4.4 Results
4.4.2 Full Wavelength Range (1.25-2.6 µm) Model Results
148
149 4.4.2.2 Measured and Optimized Particle Diameter Ratios
As discussed in Section 3.4, three different values for the endmember particle diameter ratio (measured mean, measured mode, and optimized) were used to calculate modeled mass fraction for each mixture series. Visual inspection and point counting of endmember photomicrographs shows that the particle size distributions of clay endmembers are variable (Figure 4.1). JCSS-3501, NAu-2, and SCa-3 have mean diameters close to the mean sieve diameter of 12.5, whereas SapCa-2, SWa-1, and SWy-2 have significantly smaller mean particle diameters compared to the sieve diameter (Figure 4.1). A mean particle diameter of 16.8 µm is measured for the epsomite endmember (Figure 4.1), likely due to the clumping of very small grains to form larger aggregates measurable in the transmitted light photomicrograph. Thus for all mixture suites the measured mean clay:epsomite particle diameter ratios are <1 (Table 4.2). Particle diameter modes estimated for epsomite and clay endmembers range from 2.7 µm (SWa-1) to 10.8 µm (JCSS-3501), but for all endmembers the particle diameter mode is smaller than the
measured mean particle diameter (Figure 4.1, Table 4.2). Because clay endmember particle diameter modes are similar to that measured for epsomite (JCSS-3501 is an exception), the modal clay:epsomite particle diameter ratios are larger and closer to unity than the measured mean diameter ratios (Table 4.2).
The optimized particle diameter ratios, defined as the ratio of clay:epsomite particle diameter that minimizes differences between measured and modeled mass fractions for all samples within a mixture suite, are listed in Table 4.2. In contrast to the measured values, the optimized clay:epsomite diameter ratios for the full spectrum mass fraction calculations are nearly all >1 regardless if reflectance or SSA spectra are used (NAu-2 is the exception).
150 This suggests that in order for the derived weighting coefficients (which produce the best spectral fits) calculated for the full spectral range to be converted to clay and epsomite mass fractions that best match the measured values, it is necessary to model the clay particles as being larger than the epsomite particles. Optimized particle diameter ratios calculated for each individual mixture within a series over the full spectral range are presented in Figure 4.11, which shows that values are generally greater than one and often increase as clay content decreases (e.g., JCSS-3501, SWy-2, SCa-3, SapCa-2, and SWa-1).
4.4.2.3 Modeled Mass Fractions
4.4.2.3.1 Mass Fractions Modeled with Measured Mean and Mode Diameter Ratios
Using the measured mean particle diameters of clay and epsomite (values in Figure 4.1 and Table 4.2) to convert the checkerboard model weighting coefficients to mass fractions results in consistent underestimation of clay abundance (Figure 4.12). There are large discrepancies between measured and modeled abundances, particularly for mixtures containing ~50-80 wt.% clay where the errors can be as high as 30-40 wt. % (Figure 4.12a- c). Intimate mixing model results also show that clay abundance is underestimated for nearly all mixtures when the measured mean diameter is used to calculate mass fractions (Figure 4.12d-f). Mass fraction discrepancies resulting from the intimate mixing SSA model are generally smaller by a few wt. % compared to those resulting from the checkerboard model, indicating that conversion from reflectance to SSA is an improvement for some (but not all) of the samples.
Both checkerboard and intimate mixing model results show a general improvement when the measured particle diameter mode, rather than the mean, of individual clay and
151 epsomite endmembers is used to convert weighting coefficients to mass fractions (Figure 4.13). Clay abundance calculated with the checkerboard reflectance model is still underestimated for most mixtures within the SapCa-2, SWa-1, SCa-3, and SWy-2 series.
For about a quarter of the mixtures, the intimate mixing SSA model improves abundance estimates by 1-6 wt. % over the checkerboard model results. For the remaining mixtures, the intimate mixing model leads to no improvement or an increased discrepancy between measured and modeled clay wt. %. The checkerboard and intimate mixing model results for the 20-50 wt.% mixtures show the largest discrepancies between measured and modeled clay abundance, whereas the 5 and 95 wt.% mixtures are generally the best modeled.
