K-Means Clustering of Mars Rovers APXS Oxide and Element Abundance Data
and Mapping of Classified Targets in Google Earth

Christine M. Rodrigue
Geography, CSULB rodrigue@csulb.edu

This project started as an attempt to create a laboratory exercise for my Geography of Mars class at California State University, Long Beach. I had earlier made use of MER-A (Spirit) APXS data in a lab for a multivariate statistics class and became familiar with and interested in the instrument as a result. I wanted to create a markedly different exercise for the Mars class that would use all the APXS data coming from the four Mars rovers: Mars Pathfinder/Sojourner (MPF) in Chryse Planitia, Mars Exploration Rovers A (Spirit, in Gusev Crater) and B (Opportunity, in Planum Meridiani), and the Mars Science Lab (Curiosity) in Gale Crater. The previous project had used principal components analysis in a geomorphic zonation exercise (Rodrigue 2011). This exercise would bring together all the APXS data (as of fall, 2016) and classify them using k-means clustering. K-means clustering is a non-hierarchical clustering technique that groups records into a specified number of desired categories (K), which is an arbitrary choice. I experimented with several approaches, using raw oxide and element abundance data, data reduced in dimensionality through principal components analysis before clustering, and with standardized relative abundance data. I tried K=10, K=15, and K=20, before settling on the use of standardized data and 15 categories to "test-drive" the idea before springing it on my students. In order to see whether the 15 classes made geological sense, I mapped the targets by class, using Google Earth Pro.

This article will review the process, present its results, and discuss the properties of the target clusters. It will conclude by noting a higher-order pattern among the clusters, which I call "metaclusters," and the rock and soil origination and alteration pathways they describe. Lastly, the conclusion brings in the outcomes of the eventual simplified student lab, which was utilized in the Spring 2018 section of the Geography of Mars class.

Data and Methods

All APXS-collected oxides and elements abundance data in several files were downloaded from the Planetary Data System (PDS) Geosciences Node at Washington University in St. Louis: http://pds-geosciences.uwstl.edu/. These come in a variety of layouts and formats, so they required considerable pre-processing to integrate them into a common database, in the OpenOffice/LibreOffice Calc spreadsheet. Additionally, the APXS instrument has evolved, acquiring sensitivity across a higher range of energy (electron volts), allowing it to detect peaks corresponding to a wider array of oxides and elements. The Alpha Proton X-ray Spectrometer on Pathfinder/Sojourner could not detect phosphorous pentoxide, chromium oxide, manganese oxide, nickel, zinc, or bromium. For the eleven spectra it collected, I assigned the average reading from the other three rovers for these three oxides and three elements.

The Alpha Particle X-ray Spectrometer on Spirit, Opportunity, and Curiosity can detect these six consistently. The APXS on Curiosity has sensitivity beyond the ~17,750 eV limit of the APXS on Spirit and Opportunity, up to ~26,000 eV, and at higher count frequencies, allowing it to detect gallium, germanium, rubidium, and lead more reliably than the older APXS could do. None of these four are consistently reported for all targets, so they could not be included in the clustering exercise.

In addition, there are variations in the precision and accuracy in the application of APXS to various targets, some having to do with sub-ideal conditions of instrument placement and some having to do with inherent variations in sensitivity to different elements and oxides. Another complexity is introduced by the treatment of the target surface before placement and operation of the APXS instrument. In some cases, the target is undisturbed before placement; in other cases, accumulated dust was brushed off the surface before placement; in still other cases, the surface was RATted or subjected to the Rover Abrasion Tool (RAT) to grind a hole about 45 mm in diameter roughly 5 mm down to expose relatively pristine subsurface material. The data are here simply accepted in their original condition, but these shortcomings may have affected the classification of individual APXS targets. An introduction to APXS is provided in Gellert (no date).

Once integrated into one spreadsheet, abundance data for each APXS target were standardized in Calc against the all-targets/Mars average for each oxide and element. Once converted into the common dimension of t-scores, the spreadsheet was imported into PAST 3.x (http://folk.uio.no/ohammer/past/). The data were then grouped into 15 distinctive classes of geochemically similar targets through k-means clustering (as mentioned above, 15 is an arbitrary choice). K-means clustering is an iterative process a bit like location-allocation in a statistical space with as many dimensions as there are variables (here 16 oxides and elements). Centroids are initially seeded randomly and each target is grouped with the nearest centroid. Once grouped, the centroid of each of the groups of targets is calculated and used as the seeds for the next iteration. The process continues until further adjustment of the centroids would produce positions not significantly different than those of the previous iteration.

Once each target was stably assigned to a cluster, the cluster assignments were copied back into the OpenOffice Calc spreadsheet. The clusters are given integer numbers as names, with no meaning to the numbers given other than as a tracking name. Once clustered, mean relative abundances of each standardized oxide and element among all the targets in a given class were calculated. A series of graphs was also constructed in Calc, illustrating the mean standardized abundance of each chemical by cluster, the range of standardized abundances for each chemical by cluster, their relative abundance across all 15 clusters, the relative abundance of each cluster by the four rover sites, and the alpha, beta, and gamma diversities of cluster types among the four study areas.

To map the results, I created a CSV version of the spreadsheet that conformed with the requirements of Google Earth Pro, which can open CSV spreadsheets and then convert them into Google Earth's native KML or KMZ Keyhole Markup Language formats. The resulting KMZ files can then be downloaded and opened by anyone with access to Google Earth or Google Earth Pro. Such CSV spreadsheets must, at a minimum, contain a column for the name of the record (here, APXS target) and, in decimal degrees, latitude and longitude. It may, additionally, include other columns, such as description (an expansion on the name, here the target's informal name), and anything else an author wishes to share via Google Earth, including links for more information, such as to this web page.

While conceptually straightforward, creation of target latitude and longitude was time-consuming. The APXS data available at PDS are divergent in location rendering. The rovers' positions are difficult to pinpoint on the Mars geographical grid, since there is no network of GPS satellites in orbit. Their positions have to be estimated from geometric analysis of landmarks recorded by their mast cameras and orbital imagery. Their positions at a given stopping point will be identified and converted to latitude and longitude as a designated waypoint on a rover's track. Then, the rover accomplishes its various goals in the area around the waypoint, its movements to and fro recorded in terms of turns of its wheels. The resulting position estimation, in terms of meters along X (latitude), Y (longitude), and sometimes Z (elevation), is calculated. Wheels slip and uncertainties accumulate, however, so at some point another waypoint must eventually be established to keep the rover's track and location tied to the areographical grid.

The grid itself involves further complexities. There are at least two reference systems for Mars: Viking Orbiter-based Mars Digital Image Model (MDIM) and Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA). MDIM 2.0 projects onto a reference spheroid with semi-major axis of 3,396.00 km and semi-minor axis of 3,376.80 km. MOLA uses 3,396.19 km and 3,376.20 km, respectively. MDIM was derived from stereoscopy of paired Viking Orbiter images; MOLA was based on laser altimetry. MDIM was based on Mars' center of figure (planetographic), while MOLA is based on the center of mass (planetocentric). These two centers are markedly offset on Mars due to its extreme oblateness and the gravitational distortions of the Tharsis Rise. Traditionally, cartography has used the planetographic convention, coupled with treatment of longitude as increasing with time, that is, westing, numbering from 0° at the Prime Meridian and increasing westbound. This was the custom kept with earlier Mars cartography. With MOLA based on gravitational tugs on the spacecraft carrying it, a planetocentric grid took hold and eventually eastings (numbering longitude increasing in a right-hand direction, that is, eastbound). Some maps will show longitude increasing in both directions from the Prime Meridian as is the custom for Earth. Another complication is the reckoning of the Prime Meridian: There are three slightly different definitions of the center of the Airy-0 crater selected for the Primje Meridian. These differences are consequential, especially for latitude with increasing distance from the equator. The difference amounts to roughly 0.3°, which can be about 20 km on the ground at 45° north or south. For a fuller treatment of the cartographic complexities on Mars, see Rosiek et al. (2001), Kirk (2005), and Statella (2015).

A further complication is that Google Earth Mars does not provide access to information on the datums and projections used. The MER-A and MER-B tracks accord with traverse maps produced for NASA by the University of Ohio (http://mars.nasa.gov/mer/mission/traverse_maps.html, and I was eventually able to align the locations of their APXS targets with the tracks given. With MSL, the Google Earth Mars tracks are widely off the mark and implausible (showing the rover going straight up and down steep cliffs, for example). Fernando Nogal has produced a corrected map of MSL waypoints and tracks by dead-reckoning on landmarks. My APXS location data lined up perfectly with his, rather than the default track shown with Google Earth Mars. So, to see their locations against the context of the rover's travels, it is advisable to download his KMZ file along with mine. His, named "The Martian Way - Mars Science Laboratory 'Curiosity' Route Map," can be downloaded for opening in Google Earth or Google Earth Pro at: http://www.unmannedspaceflight.com/index.php?act=attach&type=post&id=40403.

Results

The KMZ file containing Google Earth placemarks for all 901 targets in the four landing and study sites across Mars can be downloaded from https://home.csulb.edu/~rodrigue/mars/apxs/GE/tscore15/APXS15clustersTscores.kmz. Once in Google Earth -- Planets -- Mars, the file can then be opened and the icons viewed by doing searchs in Google Earth for "Pathfinder," "Spirit," "Opportunity," or "Curiosity." The Google Earth supplied traverses need to be supplemented, in Curiosity's case, by downloading and opening "The Martian Way," as described previously.

The table of mean relative abundances can be found at https://home.csulb.edu/~rodrigue/mars/apxs/GE/tscore15/15clusterstable.html. Oxides and elements that are markedly divergent from average martian relative abundances are highlighted if they exceed 1 sigma (p< 0.318) or 2 sigmas (p< 0.046), warm shade if significantly enhanced and cool shade if significantly depleted.

The 15 clusters of standardized relative abundances are depicted in the following graph: https://home.csulb.edu/~rodrigue/mars/apxs/GE/tscore15/15clusters.png. The thickness of an oxide's or element's band within a cluster is proportional to its t-score, while its location above or below 0 (Mars average) indicates whether it is enhanced or depleted in that class, respectively. If the band is more than 2 sigmas tall, it is significantly enhanced or depleted; if the band is very narrow, the cluster is close to the Mars average for that oxide or element. Some of the clusters are very markedly divergent in many of the oxides and elements, resulting in a tall bar (e.g., Cluster 11); others are comprised of a short stack of very narrow bands, marking a class that clings closely to martian norms (e.g., Cluster 6).

