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Mars Odyssey neutron data: 1. Data processing and models of water-equivalent-hydrogen distribution

2011; American Geophysical Union; Volume: 116; Issue: E11 Linguagem: Inglês

10.1029/2011je003810

2156-2202

S. Maurice, W. C. Feldman, B. Díez, O. Gasnault, D. J. Lawrence, A. V. Pathare, T. H. Prettyman,

Nuclear Physics and Applications

Journal of Geophysical Research: PlanetsVolume 116, Issue E11 Free Access Mars Odyssey neutron data: 1. Data processing and models of water-equivalent-hydrogen distribution S. Maurice, S. Maurice [email protected] IRAP, Université Paul Sabatier, CNRS, Toulouse, FranceSearch for more papers by this authorW. Feldman, W. Feldman Planetary Science Institute, Tucson, Arizona, USASearch for more papers by this authorB. Diez, B. Diez IRAP, Université Paul Sabatier, CNRS, Toulouse, FranceSearch for more papers by this authorO. Gasnault, O. Gasnault IRAP, Université Paul Sabatier, CNRS, Toulouse, FranceSearch for more papers by this authorD. J. Lawrence, D. J. Lawrence Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USASearch for more papers by this authorA. Pathare, A. Pathare Planetary Science Institute, Tucson, Arizona, USASearch for more papers by this authorT. Prettyman, T. Prettyman Planetary Science Institute, Tucson, Arizona, USASearch for more papers by this author S. Maurice, S. Maurice [email protected] IRAP, Université Paul Sabatier, CNRS, Toulouse, FranceSearch for more papers by this authorW. Feldman, W. Feldman Planetary Science Institute, Tucson, Arizona, USASearch for more papers by this authorB. Diez, B. Diez IRAP, Université Paul Sabatier, CNRS, Toulouse, FranceSearch for more papers by this authorO. Gasnault, O. Gasnault IRAP, Université Paul Sabatier, CNRS, Toulouse, FranceSearch for more papers by this authorD. J. Lawrence, D. J. Lawrence Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USASearch for more papers by this authorA. Pathare, A. Pathare Planetary Science Institute, Tucson, Arizona, USASearch for more papers by this authorT. Prettyman, T. Prettyman Planetary Science Institute, Tucson, Arizona, USASearch for more papers by this author First published: 22 November 2011 https://doi.org/10.1029/2011JE003810Citations: 53 This is a commentary on DOI:10.1029/2011JE003806 AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] For more than 7 years, the Los Alamos built Mars Odyssey Neutron Spectrometer (MONS) has measured the neutron albedo from Mars in three consecutive energy bands: thermal, epithermal, and fast neutron ranges. This paper synthesizes the teamwork on the optimization of the signal extraction, the corrections for observational biases and instrument specific characteristics. Results are presented for neutron time series with an emphasis on seasonal variations at the poles. Frost-free data are mapped on to the surface, and the apparent random nature of the counting-rate distribution per pixel is analyzed: for epithermal neutrons, the relative standard deviation is less than 0.5% equatorward of 45° and up to 2.5% above this latitude limit; for thermal neutrons it is 1% and 2.5% respectively; and for fast neutrons it is 3% and 5.5%, respectively. New science results are obtained with regards to the distribution of water-equivalent hydrogen (WEH) on Mars. Under the assumption of a single uniform distribution of hydrogen with depth, WEH abundances range from 2% near the equator to 80% at the poles, with ±2% to 4.5% relative error bars. A best approximation to a two-layered global distribution of a lower-level hydrogen-rich substrate beneath an upper layer of varying thicknesses is generated using an average hydration level of an upper layer of 2 wt %, derived in the paper by Feldman et al. (2011). Such results are discussed and compared with regard to previous publications on the MONS instrument. Key Points New data reduction scheme and results for Neutron observations on Mars New maps of frost-free thermal, epithermal, fast neutron counts, with error bars Final map of water-equivalent-hydrogen 1. Introduction [2] Since February 2002, the Los Alamos built Mars Odyssey Neutron Spectrometer (MONS), as part of the Gamma Ray Spectrometer (GRS) instrument suite on board the Mars Odyssey, has been continuously measuring the leakage flux of neutrons from Mars. Planetary neutrons are known to provide a sensitive measure of the hydrogen content [Feldman et al., 1991, 1998] of a few major elements such as Fe and Ti [Elphic et al., 1998, 2000], of rare elements such as Sm and Gd together [Maurice et al., 2000b], and of the mean atomic mass [Gasnault et al., 2001] within the top meter of a surface exposed to cosmic rays (CRs) [Lingenfelter et al., 1961]. Data processing is an important step before such interpretations can be drawn. Throughout this process, many choices and alternatives must be clearly documented to establish the accuracy, precision, and robustness of the