4.4.2.3.2 Mass Fractions Modeled with Optimized Particle Diameter Ratio
When using the optimized particle diameter ratios, the absolute differences between measured and modeled mass fractions obtained from the checkerboard model are less than or equal to 5 wt. % for all mixtures containing more than 20 wt. % clay, a significant improvement compared to results based on measured mean or mode particle diameter ratios (Table 4.3, Figure 4.14a-c). Clay mass fraction is generally under-modeled for the 5-20 wt.
% clay mixtures, and in some cases the model fails to recognize the presence of any clay, as is the case for the SWy-2 reflectance 5-20 wt. % mixtures, 5 and 10 wt. % SCa-3 and SWa-1 mixtures, and 5 wt. % NAu-2 mixture (Table 4.3, Figure 4.14c). Mass fractions modeled for SCa-3, SWa-1, and JCSS-3501 mixtures show that clay content is consistently over-modeled and epsomite under-modeled for mixtures containing 50 wt. % or more clay.
A comparison between mixture series suggests that clay mass fraction is best modeled with
152 the checkerboard model for mixtures containing 90-95 wt. % clay, whereas modeled mass fractions calculated for mixtures containing low and intermediate clay abundances deviate the most from the measured values.
Results from the intimate mixing model show that the absolute differences between measured and modeled mass fractions are very similar to checkerboard model results and they are less than or equal to 6 wt. % for all mixtures containing more than 20 wt. % clay (Table 4.3, Figure 4.14d-e). Clay mass fractions are consistently over-modeled (epsomite under-modeled) in the high clay content mixtures (50-95 wt. % clay) and under-modeled in the low clay content mixtures (5-20 wt. %) for all mixture series. Intermediate and high clay content mixtures generally result in modeled clay fractions closest to the measured values, while low clay mixtures (5-20 wt. %) tend to result in modeled mass fractions that deviate the most from the measured values. Figure 4.14 shows that the intimate mixing SSA model fails to model the presence of clay for SWa-1, SCa-3, and SWy-2 mixtures containing ≤20 wt. % clay.
4.4.2.4 Relative Uncertainty of Model Fits
The preceding section discussed modeled mass fraction results in terms of absolute discrepancies compared to known values. Though in many cases the absolute deviations are small (<5 wt. %), such values can be extremely large in terms of the relative proportion of clay or epsomite present in the mixtures. Relative uncertainties were calculated as the absolute value of the difference between measured and modeled mass fractions (calculated using optimized particle diameter ratios), divided by measured mass fraction, and multiplied by 100 (Figure 4.15). The relative uncertainties of the modeled mass fractions
153 calculated with the checkerboard reflectance model are generally between 0 and 10% for mixtures containing 50 wt. % or more clay, but the relative uncertainty increases drastically for the nontronite and montmorillonite mixtures containing ≤ 20 wt. % clay (Figure 4.15b- c). For mixtures where no clay is modeled, the relative uncertainty is 100%.
The relative uncertainties of the modeled mass fractions based on SSA spectra are similar to uncertainties calculated from reflectance spectra (Figure 4.15d-f). Relative uncertainty is generally between 0 and 10% for mixtures containing 50% or more clay but increases progressively for all mixtures containing 20% or less clay, regardless of the clay composition. No clay is modeled in the NAu-2, SCa-3, and SWy-2 mixtures containing ≤ 20 wt. % clay or the 5 and 10 wt. % SWa-1 mixture, yielding relative uncertainties of 100% for these samples (Figure 4.15e-f). Although relative uncertainty plots for expected epsomite wt. % are not shown here, they would exhibit similar increasing trends in relative uncertainty with decreasing epsomite wt. %, the one difference being that the relative uncertainty never reaches 100% since epsomite is modeled (albeit underestimated) even in mixtures containing only 5-20 wt. % epsomite.