Each cluster is additionally depicted in another graph showing the departure of each oxide and element from the martian average by the position of a square above or below 0. These may be viewed individually here:

They may be viewed, together with their Google Earth icons, in a slideshow here:

Another way of visualizing the departures of clusters from the martian averages shows each target in the cluster with its individual t-score for each of the oxides and elements as a dot. The resulting "bar chart" depicts the range of variability within each cluster for each oxide and element. The means are connected by a line.

These may also be viewed in a common viewgraphs presentation:

The distributions of the 15 clusters across the 4 rover study areas is depicted in a bar chart showing the percentage of targets in each area that fell within a particular cluster. The chart conveys the geochemical "personalities" of the four study areas: https://home.csulb.edu/~rodrigue/mars/apxs/GE/tscore15/ClustersbyMission.png.

Finally, the richness of targets and the contrasts among the sites is represented in a table repurposing biogeographical measures of "biodiversity" to show geochemical cluster diversity. That is, the number of clusters found in an area is counted up as alpha diversity or cluster richness. The total number of clusters on Mars as found in all four study areas constitutes gamma diversity or planetary cluster diversity. The contrasts between pairs of rover study areas is beta diversity, which counts only those clusters unique to either one of the paired areas. The geodiversity table may be found at:
https://home.csulb.edu/~rodrigue/mars/apxs/GE/tscore15/AlphaBetaGammaDiversityAPXSTargets.png.

Discussion of the Clusters

Each cluster is discussed in terms of its specific discrepancies from the martian average, here defined as the average of each oxide and element measured by APXS (n=901). APXS measures photon counts along a continuum of energy (eV), which are converted into weight percentages (oxides) and ppm (elements). To give each equal weight in the k-means clustering, each was converted into standard scores with respect to the martian averages for each oxide and element (now set to 0). Graphing them allowed easy visualization of their divergence from the martian average, and the pattern of divergences is the focus of the discussion. In each case, a few examples are provided as informally named targets, the missions that analyzed their spectra, and the mission-based sol on which the APXS measurement was taken. The name of the mission (MPF can be searched in Google Earth Mars as "Pathfinder"; MER-A as "Spirit"; MER-B as "Opportunity"; and MSL as "Curiosity"). Once at the right region on Mars, the sol allows tracking of the rover until the example target is found. The Google Earth icon for each cluster is also included in the discussion below to expedite finding the examples mentioned or, simply, where a given cluster is found in any of the study areas. This process can yield the geological context of each example and the cluster as a whole by examination of the high resolution imagery Google Earth Mars offers at large-scale zooming in to that location.

Here are direct links to each cluster's discussion below:

Cluster 1 [ Google Earth icon for Cluster 1]
With 112 of the 901 APXS targets, Cluster 1 (means, variability) appears to be a common Mars-typical material showing some slight modification by non-acidic water. That is, all oxides and elements are pretty close to 0 (standard score for Mars average), with some slight elevation in the oxides of iron, chromium, and potassium, as well as chlorine and bromine. These last two, halogens, form salts that dissolve readily in neutral and alkaline water (e.g. hydrogen chloride, potassium chloride, sodium bromide) and then concentrate in rinds, veins, and surface layers upon evaporation, leading to the detection of Cl and Br by APXS. Targets in this cluster are slightly enhanced in the halogens and slightly depleted in sulfur trioxide. Sulfur can signal acidic water, so its slight impoverishment here lends further support to the idea that the waters involved would be more neutral or alkaline.

The impression given by this cluster is of basaltic bedrock, regolith, or sedimentary material derived from basalt. It, thus, strongly resembles other basaltic clusters, such as Cluster 8, Cluster 6, and Cluster 5, and Cluster 15. These are all basaltic in general character, showing various mixes of basalt outcrop, float rock, regolith, or sand grain targets. What makes it stand out as its own cluster is that Cluster 1 materials show signs of having been subjected to small amounts of neutral or alkaline water moving through it, perhaps as groundwater upwelling or perhaps even as the result of condensation/freezing and evaporation/sublimation cycles. These produced a slight concentration of halogen-based compounds, perhaps just as rinds or veins. This is consistent with a rather dry site and the neutral-alkaline hydrogeochemistry believed to characterize the earlier Noachian Period (which ended roughly 3.8 Ga ago).

Examples of targets in this cluster are unevenly distributed among the rovers' study sites. Only seven were found in Gusev Crater (Spirit) and sixteen in Meridiani Planum (Opportunity), while Gale Crater yielded 89. In Gusev Crater, Cluster 1 included two targets on Alligator (MER-A, sol 380), a layered outcrop in the Cumberland Ridge area approaching Husband Hill in the Columbia Hills of Gusev Crater, two more on a similarly planar outcrop called Seminole (MER-A, sols 672-675) descending Husband Hill into the Inner Basin of the Columbia Hills, and another two on a third layered rock outcrop, Troll Montalva (MER-A, sols 1072-1079) in the Winter Haven area southeast of Home Plate (Crumpler et al., 2011; Ming et al., 2008; Berger et al., 2014).

In Meridiani, the sixteen targets were all found on the rims of two craters, Victoria Crater and Endeavour Crater. The rims, uplifted during impact, raise samples of the deep subsurface rock, typically basaltic on most of Mars. These materials may be modified subsequently by mechanical and chemical weathering, often by groundwater enriched in elements picked up during its travels through rock. So, where in Gusev Crater, Cluster 1 seemed to pick up on lightly altered volcanic materials, themselves also basaltic, in Meridiani Crater, the cluster is focussed on impactites raised up from the subsurface basalts and then subjected to interactions with fluids.

Only one of the Meridiani Cluster 1 targets was found on the rim of Victoria Crater, Dorsal_new (MER-B, sol 1463), on the inner-facing side of the rim overlooking the Duck Bay embayment of the scallop-edged crater. Examples from the eroded western rim of Endeavour Crater include two unbrushed targets on the Tisdale rock on Shoemaker Ridge of Cape York (a segment of the western rim) at the rover's first encounter with Endeavour Crater (Squyres et al. 2012). Another five were collected from the Grasberg (MER-B, sols 2990-3006) rock at the northern end of Cape York on the western rim of Endeavour Crater (Arvidson et al., 2015). These ran the gamut from undisturbed, brushed off, and RATted. Most of the rest in this cluster were found on the northern end of Solander Point, another discrete segment of the western rim lying to the south of Cape York. This group included two undisturbed targets on the Monjon rock (MER-B, sols 3422-3423) (Farrand et al., 2016), while the last member of Cluster 1 was found on an undisturbed rock just west of the Cape Tribulation segment of the western rim (RosebudCanyon, MER-B, sol 3741).

Curiosity has enountered targets in this cluster in Gale Crater far more frequently than the two MERs have at their sites, and these encounters occur throughout its travels. The cluster has turned up at Bathurst Inlet (MSL, sol 54) and Rocknest (the Et_Then targets, MSL, sols 86-91) less than half a kilometer from the landing site in rock powder samples from the MSL-specific Powder Acquisition Drill System (PADS) (Blaney et al., 2014). It was also found at several targets in Yellowknife Bay (e.g., Flaherty, MSL, sol 129; Ungava, MSL, sol 154; and Cumberland, MSL, sols 276-287) and Glenelg (e.g., Aillik, MSL, sol 322), both sites just beyond Rocknest before MSL made its turn toward Mount Sharp. Yellowknife Bay is a topographic basin on the floor of Gale Crater that is comprised of sedimentary strata of lacustrine character (Yellowknife Formation).

Cluster 1 turned up some three to six kilometers away when MSL resumed APXS sampling in the Kimberley area, an extensive area of layered sedimentary beds (e.g., the undisturbed rock target, Pine_Plains, MSL, sol 441; several drill targets on the Cumberland mudstone, MSL, sols 485-487; and the undisturbed rock, Wift, MSL, sol 633). Cluster 1 shows up again once in the Pahrump Hills, an outcrop of thinly bedded and wind-etched sedimentary rocks (the undisturbed rock target Tropico, MSL, sol 833). There's another occurrence in the Maria's Pass area in Glenelg, Square Top (MSL, sol 583) in the complex Kimberley sedimentary formation, and Sesriem Canyon (MSL, sol 1287) on the Naukluft Plateau.

Cluster 2 [ Google Earth icon for Cluster 2]

Cluster 2 (n=79) (means, variability) is a rock showing alteration or fractionation with significantly elevated silica and slightly elevated titanium dioxide. It also shows moderate depletion of magnesium oxide and iron oxide and slight depletion in calcium oxide. These were the first solid rocks analyzed by the APXS on the Pathfinder mission's Sojourner rover in Chryse Planitia at the mouths of Tiu Valles and Ares Vallis. Their pattern of enrichments and depletions was quite unexpected on a basaltic planet, triggering discussions of the possibility of the formation of evolved igneous rocks, perhaps elsewhere on Mars' highlands and transported by great outwash floods to the Pathfinder site (e.g. McSween et al. 1999; Nikolaeva and Abdrakhimov 1999). There was some reconsideration of the possibility that Mars might even have initiated plate tectonics, with the Southern Highlands having experienced the development of more felsic continental rocks (Lowman 1998). This idea was pulled up short by the finding that the Northern Lowlands show rocks of a somewhat more andesitic character, Surface Type 2, than the Southern Highlands Surface Type 1 (e.g., Bandfield et al., 2000). Attention then focussed on how neutral to alkaline aqueous alteration processes can liberate, mobilize, and concentrate silica from primitive basalts, and that might help account for the seemingly andesitic Surface Type 2 materials in the lowlands. The aqueous environment might be an ocean posited to occupy portions of the Northern Lowlands, as argued in Parker et al. (1989) or weathering and fluvial transport to the Northern Lowlands (Wyatt and McSween 20p 02). What is missing in this cluster, however, is enrichment in chlorine, bromine, and sulfur trioxide, which is associated with water on Mars. Perhaps the slight andesitic character of this cluster could, therefore, reflect more fractionation than alteration in certain contexts and aqueous alteration in other contexts. Examples include Barnacle Bill and Yogi (MPF, sols 3 and 7, respectively); Elizabeth Mahon (MER-A, sol 1157) and Gertrude Weise (MER-A, sols 1190-1199) on the eastern edge of Home Plate in the Columbia Hills of Gusev Crater; Lihir (MER-B, sol 3239) on the Matijevic Hill feature on the Cape York section of Endeavour Crater's western rim; Bonanza King (MSL, sol 722) overlooking Hidden Valley, Mojave (MSL, sol 809, 867-888) and Topanga (MSL, sol 815) in the Pahrump Hills, and Buckskin (sols 1057-1091) in the Maria's Pass area.

