# Quantification of manganese for ChemCam Mars and laboratory spectra using a multivariate model

Patrick Gasda, Ryan Anderson, Agnes Cousin, Olivier Forni, Samuel Clegg, Ann Ollila, Nina Lanza, Jens Frydenvang, Sarah Lamm, Roger Wiens, et al.

► To cite this version:

Patrick Gasda, Ryan Anderson, Agnes Cousin, Olivier Forni, Samuel Clegg, et al. Quantification of manganese for ChemCam Mars and laboratory spectra using a multivariate model. Spectrochimica Acta Part B: Atomic Spectroscopy, 2021, 181, pp.106223. 10.1016/j.sab.2021.106223. hal-03449982

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Distributed under a Creative Commons Attribution 4.0 International License
1 Quantification of Manganese for ChemCam Mars and Laboratory Spectra Using a Multivariate

2 Model

3

4 Patrick J. Gasda*¹

5 Ryan Anderson²

6 Agnes Cousin³

7 Olivier Forni³

8 Samuel M. Clegg¹

9 Ann Ollila¹

10 Nina Lanza¹

11 Jens Frydenvang⁴

12 Sarah Lamm⁵

13 Roger C. Wiens¹

14 Sylvestre Maurice³

15 Olivier Gasnault³

16 Roberta Beal¹

17 Adriana Reyes-Newell¹

18 Dorothea Delapp¹

19

20 1) Los Alamos National Laboratory, Los Alamos, NM, USA 87545

21 2) United States Geological Survey, Flagstaff, AZ, USA

22 3) Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS, CNES, Toulouse, France

23 4) Globe Institute, University of Copenhagen, Copenhagen, Denmark

24 5) Kansas State University, Manhattan, KS, USA

25

26 *Corresponding Author

27 Email: gasda@lanl.gov

28

29 Highlights

30 • High accuracy MnO calibration model for ChemCam using multivariate techniques

31 • Innovative double blending approach for predicting values in heavily skewed datasets

32

33 Abstract

34 We report a new calibration model for manganese using the laser-induced breakdown spectroscopy instrument that is part of the ChemCam instrument suite onboard the NASA Curiosity rover. The model has been trained using an expanded set of 428 manganese-bearing rock, mineral, metal ore, and synthetic standards. The optimal calibration model uses the Partial Least Squares (PLS) and Least Absolute Shrinkage and Selection Operator (LASSO) multivariate techniques, with a novel “double blending” technique. We determined the detection limit for manganese is 82 ppm using a method blank procedure and is possibly as low as 27 ppm based on visual inspection of the spectra. Based on a representative Test Set consisting of measurements on 87 standards, the double blended multivariate model shows a RMSEP accuracy of 1.39 wt.% MnO for the full blended model. Employing a local RMSEP estimate where the model performance is evaluated based on nearby test samples, the accuracy is 0.03 wt.% at the quantification limit (0.05 wt.% MnO), 0.4 wt.% accuracy at 1.0 wt.% MnO, and 4.4 wt.%

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accuracy at 100 wt.% MnO. Precision is estimated using the standard deviation of the Test Set measurements, and is ±0.01 wt.% MnO at the quantification limit, ±0.09 wt.% MnO at 1.0 wt.% MnO, and ±2.1 wt.% MnO at 100 wt.% MnO (all 1σ). This new calibration is important for understanding the variation of manganese in the bedrock with the Curiosity rover on Mars.

## Graphical Abstract

<figure><img src="image_2.png" /></figure>

## Keywords

Mars Science Laboratory

ChemCam

Manganese

Laser Induced Breakdown Spectroscopy

Multivariate calibration

## 1. Introduction

Manganese is a trace element in volcanic rocks that is typically soluble in water (as Mn²⁺) except in highly oxidizing or highly alkaline conditions, where it precipitates from water as Mn²⁺, Mn³⁺, and Mn⁴⁺ oxides and carbonates [1-2]. Reduction of Mn³⁺ and Mn⁴⁺ oxides in water can produce Mn carbonates [1-2]. Typical terrestrial basaltic rocks contain ~0.1 to 0.2 wt.% MnO [e.g., 3], and the bulk silicate Mars composition is 0.44 wt.% MnO [4], whereas terrestrial lakebed or marine deposits can have up to 62 wt.% MnO in some marine-derived manganese ore occurrences [2], and thus any composition >0.5 wt.% MnO is considered elevated. Before the Great Oxygenation Event (GOE)—before the current (e.g., less than a tenth of the present-day oxygen levels) concentrations of O₂ were present in Earth's atmosphere—there were no significant deposits of Mn [1-2]. Most economically important deposits of Mn on the Earth were deposited during or after the GOE [1-2].

We can use Mn deposits on the Earth to understand deposits of Mn on Mars that have been reported in recent literature [5-9]. The presence of Mn-rich materials on Mars adds to the picture of ancient Martian aqueous environments as habitable because Mn oxides would have provided a redox gradient from which organisms could derive energy. The quantity and speciation of Mn in martian sediments provides constraints on pH and redox potential of ancient Mars surface and sub-surface waters [5-9].

The NASA *Curiosity* rover landed in Gale crater in 2012 and has been exploring the crater and the ~5 km tall central sedimentary mound, Aeolis Mons (informally called Mt. Sharp). The sediments in Gale crater are interpreted as being deposited in a redox-stratified lake [10-12], suggesting that the crater could host Mn deposits if its water was sufficiently oxidized.

The Chemistry and Camera (ChemCam) instrument suite onboard *Curiosity* uses Laser-Induced Breakdown Spectroscopy (LIBS) to provide chemical information about targets on Mars [13-14]. The ChemCam instrument records atomic emission spectra, which can be used for elemental quantification. This is achieved using a large library of spectra of geologic standards
collected in the lab with an instrument almost identical to ChemCam. The ChemCam instrument team typically quantifies the major rock forming elements as oxides (SiO₂, TiO₂, Al₂O₃, FeO, MgO, CaO, Na₂O, K₂O) and a few minor elements (data are available from the Planetary Data System [15]). The major element quantification is determined using multivariate models [16-17] while minor, trace elements, including Mn, are calibrated using peak-fitting techniques, and univariate models [5-6, 18-21].

