Estimating Modal Abundances From the Spectra of

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. E5, PAGES , MAY 25, 1993 Estimating Modal Abundances From the Spectra of Natural and Laboratory Pyroxene Mixtures Using the Modified Gaussian Model JESSICA M. SUNSHINE AND CARLg M. PIETERS Department of Geological Sciences, Brown University, Providence, Rhode Island Spectra of samples containing multiple pyroxene components are explored as a function of modal abundance using the modified Gaussian model (MGM). The MGM, unlike other approaches, allows spectra to be analyzed directly, without the use of actual or assumed end-member spectra and therefore holds great potential for remote applications. Quantitative understanding of the spectral characteristics of lithologies which include mixtures of two or more pyroxenes is fundamental to analyzing remotely acquired spectra of terrestrial and extra-terrestrial targets. A series of mass fraction mixtures created from several different particle size fractions were analyzed with the MGM to quantify the properties of pyroxene mixtures as a function of both modal abundance and grain size. Results of this MGM analysis indicate that band centers, band widths, and relative band strengths of absorptions from individual pyroxenes in mixture spectra are largely independent of particle size. In addition, systematichanges in relative band strength as a function of modal abundance are observed, which yield particle size independent relationships that can be used to estimate modal abundances from the spectra of unknown samples. Spectra of natural samples exhibiting both zoned and exsolved pyroxenes are evaluated as examples of spectra likely to be measured from actual lithologies. Spectral properties of both pyroxene components are resolved in exsolved samples using the MGM, and modal abundances are accurately estimated to within 5-10% without predetermined knowledge of the end-member spectra. In contrast, the spectra of samples exhibiting zoned compositions are consistent with one dominant pyroxene component. This single pyroxene component has anomalously wide absorption bands and appears to represent an average composition. INTRODUCTION Pyroxenes are some of the most common rock forming minerals in the solar system. As such, remotely obtaining compositional data about pyroxenes could greatly enhance many geologic and petrologic studies, particularly those involving extra-terrestrial bodies. In visible and near-infrared reflectance spectra, pyroxenes are readily identifiable from their characteristic Fe +2 electronic transition absorption bands located near 1 I.tm and 2 I.tm [e.g., Bums, 1970; Adams, 1974, 1975]. This unique combination of absorption bands has led to the remote identification of the presence of pyroxenes on the surfaces of many solid bodies in the solar system [e.g., McCord et al., 1988]. The spectral properties of pyroxenes have been studied intensively in the past [Burns, 1970; Bell and Mao, 1972; Adams, 1974, 1975; Hazen et al., 1978; Rossman, 1980; Straub et al., 1991] and have been recently reevaluated and synthesized by Cloutis and Gaffey [1991]. These studies have convincingly shown that pyroxene spectra vary systematically as a function of major element composition. Absorptions in orthopyroxene occur at shorter wavelengths than those in clinopyroxenes, and generally move towards longer wavelengths with increasing iron content. Relationships between clinopyroxene spectra and iron content are more complex but still systematic [Cloutis and Gaffey, 1991]. These trends are useful summaries of the variability of individual pyroxene spectra with composition; however, they do not address the spectral properties of rocks which include multiple pyroxene compositions, as often occur in nature. The spectra of orthopyroxene (OPX) and clinopyroxene (CPX) mixtures have been qualitatively described by previous researchers [Adams, 1974; Singer, 1981; Cloutis and Gaffey, 1991] as having properties that are intermediate to their end-members. However, as noted by Cloutis and Gaffey [1991], spectra of pyroxene mixtures have yet to be studied intensely and their spectral properties remain poorly understood. The study presented here explores in further detail the spectra of pyroxene mixtures by examining the relationships between absorption bands and composition. Preliminary results of this research were presented by Sunshine and Pieters [1991]. Analysis begins with spectra for a suite of OPX-CPX mass fraction mixtures using samples created from several different particle size fractions. These spectra are used to quantify the properties of pyroxene mixtures as a function of both modal abundance and grain size. Analysis of these laboratory spectra yields several particle size independent relationships, one of which can be used to estimate modal abundances from the spectra of unknown samples. Spectra of natural samples exhibiting both zoned and exsolved pyroxenes are evaluated as examples of the types of spectra likely to be measured in actual lithologies. Although this study will examine the applicability of the MGM approach using relatively simple natural samples, it is a necessary first step toward extracting compositional data from pyroxenes in more complicated natural lithologies which are likely to include many other mineral constituents. Copyright 1993 by the American Geophysical Union. Paper number 93JE O /93/93JE BACKGROUND The presence of multiple pyroxene compositions can be qualitatively identified in reflectance spectra and have been described as having spectral properties intermediate to those of 9075

2 9076 SUNSH1NE AND PIETERS: ESTIMATING PYROXENE ABUNDANCES OPX and CPX [Adams, 1974; Singer, 1981; Cloutis and Gaffey, 1991]. A series of spectra of mass fraction mixtures between OPX and CPX are shown as examples in Figure 1. In the 1 region, individual OPX and CPX absorption bands are often not visually resolvable, but manifest as a single broad, and often asymmetric, composite band. The minimum of the overall absorption in the 1 Ixm region of pyroxene mixture spectra is intermediate between those found in OPX and CPX spectra. In the 2 Ixm region, the OPX and CPX absorption bands are often sufficiently well separated that both can be visually resolved in pyroxene mixture spectra, except in cases involving relatively small amounts (--<20%) of one of the end-members (cf. Figure 1). Examination of spectra of pyroxene mixtures has also revealed that these spectra, like those of most mineral mixtures, are not simple linear combinations of their end- b rs0 1.,0 z O thopyroxene 85/15 Opx/Cpx 75/25 Opx/Cpx 60/40 Opx/Cpx 50/50 Opx/Cpx 40/60 Opx/Cpx 25/75 Opx/Cpx 1 