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Figure 1. Comparison of geoanalytical scale. (A) Halemaumau crater, Kilauea, Hawaii. Photo by Molly McCanta. (B) Lava flow features, Kilauea. Photo
by Nathan Bridges. (C) Photomicrograph of basaltic magma from Kilauea Iki lava lake. Photo by Molly McCanta. (D) Scanning transmission electron
microscopy–electron energy loss spectroscopy (STEM-EELS) large grayscale high-angle dark field image of basaltic glass. Brighter areas show where
iron is concentrated; bottom left corner shows the sample edge. LIBS—laser-induced breakdown spectroscopy; XAS—X-ray absorption spectroscopy.

scale of single atoms, as is the case with standard deviations of the bulk composition grain size = beam size (ratio = 1.0), and
scanning transmission electron micros- represented by the average of the chosen grain size >> beam size (ratio = 2.5).
copy–electron energy loss spectroscopy analyses, which are randomly located. Precision values, represented by relative
(STEM-EELS; e.g., Garvie and Buseck, The model is built around a 2-D 1000 × standard deviation (RSD), are given in
1998; van Aken and Liebscher, 2002) and 1000 pixel image. Applications to Mars Table 1.
the atom probe (e.g., Kelly and Larson, exploration along with user input param-
2012; Valley et al., 2015), additional con- eters are given in McCanta et al. (2013), Single Phase Systems
siderations arise. Do the compositions of and the model itself is available at
single atoms or even tens of atoms record www.mtholyoke.edu/~pdobosh/libssim/ If only a single phase is present, then a
anything about properties of the whole lasersimR5.html. reliable bulk composition requires few
sample? Any misunderstanding of how to analyses, given the reasonable expectation
reconcile sample size and measurement RESULTS that analytical precision is as good or bet-
technique size runs the risk of leading to ter than accuracy. In our model results, six
difficulties in interpretation. Accuracies of bulk compositions for spot analyses are generally enough to gen-
multiple rock types, melt compositions, erate a statistically significant bulk compo-
This paper thus explores sampling strat- and beam conditions were calculated as a sition and account for minor heterogene-
egies that result in the most accurate function of grain size, beam size, and sam- ities; this number varies slightly with the
returned bulk rock properties from vary- pling density. Grain size here refers to relative precision and accuracy of each
ing scales of measurements, rock types, either mineral size in a crystalline rock or analytical method. These results apply to
textures, and analytical instruments. Rock ionic radius of an atom within either a chemical measurements in glasses or
characteristics (mineral and melt constitu- crystallographic matrix (mineral) or a ran- homogeneous single crystals with sizes
ents, grain size) and analytical conditions domly distributed amorphous matrix (melt). larger than the beam.
(beam size, analysis location, number of
analyses) are varied to study errors propa- Crystalline Rocks Grain Size
gated onto bulk rock compositions. The
results define the number of analyses To evaluate size ratio effects in crystal- The presence of multiple phases intro-
required to get reproducible bulk rock line rocks, basalt and dacite compositions duces complications to sampling protocols
compositions in lab and field applications. from Mt. Shasta, California, USA, were and forces consideration of the grain-size
These are broadly relevant to any type of used as program inputs. These natural to beam-size ratio. When grain size is
microanalysis, and also to sampling at field island arc samples are fully crystallized, small relative to the beam (ratio = 0.25;
scales, where the ratio of hand sampling making it difficult to obtain a bulk com- Fig. 2A), a single analysis likely samples a
size to outcrop/formation scale heterogene- position as discussed above. Experimental nearly representative portion of the assem-
ities is relevant. work (Baker et al., 1994; McCanta et al., blage, and may include all phases in the
2007) reproduced the melt-crystal assem- rock in their true proportions. Therefore,
METHODOLOGY blages, allowing bulk rock composition to archetypal bulk compositions are returned
be estimated and compared with model when the sample grain size << beam size
Grain size, beam size, phase assemblage, results. Variable grain sizes (Figs. 2A–2C), (Supplementary Table [see footnote 1]). As
and phase composition are varied using a beam sizes, and sampling densities were grain and beam size converge (grain size =
computer model to determine potential studied (see GSA Data Repository 1 Table beam size), calculated bulk compositions
effects on the accuracy of bulk rock mea- S1). For each sampling density (10, 50, or decrease in precision (Table 1). When
surements. The modeling program returns 100 locations), three data sets are shown: grain size >> beam size (ratio = 2.5), it
mineral and oxide percentages along with grain size << beam size (ratio = 0.25), becomes unlikely that any microanalysis

1GSA Data Repository Item 2017081, Table S1 (measured vs. calculated bulk compositions), is online at http://www.geosociety.org/datarepository/2017/. Questions?
Please email gsatoday@geosociety.org.

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