Spatial relationship between topography and rock uplift patterns in asymmetric mountain ranges based on a stream erosion model

Abstract

The spatial relationship between topography and rock uplift patterns in asymmetric mountain ranges was investigated using a stream erosion model in which the asymmetric rock uplift was given and erosion rates were proportional to the m-th power of the drainage area and the n-th power of the channel gradient. The model conditions were simple, and thus the effects of horizontal rock movement, diffusional processes, and erosion thresholds were neglected, and spatially uniform precipitation, lithology, and vegetation were assumed. In asymmetric mountain ranges, under realistic exponent conditions (m < n) and the above assumptions, the surface erosion rate is faster on the steeper side and slower on the gentler side. The topographic axis migrates away from the rock uplift axis toward the center of the mountain range owing to the contrast in erosion rates. This migration continues until the erosion is balanced with rock uplift. In a dynamic steady state, the topographic pattern is independent of the rock uplift rate as indicated by an analytical solution, and is prescribed by the rock uplift pattern and the exponents m and n. As the asymmetry of the rock uplift pattern increases, the topographic axis migrates a greater distance. The location of the topographic axis is related to the location of the rock uplift axis by a simple logarithmic function, for a wide range of m and n. The fit of the numerical results and the logarithmic function is particularly good when m = 0.5 and n = 1.0. If the rock uplift pattern in asymmetric mountain ranges is known, the value of n − 5m/4 can be constrained based on the logarithmic relation, assuming a dynamic steady state. On the other hand, if the value of n − 5m/4 is known in an asymmetric mountain range, the rock uplift pattern can be estimated directly from the topography. This relation was applied to the Suzuka Range in central Japan, and the value of n − 5m/4 was estimated for an assumed reverse fault motion.