Thermal Emission Spectroscopy of Microcrystalline Sedimentary Phases: Effects of Natural Surface Roughness on Spectral Feature Shape

1,2Craig Hardgrove,1A. Deanne Rogers,1Timothy, D. Glotch,1,3Jessica, Anne Arnold
1Stony Brook University, Department of Geosciences, Stony Brook, NY
2Arizona State University, United States
3University of Oxford, United Kingdom

Distinguishing between micro and macrocrystalline mineral phases can help constrain the conditions under which those minerals formed or the degree of post-depositional alteration. This study demonstrates the effects of crystal size and surface roughness on thermal infrared emission spectra of micro and macrocrystalline phases of the two most common minerals on Earth, quartz and calcite. Given the characteristic depositional and environmental conditions under which microcrystalline minerals form, and the recent observations of high-silica deposits on Mars, it is important to understand how these unique materials can be identified using remote infrared spectroscopy techniques. We find that (a) microcrystalline minerals exhibit naturally rough surfaces compared to their macrocrystalline counterparts at the 10 µm scale; and that (b) this roughness causes distinct spectral differences within the Reststrahlen bands of each mineral. These spectral differences occur for surfaces that are rough on the wavelength scale, where the absorption coefficient (k) is large. Specifically, the wavelength positions of the Reststrahlen features for microcrystalline phases are narrowed and shifted compared to macrocrystalline counterparts. The spectral shape differences are small enough that the composition of the material is still recognizable, but large enough such that a roughness effect could be detected. Petrographic and topographic analyses of microcrystalline samples suggest a relationship between crystal size and surface roughness. Together, these observations suggest it may be possible to make general inferences about microcrystallinity from the thermal infrared spectral character of samples, which could aid in reconstructions of sedimentary rock diagenesis where corresponding petrographic or micro-imaging is not available.

Reference
Hardgrove C, Rogers AD, Glotch TD, Arnold JA (2016) Thermal Emission Spectroscopy of Microcrystalline Sedimentary Phases: Effects of Natural Surface Roughness on Spectral Feature Shape. Journal of Geophysical Research, Planets (in Press)
Link to Article [DOI: 10.1002/2015JE004919]
Published by arrangement with John Wiley & Sons

Variable microstructural response of baddeleyite to shock metamorphism in young basaltic shergottite NWA 5298 and improved U–Pb dating of Solar System events

1James R. Darling, 2Desmond E. Moser, 2Ivan R. Barker, 3Kim T. Tait, 4Kevin R. Chamberlain, 5,6Axel K. Schmitt, 3Brendt C. Hyde
1School of Earth and Environmental Sciences, University of Portsmouth, Portsmouth PO1 3QL, UK
2Department of Earth Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada
3Department of Natural History, Mineralogy, Royal Ontario Museum, Toronto, Ontario M5S 2C6, Canada
4Department of Geology and Geophysics, University of Wyoming, 3006, Laramie, WY 82071, USA
5Department of Earth and Space Sciences, UCLA, Los Angeles, CA 90095, USA
6Institut für Geowissenschaften, Universität Heidelberg, 69120 Heidelberg, Germany

The accurate dating of igneous and impact events is vital for the understanding of Solar System evolution, but has been hampered by limited knowledge of how shock metamorphism affects mineral and whole-rock isotopic systems used for geochronology. Baddeleyite (monoclinic ZrO2) is a refractory mineral chronometer of great potential to date these processes due to its widespread occurrence in achondrites and robust U–Pb isotopic systematics, but there is little understanding of shock-effects on this phase. Here we present new nano-structural measurements of baddeleyite grains in a thin-section of the highly-shocked basaltic shergottite Northwest Africa (NWA) 5298, using high-resolution electron backscattered diffraction (EBSD) and scanning transmission electron microscopy (STEM) techniques, to investigate shock-effects and their linkage with U–Pb isotopic disturbance that has previously been documented by in-situ U–Pb isotopic analyses.

