Dimensionality reduction on MIR spectra of powdered silicate glasses as analogues for volcanic ashes

Rationale 
Silicate glasses are significant components of volcanic products, but spectral libraries typically provide references of crystalline materials rather than amorphous ones, even if blurred/featureless spectra are observed on planetary terrains. Thus, the Petro-Volcanology Research Group (PVRG) started an investigation of the spectral response of silicate glasses developing a database, to distribute spectral data applying the FAIR (Findable, Accessible, Interoperable, Reusable) principles ​[1]​. We have analyzed these spectra using PCA and, in particular, we focused on MIR range, in which information about silicates’ arrangement in the material is detectable ​[2].

Fig. 1: a) TAS diagram of all products. Circles:sub-alkaline , triangles:  alkaline. b) spectra of the entire dataset 

Methodology
The investigated datasets consist of MIR spectra of 20 powdered silicate glasses (<36 µm grain size) whose composition that varies greatly within TAS diagram (Fig. 1a). Spectra of silicate glasses within this range present various features, as described in ​[2]​ and depicted in Figure 1b: we can observe Christian feature (local negative at ca. 7-8 µm, hereon CF), Reststrahlen Band peak (local maximum at ca. 9-10 µm, hereon RB_peak) and transparency feature (local maximum at ca. 11.5 µm, hereon TF). CF and RB_peak depend on the chemical-structural properties of the material, whereas TF depends on the granulometry of the investigated product and it is particularly prominent for ultra-fine powders.  

​Fig. 2: The columns contain the process summary results for each dataset, see main text for explanation.​​

Steps of data analyses are shown in Figure 2 and are as follows:

I) Starting datasets 

For the principal component analysis, we considered four different starting datasets: spectra were considered between 8.17 µm, which is the highest CF among the set, and 12 µm (Full dataset in Fig. 2) and between ca 8.17 µm and 10.5 µm (Cut dataset in Fig. 2) this distinction was made to observe the influence of TF for such parameterization. Both datasets were investigated as raw spectra and as smoothed spectra  (30 points adjacent averaging technique)

II) Normalization 

Each dataset was normalized from 0 (lowest reflectance) to 1 (highest reflectance) through the formula S_norm=[S-min(S)]/[max(S)-min(S)]. This decision was taken after several try-and-fail approaches which revealed that this simple normalization leads to promising results.

III) PCA Loadings 

Regarding the full dataset, PC1 is in general in anticorrelation with the normalized reflectance values, while the PC2 is divided into a first part of the spectra that is in anticorrelation with the PC score (up to ~10.5 µm) and a second part of the spectra that correlates positively with the score (from ~10.5 to 12 µm). 
Regarding the cut dataset, the general shape of the loadings is similar to the one of the full dataset: PC1 is in general anticorrelation with the score except RB_peak, and PC2 is in general anticorrelation up to ~10.1 µm and then the correlation factor starts to grow. 

• PCA score plots 

On the full dataset the smoothing has the effect to better distinguish samples with PC1 < 0 and to map the rhyolitic samples to have similar PC1 scores, while leaving the PC2 scores almost unaffected. On the contrary, for the cut dataset the smoothing seems to affect the PC2 scores more than the PC1’s: the basaltic samples are mapped closer together after the smoothing and also the rhyolitic ones possess closer PC2 scores. On the other hand, the main difference between the cut and full datasets (either smoothed or not) seems to lay in the better distribution of samples for the cut one, having the basalt samples more separated from the rest and the rhyolitic samples nearer to each other, as well as a general better distribution of all the other samples in between. 

Conclusions and perspectives 

Firstly, it is important to assess that for each dataset the total variance explained by the PCA is significantly greater than 90 %, with the notable exception of the full non-smooth dataset that is just above it. Therefore, we assess the efficiency of the model at representing the data, especially regarding the cut and smoothed dataset that reaches up to ~97% of the total explained variance. 
Secondly in general it is important to notice how the SiO₂ content trend is well reflected by the PC1 scores, especially in the case of the cut and smooth dataset, for which it is clearly visible (see figure 2, row 4, image 4). Always regarding this specific case, the PC2 seems to be, at least partially, in anticorrelation with respect to the Na₂O+K₂O content, with basalts that have the highest PC2 values, thus giving promising preliminary results. 

References
1. Pisello A., EPSC 2022, doi.org/10.5194/epsc2022-539
2. Pisello A., Icarus 2022, 388, 115222, doi:10.1016/J.ICARUS.2022.115222.