Chemical Geology 277 (2010) 137–148

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Chemical Geology
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c h e m g e o

Optimization of laser-induced breakdown spectroscopy for rapid

geochemical analysis
J.M. Tucker a,⁎, M.D. Dyar a, M.W. Schaefer b, S.M. Clegg c, R.C. Wiens c
a
Department of Astronomy, Mount Holyoke College, 50 College St., South Hadley, MA 01075, USA
b
Department of Geology and Geophysics, E235 Howe-Russell, Louisiana State University, Baton Rouge, LA 70803, USA
c
Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA

a r t i c l e i n f o a b s t r a c t

Article history: Laser-induced breakdown spectroscopy (LIBS) is demonstrated as a quantitative technique for geochemical
Received 25 May 2010 analysis. This study demonstrates the applicability of LIBS to bulk elemental analysis of igneous rock powders.
Received in revised form 19 July 2010 LIBS spectra of 100 igneous rocks with highly varying compositions were acquired at 9 m standoff distance under
Accepted 27 July 2010
Mars atmospheric conditions. LIBS spectra were modeled using partial least squares regressions to predict major
element compositions. A series of comparative tests determined the most effective methodologies for pre-
Editor: D.B. Dingwell
processing of spectral and compositional data, and choice of calibration set. In the best cases, calculated 1−σ
Keywords:
errors are 1.6 wt.% SiO2, 1.5 wt.% Al2O3, 0.4 wt.% TiO2, 1.2 wt.% Fe2O3T, 1.6 wt.% MgO, 0.02 wt.% MnO, 1.1 wt.% CaO,
LIBS 0.5 wt.% Na2O, 0.2 wt.% P2O5, and 0.4 wt.% K2O, with totals near 100%. The largest improvement came as a result of
Quantitative analysis scaling the elemental distributions to equalize the ranges of variability. Optimal predictions for this data set were
Elemental analysis produced with calibration set compositions input as weight % oxides and not atomic fractions. Predictions were
Bulk analysis also improved when calibration sets represented the smallest range of compositional variability possible, and
ChemCam completely encompassed the compositional range encountered. Multiple calibration sets relevant to different
Mars rock types are preferred over a single all-encompassing calibration set. Baseline removal and transforming
spectral data by their first derivative do not improve predictions and can even have negative effects. These results
are directly applicable to spectra that will be acquired by the ChemCam experiment on Mars Science Laboratory,
but also apply more broadly to terrestrial LIBS applications.
© 2010 Elsevier B.V. All rights reserved.

1. Introduction are available to geologists, there has been only limited interest in
geological applications of the LIBS technique (see reviews by Harmon
Laser-induced breakdown spectroscopy (LIBS) was first proposed et al., 2005; Pasquini et al., 2007). Until very recently, very few
as an analytical technique in the mid-1960s (Runge et al., 1964) and published mineral or rock LIBS spectra existed, and the data were of
gained popularity in the 1980s with the development of sophisticated limited utility because they were acquired under disparate conditions
CCD detectors and spectrographs (Radziemski et al., 1983). The LIBS that precluded comparisons between data sets. Systematic calibration
technique involves a laser pulse focused onto a sample to create a curves, matrix corrections, and procedures for spectral processing in
small plasma from which the optical emissions are recorded complex mineral and rock samples did not yet exist.
spectroscopically. The major emitting species of the plasma are This situation is now changing as a result of upcoming NASA
neutral atoms and ions in the first few ionization states of the missions that will use LIBS for remote exploration of planetary
elements comprising the samples. LIBS spectra of geological samples surfaces. ChemCam, a standoff sensing instrument package including
typically consist of hundreds of atomic emission lines. The basis for a LIBS instrument and remote micro-imager, will provide geochemical
qualitative and quantitative chemical analysis is the dependence of analyses as part of the payload of Mars Science Laboratory (MSL)
the peak height on the abundance of that element in the sample. Curiosity rover scheduled to launch in 2011. LIBS is on the payload of
The simplicity and versatility of the LIBS technique has allowed it the Surface and Atmosphere Geochemical Explorer (SAGE) mission to
to be applied to a wide variety of materials and substances. However, Venus that was selected as one of three candidates for the next
because other robust microanalytical methods for elemental analysis mission in the New Frontiers Program of space ventures to celestial
bodies in our solar system. Other countries are also considering or
planning to use LIBS on upcoming missions.
⁎ Corresponding author. Tel.: +1 413 538 3220; fax: +1 413 538 2357.
E-mail addresses: jtucker@mtholyoke.edu (J.M. Tucker), mdyar@mtholyoke.edu
The main disadvantage of LIBS for geological samples lies in the
(M.D. Dyar), mws@lsu.edu (M.W. Schaefer), sclegg@lanl.gov (S.M. Clegg), variation of peak intensities and areas caused by interactions in the
rwiens@lanl.gov (R.C. Wiens). plasma that are in part a function of chemical composition. These

0009-2541/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemgeo.2010.07.016
138 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148