The shock-altered state of originally igneous baddeleyite grains is highly variable across the thin-section and often within single grains. Analyzed grains range from those that preserve primary (magmatic) twinning and trace-element zonation (baddeleyite shock Group 1), to quasi-amorphous ZrO2 (Group 2) and to recrystallized micro-granular domains of baddeleyite (Group 3). These groups correlate closely with measured U–Pb isotope compositions. Primary igneous features in Group 1 baddeleyites (n=5)(n=5) are retained in high shock impedance grain environments, and an average of these grains yields a revised late-Amazonian magmatic crystallization age of 175±30 Ma175±30 Ma for this shergottite. The youngest U–Pb dates occur from Group 3 recrystallized nano- to micro-granular baddeleyite grains, indicating that it is post-shock heating and new mineral growth that drives much of the isotopic disturbance, rather than just shock deformation and phase transitions.

Our data demonstrate that a systematic multi-stage microstructural evolution in baddeleyite results from a single cycle of shock-loading, heating and cooling during transit to space, and that this leads to variable disturbance of the U–Pb isotope system. Furthermore, by linking in-situ U–Pb isotopic measurements with detailed micro- to nano-structural analyses, it is possible to resolve the timing of both endogenic crustal processes and impact events in highly-shocked planetary materials using baddeleyite. This opens up new opportunities to refine the timing of major events across the Solar System.

Reference
Darling JR, Moser DE, Barker IR, Tait KT, Chamberlain KR, Schmitt AK, Hyde BC (2016)
Variable microstructural response of baddeleyite to shock metamorphism in young basaltic shergottite NWA 5298 and improved U–Pb dating of Solar System events. Earth and Planetary Science Letters 444, 1–12
Link to Article [doi:10.1016/j.epsl.2016.03.032]
Copyright Elsevier

Temperature dependent grain growth of forsterite–nickel mixtures: Implications for grain growth in two-phase systems and applications to the H-chondrite parent body

1J. Guignard, 2M.J. Toplis,2M. Bystricky, 2M. Monnereau
1European Synchrotron Radiation Facility, 71 Avenue de martyrs, 38000 Grenoble, France
2IRAP, Université de Toulouse, CNRS, UPS, Toulouse, France

Grain growth experiments in the system forsterite (Fo) + nickel (Ni) have been performed on two analogue mixtures of ordinary chondrites, with volume % of Fo:Ni (95:5) and (80:20). These two mixtures have been studied at temperatures of 1390 °C and 1340 °C, at an oxygen fugacity (fO2) three orders of magnitude below the Ni–NiO buffer, for durations between 2 h and 10 days. Microstructures and grain size distributions show that grain growth is normal and that for durations >10 h the Zener relation is verified (i.e., the ratio of Fo and Ni grain size is independent of time). Comparison with results previously obtained at 1440 °C shows a similar grain growth exponent (n∼5n∼5) for both phases, consistent with growth of forsterite by grain boundary migration, limited by the growth-rate of nickel. The details of size distribution frequencies and the value of grain-growth exponent indicate that the nickel grains, which pin forsterite grain boundaries, grow by diffusion along one-dimensional paths (i.e., along forsterite triple junctions). The derived activation energies for nickel and forsterite are 235±33 kJ/mol235±33 kJ/mol and 400±48 kJ/mol400±48 kJ/mol respectively. Within the framework of the Zener relation, this unexpected difference of activation energy is shown to be related to temperature-dependent variations in the ratio of Ni and Fo grain-size that are consistent with observed variations in Fo–Ni–Fo dihedral angle. These data thus indicate that the presence of all phases should be taken into account when considering the activation energy of growth rate of individual phases. As an application, the experimentally derived growth law for metal has been used in conjunction with temperature–time paths taken from models of the thermal history of the H-chondrite parent body to estimate the grain size evolution of metal in H-chondrites. A remarkably self-consistent picture emerges from experimentally derived grain-growth laws, textural data of metal grains in well characterised H-chondrite samples, and geochemically constrained temperature–time paths, providing the potential to use textural data of metal as a window into the thermal history of chondritic samples.

