Gravity Field Models Research Articles

Ancient selenophysical structure of the Grimaldi basin: Constraints from GRAIL gravity and LOLA topography

The Grimaldi impact basin is located near the western limb of the moon and lies to the southwest of the Oceanus Procellarum. A clearly visible positive gravity anomaly exists in its low-lying inner wall, implying a subsurface mass concentration beneath the crater. Exploration of this basin could extend our meaningful and fundamental understanding of giant impact processes as well as the structure of mare basins/craters. Limited by the low-resolution of previous gravity field models, it was once impossible to explore the structure beneath Grimaldi. The recent high-resolution gravity data from the Gravity Recovery and Interior Laboratory mission make it possible to break through this barrier. Prior to our investigation of the selenophysical structure around crater Grimaldi, we developed a flexure model that includes surface and subsurface loads. A localized admittance analysis was performed by combining high-resolution gravity data with the high-resolution topography data obtained from Lunar Orbiter Laser Altimeter. Within 2σSTD error constraints, we estimated the best-fit parameters over Grimaldi as well as two other places in its neighborhood. All the predicted admittances show a goodness of fit with their corresponding observations. The large load ratio (∼9.2) found at the Grimaldi is an indirect mirror of the dominant subsurface load, consistent with its large positive gravity anomaly in its low-lying floor. Not only the crustal thickness of 48 km but also the crustal density of 2500 kg m−3 found around Grimaldi shows a great accordance with the recent results of GRAIL. Given the best-fit parameters of f, bc and ρc, the elastic thickness Te is found to be around 28 km over Grimaldi. Taking into account the best-fit values in its neighborhood, a regional elastic thickness of 30 km could be roughly concluded around Grimaldi, which is completely in the previous ranges (20 < Te < 60 km) from Clementine. Our result of the elastic thickness is quite larger than those on the lunar nearside volcanic complexes of the recent GRAIL study. Considering fewer thermal activities occurred on the lunar limb or farside than its nearside, we can then deduce that the lithosphere could be possibly cold and therefore developed a corresponding dense elastic thickness.

Airborne Gravimetry of GEOHALO Mission: Data Processing and Gravity Field Modeling

AbstractAirborne gravimetry is a crucial method to improve our knowledge about the Earth gravity field, especially in hard‐to‐access regions. Generally, the accuracy of airborne gravimetry is several milligals, which is suitable for filling the so‐called polar gaps in satellite‐derived global gravity field models. Here some investigations based on airborne gravity measurements from the GEOHALO mission over Italy are presented. To subtract the vertical accelerations from the values measured by the gravimeter, four different versions of kinematic accelerations were derived from Global Navigation Satellite Systems (GNSS) recordings. To remove the high‐frequency noise, a low‐pass filter with a cutoff wavelength of 200 s was applied to both Chekan‐AM measurements and kinematic accelerations from GNSS. To investigate how future airborne gravity campaigns could be designed, a dedicated flight track was repeated two times showing that the equipment worked well also at higher altitude and speed. From the final best results follows an RMS of gravity differences at crossover points of 1.4 mGal, which, according to the law of error propagation, implies the accuracy of a single measurement to be mGal. To demonstrate how a satellite‐only gravity field model can be improved by airborne measurements, a gravity field model for the GEOHALO region has been computed. To compute also an improved regional geoid model, the point mass modeling (PMM) and the remove‐compute‐restore (RCR) technique, using a recent satellite‐only model and residual terrain modeling (RTM), were applied. Finally, GNSS/leveling points have been used to check the quality of the regional point mass model.

Global gravity field from recent satellites (DTU15) — Arctic improvements

Global marine gravity field modelling using satellite altimetry is currently undergoing huge improvement with the completion of the Jason-1 end-of-life geodetic mission, but particularly with the continuing Cryosat-2 mission. These new satellites provide three times as many geodetic mission altimetric sea surface height observations as ever before. The impact of these new geodetic mission data is a dramatic improvement of particularly the shorter wavelength of the gravity field (10-20 km) which is now being mapped at significantly higher accuracy. The quality of the altimetric gravity field is in many places surpassing the quality of gravity fields derived using non-commercial marine gravity observations. Cryosat-2 provides for the first time altimetry throughout the Arctic Ocean up to 88°N. Here, the huge improvement in marine gravity mapping is shown through comparison with high quality airborne data flown north of Greenland in 2009. An improvement of nearly 50% in terms of standard deviation with the airborne data was found when comparing with older gravity fields such as DTU10 and EGM08, which are the only global marine gravity fields available in the Arctic Ocean north of 80°N.

