a pca study to determine how features in meteorite reflectance spectra vary with the samples’...

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Journal of Quantitative Spectroscopy &Radiative Transfer

Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 1803–1814

0022-40

doi:10.1

n Corr

E-m

markipa

journal homepage: www.elsevier.com/locate/jqsrt

A PCA study to determine how features in meteorite reflectancespectra vary with the samples’ physical properties

Mark Paton a,n, Karri Muinonen a,b, Lauri J. Pesonen a, Viljo Kuosmanen c, Tomas Kohout a,Jukka Laitinen c, Martti Lehtinen d

a University of Helsinki, Dept. of Physics, P.O. Box 64, FI-00014 Helsinki, Finlandb Finnish Geodetic Institute, P.O. Box 15, FI-02431 Masala, Finlandc Geological Survey of Finland, P.O. Box 96, FI-02151 Espoo, Finlandd Geological Museum, University of Helsinki, P.O. Box 17, FI-00014, Finland

a r t i c l e i n f o

Available online 3 February 2011

Keywords:

Reflectance

Spectra

Meteorite

Density

Susceptibility

Analysis

73/$ - see front matter & 2011 Elsevier Ltd. A

016/j.jqsrt.2011.01.033

esponding author: Tel. : +358465714275.

ail addresses: [email protected],

[email protected] (M. Paton).

a b s t r a c t

Meteorites have advanced our knowledge of processes in the Solar System with the

application of high precision instruments here on Earth. The study of asteroids, the

source of most meteorites, has in turn given us knowledge regarding the large scale

evolution of the Solar System. Using the complementary information that asteroids and

meteorites give us the story of our cosmic backyard can be more easily read. One

efficient way to link meteorites to asteroids is by matching their respective reflectance

spectra. There have been few convincing matches because of observational and scale

differences as well as an incomplete knowledge of the light scattering physics involved.

To better interpret the reflectance data we need to know the dependencies of the

reflectance on physical properties and develop techniques for better comparisons of

data sets. For these purposes we utilise our own measurements of 26 different

meteorites together with spectra available on the NASA PDS.

We find that normalisation of reflectance at a wavelength between 1.1 and 1.3 mm

gives the closest match of spectra from meteorites common to both data sets. The depth

of the spectra bands deepens by similar amounts for different types of surface texture

alterations i.e. rock to sawn surface, rock to polished surface and rock to powdered

surface. Principal Component Analysis (PCA) is able to easily place carbonaceous

chondrites, ordinary chondrites and achondrites into distinct groups using their

reflectance spectra. We track the variation of spectral features in principal component

space by using a set of meteorite spectra synthesised from mineral and elemental

spectra. A spectral agent that reduces the reflectance at all wavelengths is required, in

addition to olivine, pyroxene and carbon, to generate a set of synthesised spectra to

match the distribution of measured spectra, in principal component space.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Meteorites contain a diverse range of over 300 mineralswith about 40 not found in terrestrial rocks [1]. Common

ll rights reserved.

mineral groups found in meteorites are silicates, oxides,carbonates, phosphides, phosphates and sulphides. Nickel–iron metal and carbon in the form of graphite or diamondare also relatively common in meteorites. Pyroxene,plagioclase and olivine are the most common and can befound in achondrites and chondrites. Table 1 shows themineral and elemental (carbon) contents of meteorites.These reflect their formation processes e.g. see Ref. [2] orRef. [3] for further details. It is generally accepted that

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Table 1Average percent weight of minerals in meteorite groups. The table is split into non-differentiated (top) and differentiated meteorites (below). A range of

weights is shown for achondrites to highlight their variability. Values for H, L and LL chondrites are an average of values measured in Ref. [4]. Carbon

references were found in Ref. [5].

Meteorite group Olivine Pyroxene Plagioclase Carbon Metal

Carbon. chondrites �7.5f (81.6)g 0f (0.9)g 0.10–5.00a,b (0.01)g

H chondrites 32.9 32.4 9.0 0.03–0.60 18.3

L chondrites 42.0 31.4 9.4 0.03–0.60 8.4

LL chondrites 51.1 26.3 9.9 0.03–0.60 2.6

Howardites – 15–60e – 0.001–0.003c o0.1

Eucrites – 45–70e – 0.001–0.003c o0.1

Diogenites – �26e – 0.001–0.003c o0.1

aRef. [6], bRef. [7], c. Ref. [8], e. Ref. [9], f. average of a CM2, C2, CI2 in Ref. [10] g. Allende CV3 Ref. [10].

Table 2Classification of chondrites. The numbers that are italicized indicate how many meteorites have been classified with the associated petrographical grade.

The numbers in the cell are the number of each meteorite in our collections [11]. Absent, sparse and distinct refer to chondrules in the meteorite. The

petrographical types 1, 2 and 3 apply to carbonaceous chondrites and are in order of decreasing aqueous alteration. The petrographical types 3, 4, 5 and 6

apply to ordinary chondrites and are in order of increasing thermal metamorphism.

Clan Group Petrographical type

1 2 3 4 5 6

Absent Sparse Abundant, distinct Increasingly indistinct

Carbonaceous Chondrites CI 5

CM 3 150

CR 78

CO 91

CV 1 54

CK 6 23 51 1

R Chondrites R 5 4, 1a 1, 2b 5c

K Chondrites K 2

Ordinary Chondrites LL 33 72 952 471 LL7 10

L 148 (3%) 464 (7%) 1368 (22%) 4443 (68%) L7 15

H 138 (3%) 1448 (23%) 3563 (40%) 2032 (34%)

EL 10 1 2 23

EH 98 11 5 6

a. R3–4, b. R3–5, c. R3–6.