data sets. On the way to science interpretation, this paper intends to provide the necessary elements for understanding most of the consistencies and discrepancies with other neutron data sets from the Mars Odyssey: the Russian-built neutron detector [Mitrofanov et al., 2002] and the neutron number density deduced from the data processing of gamma ray data [Boynton et al., 2007]. We then build on this stage by generating a global map of the water-equivalent-hydrogen (WEH) abundance under the assumption that at any latitude-longitude location, the WEH abundance is constant with depth. This new map is then compared with those same maps derived previously using past MONS data-reduction procedures [Feldman et al., 2008; Diez et al., 2008], and also using the GRS and High Energy Neutron Detector (HEND) data sets [Boynton et al., 2007; Mitrofanov et al., 2004]. We then build on the results of the companion paper [Feldman et al., 2011] to develop two layer global maps of the WEH content of a lower layer, Wdn, and its burial depth below the surface, D, by adopting a constant WEH content of the upper layer, Wup = 2 wt % WEH. This WEH content was determined from a procedure that uses the fast and epithermal counting rates developed in the paper by Feldman et al. [2011]. These new maps are then compared with those published previously [Diez et al., 2008] that assumed Wup = 1 wt % WEH. These maps then provide a foundation for future collaborative studies that require multiple data sets that bear on the present distribution of water ice near the surface of Mars, how it is lost and redistributed to other locations when the climate changes, and how it relates to the total water inventory on Mars. [3] The MONS instrument collects neutron fluxes continuously from Mars surface in three consecutive energy bands: thermal (0–0.3 eV), epithermal (0.3 eV–700 keV), and fast (0.7–5 MeV) neutron ranges. As detailed by Feldman et al. [2002a], the definitions of "thermal," "epithermal," and "fast" neutron energy ranges were made using Monte Carlo simulations of the instrument that were validated using Cf-252 and AmB neutron sources in the laboratory at Los Alamos National Laboratory. The purpose of data processing is to transform time-tagged measurements at the spacecraft into relevant neutron maps, some of which are time dependent because of seasonally changing CO2 ice precipitation at high latitudes. Since Mars orbit insertion, the instrument has been in an excellent state of health. Over more than seven years, there have been several unresolved issues regarding the detailed data processing of MONS data. This time period has permitted a better understanding of the instrument systematic biases, so that most, if not all, of those biases have been removed. Each generation of MONS data processing was built independently of its predecessors, often by different people, to limit the propagation of erroneous assumptions. Efforts were also devoted to compare the results of each approach. The initial processing of MONS data was performed by Tokar et al. at Los Alamos National Laboratory [Tokar et al., 2002] and was used for early discovery results. Subsequently, Prettyman et al. developed an independent approach [Prettyman et al., 2004a, 2004b] that has been the reference for publications between 2004 and the present. This code is currently used to deliver level-1 derived neutron data (DND) to the Planetary Data System (PDS). These products are time series of corrected neutron counting-rate data that can be used for scientific investigations. The level-1 data set includes averaged neutron data (AND), which consists of neutron maps built from DND time series data. An updated processing procedure is presented here by the instrument science team. It applies to all data collected from the beginning of the orbital mission through July 2009. Early versions of this process have been used for publications by the MONS team after 2004. Compared with earlier codes, the relative uncertainty per pixel (see section 5) has decreased by a factor of ∼2. The current processing should also apply to data that are collected after July 2009; the statistics will improve as , where N is the total number of counts in the detector. [4] Prior to the Mars Odyssey, the Lunar Prospector flew a neutron spectrometer, which consisted of a pair of 3He gas proportional counters and a large borated plastic scintillator that doubled as an anticoincidence shield for the gamma ray spectrometer [Feldman et al., 1999, 2004]. This very successful experiment provided an excellent benchmark for planetary neutron spectroscopy because of the large dynamic range of neutron composition parameters and the relative chemical homogeneity of the top few meters of the surface of the Moon from meteoritic gardening processes. In addition, knowledge of lunar surface composition enabled an absolute calibration of neutron counting rates to be fully validated [e.g., Lawrence et al., 2006]. The process we provide here follows a scheme that was developed for the neutron detector on board the Lunar Prospector [Maurice et al., 2004]. Since then, neutron spectrometers have been flying on the NASA missions Messenger to Mercury [Goldsten et al., 2007], Dawn to asteroids Vesta and Ceres [Prettyman et al., 2004b], the Lunar Reconnaissance Orbiter to the Moon [Mitrofanov et al., 2010a], and their use is planned for the European Space Agency (ESA) Bepi-Colombo Mercury Planetary Orbiter [Mitrofanov et al., 2010b]. 