G43A-0790 1340h
Mercury's Interior Structure and Geodesy
Interior structure models of Mercury have been calculated with particular focus on the core. Mercury has a very large core, compared to the other terrestrial planets, thought to consist mainly of iron and an unknown amount of sulfur. Thermal evolution models, high pressure data on iron alloys, and the magnetic measurements of Mariner 10 point to a core structure as for the Earth, with a solid inner core and a liquid outer core. We have considered a plausible range in sulfur concentration for the core and constructed Mercury models in different phases of its core evolution, from entirely liquid to entirely solid cores. Data on core material relevant for the pressures and temperatures in Mercury's core is used, and we investigate the effects of sulfur dissolving in the solid inner core. Several geodesy experiments have the potential of providing insight into Mercury's deep interior. Precise measurements of Mercury's obliquity and libration in longitude, along with the harmonic degree 2 gravitational field coefficients will determine both the polar principal moment of inertia of the entire planet and of the mantle, $C$ and $C_m$, respectively. On the other hand, Mercury's solid body tides, which are the largest of the solar system planets, are very sensitive to the core properties, and will be observed by the MESSENGER and BepiColombo missions. We calculated the moments of inertia $C$ and $C_m$ and the tidal reaction of our Mercury models, and studied their sensitivity to several core parameters.
G43A-0791 1340h
Libration dynamics of a three-layer Mercury
We studied the rotation dynamics of Mercury, assuming a three layer planet, with a solid inner core, a fluid core and an elastic mantle. In particular, we analyzed the resonance associated with the liquid core and solid inner-core, and their impact on the libration of the planet. Due to those resonances, some libration frequencies will be strongly amplified; as the resonance periods and amplifications are function of the core and inner core size and rheologic properties, this would be a way to get more information about Mercury's interior. The paper assesses the possibility to determine interior properties of Mercury from libration observations.
G43A-0792 1340h
Signature of Mercury's core on its librations
The internal structure of Mercury is the most puzzling among the terrestrial planets. The space missions MESSENGER and the upcoming BepiColombo, and ground-based radar measurements will play an important role in constraining our understanding of the structure, formation, and evolution of Mercury. The development of a complete theory of the coupled spin-orbit motion of Mercury within the Solar System is an essential complement to observational data and will improve significantly our knowledge of the planet. In order to integrate hermean core-mantle interaction in a realistic model of the Mercury's rotation, we have used the SONYR model of the solar System including Mercury's spin-orbit motion (acronym of Spin-Orbit N-bodY Relativistic model). We studied the dynamical behavior of the rotational motion of Mercury considered as a homogeneous body and as a model with two layers. The comparison of the dynamical evolution of the models of internal structure permits to clarify the impact of the core motion on the librations. The libration amplitude is not proportional to the $C_m/C$ ratio because of the non-linearity of the effect of the core-mantle interaction on the rotation. Moreover, we have computed the impact of the presence of the core on the spin rate of the planet in order to compare with recent radar observations.
G43A-0793 1340h
A new perturbation theory for fast rotators and a revised formula for spin axis precession
A new approach to the dynamics of fast rotators (e.g., the Earth, Mars and certain asteroids) is introduced. First we demonstrate in a simple case that the commonly used equation for spin axis precession needs to be revised. When we use the full dynamical equations except for wobble terms, the rate of precession is inversely proportional to the equatorial moment of inertia and not the polar one. In the case of the Earth, the revised equation implies an adjustment of about one part in one thousand in the moments of inertia. The main part of the work is the derivation of a general perturbation theory which is based on Lie series on the Lie group of rotations and the elimination of fast rotation from the averaged system. The new theory yields the revised equation for spin axis precession, along with a consistent set of equations for all possible motions, either for rigid or deformable bodies. This theory will allow accurate, long-term integrations of orbital and rotational dynamics incorporating the physics of wobble and nutation in rapidly rotating bodies such as the Earth and Mars.
