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Use of Geochemistry Data Collected by the Mars Exploration Rover Spirit in Gusev Crater to Teach Geomorphic Zonation Through Principal Components Analysis Christine M

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Use of Geochemistry Data Collected by the Mars Exploration Rover Spirit in Gusev Crater to Teach Geomorphic Zonation Through Principal Components Analysis Christine M JOURNAL OF GEOSCIENCE EDUCATION 59, 184–193 (2011) Use of Geochemistry Data Collected by the Mars Exploration Rover Spirit in Gusev Crater to Teach Geomorphic Zonation through Principal Components Analysis Christine M. Rodrigue1,a) ABSTRACT This paper presents a laboratory exercise used to teach principal components analysis (PCA) as a means of surface zona- tion. The lab was built around abundance data for 16 oxides and elements collected by the Mars Exploration Rover Spirit in Gusev Crater between Sol 14 and Sol 470. Students used PCA to reduce 15 of these into 3 components, which, after quartimax rotation, very strikingly divided the surface traversed by Spirit’s into three distinct zones. Students then used such concepts as the Bowen reaction series, typical minerals in Earth’s basalts and andesitic arcs, the periodic table, and the Goldschmidt classification, together with Pancam images from Spirit and the Mars Orbiter Camera, to interpret the surfaces over which the rover moved. Students found this foray to Mars a challenging but enjoyable project, and it made PCA memorable to them long after the class had ended. Some variant on this lab could work for multivariate statistics courses in geology, geography, and environmental science, as well as advanced courses in the content of those disciplines, particularly those dealing with zonation. VC 2011 National Association of Geoscience Teachers. [DOI: 10.5408/1.3604826] INTRODUCTION example, a transect could be taken down a catena, across a This paper presents an exercise that uses Mars Explora- wetland–upland interface, or through a seasonal surface tion Rover geochemical data to teach principal components water and groundwater boundary (Fortin et al., 2000). analysis (PCA) for geomorphic or geological zonation. The Zonation can be vertical and temporal in geological data come from the Spirit rover’s Alpha Particle X-ray Spec- usage, not just horizontal and spatial in mapping usage. trometer (APXS), which collected spectra from 93 rocks and So, for example, fossils, grain size, bulk density, and geo- soil samples (Gellert et al., 2006) during its travel over three chemistry can be used for temporal zonation and sequenc- distinctive zones on the floor of Gusev Crater. These zones ing of stratigraphic units (e.g., Patterson et al., 2000; Brown consisted of a cratered basaltic plain, the West Spur of the and Pasternack, 2004; Peterson et al., 2008). Columbia Hills with bedded materials and evaporites, and Zonation, then, is a common task in the field and labo- the northwest side of Husband Hill where very diverse ratory activities of geoscientists. The process can seem aqueous and acid–aqueous altered rocks and soils were superficially straightforward, but the zoning schemes that found. PCA is a data reduction technique that has increas- result can color analytic results. Complications include ingly been used in the geosciences since the early 1960s, scale, edge effects, spatial autocorrelation, and aggregation making its acquaintance of value in the education of geosci- effects. These distortions and biases are collectively called ence majors. The APXS data can make the technique memo- the Modifiable Areal Unit Problem or MAUP (Dark and rable to such majors as it produces a coherent zonation Bram, 2007) or the analogous Modifiable Temporal Unit from 15 different oxides and elements. Problem (MTUP). The MTUP is less commonly discussed, A classic task in the geosciences is zonation of complex largely in criminology contexts (e.g., Taylor, 2010), but it is surface patterns into areal units and demarcating transition clearly relevant to geoscientists’ work. Concern about zon- zones or boundaries between them, often along a transect ing has driven development of statistical techniques to let in the field. So, for example, a soil catena can be zoned by image processing, GIS, and statistical software handle the changes in soil particle size, underlying bedrock and rego- kinds of remote sensing, field, and laboratory data gener- lith, topographic relief, drainage, erosion and deposition ated and used by geoscientists. processes, weathering, organic matter, and geochemistry One of the common statistical techniques used in zona- (Milne 1935; Bushnell, 1942; Webster, 1973; Raynolds et al., tion is principal components analysis or PCA, a member of 2006). Ground-penetrating radar can be used along a tran- the factor analytic (FA) family of techniques. PCA is pri- sect to infer subsurface stratigraphy for geological map- marily concerned with data reduction or grouping of many ping (Baker and Jol, 2007). An environmental ecotone variables into fewer components. FA is mainly concerned might be zoned by field sampling of soils and censusing of with identifying or testing underlying factors