Cluster 3 [ Google Earth icon for Cluster 3 ]

Cluster 3 (n=35) (means, variability) appears to be mostly comprised of fractionated alkaline igneous rock, with significantly elevated levels of sodium oxide, aluminum oxide, and potassium oxide and slightly elevated levels of silica. Oxides of magnesium, iron, and chromium are, by contrast, somewhat depleted. Additionally, the aqueous alteration tell-tales of chlorine, bromine, and sulfur trioxide are slightly depleted. In terms of its balance of silica and alkali oxides, this cluster falls largely in the trachybasalt, basaltic trachyandesite, trachyandesite,and phonotephrite region.

A close Earth analogy is mugearite. Mugearite is a form of basalt containing olivine, which would argue against significant alteration by water, reïnforcing the impression given by the lower levels of halogens and sulfur trioxide in this cluster. Mugearite also features alkali feldspars, particularly the sodium-rich oligoclase. Water is indirectly a part of the picture, however, in that basaltic magma bodies produce feldspar-enriched igneous rocks in the presence of small amounts of water in the crust.

This cluster seems less ambiguously a product of fractionation than of weathering than Cluster 2. In Gusev Crater, the only examples are from Backstay (MER-A, sols 511-512) in the Columbia Hills at the Larry's Lookout area. This overlooks Tennessee Valley during the ascent up Cumberland Ridge to Husband Hill. The first rock examined by Curiosity was Jake_Matijevic, a float rock found between the Bradbury landing site and Glenelg (MSL, sol 46). Other occurrences of Cluster 3 in Gale Crater include Rocknest3_rp, a sample of rock powder taken from a depth of up to 5 cm with the MSL Powder Acquisition Drill System(PADS), this on Sol 102. Other examples come from the undisturbed surface of Monkey Yard (MSL, sol 564) in the Furnace Flats area southeast of the Kimberley formation, the undisturbed Thimble_1 and the PADS drilled powder of Stirling_RP overlooking Hidden Valley on the approach to the Pahrump Hills.

An exception to the fractionation over alteration argument may be presented by two examples in this cluster found on the western rim of Endeavour Crater by Opportunity: JeanBaptisteCharbonneau and SgtNathanielPryor (MER-B, sol 3935 and sols 3959- 3961, respectively) at Hinner's Point near the entrance to Marathon Valley south of Cape Tribulation. Given their situation along a degraded crater rim showing concentrations of smectites and other indications of aqueous alteration, these rocks have been interpreted as reflecting "alteration and oxidation relative to the host rock ... evidence for formerly enhanced fluid flow along fractures that leached the breccias and concentrated mobile ions in zones adjacent to fracture walls" (Crumpler et al. 2016).

Cluster 4 [ Google Earth icon for Cluster 4 ]
Cluster 4 (n=132) (means, variability) is close to the Mars averages for all the oxides and elements. They feature somewhat elevated sulfur trioxide and modestly depleted levels of sodium, aluminum, and silica oxides. The impression is that these common materials represent a basaltic rock or soil derived from basaltic material, which has undergone aqueous alteration. Alteration would have taken place in the presence of sulfate-acidified water or acidic fog from volcanism and hydrothermal activity and associated sulfur dioxide and hydrogen sulfide.

There are only two examples in this cluster encountered by Spirit in Gusev Crater: The first is Boroughs_Hellskitchen_side in the Gusev Plains (MER-A, sol 141) and Berkner Island soil (MER-A, sol 1013) on the eastern end of Home Plate in the Columbia Hills. This cluster is much more common in Opportunity's exploration of Meridiani Planum, which, of all the rover sites, shows the most evidence of acidic water alteration. There are several instances at the landing site, such as Robert E soil (MER-B, sol 15) and a couple dozen in Endurance Crater, such as the undisturbed rock Wopmay (MER-B, sols 260-261). A few occur on the Meridiani Plains terrain, such as the undisturbed and then brushed rock Gagarin (MER-B, sols 400-401). Roughly thirty were found in and around Victoria Crater, such as Steno undisturbed, brushed, and RATted (MER-B, sols 1311-1316). Several were also encountered along the western rim of Endeavour Crater, such as the undisturbed rock Tawny (MSL, sol 3352). Cluster 4 is as rarely encountered by Curiosity in Gale Crater as it was in Gusev Crater: The only two examples are on Sayunei mudstone rock (MSL, sol 165) in the Yellowknife area near the Bradbury landing site and Amboy, an undisturbed bedrock target at the Garden City site in the Pahrump Hills (MSL, sol 948).

Cluster 5 [ Google Earth icon for Cluster 5 ]
Cluster 5 (n=32) (means, variability) is also close to the Mars averages, indeed, slightly below, for all the oxides and elements, except it is highly enriched in iron oxide and modestly enriched in magnesium and slightly enhanced in nickel and chromium oxide. Suggestions of water, whether the halogens or sulfur, are slightly under-represented in this type. This class is consistent with olivine, an ultramafic mineral that very rapidly alters in the presence of water. Persistent olivine, then, seems contrary to the presence of large amounts of water.

That said, it has been argued that some members of this class in Gusev Crater do show signs of a continuum of alteration by groundwater moving through cracks in them and depositing dissolved iron sulfates and carbonates there through evaporation (e.g., Ruff et al. 2014). Examples of this group include the RATted rock, Peace (MER-A, sols 377-380) on the Cumberland Ridge between the West Spur and Husband Hill and Algonquin (MER-A, sols 687- 688) and Comanche (MER-A, sols 699-700) between Haskin Ridge and Allegheny Ridge east of Husband Hill. It is in this class and in Spirit's travels in the Columbia Hills that the first unambiguous in situ discovery of carbonates was made (Morris et al. 2010). Comanche had a substantial amount of carbonates, 16-34 percent by weight, comprising iron-magnesium carbonates. This finding is significant, in light of the heretofore missing carbonates that were expected to be highly abundant on a planet with a denser carbon-dioxide dominated atmosphere and the many geomorphic and geochemical signs of surface water and groundwater.

The Algonquin rocks seem to be a basaltic volcanic rock, perhaps a tephra, that show the least alteration. Comanche targets very much resemble the nearby Algonquin rocks. These may, indeed, represent their source rock before deposition of iron- and magnesium-rich carbonates leached from Algonquin or similar rocks in the vicinity by neutral pH water in contact with the atmosphere. Those waters may have been from the lake or series of ephemeral lakes posited to have occupied Gusev Crater (Morris et al. 2014) or from hydrothermal sources associated with volcanic activity in the Columbia Hills (Ruff et al., 2010). Leached iron and magnesium cations from such rocks would interact with the carbon dioxide in water to form iron and magnesium carbonates that would then be transported and concentrated in the Comanche rock joints and surfaces. Algonquin and Comanche, then, seem to be nearly identical rocks that show a source and sink series in terms of these carbonates. Peace, on the other side of Husband Hill, has been described as a sandstone comprised of similar unaltered olivine grains cemented together by iron-rich sulfates, implying a more acidic water source, perhaps the evolution of floodwaters percolating down through the Algonquin-like rock materials (Ruff et al. 2014).

Opportunity found targets akin to these in Meridiani Planum, but nearly all of these were undisturbed soil targets that were associated with æolian ripple surfaces rich in hæmatitic concretions yet low in sulfur trioxide and chlorine (Arvidson et al. 2011, Fig. 7). These included JackRussel_SoilBesi (MER-B, sol 80) on the plains between the Opportunity landing site in Eagle Crater and Endurance Crater, Ripple Crest (MER-B, sol 420) on the plains between Endurance Crater and Victoria Crater, and Juneau (MER-B, sol 2297) on the plains en route from Victoria Crater to Endeavour Crater. One member of this cluster in Meridiani Planum was an undisturbed rock or cobble: FigTree Barberton on the southeastern rim of Endurance Crater (MER-B, sol 122). This material has not yet been encountered by MSL.

This cluster is a complex grouping, a convergent evolution of materials in different circumstances towards a common profile featuring slight depression of all oxides and elements just below the martian average including those most associated with water and its evaporation (sulfur trioxide, chlorine, and bromine), as well as significant elevation of iron oxide and moderate elevation of magnesium oxide and slight elevation of nickel and chromium oxide. The general impression is that these are olivine-rich basaltic materials, whether outcrops of basalt (such as Algonquin), jointed basalt with veins of iron-magnesium carbonates (such as Comanche), sandstone comprised of basaltic sand cemented with iron-magnesium sulfates (Peace), or basaltic sand ripples with æolian-concentrated hæmatitic small spherical concretions (the Meridiani plains soil targets). The iron and magnesium oxide signal, then, is elevated from the presence of different minerals, whether olivine, iron-magnesium carbonate, or hæmatite. The general picture seems to be formation of these latter two by small amounts of water in the subsoil repetitively percolating up to and near the surface where these minerals could then precipitate in veins, vugs, or as surface rinds or cement sands into sandstone. The Columbia Hills and the plains of Meridiani found different paths to this common outcome.