chemical matrix effects are the chemical properties of a material that 2. Background
influence the ratio of a given emission line to the abundance of the
element producing that line. Chemical matrix effects are directly Laser-induced breakdown spectroscopy (LIBS) is a type of atomic
related to the elemental and molecular composition of the sample and emission spectroscopy that is closely related to the more commonly-
ubiquitously perturb the LIBS plasma. They are related to the relative used geological technique of inductively-coupled plasma atomic
abundances of neutral and ionized species within the plasma, emission spectroscopy (ICP-AES). In both these techniques (as in
collisional interactions within the plasma, laser-to-sample coupling any type of atomic spectroscopy), the analysis relies on quantized
efficiency, and self-absorption. Minor or trace elements in the sample valence-electron transitions that occur in the region of the electro-
can cause chemical matrix effects on major element emission lines magnetic spectrum recorded by the system. To produce narrow
(Tognoni et al., 2006). Additionally, local atmospheric composition emission lines with diagnostic energies, samples must be atomized,
and pressure also significantly influence LIBS plasma intensity. Local with no residual bonding remaining. After excitation, electrons decay
atmosphere and the breakdown products from the atmospheric from high-energy states to lower states, emitting energy with a
species can interact with the ablated surface material in the plasma, wavelength that is characteristic to each atom or ion.
and ambient pressure affects the amount of material ablated and the In traditional geological applications such as atomic absorption (AA)
frequency of collisions within the plasma (Knight et al., 2000; or ICP-AES, samples are commonly dissolved in solutions. LIBS differs
Effenberger and Scott, 2010). from these methods in that a pulsed high power laser is used both to
LIBS applications have benefitted from improvements in statistical ablate and excite atoms from a sample without sample preparation.
analyses in recent years (Martin et al., 2005; Munson et al., 2005), Emission from the ions and atoms in the plasma is collected by a fiber
which allow for information from the entire spectrum to be taken into optic system and analyzed by a spectrograph and CCD detector.
account as opposed to a single peak. Advanced statistical analyses are LIBS instruments have several advantages that make them well-
perhaps more needed for geochemical analyses than for other LIBS suited to planetary exploration, as well as routine field work in
applications, given the varieties of compositions and surface condi- inaccessible locations on Earth (e.g., hazardous waste facilities;
tions of unprepared geological samples. Sirven et al. (2006) was the Whitehouse et al., 2001). LIBS can be set up to operate semi-remotely,
first to apply multivariate analyses to LIBS spectra of geological with a telescope collecting the plasma light up to hundreds of meters
samples, investigating the accuracies of Cr analyses in 30 soil and 30 away (Palanco et al., 2006). No sample preparation is needed; in fact,
kaolinite samples. This study also compared partial least squares (PLS) the laser can ablate through rock coatings, making it possible to create
regression with predictions from neural network analyses. This work depth profiles of elemental concentrations. The laser can profile
was followed (Sirven et al., 2007) with a study of classification of depths up to ~ 1 mm into a rock, easily “burning” away dust layers and
different rock types by multivariate analysis of LIBS data. Clegg et al. chemical weathering coatings in a very short time (10 seconds to
(2009) applied multivariate analysis techniques to analyze the LIBS 50 minutes depending on depth and material). The laser can also be
spectra of 18 disparate igneous and highly metamorphosed rock focused to an extremely small spot size (roughly b0.5 mm at 7 m for
samples. PLS analysis was used to generate a calibration model from ChemCam), allowing analysis of small objects such as defects in
which unknown samples could be analyzed. Techniques of classifica- nuclear fuel rods or the “blueberries” observed at Meridiani Planum
tion and discrimination of geological materials by PLS-DA (partial on Mars. All elements are simultaneously analyzed, and the entire
least squares discriminant analysis), PCA (principal component analysis can be completed in seconds or minutes.
analysis), and SIMCA (soft independent modeling of class analogy) Analysis of certain elements in specific materials is complicated by
were also investigated by Clegg et al. (2009), Gottfried et al. (2009), compositional matrix effects, analogous to the matrix effects known
and Harmon et al. (2009). to complication interpretation of other types of spectroscopy, such as
This paper presents the results of a LIBS study of a suite of 100 data from electron probe micro-analysis (EPMA) and XRF. As an
igneous samples chosen to represent a broad range of compositions example of this effect in LIBS, Harmon et al. (2005) demonstrated that
and provenances with similar matrix. This larger data set provides line intensities for metallic Pb vary significantly from those of Pb in
sufficient breadth for exploration of various analytical parameters wet and dry soils. Variations in the “matrix” or composition of phases
that affect the precision and accuracy of the results, and allows in which the elements of interest reside can result in variable plasma
optimization of the technique for best application to geological temperatures, and thus in different signal intensities. However, these
materials. We here examine and characterize several different variations can be corrected with careful calibration procedures based
protocols for optimizing analytical predictions. These include the on the materials typically being analyzed. As long as the matrix
use of 1) chemical compositions expressed as atomic fractions vs. material remains the same, then variations in minor elements can be
elemental oxide weight percents, 2) two variations of partial least analyzed very well with LIBS because the matrix effects are consistent.
squares analysis (“PLS1” vs. “PLS2”), 3) different techniques for Such procedures have resulted in great advances in analysis of trace
scaling of the magnitude of input chemical compositions, 4) different elements in soils (Ciucci et al., 1996) and water (Arca et al., 1997), Pb
methods for spectral normalization and background subtraction, and in concrete (Pakhomov et al., 1996), Pb in coal (Yin et al., 2009),
5) variations on choice and size and scope of training set for analysis of carbon and graphite in iron ore slurries (Barrette and Turmel, 2001),
unknowns. Not considered in this study are variations in instrumen- and major elements in ores (Rosenwasser et al., 2001). In contrast to
tation and techniques of spectral acquisition, as was done for example matrix effects accounted for in the X-ray techniques such as EPMA and
by Gottfried et al. (2009), because the LIBS spectral data were XRF, no formalized theory with measurement of numerical constants
collected to mimic operation of the ChemCam instrument on the Mars has been developed for LIBS, so empirical corrections are applied
Science Laboratory rover. Also not considered was the dependence of when needed.
LIBS intensities on stand-off distance. ChemCam will operate up to a The traditional analytical chemistry approach to calibration in
stand-off distance of 9 m, but all spectra in this study were acquired at many types of spectroscopy uses univariate analysis, utilizing the area
a constant distance. Optimization of the above variables leads to of a single peak (or an area normalized to an internal standard) that is
significant and sometimes dramatic improvements in the predictive highly correlated with the concentration of a specific element; the
power of PLS training sets. These results allow constraints to be placed choice of which peak is used varies according to the matrix of the
on the precision of chemical data from LIBS using statistical material being studied (e.g., Buckley et al., 2000; Fabre et al., 2002;
techniques developed thus far, and lay a foundation for more Anzano et al., 2006; Thompson et al., 2006). In complex materials such
advanced statistical treatments and consideration of more variables as geologic samples, such an approach yields less quantitative results
represented in LIBS data that are now being considered. than desirable, at best. Consider the LIBS spectrum of metallic Fe
 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148 139