G43A-0794 1340h
Regional Gravity From Lunar Prospector Extended Mission Data: Results for Copernicus and Serenitatis
In the past ten years, the Moon has come fully back into focus again. This resulted in missions such as Clementine (launched in 1994) and Lunar Prospector (1998), which gathered a wealth of new information about the Moon. With the recent launch of Europe's SMART-1 mission, and the foreseen launch in the near future of Lunar-A and SELENE, together with intended initiatives by China, India and the USA, the list of lunar missions is expanded even further, and more issues about the constitution and origin of the Moon, to name a few, will be addressed. Our work focuses on processing Lunar Prospector data in order to create high resolution regional gravity fields of the Moon, that can help solve some of the outstanding issues in lunar physics. Lunar gravity has been mainly expressed in a global representation, despite the lack of tracking data over the far side of the Moon. To extract all information about the near side of the Moon, which is covered well with good quality tracking data, a global formulation is not efficient, and regional representations become of interest. A method is presented to solve for regional gravity anomalies on the lunar surface from range and Doppler tracking data residuals, at an aimed accuracy of several mGal. The method is based on a linear variational approach that linearises the relationship between the tracking data residuals and gravity anomalies. Even in the presence of severe noise of the data, it can be shown that an accuracy of 3 mGal can still be obtained without the use of regularisation, provided that the satellite altitude is low enough. Lunar Prospector tracking data have been processed for the extended mission part, which lasted from January 1999 until July 31, 1999. The data fit is typically better than 5 mm/s for Doppler data, and 3 m for range data. These data have been used in order to make solutions of regional gravity adjustments for crater Copernicus and Mare Serenitatis. Results from this work can also benefit future interpretation of SELENE data. Lunar Prospector data can now also be processed and combined with future SELENE data to solve for the lunar gravity field.
G43A-0795 1340h
The Formation of the Thaumasia Highlands: Elastic Thickness Estimates From Line-of-Sight Accelerations
The Thaumasia region of Mars defines the southeastern most portion of Tharsis. It consists of a 4-5 km high, arcuate mountain belt, the Thaumasia Highlands, which bound a 2-4 km high interior plateau that includes Solis, Sinai, and Syria Planum. Exterior to this plateau in the cratered plains, a negative free-air gravity anomaly flanks the highlands. As there in no topographic expression associated with the gravity anomaly, it represents a density contrast in the crust. We interpret this feature to result from the burial of a flexural moat created by the formation of the highlands. Raw line-of-sight (LOS) spacecraft accelerations confirm the presence of this gravity anomaly and allows for an estimate to be made of the flexural wavelength and hence the elastic thickness at the time the highlands loaded the lithosphere. As the elastic strength of the Martian lithosphere is presumed to increases over time as the planet's heat flux diminishes, its value provides an estimate of the relative timing of loading. A best-fit to the spherical harmonic gravity signal provides and elastic thickness of $\sim$20 km implying the highlands are an ancient feature (Early Noachian). This is consistent with the preservation of Early Noachian terrains on the elevated topography of the highlands and by the infilling of the adjacent trench by middle and late Noachian units, the boundaries of which, to first order, correlate with the gravity anomaly. The admittances derived from the LOS accelerations for the entire Thaumasia region, containing Noachian and Hesperian features, yield an elastic thickness estimate of $\sim$70 km. Values $>$100 km are obtained for the northwestern portion of Tharsis containing largely Amazonian units. These values indicate Tharsis development progressed toward the northwest through the Hesperian and Amazonian, consistent with the mapped geology that reflects the same trend. This suggests there has been an alteration to the underlying convection since the Early Noachian resulting in a migration in volcanic activity away from Thaumasia and the preservation of Noachian terrains on the southeast margin. Further, the style of volcanic construction has changed over this time period, transitioning from plateau building in the Noachian to the formation of large shields in the Amazonian, perhaps reflecting the changing response of the lithosphere to volcanic loads.
