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On Grain Size from Thin Sections

Grain-size distributions based on analysis of thin sections are affected by the methods used for (1) selecting grains, (2) assigning linear dimensions to each grain, (3) computing frequencies. Many combinations of methods have been proposed in the past, and they all produce valid size distribution, which may, however, be biased geometrically with respect to the desired distribution. The probabilistic relationship between the size distributions (by number) of spherical and ellipsoidal particles, and the corresponding apparent size distributions seen in thin section is discussed briefly with references to the extensive literature. Solutions to this problem exist for dilute particulate phases distributed in space according to a Poisson process, but for the commonly occurring geological case of densely packed grains in contact, no analytical solution exists. Consequently, only those sampling procedures which are geometrically equivalent to the desired standard distribution should be utilized in geological studies. Equivalent procedures are outlined following Chayes. With equivalent sampling procedures, the basic problem reduces to conversion from apparent size to true size. A numerical method is used to obtain distributions of major (a) and minor (b) axes of ellipses produced by random cuts through ellipsoids of various shapes. The analysis shows that the major axis (a) of the elliptic trace is closely related to the true intermediate axis (B) of the ellipsoid, and the minor axis (b) of the trace is related to the true minor axis (C). The ratio C/B is obtained from the difference between the cumulative distributions of the apparent axes, a and b. The sieve curve can be located between the cumulative distributions of a and b. Many apparent discrepancies in the geological literature are explained. For elliptical particles, the empirical results of Friedman are substantiated theoretically. Grid sampling combined with measurement of the apparent major axis, a, and use of number frequencies is shown to provide an efficient procedure for obtaining approximate sieve curves. Slightly closer correspondence and higher efficiency may be obtained by measurement of maximum chord length in a predetermined direction. The mathematical aspects of converting apparent axes from thin sections to distributions of true axes are outlined in the Appendix.