5/85 Opx/Cpx Clinopyroxene,/-"" mi on pa ticles ?.30 Orthopyroxene 85/15 Opx/Cpx 75/: ) 50paJCpx 60/40 Opx/Cpx 50/50 Opx/Cpx 40/60 Opx/Cpx 25/7 50px/Cpx 15/85 Opx/Cpx Clinopytoxene v ai on particles _ ?.30 Ofthopyroxene 85/1 50px/Cpx 75/25 Opx/Cpx 60/40 Opx/Cpx 50/50 Opx/Cpx 40/60 Opx/Cpx 25/7 50px/Cpx 1 5/85 Opx/Cpx Clinopyroxene Fig. 1. Reflectance spectra of the cnstatitc (OPX) and clinopyroxene (CPX) end-members and their seven mass fraction mixtures. (a) The <45 pxn particle size suite, (b) Ixm particle size suite, and (c) pxn particle size suite. The reflectance scale is noted for each CPX spectrum. For clarity, each successive spectrum is offset 5% in reflectance from the previous spectrum. member spectra. In particular, it has been noted that OPX absorptions can dominate pyroxene mixture spectra over a wide range of modal abundances [Singer, 1981; Cloutis and Gaffey, 1991]. In addition, mixtures of pyroxenes that are close in composition or continuously varying, such as zoned pyroxenes, have spectra that apparently represent an average composition and consist of broadened absorption bands [Adams, 1974; Cloutis and Gaffey, 1991]. To date, very little quantitative work has been carried out on the spectral systematics of pyroxene mixtures. Johnson et al. [1983] were able to successfully model the nonlinearity of pyroxene mass fraction mixture spectra, and several other mineral mixtures, using Hapke's [1981] radiative transfer theory. The Hapke approach is a powerful method for determining mass fractions from mixture spectra, provided the spectra of individual end-members are known [e.g., Clark and Roush, 1984; Clark, 1987; Nelson and Clark, 1988; Mustard and Pieters, 1989; Johnson et al., 1992]. However, in most remote applications, obtaining spectra of isolated endmembers, and in the case of pyroxene mixtures, spectra of individual pyroxenes, is very difficult, if not impossible. In addition, Hapke theory is explicitly dependent on grain size, a property that is also difficult to accurately assess remotely. Spectral properties of unknown end-members can be approximated by samples measured in the laboratory and a probable range of grain sizes of remote surface can be estimated. However, given the complexity of natural systems, it would be very difficult to prepare spectral libraries that include analogs which have the exact major element chemistry, minor element chemistry, and physical properties of the actual end-members. Although, spectra of different grain sizes can be synthesized from end-members of a given grain size [Johnson et al., 1992], obtaining accurate spectral analogs to the actual lithologic constituents would be particularly difficult for extraterrestrial surfaces, which undoubtedly form under different conditions and experience different weathering processes than any terrestrial samples. Even small changes in the chemistry will effect the shape, position, and strength of absorption features. Given the highly dependent nature of Hapke theory on absolute albedo and absorption features, as well as grain size, the use of spectral analogs and Hapke theory to estimate mixing ratios of unknown materials is inherently limited in accuracy. An alternative and complimentary approach to analyzing mixture spectra, which does not rely on the use of actual endmembers or spectral analogs, but extracts information from the measured spectrum itself, would therefore be useful in many situations. In previous studies, Sunshine et al. [1990] have reevaluated, tested, and modified the Gaussian model that was been used extensively by many authors [Bums, 1970; Smith and Strens, 1976; Farr et al., 1980; Clark, 1981; McCord et al., 1981; Singer, 1981; Clark and Roush, 1984; Gaffey, 1986; Huguenin and Jones, 1986; Roush and Singer, 1986]. This modified Gaussian model (MGM) more accurately describes the shape of electronic transition absorptions and was used to successfully isolate individual OPX and CPX absorption bands in pyroxene mass fraction mixture spectra. To date, the MGM has also been used to quantify the compositional systematics in the spectra of olivines [Sunshine and Pieters, 1990, 1993] and actinolites [Mustard, 1992]. The MGM refines the Gaussian approach by more accurately adhering to the physical processes that produce electronic transition absorptions. Electronic transition absorptions

3 SLrNS AND PIETERS: ESTIlVL, G PYROXENE ABUNDANCES 9077 occur when photons interact with ions in distorted crystal field TABLE 1. Microprobe Analyses of Pyroxene End-Members PP-CMP-21 PE-CMP-30 PA-CMP-47a PA-CMP-47b sites [Bums, 1970; Marfunin, 1979]. The energy, or CPX OPX CPX OPX wavelength, distribution of the absorption is determined by the asymmetry of the site the bond type, and the average distance SiO between the ion and its surrounding ligands, the average bond TtO length. The distribution of absorption energies due to a single A crystal field site is expected to be similar to a damped harmonic Fe203 (as FeO) (as FeO) (as FeO) (as FeO) FeO oscillator, or Lorentzian in shape [Liou, 1980]. However, in MgO natural mineral or lithologic samples, there are millions of unit CaO cells, and thus millions of crystal field sims. Although similar in general character, these crystal field sites will not be identical because of defects, vacancies, and substitutions. Cr203 Na20 K These irregularities, coupled with thermal vibrations, will give MnO Total rise to a statistical distribution of average bond lengths. Given the number of interactions, the central limit theorem of Wo statistics argues that the distribution of average bond lengths En should be Gaussian. Summing over a large number of Fs interactions and the irregularity of geologic samples produces a PP-CMP-21 and PE-CMP-30 are, respectively, the clinopyroxene Gaussian distribution, regardless of the underlying distribution (CPX) and the enstatite (OPX) end-members used to create the mass of any single crystal field site. Based on Gaussian distribution of average bond lengths, the energy or wavelength of fraction mixture suites. The clinopyroxene was separated from a Hawaiian volcanic bomb and the enstatite is from Webester, North absorptions can be determined, if the relationship between Carolina. PA-CMP-47a and PA-CMP-47b are, respectively, the CPX and OPX compositions of the exsolution lamellae in the exsolved average bond lengths and energy are known. Sunshine et al. pyroxene crystal from the Moses Rock Diatreme. [1990] showed empirically that energy and average bond lengths are inversely proportional; a conclusion that suggests that the energy in a crystal field site is dominated by the Coulombic potential energy. Using this physical framework, fraction