shown in Fig. 1, which has a rich variety of lines. In theory, any of these
lines could be selected for univariate analysis in which peak area or
intensity at a given channel could be used to predict Fe concentration.
When Fe is in a geological sample, this selection becomes more
complicated, for two reasons: 1) a peak or peaks representing Fe
emissions must be identified in an area where there is no overlap from
other elements; and 2) two samples with identical Fe contents may
not have identical Fe peaks areas due to interactions from other
elements in the plasma. Although the first of these may be overcome
by serendipity, the latter problem can confound quantitative analysis.
For example, the intensity of a dominant Fe line at 430.68 nm is
graphed against Fe concentration for 100 igneous rocks (to be
described below) in Fig. 2. The scatter in this line demonstrates why
this traditional analytical chemistry approach utilizing univariate
Fig. 2. Calibration curve for Fe using the height of the 430.68 nm peak plotted against
analysis does not yield quantitative results in geological samples (see
concentration (as measured by XRF) in 100 igneous rocks. The 1−σ errors on wt.%
also Clegg et al., 2009). Furthermore, not all of the lines in an Fe2O3 are ± 0.03 wt.% (Rhodes, 1988), and are thus smaller than the symbols used.
elemental spectrum are produced or detected in real geological Intensity values are normalized as described in Section 3. The scatter in this line, which
samples under experimental conditions. Many LIBS spectra of is caused by matrix effects, demonstrates why this traditional analytical chemistry
different types of geologic samples in concert with multivariate approach that employs only a single peak does not yield quantitative results in
geological samples. The non-zero intercept is a result of the contribution from
calibration techniques are thus needed for effective chemical
bremsstrahlung in the baseline, as shown in Fig. 6 and described in Section 5.4.
calibration.

3. Experimental methods wavelength than the Fe-absorption edge were estimated from the
intensity of the Compton radiation of the appropriate X-ray tube
A suite of 100 igneous rocks with a wide range of compositions (Reynolds, 1967). Mass absorption coefficients of elements with
was chosen for this study. To maximize Mars applicability, the longer characteristic radiation than the Fe absorption edge were
majority of samples are basalts by composition, but samples of higher calculated from the Compton-derived mass absorption coefficients,
and lower silica content are included to extend the range of after allowance was made for Fe and Ti intensities (Walker, 1973).
calibration to the entire range of naturally-occurring igneous rock Estimates of accuracy and precision are given in Rhodes (1988) and
compositions. The rock types represented are expressed visually by reported errors are reproduced in Table 1, row 11.
plotting Na2O + K2O vs. SiO2 (Fig. 3), a so-called total alkali-silica or For LIBS sample preparation, a few grams of sample were poured into
TAS diagram (Le Maitre et al., 1989). The distributions of the major an aluminum cup and pressed under 35 tons of pressure. No binders
elements among the samples are shown as histograms in Fig. 4. were added. LIBS analyses of the pellets were performed at Los Alamos
About 150 g of each sample were crushed to b45 μm particle size National Laboratory (LANL) using conditions configured to mimic those
(about an order of magnitude smaller than the LIBS beam diameter) in on Mars so the results would be applicable to the ChemCam instrument
a Spex tungsten carbide shatterbox in order to mitigate inhomoge- (Clegg et al., 2009). Because of known atmospheric pressure effects on
neity and equalize grain size and porosity. Different aliquots of this LIBS spectra, samples were placed in an evacuated sealed chamber filled
powder were used for both X-ray fluorescence (XRF) and LIBS. Major with 7 torr CO2 to simulate the Martian surface atmosphere. Samples
and minor elements were measured in the XRF lab at the University of were probed with a Spectra-Physics Indi Nd:YAG laser operating at
Massachusetts (under the direction of Michael Rhodes) using 1064 nm and 10 Hz, set to 17 mJ per shot. The laser was focused onto the
standard operating procedures (Rhodes, 1996; Rhodes and Vollinger, samples at 9 m standoff distance with a Newport 10x beam expander.
2004). For the XRF analysis of major elements, samples were prepared Plasma emission was collected with an 89 mm diameter Questar Field
as fused La-bearing lithium borate glass discs using a modification of Model Telescope with its standard BK7 optics replaced with fused silica
the methods of Norrish and Hutton (1969), though each sample was to extend its operational range down to the near-UV, roughly 220 nm.
first ignited at 1000 °C for several hours in order to oxidize the iron to The collected emission was directed into a 1 m, 300 μm, 0.22 NA Ocean
Fe3+ and remove volatiles. All elements (including Na2O) were Optics Solarization Resistant fiber. The fiber connected to three Ocean
measured simultaneously using a Siemens MRS-400 spectrometer. Optics HR2000 spectrometers covering the ranges 223–325 nm (near-
Intensities were corrected for nonlinear background, inter-element UV), 382–471 nm (visible), and 494–927 nm (visible/near-IR), with
interferences, and variations in mass absorption coefficient, using typical FWHM line widths of 0.2 nm, 0.2 nm, and 0.7 nm, respectively.
methods modified from those of Norrish and Chappell (1967). Mass These spectrometers are commercial instruments that use Sony CCD
absorption coefficients for elements with shorter characteristic detectors limited by read-out noise rather than dark noise, even for long

Fig. 1. LIBS spectrum of Fe metal from the visible region spectrometer. Any or all of these lines could potentially be used for calibration of the Fe concentration in an unknown.
However, in geological samples with complex chemical compositions, many of these lines do not appear.
140 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148

Fig. 3. TAS (total alkali vs. silica expressed in wt.% oxide) diagram showing rock types represented in our sample suite (Le Maitre et al., 1989). Most samples are basalts (i.e. 45–52%
SiO2, b 5% alkalis) for applicability to planetary surfaces, but the range for calibration is extended to both higher and lower silica.

