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The AAPG/Datapages Combined Publications Database
Journal of Sedimentary Research (SEPM)
Abstract
The Logarithmic Spiral: Definition and Expression of a New Graphical Representation of Results in Sedimentological Analysis
Pierre Weydert
ABSTRACT
To avoid the loss of information in the coarser and the smaller fraction, results of size analysis of sample can be plotted in three-component diagrams, also called ternary diagrams or triangular diagrams, the sample being represented by a single point. A particular disposition of triangular diagrams called a sequence of triangular diagrams can be formed by considering the grade scale (10 10) as the successive boundaries of each diagram. In this system, a sample is represented by a curve which is a logarithmical spiral, the equation being: = a e-K. Geometric and trigonometric relationships give and . Study of the variations of the K coefficient permits one to obtain the mathematical position of truncation points of log-probability curves. In this graphical representation of samples, the straight lines, which join truncation points, correspond to sedimentary populations (Visher, 1969). A spiral curve is formed by several arches of which we know the equations. These arches are homologues of the straight lines of sedimentary populations in log-probability curves. The logarithmic spiral gives: first, an equation fo the size analysis of sediments, and secondly, greater accuracy in determination and study of sedimentary populations which depend on the different modes of transport and deposit of sediment.
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