Fitting degradation of shoreline scarps by a nonlinear diffusion model

The diffusion model of degradation of topographic features is a promising means by which vertical offsets on Holocene faults might be dated. In order to calibrate the method, we have examined present-day profiles of wave-cut shoreline scarps of late Pleistocene lakes Bonneville and Lahontan. It may be assumed that these scarps were initially at least as steep as the angle of repose. Offsets range from 1 to 12 m, and present slope angles range from 9° to 29°. A parameter called apparent diffusion age, defined as half the mean square horizontal extent of the slope function of each profile, is plotted as a function of scarp offset. The points show a clear trend of apparent age increasing nearly linearly with offset. If linear diffusion held and scarps were initially vertical, apparent diffusion age would be the same for all the shoreline profiles. The increasing trend can only partly be explained by nonvertical initial scarp slope, and therefore the rate of transport of material downslope must increase significantly faster than a linear law in the range of slopes spanned by the data. The transport law must become linear at small slope to reduce scatter between profiles with varying ambient slopes. The transport law adopted for the purpose of dating is k₀(1 + 5s²), where s is local slope. The transport coefficient k₀ is correlated inversely with fan slope, suggesting that there is a dependence on the particle size distribution. A table is included that allows easy application of the model to scarps with simple initial shape.