that may not species presence and abundance along a transect. For be directly measurable themselves but which are expressed in commonalities in measurements of empirical variables (Bryant and Yarnold, 1995; Rogerson, 2006; Davis, 2002). Received 10 January 2010; revised 2 April 2011; accepted 13 April 2011; pub- PCA is more empirical and inductive; FA is more theoreti- lished online 14 November 2011. cal and in some versions can test deductive hypotheses 1Department of Environmental Science and Policy and Department of Emergency Services Management, California State University, Long about expected underlying factor structure. Beach, California 90840-1101, USA In the geosciences, PCA/FA is a common method a)Electronic mail: [email protected] underlying the unsupervised classification of remote 1089-9995/2011/59(4)/184/10/$23.00 184 VC Nat. Assoc. Geosci. Teachers J. Geosci. Educ. 59, 184–193 (2011) Geomorphic Zonation on Mars Using PCA 185 sensing imagery. It can also be performed on large data sets article. This table can be saved as a tab-delimited file for collected in the field. These could include sampling down import into a spreadsheet program. There, the data can be through a geological column, sediment core, or ice core, for further edited to fit the needs of a statistical software pro- example, or to process observations across space, as is the gram or an instructor’s goals. case in the laboratory exercise presented here. It can, thus, This table has as the record labels the “sol” or the mar- assist in both temporal and spatial zonation, making it a tian day after landing, on which the sample record was tool of increasing utility to a variety of geoscientists. For taken. The table covers the first 470 sols of Spirit’s activ- that reason, PCA/FA, particularly PCA, is increasingly ities. Martian sols are slightly longer than Earth days at 24 encountered in the geoscience literature since its discipli- h, 37 min, and 23 s, and the date of landing for Spirit was 4 nary de´but in the early 1960s (e.g., Reyment, 1961; Wong, January 2004 on Earth. The second variable is the type of 1963; Imbrie and Van Andel, 1964). For that reason, practice surface from which Spirit’s APXS took spectra on a given in its application would enhance the professional prepara- sol. These include rock undisturbed by Spirit (RU), rock tion of geoscience students, especially at the advanced brushed off (RB), rock “RATted” or abraded by the rock undergraduate and beginning graduate levels. abrasion tool (RAT), RAT fines or abrasion debris (RF), soil For all its usefulness, PCA/FA is not the most “user undisturbed (SU), soil disturbed (SD), and soil trenched friendly” approach for students. The mathematical com- (ST). The third variable is the sometimes whimsical nick- plexities are now easily handled by the common statistical name given to an individual rock or soil surface. Norm or software packages. These include SPSS, STATISTICA,MINITAB, geometric norm is a relative measure of the standoff dis- MATLAB,SCILAB, R, the freeware programs PAST and WINI- tance between the APXS and the sample surface in milli- DAMS, and others, Their widespread availability makes meters. This distance affects how much background PCA/FA accessible to undergraduate students. The under- elemental noise is included in a reading. The variable nor- lying concepts, however, are difficult to convey, because malizes the sum of all oxides to 100% to allow measure- PCA/FA represents the many variables in the analysis as ment of relative contributions by each oxide or element. T dimensions and the data collected as occupying an n- is the time in hours that the instrument took to integrate dimensional data cloud. Trying to “visualize” this is a tough the spectrum. Following these three columns are two col- sell to students! The point of PCA, especially, is to reduce umns for each of the oxides and elements. The first gives the dimensionality of the data cloud to a small number of the relative abundances of the 12 oxides (wt. %) and 4 ele- usually orthogonal components. These can then be pro- ments (parts per million), and the other reports the statisti- jected through the data cloud and aligned with most of the cal error bounds set at 62 standard deviations. The table, data points when “viewed” through various “rotations” of then, has 37 columns and 93 rows of records. the emergent model. Each of the original variables will The use of PCA on these data offers opportunities to “load” highly along one of the components (some may load encourage students’ critical thinking about examples of less dramatically on more than one component). That is, PCA they encounter in the literature or their own future most of the original variables will show strong correlations work. The data set presented here conforms to some but with one of the artificial variables, or components. The not all of the assumptions for the proper use of the tech- result for geoscientists can be a meaningful zonation of time nique, and students should be able to identify these depar- or space. PCA zonation is generated from the data them- tures and conclude that their results will be tentative.
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