M. Paton et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 1803–18141804

chondrites are primitive while achondrites have experi-enced some differentiation.

Meteorites are graded in three main ways to describepetrology, shock and terrestrial weathering. Petrographicalgrades of chondrites, shown in Table 2, attempt to describethe thermochemical equilibration with 1 being the leastaffected by thermal metamorphism and 6 being the mosteffected by thermal metamorphism. A grade 6 chondrite hasexperienced a similar degree of melting as an achondrite butwill not have experienced differentiation. The grades alsodescribe the distribution and mixing of minerals like olivineand pyroxene in the meteorite. A meteorite with a lowergrade will be more heterogeneous and a meteorite with ahigher grade will be more homogeneous.

A similar petrographical grade is not available for achon-drites as these are from differentiated bodies and have beenat least partially melted, moving them beyond the petro-graphical grade 6 used for chondrites. Achondrites areinstead organised into subgroups with similar compositionsand degrees of melting. They are sometimes organised intogroups when it is suspected they share a common parent

body. For example the subgroups Howardite, Eucrite andDiogenite meteorites (see Table 1) are thought to originatefrom asteroid Vesta and are known collectively as theHowardite–Eucrite–Diogenite (HED) group.

A grading system is employed to describe the degree ofshock received by the meteorite during an impact event.The grade increases with increasing shock pressures. Lightlyshocked meteorites may display dark shock veins whilehighly shocked impact melts will display a melted anddeformed matrix. A grading system is also used to describethe amount of degradational terrestrial weathering affectingthe meteorite sample. Terrestrial weathering first affects themetal grains, then the troilite and finally the silicates. Theshock [12] and weathering grading systems are shown inTable 3 together with more details regarding the petrogra-phical grading system introduced in Table 2.

Fortunately, pyroxene, plagioclase and olivine havediagnostic absorption bands centred at wavelengths of�1 and �2 mm in the reflectance spectra. These arewithin the range of spectrometer instruments currentlyused for asteroid observations. The bands due to pyroxene

Table 3Petrographical, shock and weathering grading systems for meteorites. The petrographical grade applies to chondrites, the shock grade system applies to

all meteorites and the weathering grading applies to ordinary chondrites.

Grade no. Petrographic (chondrites, i.e. H5, L6,

etc. see also Table 1.2)

Shock (all, i.e. S5, S6, etc.) Weathering (ordinary chondrites,

i.e. W5, W1, etc.)

1 No chondrules; very fine grained and

opaque

matrix material.

Unshocked (o5 Gpa) Minor oxide rims around metal and troilite,

minor oxide veins (o5 Ka)

2 Chondrules distinct in a matrix rich

in opaque

material. Variation in olivine and

pyroxene (45%)

Weakly shocked (5–10 Gpa) Moderate oxidation of metal, about

20–60% effected (5–15 Ka)

3 Similar to 2 except metals are

present and lower

carbon present.

Moderately shocked

(15–20 Gpa)

60–95% effected (15–30 Ka)

4 Aggregates of secondary feldspar

grains present. Variation

of pyroxene and olivine (o5%)

Strongly shocked (30–35 Gpa) 495% effected (20–35 Ka)

5 Olivine and pyroxene uniform

throughout the meteorite.

Very strongly shocked

(45–55 Gpa)

Some alteration of mafic silicates (30–45 Ka)

6 Secondary feldspar formed large

grains. Chondrules poorly defined.

Melt (75–90 GPa) Replacement of mafic silicates by clays (30–45 Ka)

1 http://pds.nasa.gov/

M. Paton et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 1803–1814 1805

and olivine have been found in reflectance spectra of alarge number of asteroids providing evidence for a linkwith meteorites. Plagioclase has proved to be difficult todetect in reflectance spectra because olivine and pyroxenetend to dominate the spectrum in the near infrared.

It is desirable to further strengthen spectral linksbetween meteorites and asteroids in order to relate resultsfrom high precision measurements of meteorites to theirasteroidal parent bodies. This has been achieved for rela-tively few meteorite samples due to the difficulties asso-ciated with comparing reflectance spectra of asteroids withthose of meteorites. While space weathering of asteroidsurfaces is generally accepted to be a major cause of spectralmismatches between meteorites, models explaining weath-ering processes on asteroids have been difficult to testbecause multiple samples of asteroidal regolith representingthe optical surface are required.

Space weathering tends to redden, darken and depletethe bands in the spectra of asteroid surfaces [13]. Theseare thought to be due to the condensation of nano-phaseiron on regolith grains due to vaporisation of materialby solar wind particles and impacts from micro-meteorites [14]. The number and relative importance ofspace weathering mechanisms, e.g. impact shocking,vaporisation–redeposition, solar wind implantation thatact on the surface are not known for asteroids. Across theSolar System it is thought that solar irradiation is domi-nant [15]. Also certain problems remain such as thetimescales suggested by experiments and observationsof asteroids e.g. see Ref. [16] and references therein.Asteroid surfaces are gardened, mixed over, by microme-teorite impacts which add to an already complicatedpicture and could account for results in different time-scales of effectiveness for each process, depending onmicrometeorite fluxes.

