The age of scarplike landforms from diffusion-equation analysis

The purpose of this paper is to review developments in the quantitative modeling of fault-scarp geomorphology, principally those since 1980. These developments utilize diffusionequation mathematics, in several different forms, as the basic model of fault-scarp evolution. Because solutions to the general diffusion equation evolve with time, as we expect faultscarp morphology to evolve with time, the model solutions carry information about the age of the structure and thus its time of formation; hence the inclusion of this paper in this volume. The evolution of fault-scarp morphology holds a small but special place in the much larger class of problems in landform evolution. In general, landform evolution means the evolution of topography as a function of both space and time. It is the outcome of the competition among those tectonic processes that make topography, erosive processes that destroy topography, and depositional processes that redistribute topography. Deposition and erosion can always be coupled through conservation-of-mass relations, but in general deposition occurs at great distance from the source region of detritus. Moreover, erosion is an inherently rough process whereas deposition is inherently smooth, as is evident from even casual inspection of shaded-relief, digital-elevation maps (e.g., Thelin and Pike, 1990; Simpson and Anders, 1992) and the current fascination with fractal representations oferoding terrains (e.g., Huang and Turcotte, 1989; Newman and Turcotte, 1990). Nevertheless, large-scale landform-evolution modeling, now a computationally intensive, advanced numerical exercise, is generating ever more realistic landforms (e.g., Willgoose and others, 1991a,b; Kooi and Beaumont, 1994; Tucker and Slingerland, 1994), although many of the rate coefficients remain poorly prescribed