Applicability and accuracy assessment of the Modified Gaussian Model (MGM) on the rock samples’ spectral interpretation

Introduction: Visible and near-infrared (VNIR) spectroscopy is fundamental to our understanding of lunar surface mineralogy. Recent lunar missions, such as Chang’e-4 and Chang’e-5/6, have returned invaluable in situ rock spectral data and small rock chips. However, interpreting the spectra of intact rock fragments remains uniquely challenging. To supplement geographically limited returned sam-ples, lunar meteorites like Northwest Africa (NWA) 4734—a highly evolved mare basalt—serve as crit-ical natural laboratories. Extensive petrological studies indicate this meteorite has undergone se-vere impact metamorphism and multistage crystal differentiation[1-4]. Despite this wealth of geochem-ical data, laboratory VNIR spectral analyses of NWA 4734 rock samples remain scarce.
The Modified Gaussian Model (MGM) is usual-ly applied to the spectral interpretation of powder samples. By mathematically deconvolving complex, overlapping absorption bands into individual Gaussian distributions, the MGM allows us to es-timate the relative abundances of mafic minerals, such as the ratio of High-Calcium Pyroxene (HCP) to Low-Calcium Pyroxene (LCP)[5-7]. While the MGM has been successfully applied to planetary remote sensing[8-9], a major limitation exists: its calibration and validation have historically relied on crushed, well-sorted powder mixtures.
Applying the MGM to intact whole rocks—which feature complex multiple scattering and shock-altered phases—has rarely been systemati-cally tested. This study aims to bridge that gap. By utilizing high-resolution petrographic analyses to establish a definitive "ground truth" HCP propor-tion via image pixel counting, the MGM’s accuracy is directly evaluated when applied to the actual VNIR spectra of the NWA 4734 whole-rock slice, providing a vital baseline for future lunar rock spectral interpretations. 
Samples and Analytical Methods:  The lunar meteorite Northwest Africa (NWA) 4734, a basal-tic rock slice (~5 × 3 × 0.8 cm), was selected for this study due to its well-documented petrology and mineralogy. To establish ground truth for spec-tral interpretation, the same sample area was ana-lyzed using both image-based and spectroscopic methods. First, backscattered electron (BSE) imag-ing and energy-dispersive X-ray spectroscopy (EDS) were performed with a scanning electron microscope (SEM) to map mineral phases and identify high- and low-calcium pyroxenes (HCP and LCP)[3-4]. The proportion of HCP relative to total pyroxene was derived via pixel counting of BSE images after grayscale thresholding, with a 5% tolerance. Second, visible to near-infrared (VNIR) reflectance spectra (450–2500 nm) of the identical area were acquired using an ASD Field-Spec 4 spectrometer under darkroom conditions. The spectra were then decomposed using the Modi-fied Gaussian Model (MGM) to extract absorption band parameters (center, width, strength) for py-roxene and olivine. The ratio of band strengths at ~1 μm and ~2 μm was used to estimate HCP abun-dance[6]. This approach allows direct comparison between petrographically determined mineralogy and spectrally derived compositions.
Results and Discussion: 1) Petrographic Characteristics
BSE imaging reveals that NWA 4734 has a di-abasic texture, with plagioclase laths (5–10 μm) and larger, fragmented pyroxene grains filling tri-angular interstices. Almost all plagioclase is trans-formed into maskelynite, indicating severe impact metamorphism. Pyroxene grains exhibit two sets of near-orthogonal cleavages and impact melt pockets, while olivine shows a “Swiss cheese” texture. These features confirm that the meteorite experi-enced both intense shock and multistage magmatic differentiation, consistent with Apollo mare bas-alts[1].
2) Mineralogical Characteristics
EPMA data show that plagioclase is uniformly anorthitic (An84-91), while pyroxene compositions vary widely (Wo11-35En3-55Fs26-81), spanning augite and pigeonite. Olivine Fa contents range from 57 to 90. Both pyroxene and olivine display Mg-rich cores and Fe-rich rims, providing clear evidence of fractional crystallization. These heterogeneities support a complex magmatic history and are con-sistent with previous studies on NWA 4734[1,3].
3) Proportion of HCP from Image Pixel Counting
Pixel counting of 21 BSE images from the cir-cular area (later measured spectrally) yielded 1,913,565 LCP pixels and 3,635,247 HCP pixels, giving a raw HCP proportion of 65.5% (Figure 1). After converting 2D areal abundance to 3D volu-metric abundance using the power 3/2 transfor-mation[10], the HCP proportion becomes 72% ± 5.4%. This value serves as the petrographic ground truth for evaluating MGM performance on rock samples.
4) Proportion of HCP from MGM Deconvolu-tion
ASD reflectance spectra of the same area show absorptions near 1000 nm and 2200 nm, with asymmetry at 1000 nm. MGM fitting with eight Gaussians achieved RMSE < 1.4% (Figure 2). The band strength ratio (CBSR) at 1 μm between two pyroxene-related Gaussians is 0.869, correspond-ing to 67–75% HCP. The CBSR at 2 μm is 0.895, yielding 66–73% HCP (Figure 3). The average HCP proportion from MGM is 71% ± 10.1%, agreeing well with the pixel counting result.
5) Error Analysis and Applicability of MGM
Errors in pixel counting include a 5% tolerance in grayscale recognition and ~2% uncounted area (cracks, unresolved minerals), resulting in RMSE of 5.4%. MGM errors include spectral fitting (<1.4%) and the CBSR-HCP calibration (~10%), giving RMSE < 10.1%. Additional measurement mismatch between ASD and SEM areas contributes ~3% uncertainty. Within errors, the two methods yield comparable HCP proportions (72% vs. 71%), demonstrating that MGM is applicable to rock samples.
References: [1] Chen J. et al. 2019, JGRE, 124, 2583. [2] Elardo, S. M. et al. 2014, M&PS, 49, 261. [3] Wang, Y. et al. 2012a, M&PSA, 75, 5170. [4] Wang, Y. et al. 2012b, GeCoA, 92, 329. [5] Sunshine, J. M. et al., 1990, JGRB, 95, 6955. [6] Sunshine, J. M., & Pieters, C. M. 1993, JGRE, 98, 9075. [7] Sunshine, J. M., & Pieters, C. M. 1998, JGRE, 103, 13675. [8] Kanner, L. C., Mustard, J. F., & Gendrin, A. 2007, Icar, 187, 442. [9] Mustard, J. F., & Sunshine, J. M. 1995, Sci, 267, 1623. [10] Pieters, C. M. et al. 1993, JGRE, 98, 17127.

Figure 1: Calculating the proportion of HCP using the image pixel counting method. The pixels with the red colors represent HCP, and the pixels with the blue
colors represents LCP.

Figure 2: Spectral fitting results of NWA 4734 using MGM.

Figure 3: The logarithmical relationship between the CBSR and the proportion of HCP. (a) the relationship at the 1 μm region, (b) the relationship at the 2 μm region (Sunshine & Pieters 1993).