**ABSTRACT: Reconstruction of Random Fluvial Topography from Preserved Stratification**

**Chris Paola, Leon Borgman**

A basic problem in the quantitative reconstruction of fluvial environments is that only rarely is the original topography completely preserved. This leads to potentially large errors in estimating the original heights of topographic features like bed forms or river channels. An additional complication is that the heights of these topographic features often vary randomly. We have developed an exact theory for the probability density of sets generated by random topography for the limiting case of zero net deposition. If the probability density function (PDF) for topographic amplitude is exponential, which includes most common PDFs, the PDF for set thickness is completely determined by the mean value ß of the exponential tail of the amplitude distribution. The mean set
thickness is 1.645 ß. The gamma distribution is a simple exponential distribution that fits many common types of fluvial topography. Gamma-distributed topography has a preservation ratio (mean thickness of preserved sets/mean topographic amplitude) of 1.645 where c_{v2}, where c_{v} is the coefficient of variation (standard deviation/mean) of the generating topography.

Application of our analysis to data from laboratory current ripples gives a predicted preservation ratio of 0.96; the measured value is 0.98. Measured dune amplitudes give a preservation ratio of 0.24, and depth data from two modern braided streams yield preservation ratios of 0.4 to 0.75 (i.e., mean preserved channel thickness is 40-75% of original channel depth). These numbers are a step toward more accurate error bounds for quantitative topographic reconstruction.

AAPG Search and Discovery Article #91003©1990 AAPG Annual Convention, San Francisco, California, June 3-6, 1990