mixtures are shown in Figure 1. Spectra for all Sunshine et al. [1990] reformulated the mathematics of the samples used in this study are obtained from to Gaussian approach to derive modified Gaussian distributions. at 5 nm sampling resolution using the RELAB bi-directional These modified Gaussian distributions are the first accurate spectrometer [Piemrs, 1983]. A standard viewing geometry of 30 ø incidence and 0 ø emission angles (measured from the mathematical description of the shape of isolated electronic transition absorption bands. Modified Gaussian distributions vertical) was chosen for these experiments. will be used to model absorption bands throughouthe analysis All spectra are analyzed with MGM as described in detail by of pyroxene mixture spectra presented here. Sunshine et al. [1990]. The MGM model deconvolves spectra into a series of modified Gaussian distributions, each EXPERIMENTAL APPROACH representing an individual electronic transition absorption band. Mathematically, each absorption band is described by a A series of reflectance spectra of nine mass fraction band strength, band center, and band width. Thus, each mixtures between enstatite (OPX) and clinopyroxene (CPX) were created for this study. The composition of the pyroxene end-members are shown in Figure 2 and listed in Table 1. This spectral data set includes a 45-75!xm particle size suite used in previous studies [Sunshine et al., 1990], as well as two additional particles size suites, <45!xm and !.tm. Spectra of all three particle size suites of pyroxene mass absorption is represented by three model parameters. The absorption bands are all superimposed onto a continuum or baseline, which is modeled as a straight line in energy, and represented by two additional parameters; a slope and an offset. Although modeling is carried out in natural log reflectance and energy [see Sunshine et al., 1990], for convenience, all MGM fits to spectra will be shown as a function of wavelength. Previous analyses have utilized an iterative nonlinear least Pyroxene Compositions squares algorithm [Kaper et al., 1966; Sunshine et al., 1990, c Appendix A] to deconvolve spectra into modified Gaussian + distributions. However, the work presented here is based on a A new fitting routine which implements the modified stochastic inversion method developed by Tarantola and Valette [1982]. The Tarantola and Valette approach allows reasonable bounds to be placed on acceptable values for the model parameters. For example, one can constrain the band centers to lie between 0.0 Mg:,Si O /. Fe Si O and 3.0!xm and the band strengths to be negative (i.e., no positive absorptions). In addition, by providing different ranges for each absorption band, one can weight the uncertainty of different regions of the spectrum. For example, absorptions on the ultraviolet edge, for which we have only Fig. 2. Compositions of pyroxenes used in this study (see Table 1): inverted triangle is the the enstatite (OPX) end-member used in mass fraction mixtures; triangle is the clinopyroxene (CPX) end-member used in mass fraction mixtures; plus sign and cross are the two pyroxenes in the exsolution lamellae of the pyroxene crystal from Moses Rock Diatreme, and the compositional zoning trends for the lunar clinopyroxene from Hollister et al. [1971] (solid lines represent continuous zoning and dashed lines connect points on opposites sides of chemical discontinuities). partial data, may be constrained to lie between 0.0 and 3.0!xm, while an absorption near 1.0!xm might be forced to lie between 0.5 and 1.5 gtm. Applying even such loose constraints to the model parameters damps the fitting process and prevents physically unreasonable solutions from being obtained. The

4 9078 SUNSHINE AND PIET S' ESTIMATING PYROXENE ABUNDANCES Tarantola and Valette approach leads to more rapid and fully reproducible solutions, and is thus a marked improvement over previous methods. LABORATORY MASS FRACTION MDCI URES Sunshine et al. [1990] previously examined the gm particle size suite of laboratory OPX-CPX mass fraction mixtures with the MGM. MGM analyses of the OPX and CPX end-members for this suite are shown in Figures 3a and 3b, respectively. The derived model parameters for these fits are listed in Table 2. Using the MGM, the spectra of both OPX and CPX can be modeled with seven absorption bands. The strongest absorptions, which dominate the 1 gm and 2 gm regions, occur at 0.91 gm and 1.83 gm for OPX and at 1.01 gm and 2.27 gm for CPX. These primary pyroxene absorptions result from electronic transitions of Fe +2 in distorted M2 octahedral sites [e.g., Burns, 1970; Marfunin, 1979]. The remaining weaker absorptions have been attributed to variety of processes, including electronic transitions of Fe +2 in M I micron particles I/ micron particles Fig. 3. Representative MGM deconvolutions of pyroxene end-member spectra. (a) The grn particle enstatite (OPX) end-member. (b) the grn particle clinopyroxene (CPX) end-member. From top to bottom in each figure: The residual error between the modeled spectrum and the actual spectrum (offset 10% for clarity), individual modified Gaussian distributions representing absorption bands, the continuum or baseline onto which these distributions are superimposed (dashed line), and the modeled spectrum plotted on top of the actual spectmm. Model parameters for these fits are listed in Table 2. sites, electronic transitions of other elements, spin forbidden absorptions, and/or charge transfer absorptions [Bums, 1970; Adams, 1974, 1975; Marfunin, 1979; Rossman, 1980; Straub et al., 1991]. For example, the absorption between 0.7 gm and 0.8 I. tm, present in this CPX spectrum, has been attributed to a charge transfer between Fe +2 and Fe +3 ions in pyroxenes [e.g., Rossman, 1980; Straub et al., 1991] and the absorption near 0.65 gm in this CPX have been attributed to Cr +3 [e.g., Bums, 1970; Adams, 1974; Marfunin, 1979; Rossman, 1980]. Although the MGM fits to the CPX and OPX spectra are quite reasonable, there is a non-random residual error in the 1 gm region of the MGM model of the OPX spectrum (Figure 3a). Note that this error is symmetric with respect to the modeled absorption band, i.e., that the peak error occurs at 0.90 I. tm while the center of the model absorption band is located at 0.91 I. tm. This systematic pattern in the residual error is diagnostic of band saturation. Band saturation occurs in reflectance spectra for absorptions involving large particle sizes and/or large absorption coefficients [cf. Clark and Roush, 1984; J. M. Sunshine et al., manuscript in preparation, 1993]. Errors due to band saturation are in sharp contrast to those that result from missing