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NASA NTRS2002

The Crustal Thickness of Mars: Accuracy and Resolution

Since the arrival of the Mars Global Surveyor (MGS) spacecraft at Mars and its entry into its mapping orbit in February 1999, the radio tracking and altimetry data from the mission have been part of the systematic mapping of the planet and used to develop very precise models of the gravity field and topography of Mars. Until the altimetry function of Mars Orbiter Laser Altimeter (MOLA) failed on June 30, 2001, the instrument had acquired close to 700 million measurements of the planet's radius, the majority of which have been used to develop a model of the topography with horizontal resolution of about 500 m and radial accuracy of better than 1 m. Concurrently, Doppler and range tracking of MGS by the Deep Space Network at X-band frequencies, with accuracies of about 50 microns/s and about 5 m respectively, have provided orbital knowledge of MGS to the few meter level and enabled the gravity perturbations of the spacecraft to be used to develop a improved gravity models of Mars. The recent models have horizontal resolutions of about 200 km, or degree 65, when expressed in spherical harmonics, and have accuracies of the order of a few mGals at the poles and about 10 mGals at the equator at the highest resolution.

Smith, David E.↗
NASA NTRS1975

The gravity field of Mars

A complete sixth-degree spherical-harmonic model of the gravitational potential of Mars has been produced from an analysis of Doppler data obtained from the radio tracking of the Mariner-9 spacecraft for over 200 orbital revolutions. The equipotential surface defined by this model is estimated to be accurate to within 100 m below 60 deg north latitude and to within 300 m above. The dominant feature of this surface is a Tharsis-related bulge which rises nearly two kilometers above the surrounding areas. Gravitational 'lows' are found to correspond to the Hellas depression and the Valles Marineris.

Reasenberg, R. D.↗
NASA NTRS2022

Constraining Venus and Mars Internal Structures from the Gravity Response to Atmospheric Loading

The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.

Mars↗
NASA NTRS1995

JPL Planetary Gravity Efforts and Techniques

The Magellan spacecraft has provided the highest resolution global gravity data set from spacecraft measurements. The X-band Doppler tracking is sensitive to harmonic degree of 120 or greater. We have developed a 75th degree and order global spherical harmonic model using a spatial constraint instead of the usual method. Results are presented for JPL Venus and Mars gravity field determination efforts and efforts are reviewed for developing higher degree models on supercomputers.

gravity fields Doppler tracking Magellan↗
NASA NTRS1999

Mars Gravity and Topography Interpretations

New models of the topography of Mars and its gravity field from the Mars Global Surveyor mission are shedding new light on the structure of the planet and the state of isostatic compensation. Gravity field observations over the flat northern hemisphere plains show a number of anomalies at the 100 to 200 mGal level that have no apparent manifestation in the surface topography. We believe that these anomalies are probably the result of ancient impacts and represent regions of denser material buried beneath the outer depositional crust. Similar anomalies are also found in the region of the north polar ice cap even though a gravity anomaly resulting from the 3 km high icecap has not been uniquely identified. This leads us to speculate that the ice cap is largely compensated and is older than the timescale of isostatic compensation, about 10(exp 15) years.

Zuber, Maria T.↗
NASA NTRS1979

Development and analysis of a twelfth degree and order gravity model for Mars

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Christensen, E. J.↗
NASA NTRS1995

The JPL Mars gravity field, Mars50c, based upon Viking and Mariner 9 Doppler tracking data

This report summarizes the current JPL efforts of generating a Mars gravity field from Viking 1 and 2 and Mariner 9 Doppler tracking data. The Mars 50c solution is a complete gravity field to degree and order 50 with solutions as well for the gravitational mass of Mars, Phobos, and Deimos. The constants and models used to obtain the solution are given and the method for determining the gravity field is presented. The gravity field is compared to the best current gravity GMM1 of Goddard Space Flight Center.

Konopliv, Alexander S.↗
NASA NTRS1986

Analysis of harmonic spline gravity models for Venus and Mars

Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.