Reference
Guignard J, Toplis MJ, Bystricky M, Monnereau M (2016) Temperature dependent grain growth of forsterite–nickel mixtures: Implications for grain growth in two-phase systems and applications to the H-chondrite parent body. Earth and Planetary Science Letters 443, 20–31
Link to Article [doi:10.1016/j.epsl.2016.03.007]
Copyright Elsevier

The oxidation state and mass of the Moon-forming impactor

1Jon Wade, 1Bernard J. Wood
1Department of Earth Sciences, South Parks Road, Oxford OX1 3AN, UK

Physical simulations of the origin of the Moon have, until recently, centred on impact, about 100 M.yr after the origin of the solar system, of a Mars-like body (10–20% Earth mass) on a near fully-accreted protoEarth. Although this model provides an explanation of the distribution of mass and moment of inertia of the Earth–Moon system it has recently been found that modification of the initial conditions greatly expands the range of permissible impactor masses. Here we take an alternative approach and consider how the oxidation state and mass of the impactor affect the chemical compositions of the product Earth and Moon. We apply the constraints that silicate Moon is richer in FeO than silicate Earth (9–13% as opposed to 8.05%), that their Hf/W ratios are both ∼25 and that they are virtually identical in isotopes of O, Ti, Si, Ni, Cr and W. We then grow protoEarth using a standard accretionary model which yields the correct mantle abundances of Ni, Co, W, Mo, Nb, V and Cr, and add to this body different masses of impactor. The impactor is assumed to be either highly oxidised (∼18% FeO), highly reduced (∼0.3% FeO) or undifferentiated and chondritic. In order to satisfy the isotopic constraints silicate Moon is assumed to be derived principally from silicate protoEarth.

We find that an oxidised or chondritic impactor of ∼0.15 ME∼0.15 ME can satisfy the isotopic constraints (most importantly ε182W), FeO contents and Nb/Ta of Earth and Moon, but leads to implausibly low Hf/W of ∼12–16∼12–16 in silicate Earth and ∼4–6∼4–6 in silicate Moon. This is because the Moon requires more impactor mantle, with low Hf/W, than Earth to reach its higher FeO content. In contrast, impact of a similar mass (10–20% MEME) of highly reduced, Mercury-like impactor on an oxidised protoEarth (∼10.7% FeO in mantle) satisfies the isotopic constraints, FeO contents, Nb/Ta and Hf/W of silicate Earth and Moon given a small amount of post-impact re-equilibration of terrestrial mantle with impactor core. The presence of a small S-rich lunar core is consistent with this reduced impactor scenario. We conclude that the geochemical properties of Earth and Moon strongly favour a reduced impactor of 10–20% MEME.

Reference
Wade J, Wood BJ (2016) The oxidation state and mass of the Moon-forming impactor. Earth and Planetary Science Letters 442, 186–193
Link to Article [doi:10.1016/j.epsl.2016.02.053]
Copyright Elsevier

The global surface composition of 67P/CG nucleus by Rosetta/VIRTIS. (I) Prelanding mission phase

1Gianrico Filacchione et al. (>10)*
1INAF-IAPS, Istituto di Astrofisica e Planetologia Spaziali, Area di Ricerca di Tor Vergata, via del Fosso del Cavaliere, 100, 00133 Rome, Italy
*Find the extensive, full author and affiliation list on the publishers website

From August to November 2014 the Rosetta orbiter has performed an extensive observation campaign aimed at the characterization of 67P/CG nucleus properties and to the selection of the Philae landing site. The campaign led to the production of a global map of the illuminated portion of 67P/CG nucleus. During this prelanding phase the comet’s heliocentric distance decreased from 3.62 to 2.93 AU while Rosetta was orbiting around the nucleus at distances between 100 to 10 km. VIRTIS-M, the Visible and InfraRed Thermal Imaging Spectrometer – Mapping channel (Coradini et al., [2007] Space Sci. Rev., 128, 529–559) onboard the orbiter, has acquired 0.25–5.1 µm hyperspectral data of the entire illuminated surface, e.g. the north hemisphere and the equatorial regions, with spatial resolution between 2.5 and 25 m/pixel. I/F spectra have been corrected for thermal emission removal in the 3.5–5.1 µm range and for surface’s photometric response. The resulting reflectance spectra have been used to compute several Cometary Spectral Indicators (CSI): single scattering albedo at 0.55 µm, 0.5–0.8 µm and 1.0–2.5 µm spectral slopes, 3.2 µm organic material and 2.0 µm water ice band parameters (center, depth) with the aim to map their spatial distribution on the surface and to study their temporal variability as the nucleus moved towards the Sun. Indeed, throughout the investigated period, the nucleus surface shows a significant increase of the single scattering albedo along with a decrease of the 0.5–0.8 and 1.0–2.5 µm spectral slopes, indicating a flattening of the reflectance. We attribute the origin of this effect to the partial removal of the dust layer caused by the increased contribution of water sublimation to the gaseous activity as comet crossed the frost-line. The regions more active at the time of these observations, like Hapi in the neck/north pole area, appear brighter, bluer and richer in organic material than the rest of the large and small lobe of the nucleus. The parallel coordinates method (Inselberg [1985] Vis. Comput., 1, 69–91) has been used to identify associations between average values of the spectral indicators and the properties of the geomorphological units as defined by (Thomas et al., [2015] Science, 347, 6220) and (El-Maarr et al., [2015] Astron. Astrophys., 583, A26). Three classes have been identified (smooth/active areas, dust covered areas and depressions), which can be clustered on the basis of the 3.2 µm organic material’s band depth, while consolidated terrains show a high variability of the spectral properties resulting being distributed across all three classes. These results show how the spectral variability of the nucleus surface is more variegated than the morphological classes and that 67P/CG surface properties are dynamical, changing with the heliocentric distance and with activity processes.

