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Abstract
Journal of Sedimentary Research, Section
B: Stratigraphy and Global Studies
Vol. 67 (1997)No.
6. (November), Pages 1060-1067
Synthetic Stratigraphy with a Stochastic Diffusion Model of Fluvial Sedimentation
Jon D. Pelletier, Donald L. Turcotte
ABSTRACT
Models of stratigraphic completeness and bed formation in fluvial depositional
environments have most often assumed that successive depositional and erosional
events deposit or erode amounts of sediment independently. This results
in a random-walk model for the total amount of deposited sediment locally
as a function of time. We consider an extension of the random-walk model
of sedimentation in an alluvial plain in which deposition or erosion is
concentrated in randomly avulsing channels and sediment transport is modeled
by the diffusion equation (Culling's model). In contrast to the random-walk
model, this model results in an anticorrelated sequence locally as a function
of time, i.e., after an area has aggraded it has a higher elevation and
a lower rate of future aggradation. In a p evious paper we analyzed the
topography generated by the model and argued that porosity variations could
be associated with topographic variations. The power spectrum S
(the square of the coefficients in a Fourier series) of one-dimensional
transects of topography and porosity horizontally and vertically in this
model have a power-law dependence on wave number k: S(k) 
k-ß, with values of ß close to those observed.
In this paper we show that the model deposits sediment with a rate depending
on time interval as a power law with exponent -3/4, more consistent with
observations than the random-walk model. The model produces an exponential
bed-thickness distribution with a skew depen ent on the sedimentation rate
of the basin in accordance with observations. We also examine the persistence
in the series of bed thicknesses as a function of depth. For the stochastic
diffusion model of sedimentation no persistence is observed. If the model
fully characterizes the autocyclic dynamics in fluvial sedimentary basins,
the lack of persistence in the synthetic bed sequences suggests that observed
persistence and cyclicity in real bed-thickness sequences must be the result
of allocyclic processes.
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