Previous Mn models used the Mn I spectral lines in the 403 nm region [6]. Lanza et al. [6] reported values of up to 20 wt.% MnO in a few targets, but the majority of targets have <1 wt.% MnO, which is consistent with the bulk silicate Mars values 0.44 wt.% MnO [4]. Applying the Lanza et al. [6] model to previous work [5] suggests that the highest concentration of Mn on Mars could be ~60 wt.% MnO. Our new study seeks to improve on the accuracy of the quantification of Mn using multivariate techniques and an expanded Mn standard set, and to compare these results with univariate techniques [e.g., 6]. Multivariate analysis techniques, including partial least squares (PLS), have been shown to accurately quantify other elements in ChemCam LIBS data [17]. As the majority of targets on Mars have 0–1 wt.% MnO, a particular goal for this study was also to improve the accuracy of the model at <1 wt.% MnO, the limits of detection, and the limits of quantification for the Mn quantification model.

## 2. Methods

### 2.1 The ChemCam LIBS Instrument

ChemCam records atomic emission spectra of targets at a standoff distance of up to 7 m away. The instrument uses a Thales pulsed laser incorporating a Nd:KGW lasing medium (1064 nm wavelength, 14 mJ/pulse, < 8 ns pulse width, 3 Hz repetition rate) focused on the targets 1.5–7 m away from the rover using a mast-mounted telescope (350–550 micron spot size depending on distance [14]). Light is collected by the telescope and travels through a 6 m fiber, separated by a demultiplexer, and analyzed with three spectrometers (UV: 240–340 nm; blue-violet, or VIO: 382–469 nm; visible and near infrared, or VNIR: 473–905 nm; [13]). The instrument on Mars has a set of calibration targets that are 1.6 m away from the instrument and mounted on the back of the rover [13, 22-23].

Each Mars observation comprises a grid ('raster') of observation points. At each point, ChemCam fires a burst of laser pulses ('shots') and collects LIBS spectra from each shot. For most analyses, the single-shot spectra are averaged into a single spectrum. The first 5 shots are contaminated by dust on Mars targets, and these first shots are not included in the average spectrum. Typically, 30 laser shots are recorded and downlinked per observation point. A raster typically consists of five to ten observation points on a single target, the points being either in a line or grid configuration, separated by 0.5–3 mrad. Depth profiles of up to 150 shots per observation point have been used on Mn-rich targets on Mars to determine relationships between Mn concentration and depth.

All calibration data for models used in this paper have been analyzed using the ChemCam testbed instrument at Los Alamos National Laboratory. This instrument is a near replica of the instrument on Mars. The mast unit (laser and telescope) is mounted 1.6 m from a test chamber. The test chamber is backfilled with ~933 pascal CO₂ to mimic the martian atmosphere. Crushed and homogenized rock material of known chemical composition ('standards') were pressed into 2.54 cm round pellets and placed in the test chamber. Typically, 5 points are recorded from each sample, where 50 shots are averaged for each point. A
calibration transfer function, calibrated using identical targets on Mars and on Earth, is used to convert laboratory spectra into Mars-like spectra for models outlined in this work [17].

## 2.2 Calibration Standards

A large calibration set has been compiled to model Mn composition over a wide range of compositions and rock matrices. The entire dataset is composed of 515 standards that include the standards from Lanza et al. [6], Clegg et al. [17], D. Anderson et al. [24], and a new set of Mn-bearing standards (minerals, ores, mixtures, and synthetic materials) [25]. The reference database contains metadata for the new Mn-bearing standards, minerals, and mixtures that have not been previously used for other models as well as all of the MnO composition data, non-normalized spectral data, mean peak area spectrum, results of outlier determination, RMSECV data, regression vectors, and Test Set predictions [25]. The full set of standards used in this study cover a compositional range from 19 ppm to 97.4 wt.% Mn. Calibration standards that are not directly from calibration standard sources (e.g., NIST), are standardized using an independent 3rd party (ACTLabs, Canada; 4Litho) using Li metaborate/tetraborate fusion ICP-MS (Inductively-Coupled Plasma Mass Spectrometry) [26]. A smaller subset (~280 standards) of the full calibration set were used for univariate peak fitting. Peak fitting is quite computationally intensive, and fitting validation requires checking each spectral fit; the smaller subset of the standard database made the process of testing and validating the dataset more streamlined.

## 2.3 Data Pre-Processing

The Python Hyperspectral Analysis Tool (PyHAT) [27] and the associated graphical interface for point spectra analysis [28] were used to preprocess the data and evaluate multivariate regression models. Each spectrum is normalized by the sum of the total emission for each of the three spectrometers, such that the normalized signal from each spectrometer sums to 1 and the full spectrum sums to 3 [e.g., 17]. We applied a “peak area” (PA) spectral binning technique [e.g., 29] after normalization. The PA technique uses the average spectrum of the training data set to define a set of local minima and maxima. For each spectrum, channels that are between each pair of local minima are then binned and assigned to the wavelength of the corresponding maximum. Defining the local minima and maxima using an average spectrum rather than on a per-spectrum basis ensures that the same bins are used in each spectrum, so the resulting “PA preprocessed” spectra are all of identical length and have identical wavelength values for the bins. The PA preprocessing method reduces the total number of channels by ~10x, greatly speeding up processing time, and consolidates the emission from spectral lines into single bins. For example, Mn signal from the range 403.313 nm – 403.952 nm, regrouping 3 emission lines, is summed into the a single 403.404 nm bin). In this example, there is no significant interferences with other elements, therefore the value of the 403.4 nm PA bin is a good approximation of the Mn contribution after continuum subtraction. In other cases, where the PA bins may represent more than one chemical element, it is the optimization of the multivariate method used afterward that will find the optimal combination to return the information on the element of interest, here Mn. However, PA pre-processing does not give access to an error in the estimation of peak areas as would a peak fitting method.

## 2.4 Univariate Models and Peak Fitting Techniques

Three univariate models are used as a baseline to compare to the multivariate methods: two peak-fitting techniques and the PA preprocessing technique. The PA preprocessed model
uses the 403.404 nm bin value for the model. For the peak-fitting models, the Mn spectral feature at ~403 nm (Figure 2) is fit with either three [6] or four Voigt line shapes. The 3-peak method uses IDL's Levenberg-Marquardt method [6, 30], and the 4-peak fit uses MATLAB's trust region reflective algorithm after a local linear background subtraction. The relationship between normalized Mn LIBS feature peak area and standard Mn composition is described by a power law [6] in all three models.