G43A-0796 1340h
Constraining Lithospheric Stress on Mars From Mars Global Surveyor (MGS) Topography, Gravity, and Crustal Thickness
The quantification of lithospheric dynamics on Mars is of fundamental importance to the understanding of Martian geologic history and surface morphology. The global stress field associated with gravitational potential energy differences (GPE) constitutes a significant fraction of the total stress field. We have obtained $0.25 \times 0.25$ degree data sets of MOLA topography and crustal thickness from \emph{Zuber et al 2000}. We calculate the GPE associated with the topography by vertically integrating density to a given lithospheric depth using either Airy isostasy assumptions or the crustal thickness model of \emph{Zuber et al 2000}. Using a finite-element thin sheet method we solve the full 3-D force-balance equations for stress magnitudes and orientations within the lithosphere associated with the horizontal gradients in GPE. We assume $\rho_{crust} = 2900~ kg m^{-3}, ~\rho_{mantle} = 3500~ kg m^{-3}, ~g = 3.7~ ms^{-2}$ and various lithospheric thicknesses. We explore both viscous and elastic rheologies. It is interesting to note that our solutions depend on the rheology only through the ratio of shear and bulk moduli for the elastic case or the shear and bulk viscosities for the viscous case. Finally, we also calculate the expected style and orientation of the associated elastic strain. To first order, all stress field solutions are consistent with a tectonically inactive region relaxing due to excess or deficit of mass. Thus topographic highs e.g., Tharsis Mons, Olympus Mons, and Alba Patera, are in deviatoric extension, while topographic lows e.g., Valles Marineras and impact basins, are in deviatoric compression. At short wavelengths, however, features are regionally supported and differences in the stress field solutions occur between the Airy isostasy and the crustal thickness models. For example, several lowlands e.g., Isidis and Argyre Planitae, are in deviatoric extension in the crustal thickness model. Increasing the lithospheric depth increases the magnitudes of stresses but does not change the deformation style. Comparisons of viscous and elastic solutions with the same ratio of the shear and bulk viscosities for the viscous case and shear and bulk moduli for the elastic case show small variations in stress magnitudes and orientations among the solutions. We compare our results with inferred fault styles and orientations e.g., \emph{Mege 2001, Montessi and Zuber 2003}. The GPE variations appear to match the radial graben features on Tharsis, as well as the wrinkle ridges at lower elevations. However, they do not predict the wrinkle ridges on the flanks of Tharsis and some grabens around Alba Patera extend into the lower topography regions beyond the area where the GPE associated stresses predict extension. Calculations of \emph{Banerdt and Glombek 2000} show the importance of flexural loading on the stress field. Their flexural loading solution provides compression at higher elevations on Tharsis that may explain some of the wrinkle ridges not predicted by GPE variations. Therefore, it appears that a combined solution of GPE inferred vertically integrated deviatoric stresses and the flexurally produced stresses will provide a better fit to the fault styles and orientations observed on Mars.
G43A-0797 1340h
MODELING OF SURFACE AND SUBSURFACE LOADS FOR THE MAJOR MARTIAN VOLCANOES: IMPLICATIONS FOR DYNAMIC MANTLE PROCESSES ON THE PLANET
In the absence of in situ geophysical measurements, modeling the relationship between gravity and topography is one of the few methods that can be used to constrain the properties of a planet's interior. In this study, we model the localized spectral admittance of the large Martian volcanoes by assuming that surface and subsurface loads are elastically supported by the lithosphere. We systematically investigate the misfit function for the entire multi-dimensional space, which includes the elastic thickness, crustal thickness, load density, crustal density, and ratio of surface to subsurface loading. Our analysis represents an improvement over previous studies in several ways. First, our methodology computes the gravity anomaly, surface deflection, and load acting on the lithosphere in a self-consistent manner. Previous studies have not been able to correctly model the case when the load density differs from that of the crust. Secondly, we calculate localized admittance and coherence functions using localizing windows that concentrate almost all of their energy ($\sim$99$%$) with the region of interest. Previous studies have employed sub-optimal windows that only concentrate about 92$%$ of their energy within the desired region. We find that the density of the Martian volcanoes is higher than what was previously published (i.e., $\sim$3200 $\pm$ 100 kg m$^{-3}$), and is more consistent with the density of Martian basaltic meteorites, which are believed to come either from the Tharsis or Elysium volcanic provinces. The elastic thickness is found to be moderately constrained for Elysium (56$\pm$20 km), Alba Patera (66$\pm$20 km), Olympus Mons (93$\pm$40 km) and Ascraeus (105$\pm$40 km). The crustal density is constrained only for Elysium (3270 $\pm$150 kg m$^{-3}$). Estimates for the density of the southern highlands crust are generally lower, and this seems to indicate that the northern hemisphere crust is more mafic in composition The crustal thickness was found not to be constrained for any of the study regions. Finally, the investigation of possible subsurface loads shows evidence for dynamic processes acting under the volcanoes in this study. We found that all volcanoes are better modeled with the presence of less dense material in the upper mantle, which is either indicative of a mantle plume or a depleted mantle composition. The only exception is for Pavonis, where intrusive material in the crust gave the best results. An active plume beneath the major volcanoes is consistent with recent analyses of cratering statistics on Olympus Mons and the Elysium rise, which indicate that some lava flows erupted as late as10-30 Myr, as well as with the radiometric age of the Shergottites which have crystallization ages of about 180 Myr.
