Analysis of fault and fluvial terrace scarps in the West Yellowstone Basin south of Hebgen Lake, Montana, indicates that, during degradation, the gradient of the scarp face and the curvatures of the basal concavity and crestal convexity of the scarp face decrease (become more rounded) with time. The pattern of degradation is identical with that predicted by a simple analytical model for degradation by creep, in which the change in elevation at a point on a hillslope is proportional to the curvature of the profile at that point. The model therefore provides the basis for morphologic dating, a technique for determining the age of a scarp by the extent to which its initial morphology has been degraded. In order to date a scarp, the coefficient of proportionality, c, must be known. The technique is probably not suitable for use on hillslopes degraded by processes other than creep.
Both the potential and the limitations of morphologic dating are demonstrated via measurements of a sequence of terrace scarps along the Madison River. The calculated relative ages are in agreement with the known relative ages, despite the fact that the gradient of the youngest scarp is significantly less than that of the older scarps.
To calculate an absolute morphologic age, c must be derived from analysis of a scarp of known age having the same aspect, must be underlain by the same material, and must be within the same climatic zone as the scarp to be dated. In the West Yellowstone Basin, a value of c = 2.00 ± 0.38 × 10−3 m2/yr was calculated from a minimum date of 7100 ± 50 yr B.P. determined by radiocarbon dating for one of the terrace scarps.
Scarps formed by normal faulting in the West Yellowstone Basin are much more difficult to date than are terrace scarps, because of the possible complexity of their initial morphology. Fault scarps formed during the 1959 Yellowstone earthquake commonly consist of an assemblage of two or more smaller scarps or are superimposed on preexisting scarps formed by one or more previous faulting events. By using a selective sampling procedure, however, one can screen out these fault scarps. In this way, it was possible to determine an age of 2,800 ± 1,100 yr for a pre-1959 fault scarp in the West Yellowstone Basin.
Because the fault and terrace scarps in the West Yellowstone area do not vary significantly in height, the morphologic dating technique proposed earlier by Nash (1980a) cannot be applied to them. The substantially modified procedure developed for the present study does not require a wide range of heights for each scarp to be dated; it can be performed using a relatively small number of scarp profiles if c is known. It is easy to use, and, when used with considerable care, it is reasonably accurate (±36%–59% in this study). It is potentially applicable to scarps in other areas.