2. Neutron Spectroscopy on Board Mars Odyssey [5] Launched on 7 April 2001, the Mars Odyssey was originally designed for a prime mission of 917 days. The mapping phase started on 19 February 2002 after the orbit had been circularized by aerobraking. The average altitude of the satellite is 400 km (384–459 km extreme). The inclination is 93°, and the orbital period is 1.975 h. Because of the availability of spacecraft resources, the prime mission was extended to achieve a communication relay for the Mars Exploration Rovers and the Phoenix Lander and the continuation of science observations though several Martian years. Recently, the orbit local time was changed from 5:30 P.M. to 3:30 P.M. with no penalty on neutron data. [6] The science objectives of this mission are to globally map the elemental composition of the surface, determine the abundance of hydrogen within the near subsurface, acquire high spatial and spectral resolution images of the surface mineralogy, provide information on the morphology of the surface, and characterize the Martian near-space radiation environment as related to radiation-induced risk to human explorers [Saunders et al., 2004]. The payload consists of a GRS suite of instruments, a multispectral Thermal Emission Imaging System (THEMIS), and a radiation detector, the Martian Radiation Environment Experiment (MARIE). The GRS suite of instruments (Gamma Ray Subsystem, Neutron Spectrometer, and HEND) measures the fluxes of neutrons and gamma rays produced by the interaction of cosmic rays with planetary material [Boynton et al., 2002; Feldman et al., 2002b; Mitrofanov et al., 2002]. [7] Within the top 1–2 m of the Martian surface, the interaction of cosmic rays (CRs) with near-surface matter produces high-energy neutrons: evaporation yields a Maxwellian energy spectrum peaking at ∼8 MeV, while spallation and charge exchange reactions yield a continuum energy spectrum with energies ranging from tens of MeV to several GeV. The neutron population at energies greater than ∼700 keV is called the fast neutron population. The threshold of 700 keV reflects our choice of a lower analog-electronic threshold of 40 keV equivalent-electron energy. Subsequent interactions of the primary neutrons with the nuclear constituents of near-surface material produce an equilibrium energy distribution both below and above the surface of the planet. The neutrons inelastically scatter on nuclei near the planetary surface, losing energy in the fast energy range, and elastically scatter on nuclei, losing energy as they pass through the epithermal regime (0.3–700 keV). The resulting flux is proportional to 1/E in the epithermal range [Fermi, 1950; Drake et al., 1988]. When the energies approach the thermal energy of the ambient soil, neutrons gain energy as fast as they lose it and thereby develop a Maxwellian velocity distribution function [Bertini, 1969]. The boundary between the epithermal population and thermal population is approximately at 0.3 eV, an energy below which neutrons are either scattered up or down by thermal motions of regolith nuclei or are significantly lost through absorption reactions. The MONS instrument is recording individually each of these neutron populations. [8] The MONS instrument is detailed by Feldman et al. [2002a], as part of the Mars Odyssey GRS instrument suite [Boynton et al., 2004]. We report here only the information useful to the data processing. The MONS detector consists of a cubical block of boron-loaded plastic scintillator. It is segmented into four prism-shaped quadrants, as shown in Figure 1. The prism segments are optically isolated from one another, and each is viewed by a separate 3.8 cm diameter photomultiplier tube (PMT). Both ends of the scintillator assembly are covered with a 0.069 cm thick sheet of cadmium to shield the ends of all prisms from thermal neutrons coming from those directions. In addition, the downward looking prism (hereafter labeled Prism-1) has its face covered by an identical cadmium sheet so that, except for two thin leakage channels at the edges of the downfacing surface of Prism-1, it responds only to neutrons having energies larger than about 0.3 eV. These energies fall within the epithermal and fast neutron energy ranges. In the epithermal range, neutrons lose energy in the neutron detector through multiple elastic scattering collisions with the hydrogen and carbon nuclei within