GRACE time-varying gravity field solutions based on PANDA software

The conventional dynamic approach for gravity filed modelling has been implemented in the PANDA (Position and Navigation Data Analyst) software. A variant of the so-called ‘two-step’ method for gravity field modelling is adopted for this purpose, where the GRACE (Gravity Recovery and Climate Experiment) orbits are derived from the GPS (Global Positioning System) data in a first step followed by a simultaneous determination of dynamic orbit and gravity filed from the GPS-derived orbits and K-band range-rate measurements in a second step. In this way, the monthly gravity field solutions complete to degree and order 96 are produced for the period Jan. 2005 to Dec. 2010. Their performance is assessed by comparing them with the official solutions, i.e., CSR RL05, GFZ RL05a and JPL RL05. A comparison in the spectral domain in terms of geoid heights reveals that the obtained solutions present the smallest degree amplitudes at degree 30–75. A further analysis of mass changes in the spatial domain demonstrates that the main signals observed from the obtained solutions are in great agreement with those from the official solutions. Remarkably, the correlation coefficients of mass changes in large river basins from the official solutions with respect to those from the obtained solutions are all above 0.97. These results demonstrate that the obtained solutions are comparable to the official solutions.

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model’s spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components $$V_{xy}$$ and $$V_{yz}$$ of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE’s inclination of $$96.7^{\circ }$$ . With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of $$V_{xy}$$ and $$V_{yz}$$ are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1’s accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data.

A new tracking mode for improved Martian gravity field measurement

The Martian gravity field has been improved significantly in terms of resolution, with the spatial resolution rising to 100 km and accuracy increasing up to the 110 degree and order, assisted by data collected in Mars exploration missions like MGS, MRO, and Odyssey. However, as the tracking data used for the Martian gravity field solution are from polar orbit at a low height (∼400 km), improvements in the low degree coefficients are possible with high orbiters and various inclinations. In our research, we simulate a future Chinese Mars mission, making use of its orbit, to investigate potential contributions to the Martian gravity field solution. As the Chinese Mars mission will include a lander, we investigate the same beam interferometry tracking mode for a more precise and accurate Martian gravity field solution. Our results show that this tracking mode will substantially improve the gravity field model accuracy in comparison with those models using only polar orbit data. Model accuracy is assessed by power spectrum analysis and precise orbit determination. All the simulation work are accomplished with our independent developed software. Our research will be a reference for the first Chinese Mars exploration mission.

Candidates for volcanoes under the ice of Antarctica detected by their gravito-topographic signal

We analyse the newest gravity field models (given in the form of spherical harmonic expansion to degree and order 2190) EIGEN 6C4 and RET 14, which consist basically from the gravity data from EIGEN 6C4 plus the bedrock topography from the Bedmap 2 model, describing the topography of the ground under ice of Antarctica. From these models we computed the gravity anomalies, the Marussi tensor of the second derivatives of the disturbing potential, the gravity invariants and their specific ratio, the strike angle and the virtual deformations. We apply these results for a selected part of Antarctica; not too far from the Lake Vostok we discovered at least two objects that might be subglacial volcanoes. We present all predictors and arguments we have available to support this hypothesis, but we are well aware that the “last word” waits for other specialists. We provide geographic coordinates on the ice cover where to dig for the possible volcanoes.