absorption bands. As discussed in later sections, missing absorption bands lead to peak errors that are larger in magnitude and that are offset from the center of the modeled absorption bands. Thus, while saturation leads to an increase in residual error, the symmetry of the resulting error is such that saturation can easily be diagnosed, yet does not effect the results of the modeling process or hinder interpretations. After successfully modeling the OPX and CPX spectra, Sunshine et ale [1990] also examined the spectra of OPX and CPX mass fraction mixtures. Qualitatively, spectra of the mass fraction mixtures, regardless of composition, are all dominated by absorptions near 1 gm and 2 gm (see Figure lb). As expected, these absorption features appear to move toward longer wavelengths with increasing proportion of CPX [Adams, 1974, 1975; Cloutis and Gaffey, 1991]. However, quantitative analysis of the gm suite using the MGM showed that the band centers of the primary absorptions (bands 5,6,8, and 9) remain essentially fixed, at 0.91 and 1.83 gm for OPX, and 1.02 and 2.29 gm for CPX, and that only the relative band strengths change as a function of CPX abundance. For example, MGM deconvolution of the 75/25- mixture spectrum (Figure 4c and Table 3) reveals that the absorption features near both 1 gm and 2 gm are each composed of two major absorption bands. The derived absorption bands are located at the same wavelengths as those in the OPX (large arrows; bands 5 and 8) and CPX (small arrows; bands 6 and 9) end-members. As anticipated from the larger proportion of OPX in this sample, the absorptions corresponding to OPX are stronger. In contrast, the 25/75- mixture spectrum (Figure 4d and Table 3) is composed of the same absorption bands, but is dominated by the absorption bands associated with CPX. Figure 5b, a summary of the band strengths and band centers for the entire gm particle size suite, illustrates a major conclusion of Sunshine et al. [1990], that while the relative band strengths systematically change with the proportion of CPX, the band centers remain essentially constant. A similar experiment is carried out here for the <45 gm and gm particle size suites of mass fraction mixtures. Model parameters derived with the MGM for the OPX and CPX end-member spectra in all three particles size ranges are listed in Table 2. Note that the fits to the OPX spectra, which include the effects of band saturation, have relatively high residual

5 SUNSHINE AND PIETF. RS: ESTIMATING PYROXENE ABUNDANCES 9079 TABLE 2. Model Parameters of Absorption Bands in the MGM,Fits to the OPX and CPX End-Members Orthopyroxene Orthopyroxene Orthopyroxene <45 micron particles micron particles micron particles Continuum E E E-6 Center Width Strength Center Width Strength Center Width Strength Band Band Band Band 4 Band Band 6 Band Band Band 9 Band rms error, % Continuum Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Band 8 Band 9 Band 10 Clinopyroxene Clinopyroxene <45 micron t articles micron r articles E E-5 Center Width Strength Cent, er Width Strength Clinopyroxene micron particles E-5 Center Width Strength 33O O.53 65O 158 -O O O rms error, % The values listed for each continuum are the offset and slope of a straight line in energy and natural log reflectance. Each absorption band is described by a center (in nm), a full width at half maximum (in nm), and a strength (in natural log reflectance). The rms error between the modeled spectrum and the actual spectrum provides a measure of the quality of the fit. errors and that this error increases with increasing particle size, yet does not effect the derived absorption band parameters. MGM deconvolutions for the 75/25 and 25/75 members of all of the particle size suites are shown in Figure 4 and the derived band parmeters are listed in Table 3. Comparisons of the model fits to these spectra show that the absorption band characteristics are quite similar for all particle sizes. As can be seen in Figure 5, absorption features in the mass fraction mixture spectra all appear to be composed of absorption bands that directly correspond to those in the OPX and CPX end-members. The band centers of these absorptions are essentially the same for all particle sizes, with the only difference between particle size suites being the absolute band strengths. These analyses suggest that absorption band centers are particle size independent and are located in the same positions as the band centers of absorptions in the end-member minerals. The band widths of individual absorptions in pyroxene mass fraction mixtures can also be evaluated. Figure 6 shows the band widths for the primary absorption bands as a function of modal abundance for the gm particle size suite. The width of each absorption band is determined by a complex function of the composition of the sample, the absorption site, of wavelength, a more complete study of a variety of pyroxene compositions would be necessary to determine the cause of this relationship. Despite the decrease in absolute width with increasing wavelength, Figure 6 shows that the width of each absorption band does not vary significantly as a function of modal abundance. Comparisons of Figures 6a, 6b, and 6c, which show similar data for all particle sizes, indicate that band widths are also largely independent of particle size. These apparently invariant band widths, as a function of both particle size and modal abundance, add to the results from the band center analysis which indicate that the absorptions in pyroxene mixture spectra are determined by those in the endmember spectra. While band centers and band widths remain fixed, the strengths of the primary absorption bands in the OPX-CPX mass fraction mixtures appear to vary systematically with modal abundance. As can be seen in Figures 4 and 5, the strength of each absorption band changes monotonically with percentage of CPX for all particle size suites. The primary OPX absorptions near 1 gm and 2 gm (large arrows) become weaker with increasing CPX content, while the primary CPX absorptions (small arrows) become stronger. This effect can be quantified by examining the relative and the partitioning of ions in different sites. While there strengths of the primary pyroxene absorption bands, i.e., by appears to be a systematic change in band width as a function calculating the "component band strength ratio" (CBSR),