G43A-0798 1340h
Mars conformant planetary interior models
We propose a set of planetary interior models in agreement with the present knowledge of the planet Mars. Our spherical, hydrostatic and non-rotating planet is constituted by a crust, parameterized by its mean density, a mantle with variable mineralogy, dependent on pressure and temperature and a partially fluid core composed of iron and sulfur. The crust thickness, the location of the core mantle boundary, the size and state of the inner-core and the concentration of sulfur in the core are adjusted to agree with the total mass and mean moment of inertia.
G43A-0799 1340h
Martian gravity field long wavelength seasonal variations model from Mars Global Surveyor radio science measurements
By using one-way and two-way Doppler X-band tracking data of Mars Global Surveyor (MGS) from March 1998 to December 2003, the determination of the time-varying zonal gravity coefficients J2 and J3 and of the second degree Love number (k2) has been undertake. The amplitudes of the temporal variations of J2, J3 and the k2 value may be compared to those of modelled signals derived from Mars GCMs (global circulation models) and to previously obtained solutions.
G43A-0800 1340h
Improvement Of The Determination Of The Seasonal Variations Of Mars Gravity Field Using Both MGS And Mars Express Tracking Data
Mars is known to show a seasonal cycle due to condensation/sublimation of atmospheric carbon dioxide at polar caps. These processes deal with about one third of the atmospheric mass and provide detectable signatures on the time-varying first zonal components of the gravity field. The Mars Global Surveyor (MGS) spacecraft has allowed detecting these signatures through the determination of the fine perturbations of its orbit. However, the precision on such a detection is not enough to provide additional constraints to the Global Circulation Model (GCM) of Mars atmosphere. This lack of precision is partly due to the fact that the tracking of a single orbiter cannot permit to separate properly each even and each odd zonal components of the gravity field. One way to separate these contributions is to use radio-tracking of two orbiters with different orbital parameters, especially different inclination or eccentricity. Such a situation is actually occurring with the Mars Express (MEX) mission, which orbit eccentricity is quite different from the MGS one (0.6 instead of 0.01). The MaRS experiment provides MEX radio-tracking data that we propose to use, along with the MGS ones, in order to improve the determination of seasonal variations of zonal components. We present preliminary results based on the first months of MEX radio-tracking. We use the GINS software, primary developed at the CNES (French space agency), for precise orbit determination.
G43A-0801 1340h
Local Gravity Fields From Mars Express Residual Doppler Data
Planetary gravity fields can be studied in detail by measuring their effect on the velocity of an orbiting probe. Two main methods of analysis of the resulting Doppler data are available. Either a complete dynamical modeling of the probe orbit yields a global spherical harmonic gravity field, or a local analysis of the residual Doppler data leads to a model of the gravity field in a given area. The very elliptical orbit of Mars Express favors the second method, since only measurements near pericenter include a significant contribution from underlying gravity anomalies. The residual line-of-sight Doppler data provided by the MaRS experiment are inverted with a Tarantola-Valette stochastic procedure, with a priori knowledge of the solution given by a full correlation matrix constrained by the Kaula rule. As a result, the Doppler data are mapped as gravity disturbances on a sphere close to the planetary surface. Mars Express gravity data are expected to be especially useful for the study of polar caps, where the gravity field is not well known at the present.
