Abstract

In ancient fluvial deposits, exposure limitations seldom allow direct measurement of channel and valley lengths—the requisite parameters for determination of channel sinuosity. However, sinuosity can be indirectly estimated from dispersion of paleocurrent data, because it is observed in modern rivers that the migration paths of ripples and dunes usually follow the local orientation of the thalweg.

A natural channel can be described to be broadly sinuous in plan. A magnified view of any small part of it is also sinuous in shape. This scale independence of shape can be observed at smaller and yet smaller scales. Fractal patterns, which also have this property, are used here to model channel plan form at the scale of bedform migration paths. It is assumed that the sinuosity of a fractal pattern represents the channel sinuosity over a single meander wavelength, and the orientations of the smallest segments of the patterns are considered to represent the bedform migration directions. An attempt has been made in this study to establish a functional relationship between the sinuosity of the patterns and the dispersion (consistency ratio) of its segment orientations. From a number of fractal patterns of different sinuosity values, the following relationship is noted:  
formula
This relationship can be used to estimate, from paleocurrent data, the sinuosity of short stretches of ancient channels whose sinuosity was steady over time, e.g., bank-stabilized (non-migrating) channels. Published data from a number of modern rivers are used to test the equation, and the goodness-of-fit hypothesis cannot be rejected at 5% level of significance.
The lateral growth of a meander generally involves a gradual increase in the sinuosity of the thalweg. A growing natural meander is modeled by grouping together a number of fractal patterns of different sinuosity values. In a group, the pattern having the maximum sinuosity value represents the thalweg at the last stage of growth, while the rest of the patterns represent the thalwegs at intermediate stages of growth. Partial removal of earlier deposits by erosion associated with the growth of meander is taken into account by excluding the parts of the fractal patterns that represent the intermediate growth stages and lie outside final meander loop. The segment orientations from all the patterns in each group are pooled and compared with the maximum sinuosity value. From a number of such groups (of different maximum values of sinuosity) the relation between the consistency ratio and the maximum sinuosity is found to be  
formula
An empirical test of this equation using data from a single ancient meandering river deposit yields satisfactory results.
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