6 ß 9080 SUNSHINE AND PIEW S: ESTIMATING PYROXENE ABUNDANCES MGM Fit to 75/25 Mixture residual MGM Fit to 25/75 Mixture residual t -... t ' -0.s j _ -. o -. o a b o.5o/,,, i,,' I'' ' I''' I ''' I ''/ t... / M Fit o.5o/,,, I''' to 25/7 I''' PX I''' Mixture I''' I '' MGM Fit to 75/25 OPX/OPX Mixture....,.., -I 50PX/O residual o.oo o.oo a) a) CE CE s0 -.s0 c I:/ micron. particles _2.501,,,,,,,,,,,, i d ø'5ø/''' [''' ' '' :''''' ' ' ' / ø'5ø/''' ''' ''' ''' '''' ' ' / o.oo o.oo -o.5o -.oo - -o.5o = -.oo -.s0 -.s0 J -zoo -zoo 25 micron particles i -z5o ,, I,,, I,,, I,,, I,, ' f Fig. 4. Representative MGM deconvolutions of spectra of mass fraction mixtures: (a) 75/25 <45 grn size particles, (b) 25/75 <45 gun size particles, (c) 75/ Ixm size particles, (d) 25/ Ixm size particles, (e) 75/ gun size particles, (D 25/ gun size particles. Large arrows indicate absorption bands from the OPX component and small arrows indicate absorption bands from the CPX component. Model parameters for these fits are listed in Table 3. Curves are as in Figure 3. where CBSR --- Band Strength of OPX component/ Band Strength of CPX component. Using the MGM, the CBSR can be derived directly from a spectrum of an unknown pyroxene mixture for both the 1 and 2 grn regions. Note that calculation of the CBSR therefore requires no predetermined knowledge of the end-member pyroxene spectra or compositions. As shown in Figure 7, the CBSR in pyroxene mixture spectra appear to vary logarithmically with modal abundance. Comparisons of Figure 7a and 7b reveal that the variations between CBSR and modal

7 SUNSHINE AND PIETERS: ESTIMATING PYROXENE ABUNDANCES 9081 abundance are quite similar for both the 1 grn and 2 grn regions. probe analyses of each of the two pyroxenes in this exsolved The logarithmic character of the CBSR is consistent with sample are given in Table 1 and illustrated in Figure 2. Since previous qualitative assessments [Singer, 1981; Cloutis and this pyroxene sample is composed of an intimate mixture of G affey, 1991 ]. two discrete pyroxenes, it is a natural parallel to the laboratory Although the absolute band strengths vary for each particle mass fraction mixtures. In addition, because the exsolution size suite (Figure 5), the correlation between relative band lamellae in this sample are physically inseparable it is strengths (CBSR) and modal abundance holds for each particle impossible to obtain spectra of the two pyroxene endsize (Figure 7). A close inspection of Figure 7 reveals that members. This exsolved sample therefore provides a parallel these variations are nearly identical for each of the three to many remote situations where end-member spectra would be particle size suites examined. To test whether this relationship unavailable. However, since the MGM, unlike other holds for larger particle sizes, an additional sample was prepared. Results from MGM analysis of a spectrum of 50/50 approaches, does not rely on end-member spectra, the lack of end-member spectra will not hinder analysis. using Ixm size particles are shown to be consistent with the results from smaller particle sizes (Figure 7). Therefore, the CBSR in pyroxene mixture spectra appear to be independent of particle size. As such, the data from all particle size suites can be combined to describe a single quantitative relationship between CBSR and modal abundance, as shown by the curves representing the best fits to all the data in Figure 7. Note that these curves tend toward positive and negative infinity as they approach the end-member compositions. This behavior is consistent with the definition of CBSR which yield values of zero and infinity, positive and negative infinity in log (CBSR), for 100% OPX and 100% CPX, respectively. These analyses demonstrate that the MGM can be successfully used to extract the spectral signatures of pyroxene end-members from spectra of OPX-CPX mass fraction mixtures. The systematic relationships among model parameters observed in these laboratory controlled samples also have several implications for modeling spectra of natural pyroxenes. First, the particle size independence of band centers, band widths, and relative band strengths (CBSR's) suggests that particle size effects can be considered minimal when modeling spectra of unknown samples. Second, the similarity of the CBSR in the 1!xm and 2!xm regions can be used to reduce the number of free parameters required to model spectra. This coupling of parameters could be particularly important for modeling spectra of natural surfaces which may have lower signal to noise ratios and/or may consist of more complicated lithologies, that include more complex overlapping absorption bands. For example, one could determine the presence of two pyroxenes absorptions from data in the 2!xm region and derive their CBSR with the MGM. The CBSR determined from the 2 tm region can then be used to constrain the relative strengths of the pyroxene absorptions in the more complicated 1 gm region. Finally, the particle size independent correlation between CBSR and modal abundance for absorption bands near 1 gm and/or 2 gm (Figure 7) provides a method for estimating modal abundances of unknown pyroxene mixtures with the MGM. The spectrum of <250 I. tm particles of this exsolved pyroxene crystal includes complex absorption features near both 1 I. tm and 2 I. tm (Figure 8). The MGM fit to the spectrum using single absorption in the 1 and 2 I. tm regions produces an unacceptable fit (Figure 8). Note in particular, that the residual error is not only quite high, but that in both the 1 grn and 2 I. tm regions the maximum errors are offset from the derived absorption bands. The peak residual errors occur at 0.98 and 2.05 gxn while the band centers are located at 0.93 and 1.8 I. tm. This offset between the residual error and the derived absorption band centers is typical for poor model fits and is diagnostic of the presence of additional bands. Including two additional absorption bands, one in the 1 I. tm and one in the 2 gm region, as indicated from examination of the residual, produces an excellent fit as shown in Figure 9. Probable absorption bands representing both an OPX component (large arrows; bands 5 and 8) and a CPX component (small arrows; bands 6 and 9)can be identified from this MGM aleconvolution. The band parameters for all nine of the absorption bands (1-9) derived from with MGM are given for the exsolved pyroxene crystal in Table 4. Note that unlike the mass fraction mixtures (Table 3), the fit to the exsolved pyroxene crystal does not include an absorption between 0.7 I.tm and 0.8 I.tm. This lack of a Fe+2/Fe +3 charge transfer band implies that the sample has not be subject to significant oxidation. Based on the MGM analysis of laboratory mass fraction mixtures discussed above, the modal abundance of CPX in the natural pyroxene mixture can be estimated by determining the CBSR of the OPX and CPX absorption bands. Data from the 1 I.tm region and the ratio of the strength of Band 