Power law olivine crystal size distributions in lithospheric mantle xenoliths

Olivine crystal size distributions (CSDs) have been measured in three suites of spinel- and garnet-bearing harzburgites and lherzolites found as xenoliths in alkaline basalts from Canary Islands, Africa; Victoria Land, Antarctica; and Pali Aike, South America. The xenoliths derive from lithospheric mantle, from depths ranging from 80 to 20 km. Their textures vary from coarse to porphyroclastic and mosaic–porphyroclastic up to cataclastic. Data have been collected by processing digital images acquired optically from standard petrographic thin sections. The acquisition method is based on a high-resolution colour scanner that allows image capturing of a whole thin section. Image processing was performed using the VISILOG 5.2 package, resolving crystals larger than about 150 μm and applying stereological corrections based on the Schwartz–Saltykov algorithm. Taking account of truncation effects due to resolution limits and thin section size, all samples show scale invariance of crystal size distributions over almost three orders of magnitude (0.2–25 mm). Power law relations show fractal dimensions varying between 2.4 and 3.8, a range of values observed for distributions of fragment sizes in a variety of other geological contexts. A fragmentation model can reproduce the fractal dimensions around 2.6, which correspond to well-equilibrated granoblastic textures. Fractal dimensions >3 are typical of porphyroclastic and cataclastic samples. Slight bends in some linear arrays suggest selective tectonic crushing of crystals with size larger than 1 mm. The scale invariance shown by lithospheric mantle xenoliths in a variety of tectonic settings forms distant geographic regions, which indicate that this is a common characteristic of the upper mantle and should be taken into account in rheological models and evaluation of metasomatic models.