominator or common scale of time. Radionuclide calibration of outcrop and basin erosion, and biological extinction are two stationary processes where rates are often compared, erroneously, on different scales of time.

Automated summary

Rates are widely used in geological sciences to characterize processes, with the numerator representing change or difference and the denominator corresponding to an interval of time. Temporal scaling examines the relationship between differences, rates, and their associated time intervals, often analyzed on logarithmic axes. Geological studies commonly involve rates dependent on denominators due to observed changes being constrained to a narrower range compared to the longer spans of geological time. When rates are dependent on denominators, comparisons must be made on a common scale of time.