A 3-peak fitting method was used for Lanza et al. ([6], Supplemental Information) and described here. The Mn lines used for the prediction correspond to the spectral feature located near 403 nm, composed of the 403.19, 403.42 and 403.56 nm lines in vacuum. LIBS physics tend to predict a Lorentz shape for the emission lines, but once the instrument resolution is convolved (peak function described best by a Gaussian shape), this yields a Voigt function [31]. These two techniques (Lorentz and Voigt functions) both return comparable results with the ChemCam data on Mars. Usually the Lorentz shape is preferred [32], but as the Mn lines are overlapping each other, the Voigt shape was favored here. Some input parameters are set in order to constrain the fit: the peak must be within ±0.1 nm of the given position from the Mars LIBS spectral library [33] and based on the uncertainty for peak positions in the NIST Atomic Spectral Database (ASD) [34]. Other uncertainty in the line position is sourced from the uncertainty in the wavelength calibration of the spectrometers. The full width at half maximum (FWHM) must be greater than the instrumental resolution (0.05 nm for UV, 0.04 nm for VIS, and 0.23 nm for VNIR) [16], but all three peaks have independent FWHM parameters.

A weak Mn line at 403.69 nm is present in standards with >1 wt.% MnO content. Hence, a 4-peak fitting method was developed for this study. The Voigt lineshape was approximated using the product between the Lorentzian and Gaussian formulas with parameters added for skewness [35]. The mixing ratio parameter describes the weighted average of the Lorentzian and Gaussian terms of the equation [35]. The skewness parameter is added to model asymmetric lineshapes introduced by the instrument. The skewness, mixing ratio, and FWHM for all four peaks were tied together and initially set as free parameters. By fitting the full database as free parameters, a distribution of the fitting results was determined. The median value of these distributions was then used to fix the parameters for the final fitting model (Mixing ratio = 0.4; skewness = -0.09; FWHM = 0.23 nm). As with the 3-peak fitting technique, the line positions are free parameters but constrained based on the uncertainty of the line position provided by NIST ASD [34] and uncertainty in the wavelength calibration of the instrument.

## 2.5 Multivariate Models

For this study, we explored several multivariate techniques: Ordinary Least Squares (OLS) [36-37], Partial Least Squares (PLS) [38], Least Absolute Shrinkage and Selection Operator (LASSO) [39], Ridge Regression [40], Elastic Net [41], Orthogonal Matching Pursuit (OMP) [42], Automatic Relevance Determination (ARD) [43], Bayesian Ridge Regression (BRR) [43], and Local LASSO Regression [44]. The PyHAT tool uses the scikit-learn Python package to implement these regression methods. All of the multivariate models were trained on data preprocessed with the PA method described above, after spectral masking and normalization. Spectral masking is used to exclude pixels outside of the useful spectral range for each spectrometer where the data are noisy [16-17].

To determine the optimal settings to use for each model, we subdivided the calibration data set into five folds, four of which were used for cross-validation and training the model, and one of which was held out as a Test Set. The folds were determined by sorting the data on the
known MnO content and then assigning samples to each fold sequentially, ensuring that all spectra of a given sample were assigned to the same fold. This approach to defining the folds ensures that there is a similar distribution of MnO compositions in each fold.

Cross validation (CV) was used to train models while avoiding overfitting. For all models, CV involves iteratively withholding one of the four training set folds and predicting the MnO content based on a model trained on the remaining three folds. Taken together, the predictions of the held-out training data give an estimate of the performance of the model, in the form of the Root Mean Squared Error of Cross Validation (RMSECV). By repeating this process for a range of model settings, the optimal settings for each model can be determined by examining the variation of RMSECV.

Cross validation was conducted for models trained on restricted composition ranges as well. The predictions of these “submodels” are typically more accurate within their specified composition range than the predictions of a “full” model trained on the full range of MnO compositions. The submodel approach requires that there be enough samples in each submodel range to remain accurate; our expanded dataset enables the submodel approach. By combining the predictions of several submodels, the overall accuracy can be improved [45]. We optimized the ranges over which the submodels were blended as described in [45] by minimizing the RMSECV of the blended training set predictions. The same blending ranges were then used to combine the Test Set predictions. Once we had a candidate calibration using optimized models, we examined the predictions of Mars measurements for which the true MnO content is unknown to ensure that results from the multivariate model passed sanity checks (e.g., that the predicted MnO content was positively correlated with Mn peaks in the spectra). The LIBS Earth calibration dataset has ~3000 spectra, but on Mars we have surpassed 800,000 individual spectra.

## 2.6 Determination of Accuracy

The accuracy of the models when predicting unknown spectra is estimated using the Root Mean Squared Error of Prediction (RMSEP) of the Test Set. As described above, the Test Set is one of five representative folds into which the full set of laboratory spectra were subdivided. Unlike the other four folds, which comprise the training set and are used to optimize model parameters and submodel blending, the Test Set is held out and treated as a true unknown (i.e., the models have never “seen” any of the Test Set data). The same Test Set is held out of all of the multivariate models and the PA univariate model and used to compare model accuracies. The univariate peak-fitting methods used a smaller subset of the same standards and thus did not use the same Test Set.

The Test Set RMSEP provides an estimate of how well the model will perform on unknown spectra. However, the actual Test Set performance often varies with composition and density of available training and Test Set samples. Typically, in composition ranges where we have more training spectra, the models have a “local” accuracy better than the overall RMSEP. Likewise, in areas where we have very few training spectra (often at the extreme high composition end), the overall RMSEP is better than the actual “local” accuracy of the model. This leads us to calculate a “Local RMSEP” that varies as a function of the predicted composition, so that the reported accuracy of predictions on Mars is representative of the actual model performance at the predicted composition [17].

To determine the local RMSEP for MnO, we generated a vector of evenly spaced positions in abundance space from 0 wt.% to 100 wt.% MnO for which we would like to determine the RMSEP. For each of these “predictions” we then calculated the local RMSEP
using the 40 nearest Test-Set predictions. We applied Gaussian smoothing to the RMSEP vs predicted composition curve to obtain a more smoothly varying estimate of local RMSEP.

