Thin section grain size analysis revisited

Existing proposals for converting thin section data to their sieve equivalents are all flawed in various ways, while questions concerning the significance of the grain size of spherical grains measured on a volume frequency basis in thin section using φ units, and of non-spherical (ellipsoidal) grains using both millimetres and φ units, have not been -satisfactorily resolved in the literature. It can be shown mathematically that the mean thin section diameters of spherical grains, or axis lengths of a series of parallel sections through ellipsoidal grains, will underestimate the dimensions of the corresponding central section (i.e. one passing through the grain centre) by 0.2023 φ when measured on a volume frequency basis. In order to approximate the effect of measuring particle size on random cuts through ellipsoidal grains, the dimensions of a series of sections cut in 49 unique directions, symmetrically arranged and evenly spread with respect to the ellipsoidal axes, were calculated. This calculation was carried out for five different ellipsoids which between them covered the mean sphericity and thin section axial ratio values normally encountered among naturally occurring quartz grain populations. The data indicated that the mean true nominal diameters (D?) of ellipsoidal quartz grains can be obtained in thin sections from the mean nominal sectional diameters (d?′) and major axes (ā′) of the central sections (derived from the observed values by multiplying the millimetre means by 1·1318 and subtracting 0·2023 from the φ means) using the following equations: A rough estimate (to within c. 5%) of both the mean nominal diameters and the mean long axes of ellipsoidal quartz grains can be arrived at by applying a simple correction factor to the mean long axis lengths as measured in thin section using either millimetres or φ units.