ABSTRACT

A methodology is discussed for reconstructing the hydraulics of an ancient flow regime, the sole record of which is now preserved in a composite set of fluviatile cross-bedding. The hydraulic interpretation of the structural and textural attributes of the deposit is achieved primarily through the application of the principles of sediment transport mechanics.

In environmental reconstruction the size of the bed material and the velocity and depth of stream flow are three fundamental parameters from which other parameters can be systematically extrapolated. Several criteria based on the competency relationships for threshold movement and suspension transport are available for estimating the paleo-velocity of stream flow. Other criteria providing a quasi-quantitative index to current velocity are: (a) the morphology of ripple and dune bed forms now preserved as sedimentary structures, (b) the character of the contact between the foreset and bottomset in a cross-bedded deposit, (c) the relative volumetric abundance of the several sets in a tabular deposit of cross-bedding, (d) the occurrence of small-scale structures in a bottomset, and (e) th angle of foreset dip.

A review of the available literature on sediment transport indicates that suspension transport becomes "appreciable" at about twice the competent (threshold) velocity. For a sediment mix, however, the competent velocity must be defined somewhat arbitrarily on account of the selective transport of certain grain sizes. Assuming that the competent velocity is identifiable with a state of general movement on a plane to incipiently-rippled bed, a reasonable estimate of its value can be obtained from the standard competency diagrams for uniform materials by simply using the median grain diameter as the representative size of the sediment mix.

Several techniques are discussed for determining stream depth. One is based on a reconstruction of the geometric characteristics of the ripples and dunes preserved in "relict" form as cross-bedded structures; whereas the other is based on an inverse path line method that depends for its effectiveness on the dispersion and sorting of particles in a bottomset (or equivalent) deposit. A knowledge of depth and velocity permits an estimate to be made of the Froude and Reynolds numbers of the flow and of the flow discharge per unit width of channel.

The selection of a representative friction or roughness coefficient presents a difficult barrier to negotiate, but even here a reasonable estimate can be made from a knowledge of stream depth and the morphology of the bed forms. Comparative data from large-scale flume experiments also provide a framework of reference for parametral reconstruction. The slope of the energy gradient (slope of the streambed) can now be derived by substituting the appropriate numerical values in the Manning or Chezy equations for stream flow. From these basic data, calculations are made for the bed shear stress, shear velocity, rate of bed-load transport and rate of dune movement along the streambed. The equation for the velocity profile between the streamb d and surface can also be specified if a value is assumed for the von Karman constant.

The deposit selected here for parametral reconstruction is very restricted in both a spatial and temporal sense. It consists of a tabular unit of medium-scale cross-bedding that was deposited as a small delta body in a basin only a few feet in depth. Overlying the deposit there is a genetically related sequence of dune cross-bedding that was deposited after the basin had been infilled and graded to a profile of equilibrium. Calculations based on a derived rate of sediment transport suggest that the deposit was laid down over a period of several days.

Because bottomset deposition connotes suspension transport, the grain size distribution within the bottomset is an index to both paleo-velocity and stream depth. Specifically, the maximum size of particle found in the bottomset is an indicator of paleo-velocity; whereas the downstream dispersion of the different size classes is an indicator of paleo-depth. In applying the inverse path line method of reconstruction to the delta body, foreset laminae were traced through the toeset into the bottomset in order to delineate successive frontal positions of the delta during its brief formative period. Careful sampling of the attenuating bottomset laminae, coupled with the extrapolation of the grain size data, indicated the approximate maximum distance of travel of the heavier size grades as hey settled out beyond the front of the delta.

A cursory knowledge is required of the hydraulic characteristics of the flow transition (flow-pattern over the foreset slope) before the dispersion data can be transposed into a numerical depth value. In this study a simplified hydraulic geometry was adopted for the flow transition. Approximate velocity profiles were sketched in for the transition zone, and inverse path lines were traced backwards from the bottomset to the hypothetical level of particle movement in the stream. Each path line was obtained by plotting at successive points along its length the vectorial resultant of the stream velocity and the settling velocity of the particle.

The particles at the limit of travel for any given size class are those that have been carried at the surface of the stream. Therefore the "ceiling height" of the path lines corresponds to the free surface of the stream and so provides a measure of stream and basin depth. An independent and confirmatory measure of depth was obtained from the morphometric characteristics of the dune bed forms preserved in the topset overlying the deltaic foreset.

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It is fortuitous that recent hydraulic researches have established the relationship between velocity, depth, bed form, and roughness coefficient for a number of sand mixes, one of which is almost identical in composition to that of the cross-bedded deposit described here. This facilitated the selection of a representative friction factor and also permitted the extrapolation of other pertinent parameters. The analysis was carried one stage further in an attempt to determine the distribution of suspended sediment in the stream flow. Here, again, the reconstruction hinged on the grain size data of the attenuating bottomset. These data were "processed" by applying the path line technique. Finally, an estimate was made of the primary angle of dip of the cross-bedding by using the calculate gradient of the streambed as a reference plane.

Parameters so derived are estimates based on a short but factual base line; that is, grain size distributions+sedimentary structuresvelocity+depthvarious extrapolated parameters. Parametral reconstruction is inevitably subject to many limitations and uncertainties, some of which are imposed by the methods and techniques presently available, and some of which are dictated by the fragmentary evidence preserved in the lithologic record. It is axiomatic, therefore, that we can only hope to reconstruct a reasonable facsimile of the natural prototype.