## 2.7 Estimation of Precision

Using the multiple observations of each sample in the Test Set, we can estimate precision of the MnO predictions. Here we take the 1σ standard deviation of each set of standard predictions (typically five averaged spectra), excluding outliers, plotted versus the mean of the Test Set predictions, excluding negative predictions. We fit a power law curve to the plotted points to arrive at an estimated precision at any given value of predicted MnO composition.

## 2.8 Limit of Detection

Two methods are used to assess limit of detection: method blanks and visual inspection. A 'method blank' procedure [46] is used where standards with zero Mn and no peaks in the region of this peak fitting is used to determine the baseline noise level. For this work, chemicals purchased from Sigma Aldrich were prepared as pellets in the same procedure used to prepare rock pellets. Four calcium sulfate and calcium sulfate plus potassium chloride mixtures (20 total spectra) were then analyzed using the same procedures as the rock standards. These spectra were fit using the 4-peak fitting procedure to determine the peak area, of what should be noise. The average peak area and 2σ standard deviation were calculated. The detection limit is where the average+2σ value intersects with the 95% confidence level of the power law regression fit of the univariate model. The method blank procedure takes into account all of the uncertainties of the spectra and fitting method [46-47]. Since there are no major emission lines interfering with the Mn LIBS spectral feature in a typical rock sample, we can determine the limit of detection for Mn based solely on the presence or absence of the peak as compared to the baseline by visual inspection. Spectra fitted above and below the method blank detection limit were visually checked to confirm the presence or absence of the Mn spectral lines.

## 2.9 Limit of Quantification

To estimate the limit of quantification (LOQ), we need to answer the question: At what predicted composition is the prediction distinguishable from zero, given the local RMSEP. Two predictions can be considered distinguishable if their RMSEPs do not overlap. Thus, if a predicted value is greater than the sum of the local RMSEP at that predicted value and the local RMSEP at zero, and greater than the limit of detection, it can be considered a valid quantification.

## 2.10 Outlier Removal

We used two different outlier identification methods from Python's scikit-learn, Isolation Forest and Local Outlier Factor (LOF) [48-49], to flag spectra as potential outliers. We experimented with training models excluding spectra identified by one or both methods as outliers but found that in general, removing the outlier spectra resulted in worse model performance: These "outliers" are spectrally distinct, but they are valid data that provide important information to the models. Thus, we kept all potential outliers in the model training set.

In the Test Set, we evaluated the predictions and investigated targets with unusually high errors. All standards, including those identified as outliers, are listed in the supplemental data [25]. Target 27-07 had large errors and all five spectra were flagged as outliers by both outlier
identification methods, so we removed it from the Test Set. One spectrum from target GBW_07701 was poorly predicted and flagged as an outlier by both methods, so it was also removed as a potential bad or mislabeled spectrum. The worst Test-Set predictions in terms of squared error were for the H-21pct standard, which is a mixture of two other Mn-bearing standards (DC11023 and JCh1). Three of the five spectra for this target were flagged as potential outliers by Isolation Forest. LOF did not mark the spectra from this target as outliers. However, given the poor prediction results compared to other Test Set samples of similar MnO content, we suspect that this target was assigned an incorrect composition. Since it was also at least partially flagged as a spectral outlier, we removed H-21pct from the Test Set as well.

Several of the highest MnO targets in the Test Set had somewhat high squared errors and were flagged as spectral outliers by Isolation Forest, but this is not surprising for extreme MnO compositions, so these targets were kept in the Test Set.

We acknowledge that removing poorly predicting samples from the Test Set may be seen as giving artificially optimistic estimates of the model accuracy. The overall RMSEP of our best model was 2.74 wt.% prior to removing these samples. The majority of the improvement in RMSEP from removing these samples results from H-21pct, for which we attribute the error to an incorrect composition rather than a problem with the model. Without that sample, the overall RMSEP drops to 1.67 wt.%. Removing 27-07 and the bad spectrum from GBW_07701 results in a RMSEP of 1.39 wt.%. Given that the 27-07 and GBW_07701 spectra had been identified as potential outliers by independent methods prior to training any regression models, we believe that removing them from the Test Set is justified.

### 3. Results

Figure 1 shows the univariate training set and power-law model fits of the data in both linear and logarithmic plots. Figure 1A-B show the model and training set for the peak-fitting univariate model, and Figure 1C-D show the model and training set for the PA preprocessed univariate method. The training sets were fit with a power law (as they were in Lanza et al., 2016) in both regression models of the form $f(x) = Ax^B$. The model parameters with 95% confidence bounds are $A = 1.687e-4$ (1.680e-4, 1.695e-4) $B = 0.583$ (0.5819, 0.5842) for the 4-peak fitting univariate method, and the model parameters are $A = 5.210e-3$ (5.176e-3, 5.245e-3) $B = 0.5465$ (0.5448, 0.5482) for the PA preprocessed univariate method. For reference, the model parameters used for Lanza et al. (2016) were $A = 4e-4$ $B = 0.5764$.

Using the method blank procedure, a noise level for Mn peak area of 1.02e-5 was calculated from the average+2σ Mn peak area of 20 spectral blanks. The point at which the noise level intersects with the 4-peak univariate model 95% confidence bounds corresponds to a detection limit of 82 ppm MnO.

Figure 2 shows examples of fits using the 4-peak method. Figure 2A shows a spectrum for a standard with 10.03 wt.% MnO to provide an example of a spectrum where all 4 Mn peaks are present in the spectrum. Figure 2B-C show the example spectra just below the detection limit. A detection limit of 27 ppm Mn was determined based on the visual inspection of 4-peak fitted spectra near the detection limit. The detection limit is consistent with the fit for a set of Mn-doped synthetic silicate and limestone standards, of which there is a standard with 27 ppm (Figure 2B). The fit of these standards may show the presence of the two strongest Mn I lines (403.19 and 403.42 nm). The fit of a standard composed of mainly Ca-sulfate (gypsum) with 19 ppm Mn may show the presence of the strongest Mn peak, but the peak is not well separated from the noise and a possible small contribution from S at 403.0 nm (Figure 2C). The residuals
plotted below the peak fit for both Figure 2B and 2C are very noisy, but the residuals in the example in Figure 2C are less well-distributed about the mean value, suggesting that this is fitting more noise than signal. Also, in Figure 2C, the 403.69 nm line, which should be the weakest Mn line in this spectral region, is modeled as stronger than the adjacent 403.5 nm line. Hence, visual inspection of the fits suggest that the detection limit could be as low as 27 ppm Mn, and the method blank procedure, which takes into account all sources of uncertainty, finds the detection limit is 82 ppm MnO.