Cluster 6 [ Google Earth icon for Cluster 6 ]
Cluster 6 (n=187) (means, variability) is a commonly encountered material, sometimes soils, including clays, and sometimes rocks, too, of martian-typical chemistry. Across the board, this is the least divergent material on Mars, with t-scores within about + 0.3. The most divergent of these is aluminum oxide, with a t-score of +0.312, which suggests the presence in this class of clays. Examples of this material have been found at all four rover sites. At the Pathfinder/Sojourner site in Chryse Planitia, Cluster 6 targets were all soils: After Deployment (MPF, sol 2); Dark Next to Yogi (MPF, sol 5); and Scooby Doo (MPF, sol 10). Cluster 6 was also found in Gusev Crater by Spirit, including Mazatzal (MER- A,sols 81-83), an undisturbed and then brushed rock on the south rim of Bonneville Crater; Kilmary Soil (MER-A, sol 227), an undisturbed soil target on the summit of the West Spur of the Columbia Hills; and Home Plate Superpesis (MER-A, sol 1209), a rock outcrop on the eastern edge of Home Plate). Opportunity found Cluster 6 targets in Meridiani Planum as, for example MontBlanc_LeHauches (MER-B, sol 60), an undisturbed soil on the rippled Meridiani plains at the edge of Eagle Crater where Opportunity landed; Amboy (MER-B, sols 2819-2940), a dozen measurements on an undisturbed rock on the northwest edge of the Cape York segment of the northwest rim of Endeavour Crater; and Thermopylae (MER-B, sols 3984-3991), an undisturbed rock target to the southwest of the Spirit of Saint Louis Crater outside Marathon Valley on the western rim of Endeavour Crater. This region produces a strong signal of smectite clays from the Mars Reconnaissance Orbiter's CRISM spectrometer (Crumpler et al. 2016), clays which form in the presence of abundant neutral to alkaline water. The presence of phyllosilicate clays might be what is picked up in the slight elevation of aluminum oxide in this cluster. This cluster has also been found by MSL. Examples in Gale Crater include Yukon (MSL, sol 161), an undisturbed rock in Yellowknife Bay near the Bradbury landing site; Shackleton (MSL, sol 400), an undisturbed rock at the Darwin Waypoint site; and Kudis (MSL, sol 1245) at the Gobabeb site overlooking the Namib barchan in the Bagnold dune field.
Cluster 7 [ Google Earth icon for Cluster 7 ]
Cluster 7 (n=16) (means, variability) is a rare class, its profile generally close to Mars averages but with nickel extremely over-represented. Zinc and magnesium are slightly more salient than the Mars average. Some of the targets in Cluster 7 are meteorites encountered on the surface, such as Barberton (MER-B, sol 122), Santa Catarina (MER-B, sol 1046), Santorini (MER-B, sols 1745-1747), and Kalos (MER-B, sol 1885). If these came from differentiated asteroids, the nickel enrichment would not be surprising. Arvidson et al., (2011) include a discussion of the many probable meteorites found by Opportunity in Meridiani Planum).

In the spirit of multiple working hypotheses, however, nickel and zinc can also be enriched through preferential alteration of olivines by aqueous, particularly hydrothermal processes (Newsom et al., 2005). Examples of the action of more diagenetic processes that can produce the nickel enrichment (and enhancement of magnesium and zinc) are Moenkopi (MSL, sol 758), Morrison (MSL, sols 767-779), and Torquas (MER-A, sol 1143). This cluster, then, comprises known meteorites as well as some targets of martian origin that may have developed similar characteristics through aqueous alteration.

Cluster 8 [ Google Earth icon for Cluster 8 ]
Cluster 8 (n=102) (means, variability) describes a picritic basalt, an unaltered representative of primitive olivine- rich magmas from the upper mantle. The material is primitive in the sense it did not evolve through fractionation in its source magma, nor has it experienced any significant alteration after emplacement, except possibly in surface rinds and joints (McSween 2015). The material is generally close to the martian average across the oxides and elements, with a slight enhancement in magnesium, sodium, and aluminum oxides. Most targets in this cluster are rocks, but there are also soils derived from them.

The archetypal example is the Adirondack rock after brushing and RATting (MER-A, sols 34-41). Adirondack was the first rock target for Spirit's APXS after landing on the basalt-covered plains of Gusev. The cluster is common throughout the floor of Gusev Crater (McSween, et al. 2006), e.g., Humphrey (MER-A, sols 55-60) on the ejecta blanket of Bonneville Crater and Mojave Joshua (MER-A, sol 150) on the basalt plains a few sols from the West Spur of the Columbia Hills. It is also found up in the Columbia Hills, e.g., Coffee Disturbed Soil (MER-A, sol 280), a disturbed soil sample on the summit of the West Spur; Irvine (MER-A, sol 600), an undisturbed rock on Husband Hill; and at Home Plate, e.g., Thoosa, the final APXS target of Spirit (MER-A, sol 2071), an undisturbed rock off the western edge of Home Plate. Cluster 8 is more rarely encountered by Opportunity in Meridiani Planum. Examples include Auk (MER-B, sol 237), an undisturbed soil target inside Endurance Crater, and Marquette (MER-B, sols 2070-2120).a rock target viewed both brushed and RATted, on the ridged Meridiani plains. It is a minor member of Gale Crater, examples including Ravalli (MSL, sol 1082) in the complex sandstone beds between Maria's Pass and Bridger Basin, and Weissrand (MSL, sol 1182) in a similarly complex sandstone terrain intermixed with sand-filled depressions and basaltic dune fields south of Bridger Basin and northwest of the Namib barchan in the Bagnold dune field.

So, the signal of picritic basalt comes across in the areas explored by the two Mars Exploration Rovers, Spirit and Opportunity, and by the Mars Science Laboratory. The signal, however, seems to come out of regionally distinct mixes of APXS targets. The overwhelmingly most common occurrence of Cluster 8 is in Gusev Crater (71 of the 102 Cluster 8 targets). Indeed, nearly a third of the 220 APXS targets in Gusev Crater fell into Cluster 8. In Gusev Crater, this cluster comprised seventy percent of the forty targets along the long traverse over the Gusev plains. These plains mainly consisted of lava and impact-gardened regolith (McSween et al., 2006). Such targets were basaltic rocks and soils derived from them up in the Columbia Hills; however, targets in this cluster were likelier to be basalt-derived soils than rocks at this location. The cluster also shows up in the Home Plate region, slightly more often rocks than soils. Home Plate is an intensely layered landscape and this yielded a wide variety of target types over a short distance, including the exposures of picritic basalt and soils or sediments derived from them.

In Meridiani Planum, the cluster is far rarer at nineteen, making up about five percent of the 370 MER-B targets. The site was chosen for access to materials potentially altered by water, i.e., the hæmatite signal noticed from orbit (Golombek et al., 2003), so the paucity of unevolved and unaltered basalt is not too puzzling. That said, there is, however, one remarkable profusion of more than half the Meridiani targets in this cluster: the Marquette Island site. This is a large igneous boulder of gabbroic texture that likely formed deep in the crust and was excavated by a distant impact, landing as an erratic in among the æolian ridged plains of Meridiani Planum (Arvidson et al., 2011). Another six can be found at different places along the western rim of Endeavour Crater, apparently material that had been excavated from the subsurface during the impact to form the rim and, so, akin to the kind of material that was lobbed out of some distant crater and landed at Marquette Island.

Cluster 8 is also rare in Gale Crater, again, a site chosen for its exposure of layered materials on Aeolis Mons, including orbitally-detected phyllosilicate clays and sulfates, both signs of water alteration. Again, it is not too odd that only twelve targets out of three hundred APXS readings in Gale Crater so far fell into this cluster. Fully eight of these came from a single active sand dune, Gobabeb, on the edge of the Namib dune field within the Bagnold Dunes complex. This was the first active dune to be analyzed by a rover, though many ripples and megaripples had been investigated earlier. The Bagnold Dunes are comprised of olivine-rich grains, unaltered by water, making the presence of Cluster 8 unsurprising.

Cluster 9 [ Google Earth icon for Cluster 9 ]
Cluster 9 (n=13) (means, variability) is a rarity. The thirteen targets in this cluster are actually distributed between just two rocks, one examined by Opportunity (Tisdale 2 Timmins 1 and Tisdale 2 Shaw 2 and 3, MER-B, sols 2694 and 2701-2702) and the other by Curiosity (Windjana, MSL, sols 612-622 and again on sol 704). Both are clastic rocks that are very highly enriched in zinc and bromine and somewhat enriched in iron oxide. They both share a slight depletion in aluminum oxide, sulfur trioxide, and calcium oxide. They differ dramatically, however, in phosphorous pentoxide (Tisdale spectacularly enriched and Windjana slightly depleted), potassum oxide (Windjana spectacularly enriched and Tisdale close to neutral), and magnesium oxide (Windjana somewhat enriched and Tisdale slightly depleted). The two rocks seem rather distinct from one another, being clustered no doubt on the force of their extreme over-representation in zinc and bromine.

Tisdale 2 appears to be a basaltic impact breccia resulting from the formation of Endeavour Crater. It is part of the Cape York uplifted rim materials on Endeavour's northwest. The fragments comprising it represent a mix of clast sizes and provenances, some basalts (perhaps sampled from depth by the impact itself) and some more typical of the Meridiani Planum surface bedrocks (Des Marais et al. 2012). The listed Tisdale rocks, however, are spectacularly enriched in zinc (Farrand et al. 2013), possibly a signal of a hydrothermal system that extracted the element from basalts and then transported and concentrated it among the Tisdale breccias (Squyres et al. 2012). Bromine, a halogen likely concentrated by evaporation of neutral pH water (Bellucci et al.2017), is also startlingly elevated with the other halogen, chlorine, very slightly depleted. Bromine and chlorine shift relative abundances in the process of evaporative concentration, with chlorine forming salts with sodium earlier in the process, leaving bromine over-represented in the remaining fluid (Rao et al. 2005). Phosphorous pentoxide is also highly elevated, a point of similarity between the listed Tisdale samples and Cluster 10, found only in Gusev Crater, discussed in the next section.

Windjana, the other rock in Cluster 9, is a sandstone found in the middle unit of a three-unit sedimentary stack (the Kimberley Formation). This middle unit, the Dillinger member, features cross-bedded thin layers of basalt-derived sandstone, siltstone, and conglomerate (Treiman et al, 2016). Windjana is divergent from Tisdale 2 in some ways, being more elevated in potassium oxide and depleted in phosphorus pentoxide. The elevation in potassium was attributed in CheMin analysis to potassium feldspar, consistent with sanidine, suggesting an unusually fractionated igneous source or at least a potassic basalt or, alternatively, aqueous alteration (Treiman et al, 2016). Diagenesis by aqueous processes is shown by the presence of manganese-rich cements on rock surfaces and in cracks, but it is unlikely to have gone so far as to produce smectite clays as suggested by the elevated potassium, because of the presence of olivines and plagioclase: These do not long persist unaltered in the presence of water (Treiman et al, 2016; Le Deit et al. 2016; Rice et al. 2017). Le Deit et al. (2016) conclude that the potassium-rich materials may have originated elsewhere, such as on the north rim of Gale Crater, and then been deposited in the Kimberley area before the build-up of Aeolis Mons/Mount Sharp (Rice et al., 2017). Despite the unusual elevation of potassium oxide, Windjana is very similar to Tisdale in its extreme elevation in zinc and bromine, which probably led K-means clustering to group them together.