the scintillator. Most of the energy is lost to proton recoils because protons and neutrons have about the same mass, and the cross section for (n, p) scattering is about four times larger than that for (n, 12C) at low energies. As the recoil protons slow down in the scintillator, they produce multiple ion-electron pairs that eventually recombine to produce photons. A collection of these photons by the PMTs produces pulses of charge that are then amplified and digitized by the neutron detector analog electronics to generate pulse-height histograms. If the neutrons deposit all of their energy in the scintillator, they will eventually be captured by a 10B nucleus to produce a second pulse in the electronics. Although the Q value of the 10B(n, α)7Li reaction is about 2.8 MeV, 478 keV of this energy goes to the gamma ray deexcitation of the first excited state of 7Li, which is populated 94% of the time in this reaction. The remaining 2.3 MeV is split between the α and 7Li recoils. Because of a pulse-height deficit in the plastic scintillator, the recoil energy appears like a 93 keV electron. The equivalent-electron energy in a plastic scintillator for heavy ions is reduced considerably because their energy-loss rate is so high that a mass-dependent portion of the lost energy goes into electrons that recombine in the molecular structure of the plastic without producing photons. The sequence of events just described is shown schematically in the upper part of Figure 1. The signature of a thermal or epithermal neutron in the scintillator is therefore a single pulse that has an amplitude that is characteristic of the 10B(n, α)7Li reaction. The signature of a fast neutron that has lost all of its energy in the scintillator is a time-correlated double pulse. The amplitude of the first pulse provides a measure of the energy of the neutron, and that of the second pulse is the same as that for a thermal or epithermal neutron. Figure 1Open in figure viewerPowerPoint Schematic overview of the MONS sensor showing several types of neutron and gamma ray interactions that dominate the data-reduction functions of the code developed here to process the MONS data. Shown on the bottom is the orientation of the sensors relative to Mars and to the velocity vector of the spacecraft: Prism-1 if looking to the nadir, Prism-2 in the direction of the velocity, Prism-4 to the rear, and Prism-3 to the spacecraft itself. [9] The orientation of the normal to each of the four prism elements of the neutron spectrometer is shown in the bottom right-hand part of Figure 1. One face will look forward in the direction of the spacecraft motion (hereafter labeled Prism-2), one backward (Prism-4), one down toward Mars (Prism-1) and one up to the spacecraft (Prism-3). Separation of the thermal and epithermal components is accomplished using the relative counting rates of the forward and backward directed prisms using a Doppler filter technique [Feldman and Drake, 1986]. This is due to the fact that the Mars Odyssey spacecraft travels faster (3.4 km/s) than a thermal neutron (1.9 km/s at 220 K) while in mapping orbit. The forward directed prism will therefore scoop up thermal neutrons, and the backward directed one will outrun them. The difference in counting rates between forward and backward directed faces thus yields a measure of the flux of thermal neutrons. A measure of epithermal neutrons is provided by the downward facing prism because it is nearly completely shielded from the outside by sheets of cadmium and the other three prisms. 3. Processing of Time Series Data [10] Our data-reduction scheme starts from science and housekeeping data returned by the spacecraft, which are time-tagged records of 19.75 s duration. Such data are binary packets, formatted on board the spacecraft and relayed through the Jet Propulsion Laboratory and the University of Arizona. The initial steps of data processing are described at the end of this section, with details moved to the appendices for clarity of the manuscript: cleaning data for corrupted and unusable records (Appendix A), neutron signal extraction from pulse-height histograms (Appendix B), and the event mode (Appendix C). The second step of data processing deals with observational biases and other instrument-specific characteristics (section 4). The third and final step is to match data normalization with our numerical simulations, which help to interpret the neutron fluxes in terms of WEH abundances. In section 5, final products are constructed: thermal, epithermal, and fast neutron counting-rate time series and/or maps, with associated error bars. [11] Along our data processing scheme, a few supplementary quantities are required: the Mars solar longitude Ls, the Mars distance to the Sun dsun, the topography at the nadir foot point, the atmospheric thickness derived from pressure P, and the ground CO2 deposits. Ls and dsun are straightforward to calculate from astronomical