Bowin, Carl↗
NASA NTRS1993

An improved gravity model for Mars: Goddard Mars Model 1

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, Goddard Mars Model 1 (GMM-1). This model employs nearly all available data, consisting of approximately 1100 days of S band tracking data collected by NASA's Deep Space Network from the Mariner 9 and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM-1 is complete to spherical harmonic degree and order 50, which corresponds to a half-wavelength spatial resolution of 200-300 km where the data permit. GMM-1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM-1 over previous models is a consequence of several factors: improved computational capabilities, the use of otpimum weighting and least squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X band tracking data from the 379-km altitude, nnear-polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM-1, particularly at high latitudes where current data poorly resolve the gravitational signature of the planet.

Smith, D. E.↗
NASA NTRS1993

An improved gravity model for Mars: Goddard Mars Model-1 (GMM-1)

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, GMM-1 (Goddard Mars Model-1). This model employs nearly all available data, consisting of approximately 1100 days of S-bank tracking data collected by NASA's Deep Space Network from the Mariner 9, and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM-1 is complete to spherical harmonic degree and order 50, which corresponds to a half-wavelength spatial resolution of 200-300 km where the data permit. GMM-1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM-1 over previous models is a consequence of several factors: improved computational capabilities, the use of optimum weighting and least-squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X-band tracking data from the 379-km altitude, near-polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM-1, particularly at high latitudes where current data poorly resolves the gravitational signature of the planet.

Smith, D. E.↗
NASA NTRS1975

Mars gravity field based on a short-arc technique

The magnitudes of 92 surface mass points at designated locations were estimated from the radio tracking data of the Mariner Mars 1971 (M9) orbiter. This result is the first mass point model of a global field. The derived surface mass distribution correlates positively with the visible topography. The Hellas basin contains a mass deficiency, in contrast to some of the lunar basins which contain mass excesses. The Mars gravity field represented by the four parameters of an optimally located mass point (superimposed on an oblate spheroid) has third- and fourth-degree harmonics comparable to those of the complete model.

Sjogren, W. L.↗
NASA NTRS1983

Planetary geodesy

The current known geodetic parameters of the planets and their moons are reviewed. A 3:2 spin-orbit resonance has been calculated for Mercury, a planet for which previous mass estimates are suggested to be inaccurate by 30 pct. The Pioneer Venus Orbiter data indicated a Venus diameter of 6051 km, a geoid surface highly-correlated with the surface topography, and regional gravity anomalies. Reflective mirrors on the surface and data from the Lunar Orbiter 4 have produced values for the principal polar moment of inertia homogeneity factor, the earth-moon mass ratio, a fifth degree and order spherical harmonic gravity model, the lunar acceleration, and the lunar potential Love number. The Mars gravity field is now estimated up to 12th degree and order spherical harmonics from Mariner 9 and Viking Orbiters 1 and 2, which also obtained new topographical data. New gravity fields and mass are being calculated for the Jovian and Saturnian moons. The outer planets' radii and rotational periods have recently been revised to greater accuracy. New data will be forthcoming from the Space Telescope and the planned Venus Radar Mapper.

Sjogren, W. L.↗
NASA NTRS2004

An Improved Model of the Crustal Structure of Mars

The first reliable model of the structure of the crust and upper mantle of Mars from remote observations was produced using data from the Mars Orbiter Laser Altimeter (MOLA) and the Radio Science investigation of Mars Global Surveyor (MGS). That model assumed a uniform crustal density and solved for the global variations in crustal thickness using a gravity field derived from preliminary MGS tracking. In that study, spherical harmonic potential coefficients were derived to degree and order 80, but crustal structure was interpreted cautiously to degree 60, or 360 km wavelength, owing to the presence of noise. Tracking normal equations have since been generated to degree 75, to degree 80 (supplemented by altimetric crossovers), and recently to degree 90, using new constants for the orientation of the spin pole and the rotation rate of Mars provided by the IAU2000 rotation model. Gravity models now incorporate tracking data coverage from the Primary and Extended MGS missions and the early phases of the Mars Odyssey mission. In the present study we exploit these advances in gravity modeling to present a refined crustal inversion, which we also interpret in the context of Mars' internal structure and thermal evolution.

