2004/02/29 by P. Fraundorf, Fraundorf, P.
Computer Science · Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Geochemistry and Geologic Mapping #Geophysics (physics.geo-ph) #Materials Science (cond-mat.mtrl-sci) #Point processes and geometric inequalities #Probability (math.PR) #Surface Roughness and Optical Measurements #cond-mat.mtrl-sci #math.PR #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.cond-mat/0403013
9 pages (3 figs, 14 refs) RevTeX, comments http://www.umsl.edu/~fraundor/covariances.html
arxiv created 2004/02/29 · openalex publication_date 2004/02/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper explores tools for modeling and measuring the compositional heterogeneity of a rock, or other solid specimen. Intuitive ``variation per decade'' plots, simple expressions for containment probability, generalization for familiar error-in-the-mean expressions, and a useful dimensionless sample bias coefficient all emerge from the analysis. These calculations have also inspired subsequent work on log-log roughness spectroscopy (with applications to scanning probe microscope data), and on angular correlation mapping of lattice fringe images (with applications in high resolution transmission electron microscopy). It was originally published as Appendix E of a dissertation on ``Microcharacterization of interplanetary dust collected in the earth's stratosphere''.