It is important to consider all possible mechanismsthat contribute to asteroid surface alteration. It is con-ceivable that an asteroid could be mis-classified if for

example it is covered in shock altered regolith [17]. Thishypothesis had been dismissed by previous workers dueto dynamical considerations [18] and the low abundanceof shocked material in our collections [19]. Given thecurrent state of meteorite–asteroid spectral links, it isnecessary that we properly understand the light scatter-ing physics from weathered and shocked material in orderto properly account for effects on asteroid reflectancespectra.

In this paper we investigate ways to improve thelinking of meteorites and asteroids through use of reflec-tance spectra and physical property measurements. Weuse meteorite spectra that include our own measure-ments from meteorites kept at the Geological Museumin Helsinki, Finland and a larger data set of reflectancespectra kept on the NASA Planetary Data System (PDS)1.We use physical property measurements (bulk densityand magnetic susceptibility obtained in the Departmentof Physics, University of Helsinki. Several issues regardingthe linking of meteorites and asteroids are investigated.

�
Normalisation of reflectance spectra from data setsobtained under different observational conditions � Unravelling of meteorite spectra into their constituent
spectra (i.e. mineral and elemental spectra)
� Effect of surface texture of the reflectance spectra
(to understand the light scattering mechanisms)
� The relationship between features in the meteorite
spectra and the physical properties for non-destructiveclassification of meteorites and possible remotesensing of asteroid physical properties

First we introduce diagnostic features in meteoritereflectance spectra that we use and their relationship tothe samples’ physical properties. Principal Component

http://pds.nasa.gov/


Analysis (PCA) is then introduced as a mathematical toolto manage the large amount of information contained inreflectance spectra. A method to analyse the variation ofmineral content in a data set of reflectance spectra isintroduced using synthesised reflectance spectra. Wedescribe a normalisation procedure for combining twodata sets of reflectance spectra obtained under differentobservational circumstances.

In the results section we discuss the combination of thetwo data sets. We use PCA to explore the data sets forcorrelations between their physical properties (bulk densityand magnetic susceptibility) and reflectance properties. PCAis used to investigate the effect of texture changes to thereflectance spectra. We track the composition, across a dataset of meteorite spectra, using a set of synthesised spectra.

2. Diagnostic features in meteorite spectra

Shown in Fig. 1 are the reflectance spectra of impor-tant minerals in meteorites namely, pyroxene, olivine,plagioclase and an important element, carbon. Reflectancespectra can be used to identify important minerals anddetermine their relative abundances. See Ref. [20] for areview of reflectance spectroscopy applied to asteroidsand meteorites. The bands in the pyroxene and olivine aredue to the electronic absorption of photons within thecrystal structure of the minerals causing a transition ofFe2 +. Olivine has three bands that combine to form onebroad band centred at around 1.0 mm. The pyroxenes havetwo separate bands one located at 0.9 mm and one at1.9 mm. For both minerals the bands are superimposed ona continuum with a strong charge-transfer absorptionband centred in the ultraviolet. The broad absorptionband of plagioclase, centred at 1.25 mm, is also causedby the transition of Fe2 + but the feature will disappear ifthe material has been shocked above 25–30 GPa.

Opaques such as amorphous carbon will severely darken(reduce the reflectance of) the spectrum and provide littlediagnostic information. Conversely free metal in the form of

Fig. 1. Reflectance spectra for pyroxene (enstatite), olivine, plagioclase

and carbon. The first bands for olivine and pyroxene are located at

around 1 mm. The second band for pyroxene is located around 2 mm.

These are the dominant minerals in ordinary chondrites and are used to

calculate abundances of the minerals. Data obtained from the USGS

Digital Spectral Library.

minerals (alloys) such as kamacite and taenite cause asmooth increase in reflectivity with wavelength [20].

One way to determine the abundance of materials inasteroids from reflectance spectra data is to use a linearcombination of the reflectance spectra from the meteor-ite’s end member minerals. However, mixing is probablynon-linear to a degree that depends on the mineraldistribution, the presence of opaques, the surface textureand the size of the mineral grains [20]. An analysis ofmaterials using a linear model may produce errors inderived abundances of the order of 10% or more. There-fore for quantitative investigations a non-linear spectralmixing model is required [21]. For large grains, where thegrain size exceeds the optical depth, a linear mixingspectral model may be appropriate [22]. Applying spectralmixing models to the reflectance spectra of meteoritesmakes the determination of mineral absolute abundancesvery difficult for several other reasons as well.

For example minerals may not be distributed homoge-neously over the meteorite surface. A reflectance spectrumtaken from one spot on the surface will then not berepresentative of the bulk mineralogy of the meteorite. Ifcarbon is mixed intimately with the silicate material this willcause absorption over the whole continuum and greatlyweaken the absorption band due to ferrous iron in thesilicate materials like pyroxene and olivine. The scatteringon a rough meteorite surface will result in increasingabsorption of light and will thereby deepen the absorptionbands. If the meteorite is ground into a powder then theabsorption bands will deepen with increasing grain size [23].

There may be other factors that make interpretationdifficult such as the influence of free metal on the overallslope of the spectrum and light scattering effects that mayarise from different illumination and observation geome-tries when comparing reflectance spectra taken usingdifferent spectrometers.

Fig. 2. Diagnostic features, used in this work, in meteorite reflectance

spectra. The areas bounded by the reflectance spectra and the dotted

lines represent the absorption bands, Band I and Band II. The peak and

minima locations are also shown. These are calculated by first dividing

out the continuum (dotted lines). The band depth is then taken from the

reflectance value of a point lying mid-point on a line connecting the

maxima each side of a band minimum and the reflectance of this band

minimum.