5 to Band 6 (-0.63/-0.32 = 1.98), in conjunction with the average of the logarithmic relationships for all particle sizes in the laboratory mass faction mixtures (Figure 7a), yields a modal abundance of 47_+4% CPX. Similarly, data from the 2 gm region (Figure 7b) and the ratio of the strength of band 8 to band 9 (-0.47/-0.20 = 2.35) suggests a modal abundance of 42_+3% CPX. These estimated abundances of CPX are remarkably self-consistent and in good agreement with visual estimates of a thin section of the sample as approximately 50% CPX. Modal estimates of 52% were also derived from over 350 NATURAL PYROXENE MIXTURES: micro-probe analyses taken along two transects perpendicular EXSOLVED PYROXENE CRYSTAL to the exsolution lamellae. It therefore appears that the modal abundances derived with the MGM are accurate to within 5-10% The successful quantification of modal abundances with the MGM in laboratory pyroxene mixtures suggests that the MGM for this sample. approach would be useful for analyzing natural pyroxene However, it should be noted that the compositional mixtures. A good candidate for MGM analysis is an apparently differences between the two pyroxenes in the exsolved mantle-derived pyroxene crystal from the Moses Rock pyroxene crystal from Moses Rock and those used in the Diatreme in southwestern Utah. Equilibrium cooling laboratory mass fraction mixtures are not terribly large, as conditions in the mantle led to the formation of 25-50!xm wide indicated in Figure 2 and Table 1. The pyroxenes in the exsolution lamellae in the Moses Rock sample, which alternate exsolved sample contain more aluminum than those used in the in composition between OPX and CPX. The results of micro- mass fraction mixtures, but their iron, magnesium, and calcium

8 ,, 9082 SUNSHINE AND PIETF S: ESTIMATING PYROXENE ABUNDANCES TABLE 3. Model Parameters of Absorption Bands in the MGM Fits to Representative Mass Fraction Mixture Spectra 75/25 75/25 75/25 <45 micron particles micron particles micron particles Continuum E E E-6 Center W. idth Strength Center Width Strene_th _ Center W_ ig_th Strength Band Band Band Band Band Band Band Band Band Band rms error, % /75 <45 micron particles 25/ micron particles 25/75 75-!25 micron particles Continuum E E E-6,, Center Width Strength Center Width Strength Center Width Strength Band Band Band Band Band Band Band Band Band Band rms error, % Values as in Table 2. contents are quite similar. Significant differences in found in lunar basalts [Papik etal., 1976]. MGM analyses composition, particularly iron content, will undoubtedly result with the spectra of pyroxenes from lunar basalts are therefore in changes in absolute band strengths and the exact values of carried out here to determine whether continuous compositional the CBSR. Compositional differences are, however, unlikely variation at the scale present in these pyroxenes can be to alter the logarithmic nature of the variations of CBSR as a detected spectroscopically. A clinopyroxene separate from function of modal abundance. Given the systematic variations lunar basalts [Adams and McCord, 1971], which of pyroxene spectra with composition, should be possible to exhibits continuous compositional zonation (Figure 2) model the compositional effects on CBSR. Nevertheless, these [Hollister et al., 1971], was chosen for this analysis. complexities need be evaluated in further detail before the The MGM deconvolution of the spectrum of <45 MGM can confidently be used to estimate modal abundances on particles of the CPX separate from is shown Figure 10 greatly from mixtures whose those examined pyroxene compositions differ here. and the derived model parameters are listed in Table 5. As expected from the reducing conditions on the moon, there is no Fe+2/Fe +3 charge transfer band in the model fit to this lunar LUNA CLINOPY OX The MGM has been a useful tool for analyzing the spectra of the laboratory mass fraction mixture spectra, as well as the natural exsolved pyroxene crystal. These samples consist of intimate mixtures of two discrete compositions, which in the case of the natural exsolved sample, occur due to near equilibrium cooling conditions. In contrast, many natural pyroxenes which form under relatively rapid cooling conditions, usually at the surface, do not reach equilibrium, and NATURAL PYROXENE MInTroES: }xm region of this MGM fit which is completely symmetric with respect to the absorption band. The peak residual error occurs at }xm and the absorption band is centered at }xm. This symmetric error is in sharp contrast, in both magnitude and character, to the error obtained in fitting the exsolved pyroxene with only one pyroxene (Figure 8). Unlike Figure 8, the symmetric residual error is not due to the presence of additional discrete pyroxene components, but as is the case for the larger particle size mass fraction mixtures, is likely the CPX spectrum. There is however, a small residual error in the 1 therefore exhibit continuous changes in composition. a result of slight saturation of the 1 }xm band. This Continuous compositional zonation is common in pyroxenes interpretation is supported by the lack of a residual error in the

9 -- SUNSHINE AND PIErE'RS. ESTIMATING PYROXENE ABUND S 9083 Strengths )f Pyroxene Absorptions ' I ' I I ' I ' I ' I ' I Primary c: c a t <45 micron particles I I ' I. I, I, I, I ß I Band Center in Microns t 2.40 A-Orthopyroxene B-85/15 C-75/25 D-60/40 E-50/50 F- 40/60 G-25/75 H-15/85 I-CIInopyroxene 0.40 "-' c: Strengths )f ' ' ' ' ' ' ' ' ' ß I " I C 't o-. : B Primary Pyroxene Absorptions,i micron particles,.;0 uo,.40,.;0 0, I, I, i,, I, I, Band Center in Microns A-Orthopyroxene B--85/15 C-75/25 D-60/40 E-50/50 F-40/60 OFOVCPX G-25/7 50PX/CPX H-15/85 I-Clinopyroxene! c ' Q _J Z C - ' Str;ngt s f I:[rim;Iry 'Pyr;xe e, bs rpt;ons ' B t A t micron particles -3.00, I, I. '. t.,.,. I Band Center In Microns t 2.40 A-Orthopyroxene B-85/15 C-7 5/25 D-60/40 E-50/50 F-40/60 G-25/75 H--15/85 I-Cllnopyroxene Fig. 5. Band centers and band strengths for the primary absorption bands in pyroxene mass fraction mixtures (denoted by letters A-I): (a) <45 laxn particles, (b) gm particles, (c) grn particles. Large arrows indicate absorption bands from the OPX component and small arrows indicate absorption bands from the CPX component. 2 I. tm region. Despite this slight saturation in the 1 I. tm region, This result is in agreement with previous visual observations the MGM fit the CPX suggests a single dominant [Adams, 1974; Cloutis and Gaffey, 1991] and is illustrated in pyroxene component. This spectrum therefore probably Figure 6a, a plot of the band widths of the primary absorptions reflects an average, or bulk, composition as suggested by from the <45!.tm mass fraction suite, the Moses Rock exsolved Adams [1974]. sample, and the CPX. The broadened absorption bands Although the general properties of the absorption bands in the lunar CPX undoubtedly reflect the zoned nature of the derived from the MGM appear to be similar to any other sample. The increased band width is likely to be statistical in pyroxene spectrum, closer inspection reveals that the band nature and due to the fact that the spectrum represents an widths of the absorptions in the CPX are unusually wide. average over a large number of different compositions. The