G43A-0802 1340h
Mass and internal structure of Phobos from close flybys by Mars-Express
Several close encounters of Phobos by Mars Express spacecraft are scheduled for 2005. This will give us the opportunity to study its mass, internal structure and particularly the assumption of a constant density. Using the perturbations induced on MEX motion by Phobos irregular shape, one can fit its first gravitational coefficients as $J_2$ and $C_{22}$ and compare them with computed harmonics based on the shape and assumed constant density. We present a simulation of this method. A first software called GINS (primary developed by CNES) is used to represent MEX motion just before the close encounter. A second software has been developed to fit the Phobos gravitational potential, using the observed velocity perturbations on MEX. It is noteworthy that it will be the first direct observational derivation of Phobos' internal structure.
G43A-0803 1340h
CONSTRAINTS ON THE TEMPERATURE AND MINERALOGY OF THE MOON FROM A JOINT INVERSION OF APOLLO SEISMIC, GEODETIC DATA AND LP-CLEMENTINE GRAVITY DATA
We show the results of a joint inversion of most of the geophysical data gathered for the Moon by the Apollo, Lunar Prospector and Clementine missions. These data constrain different parts of the Moon interior : the crust and moon upper mantle are mainly constrained by seismic and heat flux data, while the very deep Moon interior is constrained by geodetic data. Our results show that a joint analysis of seismic and heat-flux data, in the PKT terrannes, favors a crust in the range of 30-35 km, thinner than proposed in the studies published in the seventieth. More detailed analysis, taking into account lateral variations of the crust, confirm such value. Deeper, we generally find temperature of 1073K (elastic lithosphere limit) and 1473K (thermal lithosphere limit) for radius of about 1400 km and 1000 km, comparable to the depth found in thermal evolution models. Our temperature profiles suggest 70% depletion for the upper and lower mantle compared to the Earth reference of 25.7 ppb. Finally, taking a mean crustal thickness of 40 km with 1010 ppb in Th and our mantle value for the depletion, we find a bulk Th and U abundance comparable to the Earth values within the error bars, and even possibly smaller. Constraints on the core size and lower mantle are also provided, by a joint inversion of the seismic models, of the inertia factor, mean density and k2 Love number. Based on this study, our Moon model is a 40 km thick anorthositic crust with a pyroxenite cold mantle (of bulk composition 6.4% in Al2O3, 4.9% in CaO, and 13.3% in FeO ) with an magnesian model for the bulk composition of the Moon lower mantle.
G43A-0804 1340h
Topography and Gravity of 433 Eros from DSN Doppler Tracking and Altimeter Crossovers
We have used the X-band Doppler tracking of NEAR/Shoemaker spacecraft from Earth, and NEAR Laser Rangefinder (NLR) measurements to estimate the orbital state of NEAR-Shoemaker and measurement biases, as well as spherical harmonic coefficients for the gravity field and the shape of 433 Eros. Data from the 200 km. altitude orbital stage through the high inclination 35 km orbits have been used in this analysis. Crossover measurements from NLR observations have been extended to include off-nadir observations. Meter level orbital accuracy for NEAR/Shoemaker with respect to the asteroid center of mass are attainable when the NLR observations are included in the analyses, and the orbital accuracy is improved through the use of NLR crossover information. The long wavelength gravity features have been determined to fractions of a few percent of their value. The spherical harmonic model for the shape of 433 Eros has a precision of a few meters.
G43A-0805 1340h
Characterization of Instabilities in the Tidal Deformation of a Plaetary Body
In 1911, A.E.H. Love published a linear elastic model for the tidal amplitude of a uniform, compressible, self-gravitating body. Our recent numerical evaluations of the solution to Love's governing equations reveal portions of parameter space for which an infinitesimal tide raiser can raise a tide of arbitrary height. In addition, using a solution technique different from Love's, investigations have been made into the effect of allowing non-uniform, radially varying density and elasticity in Love's formulation. It has been found that the tidal instabilities persist when the body initially has a radially varying density profile. To further investigate the nature of the tidal instabilities, an exact elastic formulation of the self-gravitational collapse of a uniform sphere is considered. Analysis reveals that the instability curves observed in Love's tidal solution for a uniform sphere and in the tidal solution for a sphere with radially varying density and elasticity correspond to various unstable modes of self-gravitation.