Imhof, Matthias¹ 
(1) Virginia Tech, Blacksburg, VA

ABSTRACT: A Quantitative Stratigraphic Model Based on Nonlinear Anisotropic Diffusion

The diffusional model has been used successfully to model the transport and deposition of marine sediments. Even three-dimensional diffusion models, however, often cannot simulate erosion realistically. A steep canyon, for example, tends to be filled rapidly by sediment flowing down the sides. In reality, sediments are constantly flushed out which allows further erosion at the bottom. 
The basic assumptions of diffusional models are (1) that sediments are transported from high to low elevations, and (2) that sediments either are eroded, transported, or deposited. Both assumptions appear to be valid, and we believe that the problem is caused by the simplistic linear, isotropic diffusion model. 
We propose to couple the diffusional model with a drainage model. Assuming that sediment is transported by fluid flow, this drainage model computes direction and accumulated flow magnitude at every point of the model. The diffusion constants in the sediment model are then replaced with diffusion tensors aligned with these fluid flow directions and scaled with the fluid flow magnitudes. 
The strong fluid flow along the canyon bottom results in an aligned diffusion tensor which preferentially transports sediment through the canyon instead of into the canyon. The model becomes more complex because it contains three diffusion parameters instead of one, but these parameters are based on a physical model again and can be estimated from the drainage model. This drainage model may be costly to compute repeatedly, but algorithms such as the D8 method are readily available and easy to couple with diffusional sedimentation models.

AAPG Search and Discovery Article #90026©2004 AAPG Annual Meeting, Dallas, Texas, April 18-21, 2004.