10 .m ß 9084 SUNSHINE AND PIETF S: ESTIMATING PYROXENE ABUNDANCES ooo. o. oj o ' I ' I ' I ' I ' I ' I ' I ' Widths of Primary Pyroxene Absorptions <45 micron particles,!, I, I, i I i Band Center in Microns! A-Orthopyroxene 8-85/1 50PX/CPX C- 75/25 D-60/40 E-50/50 F- 40/60 G-25/75 H-15/85 I-Cllnopyroxene + Exso ed O Zoned Lunar Pyx ' I ' I ' I ' I ' I '! " Widths of Primary Pyroxene Absorptions : c ooo. A-Orthopyroxene B-85/1 50PX/CPX C-75/25 I)-60/40 E-50/50 F-40/ /75 H-1 5/85 I-Clinopyroxene micron particles b o oo I I, I, I I I Band Center in Microns I ' I '! ' I ' I " I ' I ' Widths of Primary Pyroxene Absorptions ooo. A-Orthopyroxene B-85/1 50PX/CPX 0-75/25 D-60/40 E-50/50 ß F-40/ /75 H-15/85 I-CIInopyroxene micron particles o. 0.8O I I, I i I, I, I, I, c Band Center in Microns Fig. 6. Band centers and band widths for the primary absorption bands in laboratory mass fraction mixtures (denoted by letters A-r). (a) <45 grn particles, (b) Ia.m particles, (c) grn particles. Figure 0a also includes values for the exsolved pyroxene crystal (pluses) and the lunar CPX (diamonds). Note the anomalously wide absorptions bands associated with the zoned lunar CPX. anomalously wide absorption bands may provide a method of remotely determining if a pyroxene is strongly zoned and therefore may indicate whether a given target formed under rapid cooling conditions. average or bulk composition. From a remote perspective, it should therefore be possible to detect variations in the bands centers of different basalts, which would correspond to relative changes in bulk pyroxene compositions. Although zoned This MGM analysis of the CPX separate suggests pyroxene in lunar basalts will have anomalously wide that pyroxenes in lunar basalts, which are also absorption bands, the residual error of the fit will be readily compositionally zoned, are likely to have spectral signatures distinguishable from a mixture of two discrete pyroxenes. that include anomalously wide absorption bands and reflect an Based on the analysis of the residual error, it should be

11 SUNSttlNE AND Pm-re ts: ESTIMATING PYROXENE ABUNDANCES o gm Region l' ' ' i,,, I,,, i,,, i,,, i, 'l 0.50j- MGM Fit to Exsolved Pyroxene Crystal-- '1 [. Sinle Pyroxen Componn residual t 10 (u ß a..o lo q- <45 gm particles ß gm particles El gm particles x gm particles Percent Clinopyroxene 2 gm Region i,,, i,, 2 ro p;rti le, i, ' Fig. 8. An unacceptable MGM fit to the spectrum of the exsolved pyroxene crystal using only one pyroxene component. Note the very large overall residual error and that the peaks of the residual error are offset from the derived absorption bands in both the 1 pm and 2 pm regions. This error is diagnostic of an insufficient number of absorption bands. Curves are as in Figure 3. 1 o q- <45 micron particles ß micron particles El micron particles x micron particles component band strength ratios vary logarithmically with modal abundance and are also independent of particle size. These results indicate that particle size effects can be considered minimal and that the MGM provides a method for estimating modal abundances from spectra of unknown pyroxene mixtures without the use of end-member spectra. The knowledge gained from this study of laboratory mass fraction mixtures was then used to interpret the results of the 100 MGM analysis of the spectrum of a natural exsolved pyroxene crystal. The spectral signatures of both OPX and CPX b Percent C!inopyroxene components in this exsolved sample were successfully resolved Fig. 7. The logarithmic relationships between the component band with the MGM suggesting that exsolved pyroxenes behave as strength ratios (CBSR) for the primary OPX and CPX absorption bands intimate mixtures of two pyroxenes. The relative band and the modal abundance of CPX in the sample: (a) absorptions in 1 pm region, (b) absorptions in 2 }xm region. The curves are the best fits to strengths (CBSR) derived with the MGM were used to estimate the data from all particle sizes and approach values for the OPX and the modal abundances in this sample and agree to within 5-10% CPX end-member compositions (0% and 100% CPX) that are consistent with both visual and microprobe estimates. Although further with the definition of CBSR (see text). studies need to be carried out to evaluate the role of possible to detect and model basalts with significant orthopyroxene and clinopyroxene components, each of which is compositionally zoned. One would therefore expect to be able to detect changes in the relative abundances of an average OPX and average CPX in such basalts using the MGM. SUMMARY AND CONCLUSIONS o co a I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' '/ 0.50j- MGM Fit to Exsolved Pyroxene Crystal-- -'] An analysis of spectra of pyroxene mass fraction mixtures has been carried out using the modified Gaussian model (MGM) developed by Sunshine et al. [1990]. These experiments provide laboratory control for interpretation of natural samples and have led to several important conclusions: (1) Using the MGM it is possible to deconvolve spectra of mixtures into absorption bands that correspondirectly to absorptions in the end-member spectra. (2) The centers and widths of the primary absorptions bands are determined by those in the end-members and do not vary with modal abundance. (3) Band centers, band widths, and relative band strengths (CBSR) are particle size independent for the particle size range studied. (4) The component band strength ratios of the primary absorptions are nearly identical in both the 1!.tm and 2!.tm regions. (5) The -J <250 micron particles - _2.00 ',,,,,,,,,,,,,,, I,, Fig. 9. An acceptable MGM fit to spectrum of exsolved pyroxene crystal. Based on analysis of the residual error in Figure 8, two additional bands were included, one in the 1 gm and one in the 2 region, representing a second pyroxene component. Large arrows indicate absorption bands from the OPX component and small arrows indicate absorption bands from the CPX component. Curves are as in Figure 3. Model parameters for this fit are listed in Table 4.