Fig. 3. Synthesized reflectance spectra of an achondrite, an ordinary

chondrite and a carbonaceous chondrite using linear combination of the

reflectance spectra in Fig. 2. Note carbonaceous chondrites usually only

have a few percent of carbon but this darkens the reflectance spectra

greatly. These spectra are only used as a guide for interpreting real

reflectance spectra.


Previous results have shown that the wavelength ofabsorption band minima varies systematically with rela-tive composition [23]. For example it is known that theolivine band minimum varies between 1.05 and 1.08 mmdepending on the Fe–Mg composition. It has also beenshown that the band area of the reflectance spectra ofpyroxene and olivine varies systematically with relativeabundance and can be predicted by measuring the BandArea Ratio (BAR), which is the area of Band II divided byBand I (see Fig. 2).

3. Principal Component Analysis

PCA is a straightforward technique for the statisticalanalysis of the variation in large data sets, e.g. seeRef. [24]. PCA can reduce the number of dimensions usedto describe the variation in the data to a low level. In ourcase we have nearly 200 spectra that we want to analyse.PCA can reduce the pertinent information in the spectra toa small number of components that can be used toexamine spectral features and grouping strategies (forclassification purposes).

The data set is first rationalised so all the spectra aresampled over the same wavelength range using the samewavelength intervals. The spectra are placed in an arraywith each spectrum a column entry. The mean spectrum iscalculated and then subtracted from the array. The resultingcolumns in the array represent vectors that describe m

points in n-dimensional space, where m is the number ofspectra and n is the number of spectral sample points.

Then the coordinate system is rotated, minimising thesum squared difference (i.e. minimising the error) of thepoints in a direction perpendicular to the axes. The axiswith the greatest variance along its length is known as thefirst principal component. The axis with the second great-est variance along its length is known as the secondprincipal component and so on with the higher dimen-sions. In this way the number of variables describing thestructure of the data is minimised.

In PCA an eigenvector is a vector that describes thelocation of the principal component axis in n-dimensionalspace after the coordinate system has been rotated. It isuseful for interpreting the results of a principal componentplot. The eigenvector will consist of n elements and eachelement maps back directly onto the original samples pointswhich are, in our case, the wavelength. The first element inthe eigenvector then directly corresponds to the first wave-length that the reflectance was sampled at. To illustratefurther take, for example, an eigenvector that corresponds tothe first principal component axis and has strong loadings(i.e. large values) in its middle elements. This will mean thatthe mid-range wavelengths of the spectrum are stronglycorrelated to the variation seen along the first principalcomponent axis.

To illustrate the application of PCA a set of artificialmeteorite spectra are synthesised from reflectance spec-tra of pure minerals and carbon. Here we use pyroxeneand olivine in addition to carbon. Various types ofmeteorites are synthesised. First there are ordinary chon-drites, with no carbon, with a more or less equal amountof olivine and pyroxene. Second there are high pyroxene

achondrites with a high ratio of pyroxene to olivine. Thirdthere is a group of high olivine content meteorites with ahigh ratio of olivine to pyroxene. Last there is a group ofcarbonaceous chondrites that vary in combinations ofolivine, pyroxene and carbon. Fig. 3 shows some of thesynthesised reflectance spectra for these meteorites.

We use a linear combination of olivine and pyroxeneas the synthesis of ordinary chondrite and achondritereflectance spectra is straightforward and we are inter-ested in qualitative investigations. Carbonaceous chon-drites are a little more complicated to synthesise andneed some careful consideration. Carbon is an opaquethat diminishes the 1 and 2 mm bands in the relativelyabundant olivine and pyroxene. The large wing of theband centred in the visible is relatively unaffected as theabsorption of light there is via a different mechanism.The generation of carbonaceous chondrite spectra usesthe following equation:

RUV ¼X4

i ¼ 1

firiðlÞ, lo0:65mm, ð1aÞ

RVIR ¼ aX2

i ¼ 1

firiðlÞþX4

i ¼ 3

firiðlÞþb, l4 ¼ 0:65mm, ð1bÞ

where fi is the fraction of mineral i, ri is the reflectance ofmineral i (at wavelength l), a is a factor introduced toreduce the depth of Band I and Band II. The term b is usedto correct for the discontinuity in the spectrum caused byintroducing the factor, a. The following spectra were usedto make up the synthesised meteorite spectrum, olivine(i=1), pyroxene (i=2), carbon (i=3) and an artificialspectrum where all reflectance values equal to zero atall wavelengths (i=4).

The factor a in equation 1 is defined as follows:

a¼ 1�f3 ð2Þ

The correction term b is defined as follows:

b¼X2

i ¼ 1

firið0:65Þ

Fig. 5. Eigenvectors for principle components 1 to 6. The eigenvectors

are offset by 0.2 from each other. Eigenvector 2 zero axis is at 0.2,

eigenvector 3 axis is at 0.4 and so on. The loading is related to the

variance on the average spectra of the whole data set. So EV-1 is flat and

so represents a similar variance over the whole wavelength range and is

related to the average reflectance.


We note that 50% or more of carbon is required to flattenthe band structure of pyroxene and olivine in these synthe-sised spectra while real carbonaceous chondrites only havea few percent carbon present. These synthesised meteoritespectra are only intended as a guide to interpreting realmeteorite spectra and to identify trends.

