CGRG Bibliography of Canadian Geomorphology
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Author : Gipp, M.R.
Date : 1999
Title : Implications of the fractal geometry of topographic surfaces to the downward continuation of seismic reflectors.
Publication : Program and Abstracts, American Geophysical Union, Spring Meeting, Boston, Massachussetts, June 1 - 4, 1999.
Issue :
Page(s) :
Abstract
As a basin fills, the roughness of its upper surface decreases. If we compare the upper surface of a sedimentary package to the lower surface of the same package, usually as delineated on seismic records, we recognize that the upper surface is controlled by, but is also smoother than, the lower surface. The intervening sediments can be considered to have acted as a filter with a gain of A(k)= exp(-mk) where k is wave number (or spatial frequency) and m is a constant that can be used to characterize the interval. Such a filter has the intuitively correct effect of attenuating the high spatial frequencies more than the low spatial frequencies, thus producing a smoother surface.The successive smoothing of topography through time is exploited by the downward continuation method of seismic interpretation, wherein the topography of a deeper surface is estimated by deconvolving a well-imaged shallower reflection through an appropriately-designed inverse filter, and fitting the result to a poorly-imaged deeper reflector. Empirical studies of glacial marine sediments on the east coast of Canada show that m does not converge onto any particular value using this method. Thus, estimates of a filter parameter in its present form do not appear to be valid. Recent understanding of the nature of topographic surfaces offers a suggestion as to how to improve the method. Topographic surfaces are now recognized as being self-affine. Their roughness, therefore, is best represented by their fractal dimension, which may be estimated by fitting a sloping line (with or without changes in slope) to the spectral estimate of the surface in the spatial frequency domain. Rough surfaces are characterized by best-fit lines with relatively steep slopes, whereas smooth surfaces are characterized by best-fit lines with shallow slopes. It is clear, then, that a realistic deconvolution operator must enhance low spatial frequencies.
Bibliography of Canadian Geomorphology