Grain-size analysis of pyroclastic samples is a standard characterizing technique and, over the last 20 years, has been increasingly used to interpret the origin of samples (for instance, Sheridan, 1971; Walker, 1971; Wohletz, 1983). Granulometric characterization of samples is an especially important tool for correlation and classification in areas where many pyroclastic deposits are encountered. Interpretation is generally needed to determine the eruption and emplacement mechanisms for the deposits sampled.
Sieving is a practical approach for classifying samples in the range of ~16 to 0.064 mm, for which standard screens are readily available (see, for instance, Folk and Ward, 1957). Above this grain size, hand counts of individual fragments are useful; below this size, settling-tube measurements, based on either a pipette method (Folk, 1976) or optical methods such as fluid suspension absorbance measurements can extend the range to near 1 µm. The wide range easily analyzed by screen sieves provides enough data to adequately characterize and interpret most tephra samples. Table A.2 presents class size intervals for clastic sediments and pyroclastic rocks. Because of the broad range of grain sizes represented by pyroclastic materials, it is common to use a logarithmic transformation of grain diameters called the phi (f ) scale (Wentworth, 1922):
for which dmm is the grain diameter in millimeters. Krumbein (1938) showed that on this scale transformation, plots of mass frequency vs phi size approximated a Gaussian distribution, which can be characterized by the use of log-normal statistics:
where d m/df = the mass per unit interval of f , Ks = a constant to normalize the distribution (usually Ks = 1), sd = the standard deviation in log units, d = particle diameter, and dm = the mode diameter of the distribution.
Tephra size data are useful for various types of interpretation. For example, Sparks et al .
(1978) discussed the importance of particle size to terminal fall velocity, which is useful in determining the amount of time required for pyroclasts to fall out of eruption plumes and clouds (Fig. A.9). Carey and Sparks (1986; Figs. 1.13 and 1.14) related maximum clast sizes to distance from source for eruptions of different magnitudes. A plot of median diameter vs distance from the source (Fig. A.10) shows the general fining of pyroclastic samples with distance for a number of different eruptions.
By using single-mode lognormal statistics, Walker (1971) characterized tephra samples of pyroclastic fall and flow origin. Wohletz (1983) described similar size data for pyroclastic surge samples. Sheridan and Wohletz (1983a) characterized size data for numerous samples of hydrovolcanic origin (see Fig. 2.20). Taken together and plotted on a sorting vs median diameter plot (Fig. A.11), these data provide a general interpretation scheme for tephra samples.
Another, more specific example illustrates the application of size data to a stratigraphic section of the Lathrop Wells scoria cone in Nevada that exhibits two main types of eruptive behavior (Wohletz, 1986): early
hydrovolcanic explosions and later Strombolian eruptions (Fig. A.12). Three types of bedforms were recognizable: scoria fall, fine ash layers of undetermined origin, and pyroclastic surge. Figure A.13 is a sorting vs median diameter plot that nicely differentiates between the three bedforms. Because of their relatively poor sorting, it was assumed that the fine ash layers had been emplaced by pyroclastic surge. Furthermore, a plot of median diameter and weight percent of fine ash (Fig. A.14) correlated the fine ash layers with similar size distributions from early hydrovolcanic samples in the cone stratigraphy and thus permitted their classification as hydrovolcanic. This interpretation was supported by a later study of pyroclast constituents, morphology, and surface chemistry.
We believe that size analysis can provide even more information about the history of fragmentation and dispersal of pyroclastic samples through mathematical analysis of individual size-frequency distributions. Sheridan et al . (1987) discussed the typical polymodality of tephra size-frequency distributions and possible types of interpretations. Typically, size-frequency distributions are analyzed as lognormal-type distributions, in which, for any particular sample, one or more lognormal subpopulations may overlap to form the total observed distribution. Because the single-mode lognormal statistics are not strictly applicable to tephra samples, we advocate the subpopulation discrimination technique established by Sheridan et al . (1987), in which microcomputer software can be applied to sieve data for fully characterized sized distributions. More recently, Wohletz et al . (1989) developed a new mathematical distribution, the sequential fragmentation/transport model, that relates distribution shapes to physical
processes of fragmentation and transport sorting, which allows a much more extensive analysis of size data. The distribution is given as
where the normalization constant (Ks ) and the transport distance factor (x/xo ) are set to unity for frequency distributions totaling 100%, gf = a parameter analogous in part to standard deviation, and gf = gf + 2 for fragmentation processes or gf = 2 for transport processes. Because the distribution shapes for the fragmentation and transport forms of Eq. (A-3) are nearly identical and because almost all tephra samples have experienced some sorting by a transporting agent, the gf = 2 form is most appropriate. Figures A. 15 through A.17 show the results when Eq. (A-3) is applied to several tephra samples. In Table A.3, we show observed ranges and expected values of gf for volcanic fragmentation and transporting process.