12 9086 SUNSHINE AND PIETERS- ESTIMATING PYROXENE ABUNDANCES TABLE 4. Model Parameters of Absorption Bands in the MGM Fit to the Exsolved Pyroxene Crystal From Moses Rock Diatreme Continuum E-6 Center Width Strength Band Band Band Band Band Band Band Band Band rms error, % O. 44 TABLE 5. Model Parameters of Absorption Bands in the MGM Fit to the Zone d Clinopyroxene Separated From Lunar Basalt Continuum E-6 Center, Width Strength Band I Band II Band III Band IV Band V Band VI rms error, % 0.92 Values as in Table 2. Values as in Table 2. composition on absolute band strength and therefore inferred modal abundances, the MGM is an excellent method for extracting the spectral signatures of end-member components, even in mixtures of samples which cannot be physically separated. Although zoned pyroxenes can also be considered intimate mixtures, the scale of mixing and the continuous compositional variations in the components, result in a continuous distribution of end-members. This continuous compositional zonation produces a spectral signature that cannot be distinguished from a single pyroxene in the MGM deconvolution. The composition of the single component is thought to represent an average composition of the zoned pyroxene. The only spectral evidence that this sample is continuously zoned is that the absorption bands are anomalously wide. These results suggest that remote spectroscopic measurements of zoned pyroxenes, which are commonly found in lithologies on the surfaces of planets, should be able to detect chances in pyroxene band centers and therefore average compositions. Finally, the presence or absence of broadened absorption bands may provide a remote method for ascertaining whether surface materials formed under extremely rapid or slow cooling conditions and therefore whether they formed at the surface or in a pluton. This study of laboratory and simple natural pyroxene mixtures is an important step in the continuing effort to accurately quantify and map relative changes in composition with remotely acquired spectra. The MGM has proven to be an excellent tool for quantifying the systematic trends that have been previously observed in pyroxene mixture spectra by many authors [Bums, 1970; Adams, 1974, 1975; Singer, 1981; Cloutis and Gaffey, 1991]. Extracting pyroxene signatures from the spectra of more complicated lithologies and/or remote data with lower signal to noise ratios will be facilitated by the quantitative understanding of absorption bands developed here, particularly the coupling of parameters, such as the relative strengths of absorptions in the 1 gm and 2 gm regions. Further studies with the MGM, such as the study of olivine spectra [Sunshine and Pieters, 1990, 1993] and the study of actinolites [Mustard, 1992], are in progress to quantify the spectral variations of other common minerals and their mixtures as a function of composition. Once a quantitative background is developed for the spectra of major rock forming minerals, this information can be explicitly and rigorously included in MGM deconvolutions of remote spectra. One of the strengths of the MGM approach is that it derives information based solely on analysis of the measured spectrum and does not rely on pre-determined or assumed end-member constituents. As such, the MGM is complimentary to methods which use Hapke theory and a library of reference spectra. Undoubtedly, a preferred approach would be to use the MGM and Hapke theory in parallel. One could, for example, use the absorptions bands derived with the MGM to aid in determining MaM fit to Lunar Clinopyroxene (; 20 appropriate spectral analogs to the model actual spectra end-memb with Hapke and 0.20 residual then use these end-members theory. Such a combined approach would include as much of our empirical and theoretical understanding of spectra as _.... possible compositional and lead makeup to a of more planetary complete surfaces. determination of the co Acknowledgments. This research effort was greatly enhanced by t technical and science input from S. Pratt and J. Mustard. Detaile reviews by R. Bums, R. Clark, and T. Hiroi led to several improvements to this paper. The microprobe facility at Brown ''' '''' ''' ''' ''' University issupportedbyfundsfromthew. M. KeckFoundationand is operated by J. Devine. All reflectance spectra were obtained using RELAB, a multiuser facility supported by NASA grant NAGW-748. Support for this research, NASA grant NAGW-28 and a NASA Graduate Fig. 10. MGM fit to spectrum of clinopyroxene separated from lunar Student Fellowship (J.M.S), are greatly appreciated. Additional basalt Curves are as in Figure 3. Model parameters for this fit financial support for parts of this research was generously supplied by are listed in Table 5. a Zonta Intemational Foundation Amelia Earhart Fellowship to J.M.S.

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