The zero reflectance spectrum (i=4) is used to subjectthe synthesised meteorite spectrum of olivine, pyroxeneand carbon to a hypothetical darkening mechanism,perhaps due to grain size effects or some other mechan-ism, across all wavelengths. This reduces the overallreflectance of the spectrum and therefore is different thanthe effect of carbon. As the contribution of the darkeningagent increases the contribution of the synthesised spec-tra will be reduced in equal amounts. This differs in thebehaviour that carbon will have in that it will also affectthe visible part of the spectrum.

Fig. 4 shows a result of PCA on the synthetic meteoritespectra plotted in principal component space. Variationsin the amounts of the minerals manifest themselves inprincipal component space in easily identifiable clusters.To associate the clusters with the correct syntheticmeteorite spectra each spectrum’s position in the arraywas used to trace the mineral spectra that were used. Forexample it is known the synthesised spectra that arecombinations of only pyroxene and olivine reflectancespectra are clustered along a diagonal line located at theextreme negative end of the x-axis. Along this line there isincreasing pyroxene up the positive y-axis and increasingolivine in the negative direction. The darkening agent hasthe effect of narrowing the spread of the spectra movingtowards the extreme positive end of the x-axis. Thecarbonaceous chondrites are easily identifiable as thetight cluster located to the right on the chart.

The clustering of the spectra can be further understoodby inspecting the eigenvectors in Fig. 5. Eigenvector one isrelatively flat compared to the others, telling us that thespread of the spectra along principal component 1 isrelated to the average reflectivity of a spectrum acrossits whole wavelength range. Eigenvector 1 defines the

Fig. 4. PCA on a set of synthesised reflectance spectra. The unfilled

triangles correspond to reflectance spectra generated from a linear

mixture of olivine and pyroxene spectra. The unfilled square symbols

correspond to reflectance spectra generated from a linear mixture of

olivine, pyroxene and zero reflectance. The filled circles correspond to a

mixture of olivine, pyroxene and carbon, using Eq. (1).

first principal component axis because most of the varia-tion in the data is due to flat spectra (i.e. carbon and thedarkening agent).

Eigenvector two shows more variation than eigenvectorone with greatest values at 1.3 and 2 mm. The variation at1.3 mm in eigenvector two tells us about the variation inBand I while the variation at 2 mm tells us about the variationin Band II. Notice in Fig. 1 that the greatest difference inreflectance between pyroxene and olivine occurs at 1.3 and2 mm. So a linear combination of these two spectra wouldresult in the greatest variations in reflectance at these points.

The band depths in the synthesised spectra change withchanging ratio of olivine to pyroxene and hence the spectrawith a deep Band I is at the extreme end of the positivey-axis and the spectra with deep Band I is at the extremeend of the negative y-axis. The darkening agent reduces theaverage reflectance together with the band depth and hencea convergence to zero is seen on the y-axis in the positive x

direction. Even though the carbonaceous chondrites containolivine and pyroxene, they are clustered tightly along the y-axis because the carbon reduces Band I and Band II relativeto the visible part of the spectrum.

A common measure of interrelation between twoquantities is the correlation coefficient. It is a measureof the linear interrelation and is often used in statistics. Itis determined by dividing the covariance of the two datasets by the product of their standard deviations. Acorrelation matrix can easily be calculated during PCAand is useful for determining relationships between datasets. For example this would be useful for comparing thedependencies of features in the reflectance spectra suchas the depths of Band I and Band II. The correlationcoefficient is as follows:

C ¼

Pðx�xÞðy�yÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPðx�xÞ2

Pðy�yÞ2

q ð3Þ

where x and y are variables of the two data sets.


4. Measurement of reflectance and data reduction

A FieldSpec FR spectrometer at the Geological Survey ofFinland was used to obtain reflectance spectra from 26meteorites representing undifferentiated (C, H, L, LL and E)to differentiated meteorites. The reflectance of each meteor-ite was sampled at 1 nm intervals from 0.35 to 2.5 mm. Thespectrometer has a spot size (footprint) with a diameter ofapproximately 5 mm. This can be the same order of magni-tude as inhomogenities in meteorites composition [1].Reflectance spectra were obtained from ten different loca-tions over the meteorite surfaces and the average was takento provide a spectrum for each meteorite that is represen-tative of its bulk composition. This type of compositespectra could be expected when observing small asteroidsor larger asteroids that are further away.

The average of the reflectance spectra of meteorites indifferent groups are shown below in Fig. 6. Noticeablefeatures are deep absorption bands in the Eucrites andthat the L chondrites are brighter (higher average reflec-tance) than H chondrites.

In addition to the averaged spectra individual reflec-tance spectra were obtained to investigate the effect ofdifferent surface textures on meteorite spectra. Reflec-tance spectra were taken of an H5 ordinary chondritesolid sample to investigate the difference between a mattsurface and a polished surface. Reflectance spectra weretaken of an L6 ordinary chondrite (Alfianello) to investi-gate the difference between a natural surface (rough andbroken) and a sawn surface. The high petrographicalgrade of both meteorites means that the compositionsare relativity homogeneous as they have experienced ahigh degree of thermal metamorphism allowing textureeffects to dominate.

Another data set of 163 reflectance spectra of meteor-ites was obtained by Bus and Binzel [24] representing asimilar range of meteorite types. The reflectance wassampled at 5 nm intervals from 0.25 to 3.0 mm. Thisset included a number of meteorite spectra taken frombulk meteorite surface and powdered meteorite samples

Fig. 6. Averaged reflectance spectra of differentiated and undifferen-

tiated meteorites obtained by the Geological Survey of Finland. The first

point of each spectrum has been normalised to a reflectance value of

unity at a wavelength of 1 mm.

allowing further investigation and comparison of textureeffects on the reflectance spectra features.