Cluster 10 [ Google Earth icon for Cluster 10 ]
Cluster 10 (n=28) (means, variability) is an uncommon type, showing significant over-representation in the oxides of phosphorous and titanium and marked enrichment in sodium and aluminum oxides. Nickel and the oxides of magnesium and manganese are slightly depleted and iron and chromium oxides more strongly depleted. Halogens are slightly but variably depressed in this group, as well, while sulfur trioxide is very consistently moderately depleted. This pattern of depletion in halogens and sulfur trioxide de-emphasizes the rôle of aqueous alteration and diagenesis, whether by neutral-alkaline or acidic fluids. The materials, then, appear to be fractionated from a basaltic magma, consistent with the presence of plagioclases and sanidines revealed by other spectrometers on Spirit.

Nearly all instances of this cluster are rocks (only two are soils) confined to Gusev Crater, all within the Columbia Hills, specifically, Husband Hill. Members of this cluster exclusive to the Spirit rover (MER-A) include: Wishstone (sols 334-335), Champagne (sols 353-357), Watchtower (sols 416-417), Methuselah (sols 469-475), Pequod (sols 481-502), Independence (sols 532-542), and Hillary (sols 630-633).

Usui, McSween, and Clark (2008) argue that the Wishstone and Champagne groups derive from tephrites high in phosphorus pentoxide. They envision these as deriving from a high plagioclase basalt eruption or, perhaps, an impact. This pyroclastic flow contained a high phosphorus mineral, merrillite, accounting for the phosphorus pentoxide signal detected by APXS. Merrillite crystals would be an addition picked up, not from cumulates in the magma chamber, but incorporated from a source engulfed and entrained by the eruption. This source material may have experienced metasomatism from CO2-rich mantle fluids and alkaline melts within the rising plume. Merrillites on Earth indicate crystallization from carbonate-rich magma from the mantle (Usui, McSween, and Clark 2008). An intriguing argument holds that the weathering of such plagioclose-rich rocks in the presence of neutral or slightly acidic pH water might have released phosphate minerals into the waters and the combination of neutral water and of the life-critical phosphorous might have made Mars quite life-friendly at least in narrow locales and at least sporadically during Noachian times (Adcock and Hausrath 2015).

Cluster 11 [ Google Earth icon for Cluster 11 ]
Cluster 11 (n=5) (means, variability) is the most eccentric and the smallest cluster of all. All five targets were taken from a single rock encountered by the Curiosity rover, Stephen (sols 627-629), a dark and resistant fracture-fill (Rice et al., 2017). Stephen is located right next to Windjana but shows marked exaggeration of enrichment compared to Windjana: drastically higher zinc, bromine, and chlorine, and the oxides of magnesium and, especially, of manganese. The scale of exaggeration in the same general directions as Windjana probably induced its statistical segregation into its own cluster.

Interestingly, the extremity of manganese oxide concentration has been argued as evidence of highly oxidizing but neutral pH fluids, which would have picked up and oxidized manganese and then precipitated the manganese oxide in cracks and fractures in the Kimberley strata. Such fluids could only have been formed in interaction with an atmosphere containing molecular oxygen, either a low oxygen atmosphere with a very long duration of water movement through rock fractures and fissures or, more plausibly, for a short duration of water movement coupled with a drastically higher atmospheric oxygen content (Lanza et al. 2015; Rice et al., 2017).

On Earth, manganese oxides appeared when its planetary atmsophere shifted from an oxygen-poor condition as oxygen built up with the advent of photosynthesis and of microbial activity. On Mars, this may indicate instead the evaporation of its oceans, lakes, and surface waters as the planet lost its atmosphere with the collapse of its magnetic field. Water vapor in the atmosphere would be photo-dissociated, with the lighter hydrogen lost from the top of the atmosphere but the heavier oxygen building up until it could be oxidized into the rocks and dust of Mars (Webster and Mullane 2016). Groundwater interacting with this oxygen buildup would then be capable of strong redox activity and the precipitation of manganese oxide to the levels seen in the Stephen material and, to less dramatic levels, in other rocks, e.g., Cluster 9, Cluster 13.

Cluster 12 [ Google Earth icon for Cluster 12 ]
Cluster 12 (n=42) (means, variability) displays a mix of oxides and elements quite close to the martian average, basaltic in general character. It shows, however, moderate enrichment in chlorine and, to a lesser extent, in bromine and magnesium. These targets have been interpreted as exhibiting a range of alteration from water and changing solutions in water (Morris and Klingelhöfer 2007; Sutter et al., 2012).

Aqueous alteration resulted in a variety of iron oxides. This variety is not distinguishable through use only of the APXS instrument, which is designed to measure iron(II) oxide: FeO. The Mössbauer spectrometer on the Mars Exploration Rovers, however, permits identification of oxidation states of iron-bearing materials and, thus, various iron oxides and minerals, including olivine, pyroxene, ilmenite, magnetite, nanophase ferric oxide, hæmatite, goethite, jarosite, and iron sulfate (Wdowiak et al. 2003; Schröder, Klingelhoefer, Tremel 2004). Many rocks in Cluster 12 showed a marked prevalence of goethite, a ferric or iron(III) oxide, containing hydroxyl, which requires enduring exposure to water to form (Morris et al. 2006). They also all contain hæmatite, a ferric oxide, which is widely interpreted as requiring the presence of water to form, particularly in acid-sulfate enriched water. Acid-sulfate alteration is associated with hydrothermal or fumarolic activity, especially in the grey crystalline form in which hæmatite is found in Meridiani Planum, where MER-B operates, and the Home Plate area, where the MER-A mission came to an end (Morris et al. 2008). While widely viewed as indicative of aqueous alteration, there are other processes not mediated by water that can produce hæmatite, including oxidation of cooling basaltic glasses (Martel 2003; Minitti, Lane, and Bishop 2005).

This cluster coïncides with a group of both outcrop and float rocks targeted by Spirit (MER-A) in the Columbia Hills called the Clovis class. Clovis rocks are characterized as poorly sorted clastic materials consistent with formation and deposition as ejecta during impact events striking basaltic materials. These were subsequently subjected to various levels of aqueous alteration, most likely by groundwater movement. Alteration is evidenced by the presence of halogens in the APXS results and the shifts in oxidation states of iron seen in Mössbauer results (Squyres et al. 2006). The Clovis class includes Clovis (sols 214-225), Ebenezer (sols 229-235), Uchben (sols 284-304), and Lutefisk,all on the West Spur of the Columbia Hills just after MER-A left the basaltic plains of the Gusev Crater floor (sols 300- 304) (Ming et al. 2006; Ming, Morris, and Clark 2007; Morris et al. 2008). The Clovis group is distinctive for the concentration of ferric oxides, notably goethite and hæmatite, in Mössbauer results. These strongly imply aqueous alteration. In addition, several others, not described as members of the Clovis group, were placed in the same category by K-means clustering. These are found around Home Plate, the final work area of the Spirit rover: Examine This (sols 1173-1179), Eileen Dean disturbed soil (sols 1239-1246), and Innocent Bystander (sols 1251-1252). These targets resemble Clovis rocks in their low olivine; moderate pyroxene, magnetite, and nanophase ferric oxide; and modest hæmatite signals in Mössbauer spectroscopy, but they do not show the moderate to strong goethite seen in the Clovis rocks (Morris et al. 2008, Fig. 4).

The cluster also shows up in Opportunity's work in Meridiani Planum (MER-B), where it is associated with rocks showing veneers, rinds, and fracture fill, which are apparently filled by leachates concentrated there by precipitation out of migrating groundwater: Escher Kirchner (sols 214-216, a float rock featuring a veneer, which was found inside Endurance Crater) (Knoll et al. 2008), Sandcherry (an outcrop rock covered with a dark veneer, sols 3138-3146, Endeavour Crater rim), and Espérance (an outcrop rock covered with a dark veneer and riven by boxwork fractures, sols 3262-3301, also along the Endeavour Crater rim) (Arvidson, R.E., et al. 2014). Espérance is notable as an identification of probable montmorillonite on Mars, montmorillote being a smectite clay that generally forms in neutral aqueous conditions (Ming, Morris, and Clark 2007; Arvidson et al. 2014). Overall, Cluster 12 seems to group together clastic rocks showing cementation by groundwater (West Spur of the Columbia Hills) or hydrothermal groundwater processes (Home Plate) or later infill of fractured and jointed rocks by groundwater alteration products (Endurance and Endeavour craters).

Cluster 13 [ Google Earth icon for Cluster 13 ]
Cluster 13 (n=28) (means, variability), too, shows pervasive aqueous alteration, but probably from sulfate-enriched water. The impacts of such water on mineral breakdown and transport and concentration of elements are quite different from those seen in Cluster 12. Where Cluster 12 produced little divergence in most oxides and elements from the martian norm, except for enhanced chlorine, bromine, and magnesium, alteration in Cluster 13 produced a strong pattern of depletion in the oxides of sodium, aluminum, silicon, and titanium, as well as in chlorine, when compared with the martian average. Sulfur trioxide is dramatically elevated and manganese is somewhat elevated. The hydrology of Noachian Mars involved waters more neutral, even alkaline, in pH, while that of Hesperian Mars, after massive volcanism, was much more sulfur enriched and highly acidic.

Cluster 13 was found only by the two Mars Exploration Rovers, MER-A in Gusev Crater and MER-B in Meridiani Planum. Between the two MER sites, this cluster was more commonly encountered by MER-A. It was not found by Mars Pathfinder in Chryse Planitia, not has it yet been found by the Mars Science Laboratory in Gale Crater. Examples of rocks and soils in this cluster found by MER-A include Paso Robles (MER-A, sol 401) and Paso Robles Light (MER-A, sol 427, climbing Husband Hill), The Paso Robles samples were soils of an unusually bright appearance, which Mössbauer analysis suggested contained ferric sulfate (Ming et al. 2006; Morris et al. 2006). Yen et al. (2008) discuss these and several other samples that wound up in Cluster 13, including Arad (MER-A, sols 723-724, between El Dorado dune field and Home Plate) and Tyrone Mount Darwin (MER-A, sol 1098, southeast and below the cap of Home Plate). They comment that these were all subsurface materials exposed by the rover's wheels, which mixed basaltic soil components in with the bright materials. They interpret the bright materials as ferric sulfate with magnesium sulfate and silica, noting that ferric sulfates form under very acidic, oxidizing conditions, possibly pyroclastic materials resulting from interactions of basaltic magma with water. Yen et al. favor a fumarolic and hydrothermic mechanism for the deposition of these materials, with fluids and fogs strongly enriched in sulfur, possibly indicative of magma degassing nearby, the fluids and vapors rising to the surface and forming condensates at and near the surface, resulting in the light colored soils.