exposures. Consequently, greater signal-to-noise levels are obtained Spectra of the 100 samples were split into a training set for
when the integration time is increased to monitor several laser shots. By calibration and a test set for prediction and error analysis, each with
contrast, the ChemCam spectrometers employ more sensitive e2v 50 samples. Except when noted, the same training and test sets were
detectors with single shot exposures. For a detailed comparison used in every comparative analysis to facilitate direct comparisons.
between this LIBS system and ChemCam, see Clegg et al. (2009). PLS regressions and predictions were performed using the Unscram-
We recorded spectra from five spots on each sample, each the bler®, a commercially-available software product from Camo Soft-
average of five 1-s exposures, representing 50 laser shots per spot. ware. Two variants of PLS are used (see Section 5.3): PLS1 regresses a
Even though the grain size is smaller than the laser spot, we probed single response variable (element) against the predictor variables
multiple spots to further compensate for inhomogeneities. It was (spectra). PLS2 regresses multiple responses against the predictors
previously determined (Thompson et al., 2006) that this sampling and explains the variance in both X and Y, taking advantage of natural
technique sufficiently accounts for the small spot-to-spot variations correlations between elements. A detailed description of mathemat-
and samples the bulk rock chemistry well in a way comparable to ical models used in the Unscrambler can be found in Martens and Næs
whole rocks. Spectra from the five spots were individually normalized (1989). The optimization tests described herein used only the major
by dividing the intensity of each wavelength channel by the total elements Si, Al, Ti, Fe, Mg, Mn, Ca, Na, P, and K.
intensity in the spectrum, which compensates for subtle variations in In all cases, the Unscrambler determines the most appropriate
laser power (Body and Chadwick, 2001). Those five normalized number of regression components (latent variables) to use based on a
spectra from each sample were then averaged to yield a single jackknife or “leave one out” full cross-validation. In this kind of
spectrum per sample, representing 250 laser shots. At the time of validation, a PLS model is built from 49 of the 50 training set samples,
these experiments, only a single spectrometer could be used at once, and the composition of the sample left out is predicted from the
so the three spectral regions were collected from different locations reduced PLS model. This procedure is repeated leaving out and
on the sample. However this issue is mitigated by combining the predicting each of the 50 samples once. The number of regression
spectra from all spots into a single average. components that yields the lowest residual variance, with a 1%
penalty per component to favor robustness, is chosen as the optimal
4. Statistical analysis number of regression components, and that number is used in
predictions of the test set.
Quantification of analytes from LIBS spectra is traditionally done by
constructing a calibration curve from standards of known analyte 5. Results
concentration and the height or area of a single spectral peak produced
by the element of interest. This technique works well when the matrix is Several different protocols for processing LIBS spectra were tested
similar between samples and the calibration set completely encom- and evaluated to determine the most effective and accurate method of
passes the range of variability. However, as noted above and in Figs. 1 calibration. Results are quantified by computing the standard
and 2, the standard univariate calibration technique is not adequate deviation of the deviation of the LIBS predictions to the known
when the matrices and compositions are highly variable, as with compositions. This quantity represents the 1−σ or RMS error in the
geological samples and multivariate calibration techniques are neces- predictions, and the values of each element for every comparative test
sary. Partial least squares regression (PLS) is well suited to situations are given in Table 1.
where there are many predictor variables (X; spectra) and few response The 1−σ errors of predictions using a randomly chosen training
variables (Y; elemental abundances), and there is a high degree of set and elemental compositions in wt.% oxides are shown in row 1 of
multicollinearity between the X variables (i.e. spectral peaks produced Table 1. These are absolute errors in units of wt.% oxide. Relative
by the same element or correlated elements). In this study, PLS errors are not reported because relative error of a prediction depends
regression is employed with varying spectral treatments and data on the magnitude of the prediction. For example, a 1−σ error of
manipulations to determine the most successful methodology and 3.11 wt.% SiO2 would represent a 4% relative error for a rhyolite
estimate the error in prediction of unknown sample compositions. (75 wt.% SiO2) and an 8% relative error for a foidite (35 wt.% SiO2).
 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148 141

Fig. 4. Histograms showing the frequency of the elemental abundances of the major elements expressed in oxide wt.% in the 100 igneous rocks. Due to the natural patterns in
compositions of igneous rocks, selecting a sample set with smooth elemental distributions is a challenge.

Thus absolute errors are more useful for quantifying the quality of 5.1. Scaling of Y variables
predictions than relative errors.
The table shows that errors are sensitive to the scale of each Because a PLS regression attempts to minimize variance in the Y
variable. The elements showing the greatest compositional ranges (Si, variables simultaneously, it will bias the principal components in the
Mg, Al, Fe, Ca) consistently yield the largest errors, and the elements direction of the Y variables with the highest variance and ignore to a
with the smallest ranges (Ti, Na, K, P, Mn) yield the smallest errors. greater extent those with ranges that are more constant in a relative
Because of the varying magnitudes of errors between elements, it is sense. To ensure the PLS assigns equal importance to all elements,
most useful to evaluate calibration models by comparing them one various methods of rescaling the elemental concentrations were
element at a time instead of considering the model as a whole. This is tested. The scaling techniques tested were:
also true because it is not necessary for each element to be predicted
by the same regression model; a single model might not simulta- 1. Each elemental concentration is divided by the maximum
neously predict all elements best. concentration of that element among the training set: Yi′ = Yi/
142 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148

Table 1
1−σ errors for each element in each calibration model⁎.

Treatment tested/element SiO2 Al2O3 TiO2 Fe2O3T MgO MnO CaO Na2O P2O5 K2O

Wt.% oxide data 3.11 1.87 0.62 1.72 2.16 0.034 1.52 0.82 0.39 0.64
Scaling method 1 2.22 1.85 0.44 1.44 1.98 0.028 1.19 0.68 0.26 0.55
Scaling method 2 3.12 1.92 0.60 1.75 2.34 0.034 1.49 0.82 0.39 0.63
Scaling method 3 2.18 1.86 0.44 1.46 1.99 0.028 1.17 0.68 0.26 0.55
Atomic fraction data 3.13 1.85 0.57 1.73 2.13 0.034 1.41 0.77 0.39 0.62
PLS1 3.66 1.85 0.43 1.73 2.01 0.029 1.22 0.68 0.27 0.52
Baseline-subtracted spectra 2.89 1.89 0.49 1.77 2.14 0.030 1.09 0.74 0.31 0.81
Spectral derivative 2.44 1.70 0.47 1.36 1.86 0.027 1.26 0.66 0.24 0.54
Deliberately-chosen training set 2.52 1.51 0.38 1.28 1.57 0.026 1.18 0.49 0.17 0.44
Split training set 1.55 1.54 0.40 1.18 1.66 0.021 1.06 0.59 0.25 0.51
XRF error (1−σ) 0.16 0.06 0.005 0.03 0.04 0.005 0.03 0.09 0.003 0.006
⁎ These absolute errors are expressed as wt.%. The errors for MnO are reported to an additional decimal point because the MnO abundance is about an order of magnitude smaller
than most other major elements. Row 1 tabulates the errors in test set predictions of using a random training set, compositions in wt.% oxide, and no compositional scaling. Rows 2–4
tabulate the errors using the same random training set with various compositional scaling methods (all in wt.% oxide). Row 5 tabulates the errors using compositions in atomic
fractions instead of wt.% oxide, scaled by scaling method 3 (standard deviation). Predicted values are converted back to wt.% oxide so the errors can be compared with the other
regressions. Row 6 tabulates the errors using individual PLS1 regressions for each element instead of a single PLS2 regression. Compositional data are in wt.% oxide and scaling is
unnecessary. Row 7 tabulates the errors using spectra with the baseline fitted and removed. Row 8 tabulates the errors when the spectra are transformed by the first derivative. Rows
1–8 all use the same random training set. Row 9 tabulates the errors using a deliberately-chosen training set, and row 10 using two training sets split on the basis of SiO2 abundance.
Rows 4 and 7–10 all use compositional data in wt.% oxide and scaled by the standard deviation. Row 11 tabulates the 1−σ errors in the XRF measurements reported by Rhodes
(1988). These errors are not considered in weighting the PLS regressions. In all cases, the XRF errors are much smaller than the errors in the LIBS predictions, but may not be entirely
insignificant.