The two data sets of meteorites were combined toform one large data set so results could be compared. Ourdata was resampled at 5 nm resolution to match the datataken by Gaffey [25]. To account for observational uncer-tainties due to viewing geometry effects the method ofRef. [24] was applied to the spectra in the data set. Firstthe reflectance spectra were normalised to unity at awavelength that resulted in the best fits between eightreflectance spectra common to both data sets. A leastsquares linear fit was made through each spectrum whilefixing the reflectance at unity, at the same wavelengththat was used for normalisation, and then the reflectancespectrum divided by the gradient of this line.

To find the wavelength location in the spectrum tonormalise the data set is described as follows. Thewavelength was varied from 0.35 to 2.5 mm in steps of0.005 mm. At each step the difference between the reflec-tance spectra of a meteorite common to both data setswas calculated and squared. This was then summedtogether for all wavelengths. This is then referred to as afit score. The procedure was then preformed for the nextmeteorite starting again from 0.35 mm.

Fig. 7 shows the fit scores for meteorites Juvinas andJohnstown. The upper line (with the large peak) is theaverage fit score of all meteorites common to both datasets. The variation of the fit score is presumably due to thefact spectra of meteorites common to both data bases arenot identical. This would be expected because a spectro-meter will only measure the reflectance from a limitedspot size on the surface of a meteorite. Mineral composi-tion can vary over scales of a cm. Also the surface texturemay vary over the surface or from meteorite to meteorite.The zone between 1.1 and 1.3 mm is considered the bestlocation to normalise the reflectance spectra in our case.This location is also convenient for examining the bandfeatures.

Fig. 7. Locating a wavelength to normalise both data sets. In the upper

panel are shown the fit (sum of squares of difference between reflec-

tance of meteorites) scores between the two data sets using eight

reflectance spectra from meteorites that are common to both data sets.

Average reflectance spectra of non-normalised [25] spectra and our

spectra (lower panel).


The result of our normalisation for reflectance spectraof a meteorite common to both data sets is shown inFig. 8. The spectra look slightly different because ourspectrum is the average of 10 spectra from all over thesurface of the meteorite while the [25] spectrum is fromone measurement. In Fig. 9, the average meteorite spec-trum of the combined data set is shown with a varianceenvelope. Most of the variance is around the location ofthe absorption bands as one may expect as the abundance

Fig. 8. The reflectance spectra from a meteorite in both data sets

(Johnstown) normalised by the technique described in Ref. [24]. The

solid line is from Ref. [25] and the dotted line is from this work. We have

normalised at 1.1 mm and divided by a line that is forced through unity

at 1.1 mm instead of 0.55 mm that was used by Bus and Binzel [26]. Note

they are very close now but it is not a perfect match due to the slightly

different shapes. The difference in shape is probably due to spot size

issues and the varying mineral content over the meteorite surface.

Fig. 9. Average reflectance spectrum (thick black line) of both meteorite

datasets normalised and combined using the method of Ref. [24] but

normalised to unity at 1.1 mm instead of 0.55 mm. The variation

envelope is also plotted on the same axis. The variance itself is plotted

using a second vertical axis (right, dashed line). The pattern of the

variance, with maximum variance offset from the peaks would be

expected if the peaks are varying in reflectance as wavelength.

of the pyroxene and olivine varies through the meteoritegroups. Our data reduction is designed to pick out thesefeatures to make comparison with physical propertieseasier.

5. Results

5.1. Minerals and spectral features

The abundance of the minerals pyroxene and olivinecan be determined by measuring the Band Area Ratio(BAR) and location of Band I (see Section 2). The resultsare often plotted by in the literature so different groupscan be identified and compared to asteroid spectra. Fig. 10shows a plot of results obtained from our spectra andfrom the NASA PDS spectra data sets. The figure showsthat the two meteorite data sets are in reasonable generalagreement; however there is some offset apparent. Webelieve that offsets between the two datasets can beexpected because Gaffey [25] took between one and threereflectance spectra from each meteorite solid surface.Each of our spectra is an average of 10 spectra taken fromdifferent locations on the meteorite. The differencesbetween the data sets may then be spot size effects dueto the varying mineral content over the surface of themeteorite.

In some cases Gaffey [25] took reflectance spectra of apowdered sample as well as from a solid surface. Stannernwas one such meteorite that had both powdered and solidsurfaces measured. In the case of Stannern it was notedthat our measurements more closely matched the reflec-tance spectra of a powdered surface than that of the solidsurface as measured by [25].

5.2. Density and band depth

Table 4 lists the new meteorite spectral measurementsmade in this work and values for selected spectralfeatures used in Fig. 10 and their physical properties.Physical properties for each meteorite are listed. The graindensity value was obtained from various references andwas either directly measured by knowing the porosity

Fig. 10. Band I minimum and Band Area Ratio (BAR) plotted. Both

datasets follow the olivine-pyroxene mixing line (not shown) except

the HEDs.