Table 1 summarizes all of the results for each full-range multivariate model, along with the best models for a given range tested. The table shows the best RMSECV accuracies along with parameter values used for each model. The full results of the RMSECV analysis is available in the supplemental materials [25]. The model with the best overall full model RMSECV is LASSO, with ±2.49 wt.% MnO. Table 1 shows that PLS models tend to give the most accurate results for the high range of values while sparser techniques (LASSO and Elastic Net) tend to provide better results in ranges with smaller MnO abundance values. Table 1 also shows that the minima of cross-validation results in small, but non-zero, values for alpha (the parameter that describes the sparseness of the LASSO regression vector).

Table 2 summarizes the results for univariate models tested. Table 2 shows that univariate models are significantly improved (±9.6 vs ±4.6 wt.% MnO) with PA preprocessing, which is mostly driven by improvements in the Test Set above 0.1 wt% MnO. However, all univariate techniques have much worse Test-Set accuracy compared to most of the multivariate models presented in Table 1, besides ordinary least squares (±5.99 wt.% MnO). Figure 3A-D shows the predicted MnO wt.% vs actual MnO wt.% of the Test Set with a 1-to-1 line for reference in both linear and logarithmic plots. Figure 3A-B show Test-Set results for the univariate peak fitting model and Figure 3C-D for the univariate PA preprocessed (Fig 2B) models.

From these multivariate model results, we designed blended submodels that took advantage of the strengths of each technique. The submodel blending process described in Anderson et al. [45] relies on a “reference” model to provide a first guess at the true composition of the target. This initial prediction, typically from a model trained on the full range of compositions, is then used to determine which submodel or combination of submodels is optimal to use for the final prediction. The best blended model uses PLS as a reference model, with the LASSO 0-10 wt.% MnO model as a low model and the LASSO full model as the high model. The predictions from these models are blended over the range 4.87-7.96 wt.% MnO, and the resulting RMSEP is 1.40 wt.% MnO.

A key innovation of the MnO calibration presented here is the use of two stages of submodel blending (“double blending”). To further improve the accuracy for low values of MnO (<1 wt.%), a ‘double blend’ model approach was used where the previously described blended model (the ‘single blend’ model) is used as a reference model, and then the 0-1 wt.% MnO LASSO model is used as a low model, and the single blend model is used as a high model. The resulting double blend model blends the 0-1 wt.% results with the single blend results over the range of 1.56 to 2.22 wt.% MnO and a full RMSEP of 1.39 wt.% MnO. (Note that although the overall RMSEP is only slightly improved with the double-blend approach, the local RMSEP at the low end is significantly better.) Figure 3E-F shows the predicted MnO wt.% vs actual MnO wt.% of the Test Set for the double blended multivariate model with a 1-to-1 line for reference in both linear and logarithmic plots.
The single-blend model is more accurate than the full 0-100 wt.% PLS model at the low end. Thus, using the single-blend predictions as the reference for the second round of blending results in significantly more accurate assignment of low-composition samples to the correct submodel, leading to significantly improved final predictions.

The results of local RMSEP and Gaussian smoothing are shown in Figure 4. Most geologic targets, and therefore most of the spectra in our training and Test Sets, have very low MnO. Thus, the distribution of MnO in our Test Set is heavily skewed toward compositions less than 1 wt.%, with a small number of high-MnO targets. Because it is unlikely that the actual accuracy of a model would abruptly change for relatively small differences in predicted composition, we applied Gaussian smoothing to the RMSEP vs predicted composition curve to obtain a more smoothly varying estimate of local RMSEP. Consequently, the local RMSEP as determined by the 40 nearest predictions varies relatively smoothly in ranges with many closely spaced Test Set predictions, but at higher values of predicted MnO, it still exhibits a “stair-step” pattern (Figure 4). The pattern occurs because a wide range of MnO predictions can have the same 40 nearest Test-Set predictions at the high MnO end.

Since applying the smoothing down to predictions of 0 wt.% has the effect of artificially increasing the apparent local RMSEP near zero, we chose to treat the upper and lower ranges separately (Figure 4B). The unsmoothed data near zero is closer to the ‘real’ accuracy of a predicted value, and it is unnecessary to over-smooth the data in the low range where we expect most predictions to fall on Mars. Hence, we chose to splice the smoothed RMSEP vs prediction curve for predictions > 5 wt.% with the unsmoothed curve for predictions < 5 wt.%. The local RMSEP at zero is also used to estimate the limit of quantification by taking the sum of the local RMSEP and the local RMSEP at a predicted value of zero. Any prediction greater than the sum of these two values can be considered to be distinguishable from zero, and therefore a valid quantification; for this model the limit of quantification is estimated as ~0.05 wt.% MnO (Figure 4C).

We have estimated 1σ precision at each value of predicted MnO composition. Figure 5 shows the variation of precision estimated using the Test Set. This is fit with a curve $f(x)=0.089x^{0.6874}$, which represents the estimated precision at a predicted value of MnO composition. Similar to RMSEP, precision scales roughly with composition, such that estimated 1σ precision at the quantification limit is ±0.01 wt.% MnO, ±0.09 wt.% MnO at 1.0 wt.% MnO, and ±2.1 wt.% at 100 wt.% MnO.

Table 3 lists the major lines present in each loading vector of the various models. The top 3 most important peak bins for that model have an “X,” and minor peak bins are labeled with an “O.” The regression vectors show that all of the multivariate models rely on a mix of Mn I and Mn II peaks to form the calibration. Since the PA preprocessing collapses a single peak or feature of overlapping or nearby peaks into a single bin, and the bin wavelength may differ from the NIST ASD wavelengths of the line(s) within it, it can be difficult to match a bin to a single Mn peak. In one case, the 453.1 nm bin has a strong Fe I interfering line. Nevertheless, we have tentatively identified the major contributions to each model regression vector and the atomic emission lines that contribute to each of these peak bins in Table 3.

