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Table 1 Summary of main physical and textural parameters in the three samples investigated. Table 1

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Fig. 1. Various ways to display textural characteristics through size (L) and number density (n or Ny) plots, and processes that they may be associated with (single or few nucleation events, multiple nucleation and | events, continuous nucleation and growth, coalescence, ripening, and collapse, see text for explanation). (a) Simple volume fraction (V¢) size distribution (VVD), (b) cumulative volume fraction size distribution. (| (c) vesicle size distributions (VSD) in terms of number density n, and (d) cumulative number density plots log(Ny>L) vs. log(L) (CVSD). Because during magmatic ascent multiple vesiculation and degassing process occur simultaneously and overprint each other, such plots call for interpretative prudence. G is growth rate and t is time.

Fig. 2. Illustrative cartoon of sampling procedure and density measurements. T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx

T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx Fig. 3. Resolution and magnification within imaging techniques. (a) Influence of minimum diameter. The dashed gray curve illustrates the error > (right y-axis) associated with misrepresentation of 1 pixel in area within a vesicle. (b) Minimum vesicle diameter measurable for various magnifications. If vesicles as small as 1 zm in diameter are present within the sample and need to be imaged, maximum magnifications of 500x are sufficient assuming a resolution of 5 pixels minimum per vesicle (arrowed dashed line).

Fig. 4. The three tested imaging strategies; (a) a 73-image grid nest, with one image randomly chosen within the previous magnification, (b) a 25-image grid nest of si- milar configuration, and (c) an example of exponential nesting, where each magni- fication possesses twice as many images than the previous one and chosen nests are not randomly located within each magnification. IMR: Image Magnification Ratio. To test the relative accuracy of the three strategies, we compare the measured number density of vesicles (Na, mm~7) in a pumice sample with a wide vesicle size range that required four different magnifications. Largest vesicles were around 5 mm, thus the lowest magnification was chosen at 5x (entire thin section). Smallest vesicles measured about 5 um, hence the largest magnification needed was around 250x (Fig. 3). Intermediate magnifications were 25x and 100x to allow sufficient size overlap between images. Fig. 5 shows that the 72-image and 25-image grid techniques produce fairly smooth decreases in number density with increasing vesicle size. Number density data from the 15-image nest are somewhat noisier but still allow adequate characterization of size distributions. From

Fig. 6. Common issues with SEM images obtained from thin sections (top), and grayscale image resulting from repairing and processing each image (bottom). (a) Vesuvius 79AD EU2 sample showing a significant amount of broken glass walls as well as extremely thin ones. (b) 3D effect caused by intersecting small objects within a somewhat thick section, and broken glass and crystal fillings within some vesicles. (c) Illustration of problems of heterogeneous grayscale variations within raw SEM images (top histogram), and conversion to homogenous grayscale levels after image processing (bottom histogram). For guidelines to avoid grayscale conversion issues, see manual in online additional material. Although the reader is directed to Sahagian and Proussevitch (1998) for complete details concerning this procedure, the stereo- logical formulations used here are summarized in Appendix A. Their method consists in deriving Ny;, the number density of objects of size i per unit volume from Naj, the number density per unit area via an expression of the probability of intersecting spheres of given sizes through their maximum cross-sectional area P;. To obtain Ny; from Nai (Appendix A), Underwood (1970) introduced a useful parameter called the mean projected height (H; , mm), which represents the mean distance between parallel planes tangential to the object boundary. For spherical particles, this equates to the characteristic diameter of each size class (L, mm). The diameter is thus used to correct Na values for intersection probabilities on the basis of the stereological assumption N= Ma (Underwood, 1970), and then corrected for the cut-effect (see To reduce the amount of time spent performing these corrections a detailed methodology that provides step-by-step guidelines on how

Fig. 5. Number of objects per melt area for different size classes measured within pumice samples from Taupo for each of the three imaging strategies. Note the good overall correspondence between the obtained curves which allows reducing the number of images required to adequately represent the sample overall. T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx

