A Random-Walk Simulation Model of Alluvial-Fan Deposition

Abstract

A digital model based on a random walk is used in an experiment to determine how well such a model is able to simulate alluvial-fan deposition. The model is three dimensional, and is dynamic with respect to both time and space. Two principal stochastic events are employed: (1) a relative uplift of the mountain area that is the source of the fan sediments, and (2) a storm event of sufficient magnitude to result in the deposition of material on the fan. These two events are assumed to follow independent Poisson processes with exponentially distributed interoccurrence times. The pattern of deposition is determined by a random walk from the canyon mouth at the mountain front, and each depositional event is assumed to occur instantaneously. The direction that each step in the walk takes is determined probabilistically by the gradient in the direction of flow, the momentum of flow, and the boundary conditions stipulated in the model. The type of flow — whether a debris flow, water flow, or eroding water flow — depends upon the thickness of erodible material in the basin. Deposition is assumed to occur over the entire length of the channel as a bad tapered in the direction of flow. Grain size of the water-flow deposits is governed by slope and velocity. Erosion is considered negative deposition and results from the exponential decline in elevation of the main stream channel at the fan apex or from water flows containing little basin sediment. Results of the simulation are printed as geologic and topographic maps of the fan surface and as geologic sections through the deposits.