The full PLS and LASSO models rely on a similar set of peak bins. For example, both models use bins located at 256 nm (Mn II), 423.6 nm (Mn I), 445.6 nm (a set of Mn I lines), and 529.9 nm (Mn II), which is the strongest feature in the PLS model. The PLS model also has a wide set of bins from 728 to 739 nm which encompassed the strongest peak bin from the LASSO full model at 728 nm (a set of Mn II lines). Interestingly, while these models do use the 403.4 nm
bin that is used for the univariate models, the multivariate models weight this feature much less than other peak bins. This fact helps explain why the univariate models that use the 403.4 peak bin or that fit the peaks in this Mn feature tend to behave poorly for very high values of Mn (Figure 3). In contrast, the LASSO model that covers the 0-10 wt.% MnO range relies heavily on the 403.4 nm peak bin, and to a lesser extent, the 259.4 nm peak bin. The LASSO model that covers the 0-1 wt.% MnO range relies more on the 259.4 nm peak bin than on the 403.4 nm peak bin.

## 4. Discussion

The goal of this study is to improve the performance of Mn quantification from ChemCam data, both for high-end observations and for typical Mars rocks with MnO abundances <1 wt.%. It is very challenging to develop a single empirical regression model that can accurately predict compositions ranging from the 10s of ppm up to a pure metal (>100 wt.% oxide equivalent). For overall model accuracy, the LASSO technique provides slightly better accuracy than PLS, and blended submodels further improve model accuracy by about a factor of two as compared to the full models on their own. For standards with <1 wt.% MnO, we found that the 0-1 wt.% MnO LASSO model improved accuracy significantly.

However, it was challenging to take advantage of the improved accuracy of this 0-1 wt.% model. The submodel approach [44] depends on a distribution model to provide a “good guess” at the true composition to correctly choose the correct submodel. When working with a submodel spanning a very narrow range, such as 0-1 wt.%, if the accuracy of the distribution model is not sufficient, measurements will not be correctly assigned to the appropriate submodel.

Our first attempts at improving the accuracy in the low range involved blending low (0-1 wt.%), medium (1-10 wt.%), and high (10-max wt.%) submodels. However, the scatter in the distribution model covering the whole range was on the order of several wt.% at the low end of the compositional range, so numerous spectra that should have been assigned to the low model were instead predicted by the medium model and vice versa. We found that no full model that we tested had sufficient accuracy to reliably and correctly assign spectra to the 0-1 wt.% model. Since the model in this case had difficulty assigning the appropriate submodel based on a reference model and more than two submodels, it led us to develop the “double blend” approach.

For the double-blend approach, we initially blend results between a 0-10 wt.% submodel and a 0-100 wt.% model. These models have broad enough composition ranges that the distribution model reliably assigns spectra to the correct model. The results of this initial submodel blending are then used as a distribution model for a second level of submodel blending between a lower 0-1 wt.% model and the initial blended results. With this double blended approach, we achieve a MnO calibration that is sufficiently accurate near zero wt.%, with a quantification limit of 0.05 wt.% MnO, allowing us to predict most geologic samples on Mars, and also performs well on high MnO contents.

It is common for multivariate regression models predicting compositions near zero to sometimes predict negative values for unknown samples. Some models can be forced to use only positive regression coefficients, but this prevents the model from taking advantage of negative correlations in the spectra and often leads to lower model accuracy. A negative composition is non-physical, so efforts were made to develop models that minimize the amount of negative value predictions. Typically, models with the best accuracy predict negative values at lower rates, which is the case here. Tests with Mars data show that ~4% of the data points have
predictions below zero. In the final implementation of this calibration for Mars data, we will
explicitly set negative predictions to zero.

The results of the multivariate model developed for this work and the univariate model
and the model developed for Lanza et al. [6] show that the new abundances are ~40% lower
relative to previously published results. A full interpretation of the new results and implications
for Mars geochemistry will be given in a future work. The geochemical interpretations of
ChemCam Mn data is not expected to markedly change however, because spectra that previously
had high predicted MnO wt.% still have high predicted values for MnO. The new multivariate
model results in a tighter distribution of MnO compositions in the 0.1 to 0.2 wt.% MnO range.
This has the effect of making higher MnO compositions stand out more prominently from more
typical bedrock targets. The change in the improved models given here are partly due to the
addition of new Mn standards. Additionally, comparing the model Test Sets in Figure 3 show
that the univariate models tend to overestimate MnO wt.% of the Test Set; the majority of the
Test Set results >1 wt% MnO are above the 1:1 line. In Figure 3A, the peak-fitting method tends
to have the highest degree of over-estimation compared to the PA preprocessed data (Figure 3C).
In Figure 3E, the Test Set tends to remain very close to the 1:1 line and does not appear to tend
towards over- or underestimating the standard MnO wt.%. Table 4 shows a comparison of the
previously published results and this model, and the new predicted values consistently decrease
by ~40% relative to the previous predictions. For observations <1 wt.% MnO as predicted by the
new multivariate model, values can change by more than 40%, become reduced to zero, or
potentially increase, but that is expected as the previous model quantification limit and RMSEP
is > 1 wt.% MnO [6].

The method blank procedure resulted in a detection limit of 82 ppm MnO, and the visual
inspection of the spectra resulted in a detection limit of 27 ppm Mn. The detection limit found by
visual inspection may be lower than 27 ppm, but currently we do not have enough standards with
very low known MnO composition in our database to make a reliable assessment. It also may be
quite difficult to find standards with <10 ppm MnO as the current fusion ICP-MS methods
reference laboratories use for our standard database have a 10 ppm detection limit for MnO [26].
Nevertheless, our detection limit results are consistent with Lasue et al. [47]; visual inspection
gives the lower limit of the detection limit, while the method blank procedure takes into account
other uncertainties and is the higher value. The method blank procedure accounts for
uncertainties in the fitting method and demonstrates that improvements could be made in how
the fitting procedure is preformed (e.g., a more robust baseline fitting method could be
developed). The low (10s ppm level) detection limit is consistent with detection limits
determined for other trace elements in LIBS spectra with no interfering peaks. For example,
Lasue et al. [47] found detection limits for Zr (66 ppm) and Co (18 ppm), despite these
measurements being performed in vacuum [47], and Payré et al. [20] found detection limits for
Li (5 ppm) and Rb (34 ppm). Payré et al. [20] used laboratory instrument very similar to
ChemCam.