Reference
Filacchione G et al. (2016) The global surface composition of 67P/CG nucleus by Rosetta/VIRTIS. (I) Prelanding mission phase. Icarus (in Press)
Link to Article [doi:10.1016/j.icarus.2016.02.055]
Copyright Elsevier

Origins of volatile elements (H, C, N, noble gases) on Earth and Mars in light of recent results from the ROSETTA cometary mission

1Bernard Marty, 1Guillaume Avice, 2Yuji Sano, 3Kathrin Altwegg, 3Hans Balsiger, 3Myrtha Hässig, 4Alessandro Morbidelli, 5Olivier Mousis, 3Martin Rubin
1Centre de Recherches Pétrographiques et Géochimiques, CRPG-CNRS, Université de Lorraine, UMR 7358, 15 rue Notre Dame des Pauvres, BP 20, 54501 Vandoeuvre lès Nancy, France
2Ocean and Atmosphere Research Institute, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa-shi, Chiba 277-8564, Japan
3Physikalisches Institut, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland
4Laboratoire Lagrange, Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, Boulevard de l’Observatoire, BP 4229, 06304 Nice Cedex 4, France
5Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France

Recent measurements of the volatile composition of the coma of Comet 67P/Churyumov–Gerasimenko (hereafter 67P) allow constraints to be set on the origin of volatile elements (water, carbon, nitrogen, noble gases) in inner planets’ atmospheres. Analyses by the ROSINA mass spectrometry system onboard the Rosetta spacecraft indicate that 67P ice has a D/H ratio three times that of the ocean value (Altwegg et al., 2015) and contains significant amounts of N2, CO, CO2, and importantly, argon (Balsiger et al., 2015). Here we establish a model of cometary composition based on literature data and the ROSINA measurements. From mass balance calculations, and provided that 67P is representative of the cometary ice reservoir, we conclude that the contribution of cometary volatiles to the Earth’s inventory was minor for water (≤1%), carbon (≤1%), and nitrogen species (a few % at most). However, cometary contributions to the terrestrial atmosphere may have been significant for the noble gases. They could have taken place towards the end of the main building stages of the Earth, after the Moon-forming impact and during either a late veneer episode or, more probably, the Terrestrial Late Heavy Bombardment around 4.0–3.8 billion years (Ga) ago. Contributions from the outer solar system via cometary bodies could account for the dichotomy of the noble gas isotope compositions, in particular xenon, between the mantle and the atmosphere. A mass balance based on 36Ar and organics suggests that the amount of prebiotic material delivered by comets could have been quite considerable – equivalent to the present-day mass of the biosphere. On Mars, several of the isotopic signatures of surface volatiles (notably the high D/H ratios) are clearly indicative of atmospheric escape processes. Nevertheless, we suggest that cometary contributions after the major atmospheric escape events, e.g., during a Martian Late Heavy Bombardment towards the end of the Noachian era, could account for the Martian elemental C/N/36Ar ratios, solar-like krypton isotope composition and high 15N/14N ratios. Taken together, these observations are consistent with the volatiles of Earth and Mars being trapped initially from the nebular gas and local accreting material, then progressively added to by contributions from wet bodies from increasing heliocentric distances. Overall, no unified scenario can account for all of the characteristics of the inner planet atmospheres. Advances in this domain will require precise analysis of the elemental and isotopic compositions of comets and therefore await a cometary sample return mission.