Ymax. This rescales all elemental distributions between the ratio of wt.% oxide (analogous to the example in Clegg et al., 2009). The
minimum to maximum concentration and 1. atomic fraction of Si is the same (0.2) regardless of which end-
2. The minimum concentration of an element is subtracted from each member cation is present. However, because Mg and Fe differ
concentration of that element, and this value is divided by the substantially in their atomic mass, the weight percent of SiO2 differs
range (the maximum minus the minimum value of that element between the two end-members (59.9 wt.% SiO2 for enstatite and
among the training set): Yi′ = (Yi–Ymin)/(Ymax–Ymin). This rescales 42.9 wt.% for ferrosilite). A calibration curve using wt.% oxide of
all elemental distributions between 0 and 1. enstatite and ferrosilite would show differing amounts of SiO2, even
3. Each elemental concentration is divided by the standard deviation though the two should respond with similar Si emission line
of that element's distribution: Yi′ = Yi/σy. This rescales all elemen- intensities. This example implies that geological standards should be
tal distributions to have a variance of 1. converted to atomic fractions before fitting calibration curves.
However, our results show that atomic fraction predictions are
Elemental abundances predicted from the LIBS spectra in the test worse than wt.% oxide predictions in all elements except Al, as shown
set are now scaled, and must be “unscaled” by the reverse of the in Table 1, row 5. The reason for this surprising result is best
scaling formulas, using the elemental minima, maxima, and standard understood by considering the effects of error propagation. Calculat-
deviations from the training set. The resulting 1−σ errors are shown ing the known atomic fraction of a single element for comparison to
in rows 2–4 in Table 1. The second method (row 3) produced errors LIBS predictions incorporates the error from all wt.% oxide values
comparable to the original model without scaled compositions (row determined by XRF, and is especially affected by incomplete analyses
1), and the first and third methods (row 2 and 4) showed significant (e.g., those lacking H2O, SO3, or CO2) or those that do not sum to 100%.
improvements in the errors of all elements except Al, where the errors Thus there is more inherent error in atomic fraction values than wt.%
are comparable. In general, the elements showing the most oxides in the training set. Moreover, when using atomic fractions in
improvement in terms of percentage are those with the lowest the training set, predictions in the test set are returned as atomic
compositional ranges; the ones “ignored” in the original PLS2 model. fractions, which must then be converted back to wt.% oxide for
Because of the significant improvements in doing so, all subse- geochemical interpretations. This last conversion incorporates all the
quent models use scaled compositions according to the third method. errors in the LIBS predictions of all elements, which are much greater
It must be noted that rescaling is only appropriate when the original than the errors in the XRF analyses. It also assumes a normalization to
elemental distribution is approximately Gaussian. Some kind of 100%, i.e. a complete analysis, which may not be a good assumption
rescaling technique is highly recommended when multiple Y when volatiles and other unanalyzed elements are excluded.
variables with disparate ranges are modeled simultaneously. Another explanation of this result is that the samples used in this
study are of similar mineralogies and not composed of extreme end-
5.2. Atomic fraction vs. wt.% oxide members like the example of pyroxenes above. Thus, the wt.% oxide
stoichiometry is nearly identical to the atomic fraction stoichiometry.
Regardless of how they are performed, geochemical analyses are A comparison between the atomic fraction values and wt.% oxide
almost always reported in elemental wt.% oxides. Reporting a values has R2 N 0.96 for each element (Fig. 5).
chemical analysis as wt.% oxides assumes a specific valence for each For the reasons stated above, all subsequent comparisons are done
cation and assumes oxygen is the only anion. These assumptions using wt.% oxides as inputs and products of the regression models.
break down when considering sulfides or halides, but are broadly
applicable to other rock types. However, techniques such as LIBS (and 5.3. PLS1 vs. PLS2
the X-ray techniques typically employed for bulk analysis) physically
respond to the atomic fraction or atoms per formula unit of a given There are many permutations of partial least squares analysis. All
element, not its oxide weight percent (a somewhat artificial of them share the advantage of utilizing all available predictors and
construction), and the two are not equivalent. eliminating multicollinearity; this is why PLS analysis is routinely
A comparison of the two pyroxenes enstatite (MgSiO3) and more successful than standard univariate analysis at predicting
ferrosilite (FeSiO3) illustrates the inequality of atomic fraction and elemental concentrations. Two variations of PLS were used here
 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148 143

squares of the values across each row as a crude quantitative measure of

the degree of intercorrelation of each element.
Our results show that predictions using PLS2 are superior to PLS1
predictions only for Si and Fe (by 40% and 15%, respectively), and the
two PLS variations are comparable for the other eight elements
(Table 1, row 6). Table 2 shows that Si and Fe exhibit the highest
degrees of intercorrelation, and thus the improvements in the
prediction of these elements using PLS2 over PLS1 can then be
ascribed to their higher degree of intercorrelation.
The lack of improvement in less intercorrelated elements might
result from optimization of a PLS2 model to all elements simulta-
neously. This is evidenced by the fact that the jackknife validation for
the scaled PLS2 model is optimized with only four regression
components, whereas some of the PLS1 models are optimized with
up to eight. Another reason for the lack of improvement between PLS1
and PLS2 for the majority of elements might be the very large number
of X variables. There are 6144 X variables and only 10 Y variables. So,
any improvements that the correlations among the Y variables give
the model are swamped by the enormous numbers of number of
channels that contribute nothing to the regression.
We conclude that when a large number of X variables is used, there
should be little difference between PLS1 and PLS2 except for highly
intercorrelated elements, but this will be greatly dependent on the
particular data set. Although the computation time is increased for PLS2,
there is no major disadvantage to using PLS2 routinely (predictions are
no worse), and PLS2 is used in all other tests in this study.