Fig. 7. Illustration of the influence of how magnification cutoffs are chosen within a Vesuvius 79AD pumice. (a) A plot of Na vs. equivalent diameter L for each magnification (1-4) results in decreasing Na with increasing L for each decreasing magnification. A certain amount of overlap is required for the FOAMS program (or the operator) to choose the best Na coverage per size range. (b) Vesicle volume distribution histograms resulting from several magnification cutoff trials; the first cutoff technique tested consisted in arbitrarily choosing boundaries at order of magnitude size changes, the second technique involved minimizing slope differences between the Na curves of two overlapping magnifications (resulting cutoffs reported as round symbols), and the third method minimized Na changes (resulting cutoffs reported as dotted lines and arrows). (c) The best result for this pumice clast was obtained using the Na-minimizing method. Notice that there are still some irregularities in the resulting curve. Overlapping size bins for adjacent magnifications ensures that all vesicle sizes are adequately represented. We illustrate a method of merging data from different magnification images using an example of pumice from Vesuvius (79AD eruption, white magma, EU2 unit; Gurioli et al., 2005). Pumice clasts contain vesicles of sizes varying between 0.001 and about 4mm. Four magnifications are chosen to FOAMS is a Matlab™-based program designed to facilitate the measurement and stereological conversion of objects within a set of one to twenty images. All the details on the program's structure are available on the web (http://www2.hawaii.edu/~tshea/), and a simple

Fig. 8. FOAMS “Init” (top) and “Result” (bottom) user interfaces and graphical contents. T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx

Fig. 9. Density measurements (bottom x-axis) and corresponding vesicularities (top x-axis) for (a) Makapuu lava flows including three physically distinct units (pahoehoe, ‘a’a, transitional), (b) Villarrica basaltic scoria samples including some very low density samples of golden pumice, and (c) Vesuvius 79AD EU2 pumice samples Large stars represent chosen samples within all three eruption units and small stars stand for lower and higher density clasts that were also investigated in other contributions (Gurioli et al., 2005, 2008).

T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx

T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx Fig. 11. Influence of adding or discarding images of increasing magnifications for (a) Makapuu lavas (bottom section only), (b) Villarrica scoria, and (c) 79AD Vesuvius EU2 pumice. In each case, the distribution resulting from using only lower magnification imagery is shown in gray. Here, a 5-pixel diameter was used to generate these distributions, thus the lower size limit corresponds to the point under which the uncertainty for each misrepresented pixel is greater than 5%. Vesicle number densities corrected for melt (Nycorr) calculated for each combination of magnifications are also reported.

T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx Fig. 12. Vesicle number density per area (Na) measured in the investigated samples. (a) Makapuu, (b) Villarrica, (c) Vesuvius. Gray dotted lines correspond to the resolution limit allowed by various minimum diameters. Under these boundaries, Na values used to obtain Nys are discarded. Typically, a maximum uncertainty of 5% is allowed. Any vesicle smaller than this is thus considered noise. For Makapuu the best choice of minimum diameter is probably situated around 15-20 pixels, for Villarrica at about 5-10 pixels, and at Vesuvius 5 pixels.

T. Shea et al. / Journal of Volcanology and Geothermal Research xxx (2009) xxx-xxx Fig. 13. Vesicle size distributions in terms of volume fraction (VVD), cumulative size distributions (CVVD), size distributions in terms of number density (VSD), and cumulative number density plots (CVSD) for (a) Makapuu transitional lava, (b) Villarrica scoria, and (c) Vesuvius 79AD pumice. Vesicularities are reported in VVD plots. Gray dotted line: represent minimum diameter boundaries; i.e. the limits under which any vesicle smaller than a given diameter in pixels will be discarded. Black dashed lines are limits beyond whict bins possess less than 5 vesicles each.