5. Conclusions

We have developed a multivariate model to predict the abundance of MnO in rocks using
the ChemCam LIBS instrument on Mars. To further improve predictions compared to the
previous univariate approach, our method involves several multivariate models optimized for
different ranges of abundance, with a special effort to ensure continuity between these ranges.
The quantification limit of ~0.05 wt.% MnO and local RMSEP values of 0.03 wt.% MnO at the
quantification limit and 0.4 wt.% MnO at the predicted 1.0 wt.% MnO, with ±0.01 and ±0.09 1σ
precision, respectively, will enable this model to accurately distinguish small variations of MnO
in martian rock and soil targets and greatly aide in the interpretation of these variations.

The innovative double-blending approach used here is promising for any chemometric
calibration in which the expected distribution of compositions is heavily skewed and a full model
does not possess the necessary accuracy to reliably assign spectra to the appropriate sub-model at
the extreme end of the composition range.

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<table><caption>Table 1: Cross Validation Results for Multivariate Models.</caption><thead><tr><th>Model Range (MnO wt.%)</th><th>Method</th><th>RMSECV</th><th>Alpha<sup>a</sup>/Fold<sup>b</sup></th><th>L1 Ratio<sup>c</sup></th></tr></thead><tbody><tr><td rowspan="14">Full</td><td>LASSO</td><td>2.486</td><td>8.43E-05</td><td></td></tr><tr><td>PLS</td><td>2.620</td><td>15</td><td></td></tr><tr><td>Ridge</td><td>2.589</td><td>1.48E-03</td><td></td></tr><tr><td>Elastic Net</td><td>2.488</td><td>9.68E-05</td><td>1.000</td></tr><tr><td>Elastic Net</td><td>2.565</td><td>3.28E-05</td><td>0.990</td></tr><tr><td>Elastic Net</td><td>2.587</td><td>1.30E-05</td><td>0.950</td></tr><tr><td>Elastic Net</td><td>2.589</td><td>7.85E-06</td><td>0.900</td></tr><tr><td>Elastic Net</td><td>2.592</td><td>2.85E-06</td><td>0.700</td></tr><tr><td>Elastic Net</td><td>2.594</td><td>1.84E-06</td><td>0.500</td></tr><tr><td>Elastic Net</td><td>2.596</td><td>1.13E-06</td><td>0.100</td></tr><tr><td>Local LASSO</td><td>2.200</td><td></td><td></td></tr><tr><td>OMP</td><td>2.956</td><td></td><td></td></tr><tr><td>OLS</td><td>5.989</td><td></td><td></td></tr><tr><td>ARD</td><td>4.456</td><td>8.43E-05</td><td></td></tr><tr><td>BRR</td><td>3.323</td><td>8.43E-05</td><td></td></tr><tr><td>10-Max</td><td>PLS</td><td>6.945</td><td>4</td><td></td></tr><tr><td>1-Max</td><td>LASSO</td><td>6.717</td><td>9.33E-03</td><td></td></tr><tr><td>1-10</td><td>PLS</td><td>1.329</td><td>5</td><td></td></tr><tr><td>0-15</td><td>Elastic Net</td><td>0.437</td><td>1.40E-07</td><td>0.725</td></tr><tr><td>0-10</td><td>LASSO</td><td>0.296</td><td>4.53E-05</td><td></td></tr><tr><td>0-5</td><td>Elastic Net</td><td>0.192</td><td>8.70E-07</td><td>0.900</td></tr><tr><td>0-2</td><td>LASSO</td><td>0.103</td><td>2.32E-05</td><td></td></tr><tr><td>0-1</td><td>LASSO</td><td>0.066</td><td>5.93E-06</td><td></td></tr><tr><td>0-0.1</td><td>Elastic Net</td><td>0.021</td><td>1.10E-06</td><td>0.950</td></tr></tbody></table>

<sup>a</sup>The alpha value represents the sparsity parameter for the LASSO, Ridge, Elastic Net, ARD, and BRR methods.

<sup>b</sup>The fold value represents the number of k-folds used in the cross validation.

<sup>c</sup>The L1 ratio represents the mixing ratio for Elastic Net, which is a combination of Ridge regression and LASSO.

<table><caption>Table 2: Summary of Root Mean Square Error of Prediction (RMSEP) for selected data ranges of univariate models.</caption><thead><tr><th>[wt.% MnO], N (in Test Set)</th><th>Univariate (PA pre-processed)</th><th>Univariate (peak-fitting)</th><th>Lanza et al., 2016<sup>c</sup></th></tr></thead><tbody><tr><td>&gt;5, 35</td><td>16.0</td><td>21.6</td><td></td></tr><tr><td>1–5, 10</td><td>0.96</td><td>1.9</td><td>2.8</td></tr><tr><td>&lt;1, 378<sup>a</sup></td><td>0.36</td><td>0.8</td><td></td></tr><tr><td><strong>Full, 423<sup>b</sup></strong></td><td><strong>4.6</strong></td><td><strong>9.6</strong></td><td><strong>11.6</strong></td></tr></tbody></table>

<sup>a</sup>The peak fitting univariate model uses N=134.

<sup>b</sup>The peak fitting univariate model uses N=178.

<sup>c</sup>The full model in [6] uses 26 standards, where 8 standards had compositions 0.43–5.95 wt.% MnO.
<figure><img src="image_3.png" /><figcaption>Figure 1: Comparison of the standard wt.% MnO composition with the normalized peak area or peak bin for the 4-peak fitting and PA preprocessed univariate models with training data (black dots), model fit curve (solid black line), and 95% confidence bounds on the model fit (dotted black curves). A) Linear scale power law univariate model of the 4-peak fit of the 403.4 nm spectral feature. B) Logarithmic scale power law fit of the 4-peak fit univariate model. C) Linear scale power law fit of the PA preprocessed univariate model using the 403.4 nm peak bin. D) Logarithmic scale power law fit of the PA preprocessed univariate model.</figcaption></figure>

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<figure><img src="image_4.png" /></figure>

Figure 2: Background subtracted LIBS laboratory spectrum for a A) Mn ore mixture (JMN1 and JB1B standards) with 10.03 wt.% MnO, B) synthetic silicate standard with 27 ppm Mn, C) a gypsum rock standard with 19 ppm Mn. The Mn peak feature is fitted with 4 Voigt lines (red dashed curves) which sum to the green curve that closely matches the data (black). Residuals of the fits are offset (black dots) below the data for clarity. Each spectral line, including those not modeled, are labeled in Fig 2A. Note that the scale of Figure 2A is an order of magnitude larger than Fig 2B and 2C.