Table 4Properties of major features in meteorite reflectance spectra. There are 32 reflectance spectra from 26 different meteorites. A dash indicates there was no

feature present as defined in Fig. 2. Wellman 1 is taken from a matt surface and Wellman 2 is taken from a polished surface. Allegan has reflectance taken

from two different directions. Bjurbole 1–4 are reflectance spectra taken from four different fragments of the same meteorite. Alfianello 1 is taken from a

rough natural surface while Alfianello 2 is taken from a sawn surface. The density and magnetic susceptibility data are from measurements made by

Kohout et al. [27] and Kohout [29]. The asterisk (*) indicates meteorites common with the meteorite set obtained by Gaffey [25]. A blank cell means no

data is available. A dash (–) in a cell means it has the same value as the preceding row.

No. Meteorite Type Min I Min II BAR rbulk (kg m�3) M (10�8 m3 kg�1)

1 Johnstown Diogenite 917 1910 2.32 3140 461

2 Stannern (*) Eucrite 935 1989 1.43 2910 1196

3 Sioux County (*) Eucrite 928 1987 2.74 2740 80

4 Juvinas (*) Eucrite 946 1983 1.97 2880 70

5 Norton County Aubrite 1934 2970 12,222

6 Tieschitz (*) H3 920 1997 1.155 3230 11,753

7 Menow H4 939 1940 0.838 3090 30,688

8 Bielokrynitschie H4 937 1937 0.563 3447 29,994

9 Castalia (*) H5 928 1964 0.123 3420 13,941

10 Wellman 1 H5 929 1945 0.707 3710 20,326

11 Wellman 2 H5 960 1925 0.915 – –

12 Allegan 1 (*) H5 933 1936 0.989 3070 21,894

13 Allegan 2 (*) H5 933 1936 0.989 – –

14 Stalldalen H5 936 1924 0.62 3570 31,182

15 Nammianthal H5 938 1965 0.798 3490 531,573

16 Agen H6 949 1953 0.525 3384

17 Cape Girardeau H6 934 1789 0.675 3410 25,163

18 Vernon County H6 939 1876 0.62 3250 42,095

19 Souslovo L4 957 1950 0.536

20 Bjurbole 1 L4 956 1950 0.594

21 Bjurbole 2 L4 945 1950 0.439

22 Bjurbole 3 L4 990 1980 0.384

23 Bjurbole 4 L4 960 1944 0.586

24 Sevrukovo (*) L5 933 1986 0.924 3500 10,445

25 Ausson (*) L5 928 1948 0.744 3290 6910

26 Durala L6 972 1794 0.453 3320 8296

27 Pacula L6 957 1949 0.446 3260 7379

28 Kisvarsany L6 960 1954 0.389 3250 7700

29 Alfianello 1 (*) L6 974 1924 0.261 3260 8054

30 Alfienello 2 (*) L6 945 1780 0.435 – –

31 Nyirabrany LL5 949 1958 0.52 3190 1570

32 Allende (*) CV3 1018 1934 0.63 2957 342

Fig. 11. Values of correlation coefficients (Eq. (3)) comparing ordinary

chondrite spectra and physical properties (bulk density and magnetic

susceptibility for 57 ordinary chondrite meteorites, H and L). A weak

positive correlation is seen between the reflectance of the Band I and

Band II minimum reflectance and the physical properties.


and bulk density or calculated knowing the mineralcontent. The bulk density and magnetic susceptibilityare also listed.

To first order, one might expect that the density wouldincrease with increasing free iron as the abundance ofolivine and pyroxene (the reduced iron) decreases. Thisrelationship is known as Prior’s law or on a Urey–Craighplot which is more representative for specific groups ofmeteorites. This relationship would manifest in themeteorite spectra as a decrease in band depth as theabundance of reduced iron decreases. This is what we seein Fig. 11 because the band minimum reflectance isincreasing, with increasing density, and the interbandpeak is decreasing, with increasing bulk density. Theweakness of the correlation is probably due to the factthat bulk density is not directly representative of soliddensity due to pores. It would be best to use grain density.However, there are very few measurements of graindensity available such that model calculations are difficultto interpret with any degree of confidence.

The magnetic susceptibility would be expected toincrease with increasing metallic iron content e.g. seeRef. [27] and references therein. In Fig. 11 the reflectancevalues corresponding to the band minima are positively

correlated to the magnetic susceptibility which suggeststhat as the amount of reduced iron decreases the amountof free iron is increases as one would expect. However one

Fig. 13. Eigenvectors (EV) from PCA of the meteorite reflectance spectra

data set. EV-2 shows that the maximum variation in reflectivity is at

around 1 and 2 mm while EV-3 is most strongly correlated to variation in

reflectivity around 1.2 and 1.8 mm. EV-2 and EV-3 have been offset by

0.15 and 0.3, respectively, on the y-axis and the dotted lines are the

zero axes.


would expect the correlation with magnetic susceptibilityto be stronger than with the bulk density if the metalliciron was really increasing.

We conducted a similar analysis of the properties ofthe spectral features such as band depth, band locationand BAR. The physical properties tended to correlatestrongest with band depth and band position and mostweakly with gradient.

5.3. Texture effects and band depth

The result of our Principal Component Analysis of themeteorite reflectance spectra is shown in Fig. 12. The firstthree principal components were considered as they containthe majority of variance in the data. The correspondingeigenvectors for Fig. 12 together with that for Eigenvector 2are shown in Fig. 13. Eigenvector 1 has strong loadings closeto the locations in wavelength space corresponding to theabsorption bands at �1 and �2 mm (i.e. Bands I and II) thatare diagnostic of the mineral pyroxene. Eigenvector 2 has astrong loading at approximately 0.5, 1.2, 1.8, and 2.5 mm.Eigenevector 3 has a strong loading close to the location ofthe bands found at �1 mm and is relatively flat thereafter.Eigenvector 1 and 3 were used in Fig. 12 as Eigenvector 2has strong loading at numerous places that would makeinterpretation complicated.

