M.C. McCanta¹, M.D. Dyar², P.A. Dobosh³

1 Dept. of Earth and Planetary Sciences, University of Tennessee, Knoxville, Tennessee 37996, USA
2 Dept. of Astronomy, Mount Holyoke College, South Hadley, Massachusetts 01075, USA
3 Dept. of Computer Science, Mount Holyoke College, South Hadley, Massachusetts 01075, USA

Abstract

Geologists are commonly faced with questions relating to representative sampling at all scales: outcrop to formation, hand sample to bulk rock, microanalysis to overall chemistry. A new computer model allows quantitative answers to the question of how many different microanalysis spots are needed to determine different bulk properties of a rock for any type and scale of measurement, including whole rock composition and oxidation state. The relationships among grain size, glass ordering, and microbeam size, the composition and heterogeneity of the rocks studied, and the location of the analyses relative to textural features are all important. These variables can be grouped into those that affect the heterogeneity (H) of the material versus the scale of measurements (M) being used. For rocks where H (grain size, glass long- or short-range ordering, or composition) <<M (beam size), an average of fewer than ten analyses will yield a representative bulk rock composition no matter how heterogeneous the phase assemblage. For rocks where H ≥ M, hundreds of analyses may be needed to result in acceptable analytical precision. Guidelines for how many samples/analyses are needed to represent geologic materials at any scale are presented.

Manuscript received 7 Mar. 2016; Revised manuscript received 25 Oct. 2016; Manuscript accepted 1 Dec. 2016; Published online 21 Mar. 2017

10.1130/GSATG290A.1