Reference
Marty B, Avice G, Sano Y, Altwegg K, Balsiger H, Hässig M, Morbidelli A, Mousis O, Rubin M (2016) Origins of volatile elements (H, C, N, noble gases) on Earth and Mars in light of recent results from the ROSETTA cometary mission. Earth and Planetary Science Letters 441, 91–102
Link to Article [doi:10.1016/j.epsl.2016.02.031]
Copyright Elsevier

Coesite in suevites from the Chesapeake Bay impact structure

John C. Jackson1, J. Wright Horton Jr.1, I-Ming Chou2 and Harvey E. Belkin1
1U.S. Geological Survey, Reston, Virginia, USA
2Sanya Institute of Deep-Sea Science and Engineering, Sanya, China

The occurrence of coesite in suevites from the Chesapeake Bay impact structure is confirmed within a variety of textural domains in situ by Raman spectroscopy for the first time and in mechanically separated grains by X-ray diffraction. Microtextures of coesite identified in situ investigated under transmitted light and by scanning electron microscope reveal coesite as micrometer-sized grains (1–3 μm) within amorphous silica of impact-melt clasts and as submicrometer-sized grains and polycrystalline aggregates within shocked quartz grains. Coesite-bearing quartz grains are present both idiomorphically with original grain margins intact and as highly strained grains that underwent shock-produced plastic deformation. Coesite commonly occurs in plastically deformed quartz grains within domains that appear brown (toasted) in transmitted light and rarely within quartz of spheroidal texture. The coesite likely developed by a mechanism of solid-state transformation from precursor quartz. Raman spectroscopy also showed a series of unidentified peaks associated with shocked quartz grains that likely represent unidentified silica phases, possibly including a moganite-like phase that has not previously been associated with coesite.

Reference
Jackson JC, Horton JW Jr., Chou I-M and Belkin HE (2016) Coesite in suevites from the Chesapeake Bay impact structure. Meteoritics & Planetary Science (in Press)
Link to Article [DOI: 10.1111/maps.12638]
Published by arrangement with John Wiley & Sons

The two Suvasvesi impact structures, Finland: Argon isotopic evidence for a “false” impact crater doublet

Martin Schmieder1,2 et al. (>10)*
1Lunar and Planetary Institute, Houston, Texas, USA
2NASA Solar System Exploration Research Virtual Institute (SSERVI)
*Find the extensive, full author and affiliation list on the publishers website

The two neighboring Suvasvesi North and South impact structures in central-east Finland have been discussed as a possible impact crater doublet produced by the impact of a binary asteroid. This study presents 40Ar/39Ar geochronologic data for impact melt rocks recovered from the drilling into the center of the Suvasvesi North impact structure and melt rock from glacially transported boulders linked to Suvasvesi South. 40Ar/39Ar step-heating analysis yielded two essentially flat age spectra indicating a Late Cretaceous age of ~85 Ma for the Suvasvesi North melt rock, whereas the Suvasvesi South melt sample gave a Neoproterozoic minimum (alteration) age of ~710 Ma. Although the statistical likelihood for two independent meteorite strikes in close proximity to each other is rather low, the remarkable difference in 40Ar/39Ar ages of >600 Myr for the two Suvasvesi impact melt samples is interpreted as evidence for two temporally separate, but geographically closely spaced, impacts into the Fennoscandian Shield. The Suvasvesi North and South impact structures are, thus, interpreted as a “false” crater doublet, similar to the larger East and West Clearwater Lake impact structures in Québec, Canada, recently shown to be unrelated. Our findings have implications for the reliable recognition of impact crater doublets and the apparent rate of binary asteroid impacts on Earth and other planetary bodies in the inner solar system.