ephemerides. The topography at the nadir is smoothed to 5° to match the instrument response function. Atmospheric pressure and CO2 deposits require the use of a global circulation model (GCM) [Forget et al., 1999] to account for the spatial and temporal variations of these quantities. The incorporation of GCM data into our model is the subject of Appendix D. Instrument Event Definitions [12] To understand the following discussion, the reader should be aware of the instrument event definitions. Two categories of events are recognized by the MONS front-end electronics [Feldman et al., 2002a]. A category-1 event is a first scintillator interaction having energy in the range 40 keVeq < E < 630 keVeq (subscript eq stands for electron-equivalent light output) that is not followed by a second interaction within 25.6 μs. Another characteristic is that the interaction should be registered in only one or two prism segments of the neutron sensor. Any prompt interaction having energy greater than 2.55 MeVeq (regardless of the number of sensor elements that register energy above threshold) will be identified as a CR. After detection, no second interaction is looked for, and the event is counted in a dedicated CR scalar. [13] A category-2 event is a prompt scintillator interaction having energy in the range 40 keVeq < E < 2.55 MeVeq that deposits energy in one or two prism segments only, which is followed by a second interaction that is detected in one or two prism segments within a 25.6 μs gate window beginning with the time of the first interaction. The second interaction must have energy in the range 40 keVeq < E < 630 keVeq. Any event that does not satisfy these criteria is ignored but is nevertheless accounted for in a dedicated dead-time counter. For every category-2 event identified by onboard classification firmware, information used in the present paper to determine the energy spectrum of fast neutrons aboard Mars Odyssey consist of (1) a 5 bit prompt analog-to-digital converter (ADC) address, (2) a 6 bit delayed ADC address, (3) a 4 bit prompt interaction sensor ID, (4) a 1- it delayed interaction sensor ID, and (5) an 8 bit digitized time to second pulse. The prompt and delayed ADC addresses give the pulse height of the prompt and delayed interactions, respectively. Each of the four prompt interaction ID bits identifies a unique prism that detects energy deposition above threshold. Only one or two prisms are allowed for analysis. The delayed ID bit identifies only whether the second interaction occurred in one or two prisms. Here again, three- and four-prism events are rejected by the onboard event classifier. Event-mode data consist of the first 84 three-byte events in each accumulation time interval. All succeeding events are counted in a histogram format without recording details of the separate interactions. [14] Data used by this data-reduction code have been collected through two different modes: event mode and histogram mode. Category-1 data are collected only in the histogram mode. For each prism the counts in the histogram mode are collected during an integration time of 19.75 s and stored in 64 channels that correspond to electron-equivalent energy-deposition levels. The acquired category-1 spectra are merged into (4, 64) sized tables of integers. Histograms of these spectra, averaged over measurements acquired during the first quarter of 2003 and normalized to counts per second are displayed in Figure 2. Figure 2Open in figure viewerPowerPoint Histograms of counts in Prisms-1, -2, -3 and -4 averaged over category-1 measurements acquired during the first quarter of 2003 in counts/s. [15] The event mode collects the history of double-interaction events. Each measurement records the detection of an interaction, the prism recording the interaction, and the type of interaction (first or second interaction). The resulting information is coded in 252 byte data packets. Supporting data are added, namely universal time (UTC), Julian day and sol (Mars day) for the time baseline, orbital information (longitude, latitude, altitude of the satellite), satellite attitude information (the spacecraft orientation relative to a coordinate system with origin at the subsatellite point, z axis pointing radially away from the surface, x axis pointing along the spacecraft velocity vector, and y axis that completes a right-handed coordinate system), and proxies of the measurement quality (amount of dead time during measurement and cosmic ray intensity). Data Selection [16] Data range from 8 February 2002 to 31 July 2009 for this paper. Considering a 19.75 s accumulation time, we are looking potentially at ∼12 million data points. However, the initial MONS data set consists of 9.6 million data points, which amount to 80% of the total possible returned by the instrument. In a series of processes described in Appendix A, suspicious data are removed: (1) saturation by solar energetic particle (SEP) events, (2) spurious data points that are out of range, (3) spacecraft orientation anomalies, (4) overflow of onboard acquisition processing, also called dead time, (5) early in the mission, bad registration of the data, and (6) issues near the equator when the instrument clock is reset. Some records can be flagged for two or more reasons. At the end of this filtering, ∼14% of available data are removed. Because of the long duration of the mission, there are sufficient data remaining that the removal of these data is of no consequence. Signal Integration [17] Neutron counting rates are measured by the four prisms of the MONS instrument using two independent front-end electronics. The first builds up pulse-height histograms (also called category-1 data) from all first interactions to obtain epithermal and thermal counting rates. The signal integration is described in detail in Appendix B. The key point of this procedure is the localization of the peak associated with the neutron capture by 10B. The shape of this peak requires correction for nonlinearities of the ADC. It also moves with respect to the high-voltage setup. We force it to a certain channel before integration of the signal under the peak, with a special care taken for the background estimate. [18] The energy deposition of fast neutrons that have lost all of their energies in Prism-1 is used to determine the energy of fast neutrons. A fast neutron is identified if the first pulse is followed by a second interaction within 25.5 μs, which corresponds to an energy that is above the second-interaction threshold but below 630 keVeq. The first and second interactions are analyzed separately. The second pulse is carefully analyzed to eliminate after-pulsing [Feldman et al., 1991]. The first four channels of the first-interaction spectrum, after after-pulsing removal, are used, which provide an optimum signal-to-noise ratio versus counting rate for our study. This part is described in detail in Appendix C. [19] At this point, four scalar values have been extracted: Prism-1, Prism-2,and Prism-4 counting rates from category-1 histograms and fast counting rates from Prism-1 in the event mode. 4. Reduction of Systematic and Random Uncertainties [20] Time series data require treatment for measurement biases: detector background, altitude variations of the spacecraft, and look direction of the detectors, as well as for the variations of the environmental conditions: cosmic ray flux and atmospheric pressure. There are also variations within the data, whose origin is unknown, which are well localized in time but cannot be corrected for. These effects apply differently in the four-scalar data, but with different magnitudes. Background [21] Detector background results from the interaction of cosmic rays with the Mars Odyssey spacecraft. This contribution was determined during cruise, between the instrument first activation (2 May 2001) and Mars orbit insertion (on 23 October 2001). During this period, the interplanetary medium was relatively quiet, thereby allowing a determination of the baseline energy spectrum of neutrons produced on a spacecraft of the Mars Odyssey class by cosmic rays. Backgrounds for thermal and epithermal neutrons were so small during cruise that they were not measurable [see Prettyman et al., 2004a; Feldman et al., 2004]. Around Mars, the spacecraft background for thermal neutrons from Mars scattered by spacecraft material into the detector were subtracted using the Doppler filter technique and that for the epithermal neutrons was estimated using both the Prism-4 and Prism-3 results. A detailed study of fast neutron spectra during cruise can be found in the work by Feldman et al. [2002a]. The correction for background is applied only to the fast neutron flux. Integration of the fast neutron spectrum over the energy range at which the fast signal is evaluated provides the ability to determine background counting rates in Mars orbit. It was measured to be 0.12 counts/s. This value is scaled to the cosmic ray flux and is subtracted from the signal. Spacecraft Altitude [22] The orbit of the spacecraft is slightly elliptical. Therefore, its altitude with regard to Mars mean sphere changes with time (Figure 3 for 6–7 April 2002). The maximum range over the mission is 384–459 km. We normalize the data to 450 km, using a simple solid-angle law [Maurice et al., 2004]. A 6% correction factor is shown in Figure 4 for the entire data set. At this point, the ±7 km height of the Martian mountains, at the resolution of the instrument, is not accounted for in determining the distance of the spacecraft to the surface because the area of these mountain peaks is generally much smaller than the spatial resolution of the MONS. Figure 3Open in figure viewerPowerPoint Spacecraft altitude over the mean sphere as a function of time. Figure 4Open in figure viewerPowerPoint Correction coefficient as a function of altitude and latitude. Latitude Offs