This cluster is also seen at the end of the mission on the northwestern sides of Home Plate between sols 1863 and 2024 (John Wesley Powell, Sackrider, Olive Branch, and Penina). With the exception of John Wesley Powell (sol 1863), these are all disturbed soil samples, similar to the Paso Robles, Tyrone Mount Darwin, and Arad Samra targets found earlier: bright soils covered by a veneer of basalt-derived soils and exposed by the rover's wheels. Home Plate has been interpreted as an accumulation of pyroclastics caused by explosive interactions of basaltic magma and water similar to the earlier targets' context (Yen et al. 2008).

MER-B found examples of this group in several targets at two nearby sites on the Murray Ridge section of the western rim of Endeavour Crater: Pinnacle Island (sols 3546-3564) and Stuart Island (sols 3573-3577). These were not bright soils exposed by the rover's wheels but, instead, were small basaltic rocks from a fracture zone that had been inadvertently overturned by the rover. This disturbance revealed a relatively bright coating of sulfate-rich material that had been, like the Gusev soils, covered by a thin deposit of other materials. Unlike the pyroclastic-derived Gusev materials, these originated as impact-brecciated basalt subsequently subjected to subsurface precipitation of sulfates (Arvidson et al. 2016. Another instance of Cluster 13 was found by Opportunity earlier in its traverse: Gagarin RAT (sol 403, Meridiani plains near Vostok Crater). This was a flat rock with an interior dominated by sulfate-enriched material (iron-, calcium-, and magnesium-sulfates). This was covered by a thin veneer depleted in sulfates and enriched in oxides of aluminum and silicon, probably from the ubiquitous martian dust, and in oxides of sodium, potassium, chlorine, and phosphorous, perhaps from salt concentration during recurrent formation and evaporation of thin films of water at rock surfaces (Knoll et al. 2008).

Cluster 14 [ Google Earth icon for Cluster 14 ]
Cluster 14 (n=18) (means, variability) shows a number of divergences from the martian average, as well as a high degree of agreement among cluster members on the magnitude of most of those divergences. Sulfur trioxide is significantly enriched and calcium oxide is spectacularly over-represented. Silica is significantly under-represented, and the oxides of titanium, aluminum, iron, and sodium are markedly depleted, while magnesium oxide is somewhat depleted. These are materials strongly altered from martian norms. The high enrichment in the sulfur and calcium oxides is consistent with precipitation of calcium sulfates in the cracks and fractures of rock.

Spectra taken by the ChemCam on MSL of one of the rocks in this cluster (Mavor) indicated elevation, not only of calcium and sulfur, but of hydrogen, suggesting that these fill materials are hydrated calcium sulfates, perhaps gypsum and/or the less hydrated bassanite (Nachon et al. 2014). These precipitate at relatively low temperatures and destabilize at warmer temperatures, where the anhydrite version of calcium sulfate forms and is stable at warmer temperatures (Vaniman et al. 2017). The presence of hydrated forms of calcium sulfate, then, not only attests to the presence of water, but also the non-hydrothermal temperatures at which precipitation occurred (Lowell and Yao 2002). As an aside, similar targets analyzed only by ChemCam, not APXS, also showed depletion in all other elements, consistent with the APXS-derived Cluster 14 targets.

As to the source of the calcium in the calcium sulfate, calcium dissolves from calcium plagioclase and high-calcium pyroxene in basaltic rocks into water, including groundwater welling up in or moving through fractured bedrock or regolith. In water it can then encounter and combine with sulfur, if it is available.

The ultimate source of that sulfur was introduced into the then much denser carbon dioxide atmosphere of Mars by volcanic activity (sulfur dioxide or SO2 and hydrogen sulfide or H2S) (Halevy et al. 2007; Gaillard and Scaillet 2009; Levine and Summers 2011). These sulfur species would oxidize into sulfur trioxide or SO3 (which APXS can measure). Sulfur trioxide would dissolve in water to form sulfuric acid or H2SO4. Alternatively, it could dissolve into atmospheric water to form sulfurous acid or H2SO3, which could then oxidize in the atmosphere into sulfuric acid. Sulfuric acid then could condense onto the surface, dissolving into surface waters that could exist in the denser sulfur dioxide enriched carbon dioxide atmosphere of Noachian times (Levine and Summers 2011). There, it could trigger the formation of sulfate minerals and sedimentary beds, which could themselves become the source of sulfate-enriched fluids subsequently migrating through veins and joints in rocks (Nachon et al. 2014).

Very importantly, sulfuric acid acidifies surface and groundwater enough to interfere with the formation of carbonates that would normally be expected to form in waters in contact with a carbon dioxide atmosphere. The near absence of carbonates has been one of the big puzzles on Mars (Ehlmann and Edwards 2014; Ruff et al., 2014; Gaillard et al. 2013; Bibring et al. 2006). Carbon dioxide dissolves in water to form carbonic acid, which can be deprotonated into bicarbonate ions (HCO3-) or further into carbonate ions (CO32-). These can combine with a variety of cations to form familiar carbonates, such as calcium carbonate (limestone, largely CaCO3), calcium-magnesium carbonate (dolomite or CaMg(CO3)2), and iron carbonate (ferrous carbonate or FeCO3). Mars has hardly any carbonates, despite its carbon dioxide dominated, once denser atmosphere and evidence of standing water and even oceans. The puzzle can be resolved by reference to the sulfuric chemistry of Late Noachian and Hesperian Mars and its interference with carbonate formation and reactions with existing carbonates. Of relevance to Cluster 14, calcium carbonate would combine with sulfuric acid to produce carbonic acid and calcium sulfate.

Volcanic activity, the source of sulfur species in Mars' atmosphere and, later, surface and subsurface waters and minerals, intensified on Mars roughly 4.1 Ga ago or even earlier, as the Tharsis complex began emplacement. Volcanism continued very actively from several volcanic centers until about 3.5 Ga ago, tapering down by 3.0 Ga ago, and dwindling to sporadic and localized events, mostly around Tharsis, since then (Gaillard et al. 2013; Ehlmann et al. 2011; Carr and Head 2010; Werner 2009). It should be noted that crater count analyses of the major volcano calderas indicates that there have been eruptions as recently as 100 Mya (Robbins et al. 2011).

The volumes entailed in the eruptions during the most intense activity would have placed large amounts of sulfur dioxide (SO2) and hydrogen sulfide (H2O) in the martian atmosphere. These quickly react with atmospheric water vapor to form sulfuric acid (H2SO4) in the atmosphere. Under modern martian conditions, SO2 cannot withstand photodissociation in the atmosphere for more than a day and, indeed, neither it nor sulfur monoxide are evident in Mars' atmosphere at the present (Nakagawa et al. 2009). Under the denser atmosphere of Noachian Mars, however, it could well last for a duration a couple of orders of magnitude longer, enough to enable its conversion to H2SO4 (Levine and Summers 2008).

Precipitation of sulfuric acid in water would acidify any surface waters and groundwaters, triggering a drastic change in the aqueous geochemistry of Mars, called by Bibring and colleagues the Theiikian Period (Bibring et al. 2006). This may be the major factor accounting for the vanishingly small presence of carbonates on martian surfaces (Bibring et al. 2006; Webb 2004; Levine and Summers 2008). Besides interfering with the production of carbonates, sulfuric acid rain also would result in the formation of sulfates, such as the calcium sulfates of Cluster 14, and a series of other sulfates, depending on which metal cations were available, temperature, pressure, and pH (Fan et al. 2006).

Indeed, calcium sulfate has been directly detected by the Mini-TES spectrometer on the MER-B and MSL rovers, commonly in veins prominent on the surface of rocks. This identification reïnforces the impression given by Cluster 14, with its over-representation of sulfur trioxide and calcium oxide.

Targets in Cluster 14 include two rocks on the northwestern rim of Endeavour Crater investigated by Opportunity: Homestake (MER-B, sols 2764-2767), described in Squyres et al. 2012, was the first detection of calcium sulfate on Mars, and Ootsark (MER-B, sols 2974-2976) (Yen et al. 2014). The cluster was also detected in three areas of Gale Crater by Curiosity: the Mavor rock in the Yellowknife Bay area not far from the landing site (MSL, sol 158) (Nachon et al. 2014)c; the Coalville (MSL, sol 930) and Alvord rocks near the Pahrump Hills (MSL, sols 935-937) (Berger et al. 2015); and Palmwag (MSL, sol 1275) (Hurowitz et al. 2017) and Rossing (MSL, sol 1287) in the Naukluft Plateau area.

Cluster 15 [ Google Earth icon for Cluster 15 ]
Cluster 15 (n=72) (means, variability) is widely distributed, found by all rovers except among the eleven targets of Mars Pathfinder/Sojourner. It occurs most commonly on soil targets, whether undisturbed or disturbed. It is also found on a number of rock targets, most of which had not been brushed, RATted, or drilled. The oxides and elements cling closely to the martian averages, except that chromium(III) oxide, Cr2O3, is somewhat elevated. This cluster captures the martian soil, which is strikingly homogeneous across Mars, representing the breakdown of local rocks (basaltic on most of Mars), together with fines picked up in duststorms and then sifted down around the planet, where it forms a cover on undisturbed rocks.

These fines include oxidized iron and particulates derived from unaltered olivine and pyroxene, that is, from minerals showing little to no presence of water. The oxidized iron includes magnetite or ferrous-ferric oxide (Fe3O4 or FeO.Fe2O3), in results from the Mössbauer spectrometer, another rover instrument. Chromium(III) can sometimes substitute for either or both of the iron(III) in the ferric iron (FeO.CrFeO3 or FeO.Cr2O3)), perhaps accounting for the modest elevation in average chromium oxide (Cr2O3) picked up by the APXS.