5.4. Normalization of spectral data and baseline subtraction

In another set of analyses, an additional procedure (Schaefer et al.,

2008) for further spectral normalization was employed. After spectra
were normalized to total intensity and combined, they were scaled back
up by a factor of the sum of the sums of all original spectral intensities. A
baseline was then fitted to the spectrum and removed to test the analysis
sensitivity to the baseline. In LIBS spectra, baselines are often considered
complicating factors (Cremers and Radziemski, 2006), and standard
procedure is to use a gated spectrometer that significantly reduces the
broad baseline. As an example of baseline fitting and removal, a typical
basalt spectrum from the red/NIR spectral region is shown in Fig. 6.
Fig. 5. Chemical analyses for the 100 samples in our data set expressed as atomic
fractions vs. wt.% oxides for Si/SiO2 (upper) and Al/Al2O3 (lower). All other elements Our results show that PLS2 analysis performed using baseline
show similar correlations. The apparent greater degree of Si correlation in high-silica subtracted spectra predicts elemental concentrations that are either
samples is an artifact of the samples used in this study and not more generally comparable to or worse than with the analysis using spectra without
characteristic of igneous rock analyses. These plots are not perfectly straight lines baseline removal (Table 1, row 7). Perhaps the baseline, which is
because the calculation of atomic fraction from wt.% oxides (as reported by XRF)
incorporates the error from all wt.% oxide values, and is especially affected by
primarily caused by bremsstrahlung (specifically thermal bremsstrah-
incomplete analyses (e.g., those lacking H2O, SO3, or CO2) or those that do not sum to lung—optical and infrared continuum emissions originating from
100%. Thus there is more inherent error in the atomic fraction values than in the wt.% Coulomb interactions between electrons and positive ions in the
oxide values in the training set. plasma), is relatively consistent and systematic at a given standoff
distance for samples of similar composition, and thus its removal does
(Martens and Næs, 1989; Malinowski, 2002). PLS1 regresses a single not improve the quantitative nature of the spectral peaks.
response variable (element, vector x) against the predictor variables To test this hypothesis, we selected a subset of 10 samples with the
(spectra, matrix Y). PLS2 regresses multiple responses (elements, widest variety of compositions to investigate systematics and
matrix X) against the predictors and explains the variance in both X compositional dependences of the baseline that was subtracted
and Y, taking advantage of the natural well-known correlations using the technique mentioned above. These subtracted baselines
between elements in igneous rocks. The preceding analyses in are shown in Fig. 7. This preliminary analysis yields some interesting
Sections 5.1 and 5.2 used only PLS2. In general, PLS2 will outperform results that will be pursued more rigorously in future work. First, the
PLS1 when there is a high degree of intercorrelation between the Y maxima of the baselines appear to be around the yellow to red region
variables. This should be the case with geologic materials, where of the spectrum, roughly 540–650 nm in these data. The overall shape
elemental variations can be very systematic. of the baseline and the positions of the broad features do not change at
To test the connection between the two variants of PLS and elemental all. Very broad peaks are present that appear roughly correlated with
intercorrelation, we computed a correlation matrix for all 100 samples spectral regions where there are many emission lines. These broad
between each element (Table 2). The strong correlations shown in the peaks are likely to be due to unresolved light scattered from a strong
table can be understood as the result of igneous rock chemistry and emission line or a series of emission lines. The bremsstrahlung is the
petrogenesis. For example, Fe and Mg are negatively correlated with Si in even broader distribution beneath the individual broad peaks.
this data set, a result of mafic/felsic mineralogical variations; and K is Theoretically, the shape and position of the bremsstrahlung should
positively correlated with Si, a result of its incompatibility in silicate only be affected by the velocity distribution of the electrons in the
melts. In the table, a “correlation factor” is computed by summing the plasma, and at consistent laser power, standoff distance, and spectral
144 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148

Table 2
Matrix of correlation coefficients between pairs of compositional variables. A correlation coefficient is computed between each pair of elements over all 100 samples. The high
positive and negative correlations can be understood by the principles of igneous chemistry. The “correlation factor” is the sum of the squares across each row and is thus a
quantitative measure of the degree of intercorrelation of each element. Si, having the highest correlation factor, is the most intercorrelated element.

SiO2 Al2O3 TiO2 Fe2O3T MgO MnO CaO Na2O P2O5 K2O Correlation factor

SiO2 1 0.38 −0.68 −0.85 −0.70 −0.77 −0.70 0.51 −0.45 0.80 4.0
Al2O3 0.38 1 −0.63 −0.32 −0.80 −0.19 0.21 0.57 −0.57 0.15 2.0
TiO2 −0.68 −0.63 1 0.69 0.58 0.57 0.14 −0.48 0.82 −0.37 3.1
Fe2O3T −0.85 −0.32 0.69 1 0.42 0.91 0.59 −0.37 0.36 −0.67 3.4
MgO −0.70 −0.80 0.58 0.42 1 0.29 0.18 −0.71 0.49 −0.53 2.8
MnO −0.77 −0.19 0.57 0.91 0.29 1 0.58 −0.16 0.37 −0.62 2.7
CaO −0.70 0.21 0.14 0.59 0.18 0.58 1 −0.25 −0.14 −0.78 2.0
Na2O 0.51 0.57 −0.48 −0.37 −0.71 −0.16 −0.25 1 −0.20 0.40 1.7
P2O5 −0.45 −0.57 0.82 0.36 0.49 0.37 −0.14 −0.20 1 −0.08 1.8
K2O 0.80 0.15 −0.37 −0.67 −0.53 −0.62 −0.78 0.40 −0.08 1 2.7