Reference
Schmieder M (2016) The two Suvasvesi impact structures, Finland: Argon isotopic evidence for a “false” impact crater doublet. Meteoritics & Planetary Science (in Press)
Link to Article [DOI: 10.1111/maps.12636]
Published by arrangement with John Wiley & Sons

Multiple precursors of secondary mineralogical assemblages in CM chondrites

Isabella Pignatelli1,2, Yves Marrocchi1,2, Lionel. G. Vacher1,2, Rémi Delon1,2 andMatthieu Gounelle3,4
1Université de Lorraine, CRPG, UMR 7358, Vandoeuvre-lès-Nancy F-54501, France
2CNRS, CRPG UMR 7358, Vandoeuvre-lès-Nancy, France
3IMPMC, MNHM, UPMC, UMR CNRS 7590, 75005 Paris, France
4Institut Universitaire de France, Maison des Universités, 75005 Paris, France

We report a petrographic and mineralogical survey of tochilinite/cronstedtite intergrowths (TCIs) in Paris, a new CM chondrite considered to be the least altered CM identified to date. Our results indicate that type-I TCIs consist of compact tochilinite/cronstedtite rims surrounding Fe-Ni metal beads, thus confirming kamacite as the precursor of type-I TCIs. In contrast, type-II TCIs are characterized by complex compositional zoning composed of three different Fe-bearing secondary minerals: from the outside inwards, tochilinite, cronstedtite, and amakinite. Type-II TCIs present well-developed faces that allow a detailed morphological analysis to be performed in order to identify the precursors. The results demonstrate that type-II TCIs formed by pseudomorphism of the anhydrous silicates, olivine, and pyroxene. Hence, there is no apparent genetic relationship between type-I and type-II TCIs. In addition, the complex chemical zoning observed within type-II TCIs suggests that the alteration conditions evolved dramatically over time. At least three stages of alteration can be proposed, characterized by alteration fluids with varying compositions (1) Fe- and S-rich fluids; (2) S-poor and Fe- and Si-rich fluids; and (3) S- and Si-poor, Fe-rich fluids. The presence of unaltered silicates in close association with euhedral type-II TCIs suggests the existence of microenvironments during the first alteration stages of CM chondrites. In addition, the absence of Mg-bearing secondary minerals in Paris TCIs suggests that the Mg content increases during the course of alteration.

Reference
Pignatelli I, Marrocchi Y, Vacher LG, Delon R and Gounelle M (2016) Multiple precursors of secondary mineralogical assemblages in CM chondrites. Meteoritics & Planetary Science (in Press)
Link to Article [DOI: 10.1111/maps.12625]
Published by arrangement with John Wiley & Sons

The Red Edge Problem in asteroid band parameter analysis

Sean S. Lindsay1,2, Tasha L. Dunn3, Joshua P. Emery2 and Neil E. Bowles1
1Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, UK
2Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, USA
3Department of Geology, Colby College, Waterville, Maine, USA

Near-infrared reflectance spectra of S-type asteroids contain two absorptions at 1 and 2 μm (band I and II) that are diagnostic of mineralogy. A parameterization of these two bands is frequently employed to determine the mineralogy of S(IV) asteroids through the use of ordinary chondrite calibration equations that link the mineralogy to band parameters. The most widely used calibration study uses a Band II terminal wavelength point (red edge) at 2.50 μm. However, due to the limitations of the NIR detectors on prominent telescopes used in asteroid research, spectral data for asteroids are typically only reliable out to 2.45 μm. We refer to this discrepancy as “The Red Edge Problem.” In this report, we evaluate the associated errors for measured band area ratios (BAR = Area BII/BI) and calculated relative abundance measurements. We find that the Red Edge Problem is often not the dominant source of error for the observationally limited red edge set at 2.45 μm, but it frequently is for a red edge set at 2.40 μm. The error, however, is one sided and therefore systematic. As such, we provide equations to adjust measured BARs to values with a different red edge definition. We also provide new ol/(ol+px) calibration equations for red edges set at 2.40 and 2.45 μm.

Reference
Lindsay SS, Dunn TL, Emery JP and Bowles NE (2016) The Red Edge Problem in asteroid band parameter analysis. Meteoritics & Planetary Science (in Press)
Link to Article [DOI: 10.1111/maps.12611]
Published by arrangement with John Wiley & Sons