It should be noted that there are only two anomalously high readings of Cr2O3, which pulled the mean t-score for Cluster 15 from 0.767 to 1.114. Both readings were from a single undisturbed rock in the Columbia Hills, Gusev Crater (Assemblee Gruyère and Assemblee APXS). This rock is described as anomalously evolved towards an aluminous, montmorillonite-like composition, and more akin to a few other targets that fell in Cluster 10 (Hurowitz and McLennan 2007). Indeed, these two targets are found in the middle of the only concentration of Cluster 10 on Mars: the Husband Hill area of the Columbia Hills. Examining them more closely, they do have elevated Al2O3 compositions, also rather deviant in Cluster 15. They are somewhat eccentric in other oxides and elements, too, but not sharing their deviant readings with any other cluster and, so, may be been deposited in Cluster 15 for want of a better suited cluster.

More typical examples of Cluster 15 in Gusev Crater include Bighole Trico (MER-A, sol 115), a trench cut by Spirit's wheels into soil on the Gusev plains about midway between Missoula Crater and Lahontan Crater (Karuntatillake et al. 2007). Another, also in Gusev Crater, is Polyphemus (MER-A, sols 1981-1995), located on the western edge of the Home Plate area near the final resting place of the Spirit rover. The Polyphemus soil targets had been RATted, exposing the unaltered basaltic grains that are common among Cluster 15 targets. Altogether, 13 of MER-A's 220 targets fell into Cluster 15.

Cluster 15 has also been found by MER-B in Meridiani Planum (28 targets of MER-B's 370). One example is Tarmac found near the Opportunity landing side in Eagle Crater (MER-B, sol 11). Tarmac is deemed representative of Meridiani Planum soils that are basaltic in origins. The Mössbauer Spectrometer can differentiate various iron species, where APXS can only discern iron(II) oxide (FeO). MS analysis describes Tarmac and similar soil targets as dominated by olivine, pyroxene, and nanophase ferric oxides (Morris et al. 2006). As with many of the Cluster 15 occurrences in Gusev Crater, the impression here is of a soil built from unaltered basaltic grains admixed with the ferric oxides in the ubiquitous martian dust (Banin 1992), which forms coverings, drifts, alteration rinds, and crusts all over Mars (Bishop et al. 2002; Morris and Klingelhöffer 2007). Other examples found by MER-B include Rocknest_Void_Soil, an undisturbed soil on the interior slope of southwest Endurance Crater (MER-B, sol 249) and Liver Eating Johnson, an undisturbed soil amid regolith and ripples on the outer western rim of Endeavour Crater on the west side of Cape Tribulation just north of Marathon Valley (MER-B, sol 3925) (Crumpler et al. 2016).

Cluster 15 has also been found 31 times among the 300 Gale Crater targets. Examples include PortageRP (MSL, sol 89), a soil sample from a wheel print in the wind drift material at the Rocknest work site. The Rocknest waypoint was about 400 m east of the Bradbury landing site en route to the Yellow Knife Bay and Glenelg detour before MSL headed for Mt. Sharp. Portage exemplifies a "...representative regional composition of unaltered basaltic host rocks ... similar to typical upper Martian crust" (Bridges et al. 2015: 6). It is depicted in Schmidt et al. (2014) as quite similar to Gusev basaltic soils, particularly Adirondack_asis and several from Home Plate, which are also in Cluster 15. Portage is often used as a baseline against which to compare relative element and oxide abundances in other rocks and soils on the floor of Gale Crater (e.g., Berger et al., 2014; Gellert et al. 2015; Gellert et al. 2016). Similar soils have been found at several locations along the MSL traverse. Gobabeb Scoop2 (MSL, sol 1225) is one of these, a soil sample taken from a barchan dune (Namib) in the Bagnold Dunes, roughly 7 km from the landing site and Rocknest. The site was chosen as representative of a strong olivine signal, implying no water alteration, and its high æolian activity (Achilles et al., 2017: 2347), and several samples were subjected to the full array of MSL instrumentation. The dunes here are quite active, unlike the sand and soil at Rocknest, which removes the global Mars dust component (Ehlmann et al. 2017), yet Gobabeb Scoop2 remains within Cluster 15, suggesting that it is the unaltered basalt (olivine) component that actually drives the character of the cluster more than the ferric oxide common in the global dust.

Conclusions

K-means clustering within PAST flexibly classifies APXS targets into coherent groups, the number of which is an arbitrary choice. I had experimented with reducing the database by performing quartimax and varimax rotated principal components analysis in SPSS first and then using k-means clustering to yield 10 and 20 clusters but, since the goal was creation of a manageable lab exercise for my Geography of Mars class, I decided that the extra layer of interpretation of the underlying components might be excessive. I then tried k-means clustering on the t-scores of the APXS readings on an intermediate number of classes, 15, with some apprehension, since k-means clustering in PAST sometimes founders on large databases. The software was able to perform the classification, however, and the groupings that emerged make sense, as seen in the discussion above.

Emergent metaclusters

There seems to be another, underlying structure beneath the 15 classes, however. That is, the 15 clusters can be organized into 5 "metaclusters" or clusters of similar clusters. The viewgraphs showing relative abundances of oxides and elements have been reorganized by metacluster, each with a distinctive background coloring:

One of these is a one-cluster metacluster comprised of Cluster 7 or meteorites and possible meteorites (shown with a brown background). The relative distribution of oxides and elements is pretty close to the Mars norm, except for high over-representation of nickel. It should be noted that there are some aqueous alteration processes operating on olivine, especially in hydrothermal contexts, that can mobilize and concentrate nickel and zinc (which is also enhanced in nearly all samples in this cluster).

The second group is basaltic rocks and soils largely derived from them, showing little alteration or diagenesis. These, shown with a black background, comprise clusters 6, 8, 15, and 5. Their mean relative abundances are close to the Mars norm, some with one or two excursions from the norms that pulled them into separate clusters.

The third metacluster contains three clusters, 2, 3, and 10, set off with a red background. These three show relative depletion in magnesium oxide, iron(II) oxide, chromium oxide, manganese oxide, and sulfur trioxide, while chlorine, bromine, zinc, and calcium oxide are at Mars norms or slightly below. Meanwhile, silica is slightly to significantly over-represented, while the oxides of sodium, aluminum, and potassium range from Mars-neutral to significantly over-represented. The oxides of phosphorous and titanium range from very slight depletion to extremely high over-representation. The impression is of targets comprised of fractionated igneous materials, such as andesitic basalts, andesites, even granites, representing evolved magma derived materials.

The fourth metacluster, shown with a blue background, brings together four clusters, 1, 12, 9, and 11. These form a series featuring enhanced levels of chlorine and bromine and seem to involve the alteration or diagenesis of basaltic materials by neutral or alkaline water, most commonly small amounts of groundwater, with evaporation concentrating the two halogens. Cluster 1 shows Mars-typical relative distributions of oxides and elements with a slight over-representation of chlorine, bromine, and iron(II) oxide. Cluster 12 is also Mars-typical, except for a more marked enhancement of the two halogens, together with enhancement in magnesium oxide. Cluster 9 strongly exaggerates bromine, zinc, and potassium oxide, with smaller enhancements in chlorine and magnesium oxide. Cluster 11 (with only 5 targets) shows extreme over-representation of chlorine, bromine, zinc, and the oxides of potassium and magnesium.

The fifth metacluster groups together clusters 4, 13, and 14 and is shown with a green background. These are unified by over-representation of sulfur trioxide and bring to mind the sulfuric acid and sulfate geochemistry of the Theikiian period (Late Noachian through Hesperian periods) as characterized by Bibring et al., (2006). Cluster 4 is close to Mars norms for all oxides and elements, except for a noticeable enhancement in sulfur trioxide. Cluster 13 raises sulfur trioxide into extreme over-representation, with manganese oxide noticeably elevated and significant depletion in silica and marked depletion in chlorine and the oxides of sodium, aluminum, and titanium. Cluster 14 shows dramatic over-representation of sulfur trioxide and significant depletion in silica, with marked under-representation in the oxides of sodium, aluminum, titanium, and iron, with an odd and extreme over-representation in calcium oxide, perhaps indicating calcium sulfates precipitated in joints and cracks.

These groupings are visible in various diagrams of the associations among particular elements and oxides, such as ternary SAF diagrams of silica, alkali, and ferromagnesium oxides, ternary AFM diagrams (alkali oxides of sodium and potassium; iron oxide, here only FeO; and magnesium oxide), and scatterplots of sulfur trioxide and the halogens and of silica and the alkali oxides.

Origination and development pathways linking the clusters and metaclusters

In a manner of speaking, these five metaclusters themselves seem to fall into three starting points, one of which then departed on two different historical trajectories. Seven of the clusters are essentially basalts or soils based on basaltic grains. Of these, clusters 6, 8, 15, and 5 were grouped into the basaltic metacluster showing little evolution or alteration. This is the dominant starting point and the one from which the two aqueous alteration pathways diverge.

Clusters 1 and 4 are also Mars-typical basaltic in character but showing slight elevations in two different aqueous alteration or diagenetic pathways. Cluster 1 shows elevation in halogens, marking evaporative concentration of neutral or alkaline waters, and this is an alteration pathway developed progressively more strongly in clusters 12, 9, and 11. Cluster 4 is basaltic in character but with a slight elevation in sulfur trioxide and the sulfur/sulfate signature and the acidic aqueous alteration or diagenetic pathway is exaggerated in clusters 13 and 14.

Cluster 7, comprised of apparent meteorites, is the second starting point, basically Mars-typical in all oxides and elements except for high elevation in nickel and faint elevations in zinc and magnesium. The origins of most of these, no matter how similar to Mars, are exogenous to Mars, but the cluster may possibly also include a few targets originating as martian basalts and then subjected to hydrothermic alteration that led to the concentration of the fluid-mobile zinc and magnesium, as well as nickel. Alteration or diagenesis of meteorites might obscure meteoritic origin in the clustering process and, so, this origin isn't as obviously fruitful as the conventional martian basalts. Some of the targets grouped into this class, however, may not be meteoritic at all, but the result of extreme alteration of Mars-indigenous materials by hydrothermal processes.