Fig. 14. Influence of minimum measured vesicle size (in pixels per diameter) on the calculated Nvcorr for (a) Makapuu lavas, (b) Villarrica scoria, and (c) Vesuvius white pumice. In all cases the obtained number densities are extremely dependent on the choice of the smallest resolvable vesicle size (in pixels). Number densities obtained using VSD fitted curves (Nvst) are also shown as black squares. Notice the general disagreement between the two values for samples containing a high density of vesicles (Villarrica and Vesuvius) and the good concordance with Makapuu lavas. Zones filled with increasing gray shades report errors associated with misrepresentation of 1 pixel. Another issue inherent to the acquisition of results through binning and stereological conversion to 3D is that individual data are inevitably lost in the process. This means that statistical analysis of the data will have to be done directly on distribution curves with no real decision on how large the bins are and how many objects they typically contain. Even so, distribution fitting is still possible using geometric binning, as it appears that most distributions fall within the logarithmic family (log- normal, Weibull, logistic and exponential, Proussevitch et al., 2007a). Because few distributions are normal, we recommend avoiding the use of the mean and using modes instead. The actual “log-normal” mean can still be obtained through the normal mean and standard deviation derived from the geometrically binned distribution. We showed that the choice of the minimum number of pixels necessary to adequately represent a vesicle is crucial since it has a large influence on measured estimates of Ny. For small increases in minimum resolvable diameter, number density can drop by an order of magnitude. This decrease was observed to be stronger with increasing explosivity: each 5 pixel increase in the input threshold diameter resulted in about 5, 15, and 30% decreases in Nycorr for Makapuu, Villarrica and Vesuvius samples respectively. Thus, to obtain accurate measurements of Ny,o;;, it is crucial to select minimum diameters that ensure that the measured vesicles are above “noise” level. Uncertainties within Nycor; will then mostly depend on the accuracy of vesicularity measurements used to calculate number density per melt volume. The errors associated with misrepresentation (addition or omission) of 1 or several pixels

Please cite this article as: Shea, T., et al., Textural studies of vesicles in volcanic rocks: An integrated methodology, J. Volcanol. Geotherm. Re (2009), doi:10.1016/j.jvolgeores.2009.12.003 a single value of exponent d~2.5, close to the value anticipated for Apollonian packing (Blower et al., 2001), could apply to most vesicular samples, from lava flows to pumice. In the literature, however, varying d exponents have been found: d=2.5 in Basaltic scoria from Izu Oshima subplinian eruption (Blower et al., 2002), 2.8 within Stromboli basaltic scoria (Bai et al., 2008; Polacci et al., 2008; Note that their form of Eq. (B.6) expresses measurements as volume instead of radius), 2.8 in Etnean basaltic scoria (Simakin et al., 1999), 2.7-2.9 in Plinian basaltic scoria (Sable et al., 2006), 3.3 in rhyodacitic

Julia Hammer

Textural studies of vesicles in volcanic rocks: An integrated methodology

Abstract:Vesicles in volcanic rocks are frozen records of degassing processes in magmas. For this reason, their sizes, spatial arrangements, numbers and shapes can be linked to physical processes that drive magma ascent and eruption. Although numerous techniques have been derived to describe vesicle textures, there is no standard approach for collecting, analyzing, and interpreting vesicular samples. Here we describe a methodology for techniques that encompass the entire data acquisition process, from sample collection to quantitative analysis of vesicle size and number. Carefully chosen samples from the lower, mean and higher density/vesicularity endmembers are characterized using image nesting strategies. We show that the texture of even microvesicular samples can be fully described using less than 20 images acquired at several magnifications to cover efficiently the range of existing vesicle sizes. A new program (FOAMS) was designed to perform the quantification stage, from vesicle measurement to distribution plots. Altogether, this approach allows substantial reduction of image acquisition and processing time, while preserving enough user control to ensure the validity of obtained results. We present three cameo investigations — on basaltic lava flows, scoria deposits and pumice layers — to show that this methodology can be used to quantify a wide range of vesicle textures, which preserve information on a wide range of eruptive conditions.

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Figure 1 – uploaded by Julia Hammer

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