The distribution of the meteorite groups in principalcomponent space are then easily explained by examiningthe eigenvectors 1 and 3. In Fig. 12 the carbonaceouschondrites cluster to the right of the diagram as they haverelatively flat spectra. The HEDs then cluster to the left asthey have relatively deep absorption bands. The spreadalong the y-axis for the ordinary chondrites could beexplained by the presence of olivine and pyroxene in

Fig. 12. Principle Component Analysis of 196 meteorite reflectance

spectra including 33 new measurements from this work combined with

163 measurements retrieved from NASA’s PDS [25]. The spectra have

been normalised and divided by their gradient as explained in Sect. 3.

The three meteorite clans (groups) are shown. Individual meteorites

from these clans are identified with their own symbols and labelled with

their surface condition. Wellman and Alfianello are from spectra

obtained from this work.

these meteorites whose relative ratio of abundance variesover the ordinary chondrite group.

From measurements by Gaffey [25] the reflectancespectrum from a rock surface has smaller absorption bandswhen compared to powdered surfaces. Also an increase inthe roughness of the rock surface will increases the banddepth. This agrees with measurements made by Harloff andArnold [28] and shown in Fig. 2. A similar effect occurs withthe ordinary chondrites. In our reflectance spectra, whencomparing a matt and a polished surface, the polishedsurface has deeper absorption bands than found in thereflectance spectrum from the matt surface which suggeststhat the polished surface is rougher.

One explanation suggested by Harloff and Arnold [28] forthis contradictory result may be that exposed pore spacesactually increase roughness after polishing. The Wellmanmeteorite was inspected with a microscope at 50� magni-fication. The polished surface was found to contain manymetal inclusions and there were some pits in the surfacethat look like they had rusted inner surfaces. The reflectancespectrum from the rock surface has deeper absorptionbands than found in the reflectance spectrum from thesawn surface as would be expected with a rougher surface.

5.4. Shock grade and average reflectance

Fig. 14 shows the PCA results using a combineddata set of real meteorites and the synthesised spectraintroduced in Section 3. One can see the achondritesoccupy a similar PCA space as the high-pyroxene synthe-sised meteorites in Fig. 4. The carbonaceous chondritesin Fig. 14 occupy a similar region as do the synthesisedcarbonaceous chondrites in Fig. 4. The ordinary chon-drites are constrained along the y-axis suggesting more orless equal amounts of olivine and pyroxene as in Fig. 4.However they are spread quite widely along the x-axis

Fig. 15. Shock grade plotted against average spectral reflectance. Within

individual meteorite groups the shock grade increases with decreasing

average reflectance. There is an anomalous point in the H5 group.

Fig. 14. Principal Component Analysis of real meteorite spectra. The PCA

was conducted on a combined set of artificial spectra shown in Fig. 4 and

real meteorite spectra (shown here). The data set was not normalised in

order to examine darkening effects. The carbonaceous chondrites are

approximately in the location of principle component space occupied by

the artificially generated carbonaceous chondrites in Fig. 4. The HEDs occupy

an area corresponding to high pyroxene content as would be expected.


(principal component 2) which suggested they vary a lotin average reflectivity.

Fig. 15 shows the shock level of meteorites against theaverage reflectance of their spectra. An interesting trendmay be apparent in that the reflectance spectra withinmeteorite groups become darker with increasing shocklevel. The low number of meteorites with both shock gradesand reflectance spectra is very small so this interpretation isproblematic. However it may be an explanation to why adarkening agent is required to provide a similar distributionof synthesised spectra (see Fig. 4) to the meteorite spectra inprincipal component space.

There may be several reasons for darkening related toshock or inclusion or varying mineral content such as theinclusion of free metals or carbon. The darkening processcould be due to the shock received during ejection from the

parent body. In fact the process of shock darkening is wellknown e.g. [19] and is due to shock induced production oftiny inclusions within silicates. Some highly shocked ordin-ary chondrites are fine grained and almost black.

6. Conclusions

Relationships between the reflectance spectra and phy-sical properties of bulk density and magnetic susceptibilitywere found to be correlated positively with reflectanceabsorption band minima and negatively correlated withband maxima in the ordinary chondrites. The sign of thecorrelation was expected but the magnitude of the correla-tion for magnetic susceptibility was surprisingly weak.

The meteorites, within their groups, were found tohave some agent or process acting to darken the spectraacross the whole wavelength range. A trend was noticedthat as shock grade increased that the average reflectancespectra decreased. Surface texture was found to have aneffect comparable in magnitude to the offset between thetwo data in terms of their spectral features. We note thata polished surface had the surprising effect of deepeningthe absorption bands. This may be due to micro cracksgenerated during the polishing process together with theexposure of pore holes.

PCA was found to be a good tool for classificationpurposes when applied to meteorite reflectance spectraand could easily distinguish between the major meteoriteclans. It was found to be a good technique for comparingmeteorites to each other and identifying interestingtrends especially when combined with a dataset ofartificial meteorite spectra synthesised out of knownmineral reflectance spectra.

Particularly the abundance of pyroxene in achondriteswas noticeable and the tight grouping of the carbonac-eous chondrites gave away their presence in the data set.Interestingly there appeared to be a darkening agent,acting across all wavelengths that effected the distribu-tion of the achondrites in principal component space.

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