The third starting point, also difficult to trace into aqueous alteration pathways, lies in evolved magmas. These are found in clusters 2, 3, and 10. None of these show the slightest elevation in chlorine, bromine, or sulfur trioxide, implying that the shifts in the other oxides and elements are not the result of aqueous modification. All of them are depleted slightly or strongly in iron(II) oxide and magnesium oxide. All are slightly or strongly elevated in silica. Cluster 2 is neutral in the alkali oxides (sodium and aluminum), while clusters 3 and 10 are markedly elevated in these, while Cluster 10 is markedly over-represented in the oxides of phosphorous and titanium. Since silica can be liberated from source rocks, mobilized, and concentrated in sink materials by neutral to alkaline water moving through basalts, there is a possibility that Cluster 2 is more altered than evolved, but the other signs of neutral to alkaline water are not present.

In all, then, there seem to be three starting points for the materials on the martian surface that were investigated by APXS and here grouped into 15 clusters: basalt/basaltic materials, meteoritic materials, and evolved materials. One cluster is mostly, if not all exogenous, while the two other starting points represent three different martian development pathways: little to no alteration or diagenesis of either basaltic or evolved materials, alteration or diagenesis of basaltic materials by neutral to alkaline water, and alteration or diagenesis of basaltic materials by acidic water.

The aqueous development pathways are linked to changes in the martian atmosphere. Neutral or somewhat alkaline aqueous processes are associated with the Noachian period, especially its early and middle phases, and possibly reaching into the later pre-Noachian (an increasingly recognized period, representing the accretion of the planet up until the point of crater saturation where it becomes impossible to age surfaces). The martian atmosphere was much denser, in places warm enough to support water's liquid phase, judging from dendritic channel networks and suggestions of lakes and oceans. This would be the time supporting neutral or somewhat alkaline aqueous alteration and diagenetic processes, which in places generated phyllosilicate clay formation. In the APXS data, this would be implied by elevation in chlorine and bromine, which readily dissociate out of salts dissolved in water generally without affecting water pH and then concentrate and precipitate out of evaporating water.

Later in Mars' history, from the Late Noachian into the Hesperian, drastic changes affected the martian atmosphere. Mars gradually lost its atmosphere, a process triggered at least in part by the collapse of its dipole magnetic field and the protection it offered against a (then stronger) solar wind. Even as its density declined, there were shifts in the gasses present, with an increase in sulfur dioxide and hydrogen sulfide as volcanic activity ramped up. This altered hydrochemistry, producing sulfuric acid and marked acidification of surface and groundwaters, resulting in the formation of sulfate minerals, such as calcium sulfate, magnesium sulfate, and iron sulfates, often precipitated as rinds or in cracks and joints. In the APXS data, this is reflected in the presence of sulfur trioxide and sometimes in elevation of calcium oxide or iron oxide.

Many of the clusters in the basaltic metacluster may indicate that, as on Earth, there was geographic variability in the availability of water in deep time. These materials sometimes represent primitive basalts rich in olivines and pyroxenes and the presence of these minerals on the surface is a contraindication to the presence of water, since they alter so readily in the presence of even small amounts of water. Some of these materials may not have been exposed to the atmosphere until the advent of "modern" Mars, the Amazonian period, which goes back roughly 3 billion years. The Amazonian is exceptionally dry, the atmosphere so thin that what small amounts of water there are can only exist as ice or vapor. The dominant erosive force, ironically, is wind, low force wind operating over billions of years. Surface geochemistry, then, is dominated by oxidation and anhydrous iron oxides. The APXS data may indicate these with the one iron oxide it detects, iron(II) oxide (but this may also be associated with iron sulfates and hæmatites, which require water to form), so the Amazonian atmospheric signal is ambiguous. More basaltic materials from whichever time period show up in APXS data as neutral to elevated oxides of iron, magnesium, manganese, chromium, and, sometimes, calcium, as well as depletion in felsic oxides. The persistence of olivines and pyroxenes on the surface does indirectly speak to the extreme aridity of Amazonian Mars, but these minerals cannot be directly detected or inferred through APXS.

How the student lab turned out

Since this project originated in the construction of a lab for my Geography of Mars class, the next step entailed having student groups experiment with a 4-cluster number request in k-means clustering, to see if APXS targets will be allocated to the emergent metaclusters seen here. I had students select 4 clusters because the fifth cluster comprised so few targets, even if of unique origination. The students also learned to create KMZ files in a spreadsheet for mapping in Google Earth Mars to help them see if their clustered APXS targets make geomorphic sense spatially.

The Geography of Mars students in the Spring 2018 section did carry out this process. As expected from the iterative location-reallocation process of K-means clustering from randomized initial seeds, there were some differences among the labs turned in by the sixteen students, and these differences led to the emergence of a fifth cluster among the ensemble of student labs, despite the request for 4 clusters.

In general, the group's results conformed to the 4 metaclusters: basaltic, evolved magma-derived, alteration by neutral/alkaline water, and alteration by acidic water. Most students' results placed the meteorite-dominated group with the basaltic metacluster. Eight of the sixteen reported exactly these 4 clusters.

Three students' 4 clusters did not include the acidic alteration group at all, while one other produced 2 acidic alteration groups (one with enhanced calcium oxide, perhaps picking up on calcium sulfate deposits at the expense of detecting neutral-aqueous altered materials). Three students did not detect evolved magma derived materials at all, while another three detected 2 such categories. When 2 evolved magma categories were differentiated, they would bifurcate between silica-enriched and alkali oxide-enriched. Two students did not extract a category for neutral-water altered materials, while another differentiated 2 such categories: One replicated the conventional neutral-aqueous metacluster while the other pulled out the five "Stephen" targets (Cluster 11 in my original scheme), featuring extreme enrichment in the two halogens and zinc. While most of the students' results placed the meteoritic group in their broader basaltic cluster, three of the students' results extracted them as a separate cluster, displacing evolved magma derived or acid-aqueous altered clusters in the process.

As a group, students extracted 5 clusters in total: basaltic was universally pulled out, evolved magma derived was recognized by thirteen and sometimes bifurcated into silica and alkali-oxide subtypes, neutral-aqueous altered materials were recognized by fourteen (with one bifurcated into extreme and less extreme variants), acid-aqueous altered by thirteen (with one specifically pulling out calcium sulfate as a distinct subtype), and three picked out the meteoritic group (with thirteen placing these materials among the basalts). As a collective, they reproduced the metaclusters that emerged when I manually grouped my 15 original clusters.

When the two approaches to classifying the APXS targets are compared, the 4 cluster approach tended to obscure some of the diversity of the APXS targets under the basalt banner. The targets showing very small deviations in the direction of magma evolution (Cluster 2), neutral aqueous interaction (Cluster 1), and interaction with acidic water (Cluster 4) would be deemed basaltic by the clustering algorithm when so few clusters are requested. These deviations were picked up when k-means clustering was forced to differentiate a far larger number of clusters and then could be spotted and retained during the subjective process of reducing the number of 15 clusters to 5 metaclusters. The outcome was that my basaltic metaclass contained 393 targets, while the fifteen students' averaged 626.4 targets. Where there were 142 targets in my evolved magma derived metacluster, students detected 120.3 such targets on average. My neutral/alkaline aqueous altered metacluster contained fully 172 targets, but the student collective detected only 25.4 in their corresponding cluster. The targets in the acidic aqueous altered metaclass comprised 178, while students placed an average of 123.5 in the corresponding class. Where I had identified 16 targets as likely meteorites, the student group counted 5.4 such targets. So, by asking for 4 clusters at the start, basalt tamped down the signals of the other 4 metaclusters.

Here is a link to viewgraphs comparing the 15 clusters to 5 metaclusters aggregation results to those of students requesting 4 clusters (and getting 5 as a collective):

Future work

The database is already out of date: It took me about a year to consolidate the database and reconcile latitudes and longitudes, construct the KMZ, analyze the results for my instructional needs, and write up the outcome in the interstices of my schedule. The lab activity based on it turned out quite successful: Students got to work with the consolidated database, practice using k-means clustering and interpreting its results in light of what they'd learned about the origins and evolution of Mars' crust and atmosphere, learned how to do mass imports of spatial data into Google Earth Pro for mapping their classifications, and materially help me validate my own cluster and metacluster target classification system. Their classification schemes echoed my own results, but there was masking of some magma evolution and aqueous alteration and diagenesis going directly to the final reduced classification rather than taking the "scenic route" through forcing a detailed classification and then aggregating similar clusters to the five emergent metaclusters. I would recommend that longer process to create a stable classification of martian rocks and soils that allows interregional comparisons on a common base. The general approach might be useful for other rover instruments as well, such as the Mössbauer spectrometer (MER-A and MER-B) and the Sample Analysis at Mars (SAM) and the Chemistry & Mineralogy X- Ray Diffraction (ChemMin) instrument on MSL. It might work for orbiter based spectrometers, too (Mars Global Surveyor Thermal Emission Spectrometer; Mars Reconnaissance Orbiter Compact Reconnaissance Imaging Spectrometer for Mars; Mars Odyssey Thermal Emission Imaging System and Gamma Ray Spectrometer; Mars Express Omega IR Mineralogical Mapping Spectrometer).

Curiosity and Opportunity (until the massive dust storm of 2018 shut it down, possibly permanently), meanwhile, have relentlessly added targets, and the new materials can be expected to create changes in the clustering results. The process described here, however, is very labor-intensive. It would be useful if the process of mapping each target were routinized and reported in a uniform format on the PDS. Reading of the spectra and latitude-longitude information could be programmed and automated, along with the performance of k-means clustering at desired numbers and then the graphs used here automated. The outcome could then be an interactive GIS allowing users to customize analysis to suit their own interests in the geochemistry of martian surfaces.

I may go through the whole process once more, should Opportunity finally be deemed unrecoverable, as that would be a fitting end-point pending the arrival of Mars 2020 and ExoMars and the continuing exploration by Curiosity. As with most web sites, this one, then, is "under construction."

Acknowledgements

I wish to thank the following students in the CSULB GEOG 441/541 course in Spring 2018 who participated in this lab and contributed their data:
  • Juan Arias
  • Ruby Bollo
  • Mary Bunting
  • Jason Callanan
  • Brian Carroll
  • Kyle Drake
  • Enadina Lozano
  • Chloe Marchman
  • Sawyer Marks
  • Edgar Martinez
  • Randall McKean
  • Nina Miller
  • Devon Sharp
  • William Shaw
  • Brooke Shorey
  • Salena Tach

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Maintained by Christine M. Rodrigue

Last revised: 06/18/19