acquisition parameters; this is consistent with observations. Second, 5.5. Spectral derivatives
the height or total area of the baseline should theoretically be affected
by the relative abundances of the ions in the plasma and their effective A commonly-employed technique in spectral analysis is transfor-
atomic numbers. Numerically, the strongest correlations between mation of spectral data by first or higher-order derivatives. Spectral
total baseline area and composition are seen with MnO, Na2O, and derivatives are useful to analytical spectroscopy because they
Fe2O3T. Fig. 7 also shows how the total baseline area correlates with emphasize spectral peaks and deemphasize flatter areas such as the
specific elements. In the top panel of Fig. 7, colors represent Fe2O3T baseline. In a spectral derivative compared to its parent spectrum
content, and in the bottom represent Fe2O3T + Na2O, showing the (Fig. 8), the peaks remain strong and the baseline is reduced to 0. We
positive correlation between total baseline area and those elements. tested the effect of this procedure by computing first order spectral
Mn is likely not the cause of the differences in baseline because MnO derivatives using Savitzky–Golay parabolic smoothing with a variety
abundances are about two orders of magnitude smaller than Fe2O3T, and of numbers of smoothing points from 3 to 11. Little difference is
its correlation with baseline area is therefore a result of the strong observed with different numbers of smoothing points, as long as the
intercorrelation between Mn and Fe (shown in Table 2), the result of number is lower than the width of the peaks.
simple cation substitution. The correlations between baseline area and The resulting PLS2 prediction errors when all spectra are
Na2O and Fe2O3T might indicate that these two elements either couple transformed by their first derivative are shown in Table 1, row 8,
most efficiently with the laser or are ionized most efficiently, or both. By and are completely comparable to PLS2 predictions on the raw spectra
far, Fe displays the most lines in a LIBS spectrum, and Na the single most (row 4). This implies that either there is no improvement in the
intense line (590 nm). Quantitatively, these elements thus appear to quantitative nature of peaks using spectral derivatives, or any
couple most efficiently with the laser, i.e. they are overrepresented in improvement is countered by elimination of the baseline, which
the plasma compared to the other elements, which could explain why was shown to be sensitive to the composition. Further, spectral
they appear correlated with the baseline area. The compositional derivatives will tend to emphasize only the strongest peaks in the
dependence in the baseline magnitude persists even in the spectral spectra, and can detrimentally deemphasize low-intensity peaks. If a
channels where there are no atomic emission peaks, and removal of the peak rises only slightly above the baseline, as is the case with peaks
baseline could therefore slightly worsen predictions as the composi- from minor and trace elements, the derivative will flatten the peak
tional information contained in the empty spectral regions is eliminated. and quantitative information therein will be lost.

Fig. 6. Comparison of a spectrum from the visible/near IR spectrometer of a typical basalt with and without the baseline. As seen in the upper spectrum, the magnitude of the baseline
is often comparable to the height of the peaks, and thus slight variations in the baseline can undesirably affect the total height of smaller peaks.
 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148 145

Fig. 7. Baselines from 10 spectra with widely varying compositions. Colors are increasing from purple to red with Fe2O3 (total) (upper) and Fe2O3 (total) + Na2O (lower) contents.
The overall position and shape remains consistent across all compositions. The colors increasing from blue/purple at the bottom to red at the top in both panels indicate that the total
baseline area is positively correlated with Fe2O3 (total) and Na2O contents, likely due to the disproportionate influence these two elements have on the total spectral intensity.

The use of spectral derivatives is therefore not recommended preceding tests, the 100 spectra were arbitrarily divided on the basis
when the entire spectrum is considered for quantification. It is of odd and even sample numbers into two groups, one to create the
however still a good means for baseline elimination, because training set and a second for the test set. To test the importance of the
predictions were not worsened as they were with formal baseline training set, a new set of 50 samples was selected from the starting
removal (Section 5.4). This procedure may thus prove useful in other 100 samples that included samples exhibiting the highest and lowest
applications, such as the comparison of LIBS spectra taken at different values of all 10 major elements, and regularly spaced samples in
standoff distances or laser powers. between.
Predictions using this training set are better or comparable for all
5.6. Deliberate training set elements, except Si (Table 1, row 9). A notable example of
improvement is with Na, in which case the original training set
Any kind of regression works best when the training set fully encompassed a range from approximately 0 to 5 wt.% Na2O, and the
encompasses the range of variation encountered in the test set so that highest Na2O value in the whole set is 6.08. Predictions of this one
extrapolation beyond the range of the training set is avoided. In all the sample are often poor, skewing the statistics of the quality of the

Fig. 8. An example spectrum (solid line) in a narrow spectral region and its first order derivative (scaled by 5×, dashed line) using Savitzky–Golay parabolic smoothing with one
adjacent point.
146 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148

Fig. 9. Comparison of values of all elements for the 50 test set samples using the deliberately-chosen training set (left graph in each plot) and the split training set (right graph), with
1:1 lines. These were the two most successful calibrations. The x axis in all cases is the wt.% of the oxide measured by XRF, while the y axis shows the predicted value for that oxide.
Deviations from a 1:1 line are used to calculate the absolute error associated with predictions, and 1−σ error bars are shown.

predictions. With this sample now in the training set, the Na 5.7. Split training set
prediction error improves by almost 30%. The reason why the Si
error is slightly worse is unclear, but may have to do with the slightly Attempting to describe the entire range of geochemical variability
greater range of Si encompassed in the training set compared to the in the calibration model may not be the most useful approach. To test
original training set. the effectiveness of smaller training sets, the 100 samples were split
 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148 147

