10:45 AM - 11:00 AM
[SMP26-01] Skew-normal peak fitting of cathodoluminescence on shocked quartz: a statistical model for impact pressure estimation
Keywords:cathodoluminescence, impact, spectral deconvolution, Bayesian statistics
Impact pressure is a key parameter to understand an impact cratering on celestial body, one of the ubiquitous processes on terrestrial planets, satellite and asteroidal bodies. Recent studies qualitatively revealed that cathodoluminescence (CL) spectra of shocked quartz depend on impact pressure [1, 2] as also found in alkali feldspar [3]. However, since CL spectra of shocked quartz have broad and skewed peaks, it has been difficult to obtain a quantitative relation between CL spectra and impact pressure by using spectral deconvolution.
In this study, we propose a statistical model that decomposes CL spectra of experimentally shocked quartz at various impact pressures into several peaks by utilizing skew-normal distributions, instead of normal distributions. The samples of shock-induced quartz were obtained by shock experiments done in Chang et al. (in prep). According to the experiments, the peak pressures of the samples reach 0 GPa to 40 GPa in 5 GPa increments. Also, the CL spectra of the samples were analyzed with SEM (JEOL: JSM-5410) combined with a grating monochromator (Oxford: Mono CL2) at the Okayama University of Science. The obtained CL spectra were corrected by standard lamp. Using Monte-Carlo sampling and Akaike information criterion, we estimate the number of skew-normal peaks and four parameters for each peak, i.e., location, scale, shape, and weight. A mixture of skew−normal distributions provides a better fitting model for CL spectrum of shocked quartz than a mixture of normal distributions. Moreover, it is statistically revealed that among the four parameters of a skew-normal distribution, weights of peaks change with impact pressure.
We also demonstrate that the quantitative relation between weights of CL peaks and impact pressure can be utilized for an estimate of impact pressure based on CL spectra of shocked quartz. Here, we divide the CL data of shocked quartz into two data sets, i.e., training and validation data sets. Then, we calculate a posterior probability of impact pressure of the validation data set by comparing posterior distributions of CL weights of the validation data sets with those of the training data sets. As a result, the actual pressure of the validation data set tends to have the highest posterior probability. The proposed method is as precise as a conventional impact pressure estimation via Planar Deformation Features (PDFs) while the dynamic range would be wider than the conventional method. Additionally, The proposed method is more convenient than the other. The improvement in the efficiency in estimation of paleo impact pressure would drive investigations of impact cratering processes. Also, a fitting via skew-normal distribution could contribute to deconvolution of spectra other than CL spectrum of shocked quartz.
[1] Chang et al., (2016) JpGU Meeting, PSS11-P21.
[2] Chang et al. (in prep)
[3] Kayama et al. (2012) JGR Planets 117 (E9).
In this study, we propose a statistical model that decomposes CL spectra of experimentally shocked quartz at various impact pressures into several peaks by utilizing skew-normal distributions, instead of normal distributions. The samples of shock-induced quartz were obtained by shock experiments done in Chang et al. (in prep). According to the experiments, the peak pressures of the samples reach 0 GPa to 40 GPa in 5 GPa increments. Also, the CL spectra of the samples were analyzed with SEM (JEOL: JSM-5410) combined with a grating monochromator (Oxford: Mono CL2) at the Okayama University of Science. The obtained CL spectra were corrected by standard lamp. Using Monte-Carlo sampling and Akaike information criterion, we estimate the number of skew-normal peaks and four parameters for each peak, i.e., location, scale, shape, and weight. A mixture of skew−normal distributions provides a better fitting model for CL spectrum of shocked quartz than a mixture of normal distributions. Moreover, it is statistically revealed that among the four parameters of a skew-normal distribution, weights of peaks change with impact pressure.
We also demonstrate that the quantitative relation between weights of CL peaks and impact pressure can be utilized for an estimate of impact pressure based on CL spectra of shocked quartz. Here, we divide the CL data of shocked quartz into two data sets, i.e., training and validation data sets. Then, we calculate a posterior probability of impact pressure of the validation data set by comparing posterior distributions of CL weights of the validation data sets with those of the training data sets. As a result, the actual pressure of the validation data set tends to have the highest posterior probability. The proposed method is as precise as a conventional impact pressure estimation via Planar Deformation Features (PDFs) while the dynamic range would be wider than the conventional method. Additionally, The proposed method is more convenient than the other. The improvement in the efficiency in estimation of paleo impact pressure would drive investigations of impact cratering processes. Also, a fitting via skew-normal distribution could contribute to deconvolution of spectra other than CL spectrum of shocked quartz.
[1] Chang et al., (2016) JpGU Meeting, PSS11-P21.
[2] Chang et al. (in prep)
[3] Kayama et al. (2012) JGR Planets 117 (E9).