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<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>
Figure 3: Comparison of the standard wt.% MnO vs the model predicted wt.% MnO composition for the 4-peak fitting and PA preprocessed univariate models with the double blended multivariate model Test Sets (black dots) and one-to-one line (solid black line). A) Linear scale univariate model of the 4-peak fit of the 403.4 nm spectral feature. B) Logarithmic scale 4-peak fit univariate model. C) Linear scale PA preprocessed univariate model using the 403.4 nm peak bin. D) Logarithmic scale PA preprocessed univariate model. E) Linear scale double blended multivariate model. F) Logarithmic scale double blended multivariate model.

<table><caption>Table 3: Potential Identification of Major Contributions to Peak Bins in Model Regression Vectors.</caption><thead><tr><th>PEAK BIN (NM)</th><th>NIST (NM)</th><th>IDENTIFICATION</th><th>PLS FULL</th><th>LASSO FULL</th><th>LASSO 0-1</th><th>LASSO 0-10</th></tr></thead><tbody><tr><td>256.0</td><td>255.766</td><td>Mn II</td><td>O</td><td>O</td><td></td><td></td></tr><tr><td>259.4</td><td>259.450</td><td>Mn II</td><td></td><td></td><td>X</td><td>X</td></tr><tr><td>303.2</td><td>303.192</td><td>Mn II</td><td></td><td>O</td><td></td><td></td></tr><tr><td>304.8</td><td>304.793</td><td>Mn I</td><td></td><td>O</td><td></td><td></td></tr><tr><td>403.4</td><td>403.421</td><td>Mn I</td><td>O</td><td></td><td>X</td><td>X</td></tr><tr><td>408.9</td><td>408.409</td><td>Mn I</td><td>O</td><td></td><td></td><td></td></tr><tr><td>423.6</td><td>423.633</td><td>Mn I</td><td>X</td><td>X</td><td></td><td></td></tr><tr><td>445.6</td><td>445.284</td><td>Mn I</td><td>X</td><td>O</td><td></td><td></td></tr><tr><td></td><td>445.707</td><td>Mn I</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>445.880</td><td>Mn I</td><td></td><td></td><td></td><td></td></tr><tr><td>453.1</td><td>453.130</td><td>Mn I<sup>a</sup></td><td></td><td></td><td>X</td><td></td></tr><tr><td>529.9</td><td>530.392</td><td>Mn II</td><td>X</td><td>X</td><td></td><td></td></tr><tr><td>614.3</td><td>612.76</td><td>Mn II</td><td>O</td><td></td><td></td><td></td></tr><tr><td>723.5</td><td>722.668</td><td>Mn II</td><td>O</td><td></td><td></td><td></td></tr><tr><td>728.1</td><td>728.217</td><td>Mn II</td><td></td><td>X</td><td></td><td></td></tr></tbody></table>

a) Inferring strong Fe I line
<figure><img src="image_11.png" /><figcaption>Figure 4: Local RMSEP as a function of predicted MnO wt.%. The solid black curve labeled "Smoothed >5 wt.%" is the result of splicing the unsmoothed curve below ~5 wt.% with a smoothed version of the curve for higher values. A) Shows the full range of data and B) shows the range of data in the lower part of the range. C) The local RMSEP near zero demonstrates how the limit of quantification is calculated at the point where the local RMSEP + local RMSEP at 0 wt.% MnO intersects the one-to-one line.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 5: Precision estimated using the standard deviation versus mean of each set of Test Set prediction of MnO (points) and fit with a curve (line).</figcaption></figure>
<table><caption>Table 4: Selected Mars Targets Comparing Multivariate and Univariate MnO wt.% Predictions</caption><thead><tr><th>Sol</th><th>Target</th><th>Obs #</th><th>Multivariate<br>Prediction<br>(MnO wt.%)</th><th>Univariate<br>Prediction<br>(MnO wt.%)<sup>a</sup></th></tr></thead><tbody><tr><td>342</td><td>Caribou</td><td>5</td><td>13.6</td><td>49.98</td></tr><tr><td>342</td><td>Caribou</td><td>6</td><td>0.16</td><td>0.31</td></tr><tr><td>342</td><td>Caribou</td><td>7</td><td>0.14</td><td>0.17</td></tr><tr><td>342</td><td>Caribou</td><td>8</td><td>0.09</td><td>0.42</td></tr><tr><td>342</td><td>Caribou</td><td>9</td><td>0.14</td><td>0.31</td></tr><tr><td>342</td><td>Caribou</td><td>10</td><td>0.15</td><td>0.37</td></tr><tr><td>514</td><td>Harrison</td><td>5</td><td>5.42</td><td>17.17</td></tr><tr><td>514</td><td>Harrison</td><td>6</td><td>0</td><td>0.04</td></tr><tr><td>514</td><td>Harrison</td><td>7</td><td>0</td><td>0.07</td></tr><tr><td>514</td><td>Harrison</td><td>8</td><td>0</td><td>0.06</td></tr><tr><td>611</td><td>Stephen</td><td>1</td><td>6.54</td><td>17.35</td></tr><tr><td>611</td><td>Stephen</td><td>2</td><td>4.26</td><td>8.86</td></tr><tr><td>611</td><td>Stephen</td><td>3</td><td>4.28</td><td>11.94</td></tr><tr><td>611</td><td>Stephen</td><td>4</td><td>2.83</td><td>6.23</td></tr><tr><td>611</td><td>Stephen</td><td>5</td><td>2.6</td><td>5.18</td></tr><tr><td>611</td><td>Stephen</td><td>6</td><td>3.06</td><td>6.94</td></tr><tr><td>611</td><td>Stephen</td><td>7</td><td>3.29</td><td>7.43</td></tr><tr><td>611</td><td>Stephen</td><td>8</td><td>3.25</td><td>7.99</td></tr></tbody></table>

a) Lanza et al. [6]

## Acknowledgements

The authors acknowledge NASA, CNES, and the Jet Propulsion Laboratory for the development of ChemCam instrument suite and the Curiosity rover, respectively. JPL for their support and the operation of the Curiosity rover mission on Mars. NASA Mars Exploration Program and CNES for funding. J. Frydenvang acknowledges the Carlsberg Foundation for funding.

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