into a high-silica group consisting of 26 samples and a low-silica Table 3

group of 74 samples, with the cutoff at 52 wt.% SiO2 (between basalt Predictions of a single sample composition (Juan de Fuca Ridge, cruise 152, sample 26-1
Liias, 1986) from 10 different spectra using the randomly-split training set model. In
and basaltic andesite). These two groups were themselves split nearly all cases, the predictions lie within the established 1−σ error. In all cases, the
randomly in half into test sets and training sets, and separate PLS standard deviation of the 10 measurements is much smaller than the magnitude of the
regressions were used to predict compositions of the two new test 1−σ error.
sets. The low-silica group was scaled by the standard deviation of its
SiO2 Al2O3 TiO2 Fe2O3T MgO MnO CaO Na2O P2O5 K2O
training set (the third method described in Section 5.1). The high-
1 47.49 14.95 2.78 15.12 4.29 0.22 11.23 3.13 0.57 0.45
silica group was not normalized because it contained too few samples
2 49.71 14.22 2.37 13.93 4.75 0.21 10.52 3.17 0.51 0.88
to approximate a Gaussian distribution. The low-silica training set was 3 48.56 14.61 2.63 15.37 4.40 0.22 10.71 3.04 0.39 0.34
used to predict compositions of the low-silica test set and the high- 4 50.25 14.79 2.31 14.23 4.22 0.20 10.46 3.11 0.31 0.36
silica training set used for the high-silica test set. The results of the 5 50.37 14.39 2.31 13.58 5.00 0.20 10.70 2.96 0.36 0.44
two sets of compositions were combined for direct comparison to the 6 49.92 14.60 2.27 14.76 4.06 0.21 10.56 3.14 0.26 0.42
7 50.73 14.41 2.13 13.55 4.79 0.20 10.54 3.11 0.30 0.45
models where the samples are not split.
8 51.18 13.60 2.20 14.11 5.04 0.20 10.04 2.98 0.26 0.59
Results using the split training sets are superior (sometimes 9 50.25 14.10 2.30 14.01 5.19 0.20 10.24 3.05 0.36 0.54
considerably) or comparable to the original 50-sample training set 10 49.63 14.47 2.35 14.55 4.51 0.21 10.58 2.98 0.33 0.59
(Table 1, row 10), showing the promise of this approach. This σ 1.08 0.38 0.20 0.62 0.38 0.01 0.31 0.08 0.10 0.16
μ 49.81 14.41 2.36 14.32 4.62 0.21 10.56 3.07 0.37 0.51
technique yields by far the lowest error in Si. Si always has the
XRF value 49.42 12.93 2.44 15.34 6.1 0.25 10.3 2.51 0.24 0.18
greatest compositional range, and thus the largest error of any 1 − σ 2.18 1.86 0.44 1.46 1.99 0.03 1.17 0.68 0.26 0.55
element. Here, when the Si range is cut essentially in half, it is now error⁎
comparable to the other elements with large ranges (Al, Mg), and the ⁎ Table 1, row 4.
magnitude of the error is also comparable to those elements.
A comparison is also shown in Fig. 9, which includes graphs of
predicted vs. measured of each element for the samples in this and the low. The same systematic trends were not observed across the
deliberate training set (Section 5.6). Note that the two test sets samples in the predicted set (Fig. 9), indicating that these are
represent different samples, so the ranges of each element are not the characteristic of the sample, and not the calibration. In 93 of 100
same. However, it is apparent that both training sets predict the predictions, the elemental value predicted is within the established 1
compositions of various elements very well. −σ error for this model.
An ideal training set should span the smallest compositional range
possible to minimize errors but must also fully represent the variation 6. Conclusions
in unknown samples. On Mars, where most rocks are basaltic in
composition, restricting the training set to low-silica samples would This study has demonstrated the ability of standoff LIBS to provide
improve the predictions of most analyses. But encountering a high- accurate and precise major element chemistries of geologic samples.
silica sample would potentially be very interesting, and excluding Our prescription for a successful calibration involves the following
high-silica samples from the training set would bias it against accurate procedures: For input into a training set, elemental distributions
compositional determinations of such samples. It seems that use of should be scaled to correct for the vastly differing ranges among the
multiple different training set calibrations might be necessary, in elements. The units of quantification should be wt.% oxide and not
combination with informed inspection of the data. A useful protocol atomic fraction to avoid inaccuracies due to error propagation and
might include initial application of a “universal” broad training set incomplete analyses. The choice between PLS1 and PLS2 should be
that encompasses all possible expected ranges of elements likely to be based on the degree of intercorrelation between the elements. Choice
encountered, in order to gain a preliminary estimate of the of training set should be focused on using multiple smaller calibration
composition and to guide selection of which specialized training set sets after application of a single all-encompassing calibration set. This
is appropriate. This would then be followed by use of a more specific will allow the calibration to both encompass the entire range of
calibration developed on samples similar to the unknown. For variability of unknown samples and to be small so that accuracy and
example, a spectrum with unusually high Si peaks might best be precision can be maximized.
interpreted using a training set based on sedimentary samples. While this study has demonstrated the possibility of LIBS to
Spectra with Si and Fe lines similar to those common in basalts might produce geochemically valuable information, other analyses are
use a basalt-centered training set. Finally, a spectrum with intense C needed to further understand the connection between LIBS spectra
or S peaks would clearly be better served by application of a and geochemical quantities. One factor demanding further study is
carbonate- or sulfate-specific calibration suite. the importance of the bremsstrahlung, or baseline. With consistent
experimental conditions (standoff distance, laser power and focus),
5.8. Precision the shape and area of the bremsstrahlung were shown to be reflective
of the bulk composition, specifically Fe and Na. However, dedicated
To further benchmark precision, a single sample (a mid-ocean studies of pure elements and simple compounds with more extreme
ridge basalt from the Juan de Fuca Ridge, Liias, 1986) was run 10 times varieties in composition and atomic number are needed to system-
over the course of the experiment to assess consistency in the LIBS atically relate composition to baseline in LIBS spectra. Additionally,
measurements. Predictions of the major elements are made for each the procedure of taking the spectral derivative should be tested as an
of the 10 spectra of this sample using the randomly chosen training alternative to formal baseline removal when such a procedure is
set with scaled compositions, and the results are shown in Table 3. necessary. Systematic experiments are also underway to determine a
Even though other calibrations yielded smaller errors than the precise distance correction. Preliminary results indicate it may not be
randomly chosen training set, this sample fell into the training sets sufficient simply to adjust for the different solid angle observed.
of those calibrations, and the test set of the random one. Prediction of We note that the PLS regression models used here, which give very
this sample could be strongly biased if it were included in the training useful results, are probably not the most efficient way to interpret
set of the calibration used. these data. Additionally, there is an enormous amount of multi-
The predictions of some elements in this sample, like Si, Ti, and Ca collinearity, or redundancy in the spectra from multiple peaks of the
show deviations around the true value. In contrast, elements in this same element and multiple spectral channels within each peak. With
sample, like Mn and Na, are predicted consistently slightly high or N6000 regressors, it is difficult to determine which spectral lines are
148 J.M. Tucker et al. / Chemical Geology 277 (2010) 137–148

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We are grateful for support from NASA grants NNG06GH35G and 0003702963905538.
NNX09AL21G, and from LANL internal funding. We also thank Palanco, S., López-Moreno, C., Laserna, J.J., 2006. Design, construction, and assessment
of a field-deployable laser-induced breakdown spectrometer for remote elemental
Professor Bradley Schaefer of Louisiana State University and Marco sensing. Spectrochim. Acta B 61 (1), 88–95. doi:10.1016/j.sab.2005.12.004.
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