Zuber, M. T.↗
NASA NTRS1993

Analyzing Martian winds and tracer concentrations using Mars Observer data

During the courses of a day, the Mars Observer spacecraft will acquire globally distributed profiles of the martian atmosphere. It is highly desirable that this data be assembled into synoptic weather maps (complete specifications of the atmospheric pressure, temperature, and winds at a given time), which can in turn be used as starting points in the study of many meteorological phenomena. Unfortunately, the special nature of the Mars Observer data presents several challenges above and beyond the usual difficult problem of data initialization. Mars Observer atmospheric data will consist almost exclusively of asynoptic vertical profiles of temperatures (or radiances) and pressures, whereas winds are generally in balance with horizontal gradients of these quantities (which will not be observed). It will therefore be necessary to resort to dynamical models to analyze the wind fields. As a rule, data assimilation into atmospheric models can result in the generation of spurious gravity waves, so special steps must be taken to suppress these. In addition, the asynoptic nature of the data will require a four-dimensional (space and time) data assimilation scheme. The problem is to find a full set of meteorological fields (winds and temperatures) such that, when marched forward in time in the model, they achieve a best fit (in the weighted least-squares sense) to the data. The proposed solution is to develop a model especially for the Mars Observer data assimilation problem. Gravity waves are filtered from the model by eliminating all divergence terms from the prognostic divergence equation. This leaves a diagnostic gradient wind relation between the rotational wind and the temperature field. The divergent wind is diagnosed as the wind required to maintain the gradient wind balance in the presence of the diabatic heating. The primitive equations of atmospheric dynamics (with three principal dependent variables) are thus reduced to a simpler system with a single prognostic equation for temperature - the variable that will be best observed. (This balance system was apparently first derived by Charney as a first-order Rossby number expansion of the equations of motion). Experience with a full primitive equation model of the martian atmosphere indicates that a further simplification is possible: at least for short-term integrations, the model can be linearized about the zonally symmetric basic state.

Houben, Howard C.↗
NASA NTRS1978

Theoretical models for Mars and their seismic properties

Theoretical seismic properties of the planet Mars are investigated on the basis of the various models which have been proposed for the internal composition of the planet. The latest interpretation of gravity-field data, assuming a lower value of the moment of inertia, would require a less dense mantle and a larger core than previous models. If Mars is chondritic in composition, the most reasonable models are an incompletely differentiated H-chondrite or a mixture of H-chondrites and carbonaceous chondrites. Seismic profiles, travel times, and free oscillation periods are computed for various models, with the aim of establishing which seismic data is crucial for deciding among the alternatives. A detailed discussion is given of the seismic properties which could - in principle - help answer the questions of whether Mars' core is liquid or solid and whether Mars has a partially molten asthenosphere in its upper mantle.

Okal, E. A.↗
NASA NTRS1972

Mars lander position estimation in the presence of ephemeris biases.

The process of estimating the location of a spacecraft landed on the surface of Mars is investigated through the application of statistical estimation techniques to earth-based radio tracking data. The spacecraft location and the tracking geometry and schedule are consistent with Viking-type mission constraints. With mission control requirements in mind, the investigation is restricted to analysis of a short data arc (approximately 3 days). Statistics of the spacecraft location are obtained through analysis of (direct-link) tracking data for the landed spacecraft and through simultaneous analysis of tracking data for both a landed and an orbiting spacecraft. These estimates include the effects of model uncertainties in the ephemeris of Mars, tracking station locations, the Mars rotational period, the Mars gravity field, and the orientation of Mars axis of rotation. The most significant of these effects is shown to be due to the Mars ephemeris uncertainty. A dual spacecraft tracking technique is presented for substantially reducing these ephemeris effects.

Blackshear, W. T.↗
NASA NTRS1993

An inversion of geoid and topography for mantle and crustal structure on Mars

Mars has the largest amplitude geoid anomalies and surface topography known on the terrestrial planets. A number of prior studies have analyzed Martian gravity anomalies and topography in terms of isostasy and flexure of the crust and lithosphere. Other studies have emphasized the role of mantle convection in producing gravity anomalies and topography in some regions of Mars. Geoid and topography observations for simultaneous estimates of density anomalies in the crust and mantle of Mars are inverted. In performing this study, a recent degree 50 spherical harmonic expansion of the Martian gravity field (GMM-l) and a corresponding resolution expansion of the USGS Mars topography model are used. However, our analysis is restricted to harmonic degrees up to L equals 25, which are better determined than the higher harmonics. This provides a half-wavelength horizontal resolution of 425 km.

Kiefer, Walter↗