A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model

The paper is about a methodology to combine a noisy satellite-only global gravity field model (GGM) with other noisy datasets to estimate a local quasi-geoid model using weighted least-squares techniques. In this way, we attempt to improve the quality of the estimated quasi-geoid model and to complement it with a full noise covariance matrix for quality control and further data processing. The methodology goes beyond the classical remove–compute–restore approach, which does not account for the noise in the satellite-only GGM. We suggest and analyse three different approaches of data combination. Two of them are based on a local single-scale spherical radial basis function (SRBF) model of the disturbing potential, and one is based on a two-scale SRBF model. Using numerical experiments, we show that a single-scale SRBF model does not fully exploit the information in the satellite-only GGM. We explain this by a lack of flexibility of a single-scale SRBF model to deal with datasets of significantly different bandwidths. The two-scale SRBF model performs well in this respect, provided that the model coefficients representing the two scales are estimated separately. The corresponding methodology is developed in this paper. Using the statistics of the least-squares residuals and the statistics of the errors in the estimated two-scale quasi-geoid model, we demonstrate that the developed methodology provides a two-scale quasi-geoid model, which exploits the information in all datasets.

Analysis of local covariance functions applied to GOCE satellite gravity gradiometry data

GOCE Level 2 products of corrected gravity gradients in Local North-Oriented Frame were used in this study. We analyzed four accurately measured elements of the gravity tensor, which were transformed to disturbing gravitational gradients. The investigation was carried out in the restricted region of dimension 20° × 20° covering the south part of Europe. We applied several types of analytical covariance functions in a local approximation, which have the best fit to the empirical covariances calculated from the disturbing gravitational gradients in particular sub-regions. At first, we have investigated four different types of the 1-dimensional covariance function. Obtained results show that the Gaussian covariance function approximates the empirical covariances the best from tested functions. Moreover, a time stability of calculated parameters of the covariance functions was studied by assuming GOCE data from different time periods. In the second experiment, we have compared two types of the 2-dimensional covariance function, which also enables a spatial stochastic modeling. The second study revealed that the least-squares collocation using the 2-dimensional local covariance function can produce the local grid of GOCE disturbing gravitational gradients directly from GOCE Level 2 products right below GOCE orbit, which in general fits well with the recent Earth’s global gravity field models and might have some advantages. Such local grids can be useful for specific tasks, e.g. mutual comparing of GOCE data collected during particular time periods.

Characterizing Drought and Flood Events over the Yangtze River Basin Using the HUST-Grace2016 Solution and Ancillary Data

Accurate terrestrial water storage (TWS) estimation is important to evaluate the situation of the water resources over the Yangtze River Basin (YRB). This study exploits the TWS observation from the new temporal gravity field model, HUST-Grace2016 (Huazhong University of Science and Technology), which is developed by a new low-frequency noise processing strategy. A novel GRACE (Gravity Recovery and Climate Experiment) post-processing approach is proposed to enhance the quality of the TWS estimate, and the improved TWS is used to characterize the drought and flood events over the YRB. The HUST-Grace2016-derived TWS presents good agreement with the CSR (Center for Space Research) mascon solution as well as the PCR-GLOBWB (PCRaster Global Water Balance) hydrological model. Particularly, our solution provides remarkable performance in identifying the extreme climate events e.g., flood and drought over the YRB and its sub-basins. The comparison between GRACE-derived TWS variations and the MODIS-derived (Moderate Resolution Imaging Spectroradiometer) inundated area variations is then conducted. The analysis demonstrates that the terrestrial reflectance data can provide an alternative way of cross-comparing and validating TWS information in Poyang Lake and Dongting Lake, with a correlation coefficient of 0.77 and 0.70, respectively. In contrast, the correlation is only 0.10 for Tai Lake, indicating the limitation of cross-comparison between MODIS and GRACE data. In addition, for the first time, the NCEP/NCAR (National Centers for Environmental Prediction/National Center for Atmospheric Research) vertical velocity data is incorporated with GRACE TWS in the exploration of the climate-induced hydrological activities. The good agreement between non-seasonal NCEP/NCAR vertical velocities and non-seasonal GRACE TWSs is found in flood years (2005, 2010, 2012 and 2016) and drought years (2006, 2011 and 2013). The evidence shown in this study may contribute to the analysis of the mechanism of climate impacts on the YRB.

Using radial basis functions in airborne gravimetry for local geoid improvement

Radial basis functions (RBFs) have been used extensively in satellite geodetic applications. However, to the author’s knowledge, their role in processing and modeling airborne gravity data has not yet been fully advocated or extensively investigated in detail. Compared with satellite missions, the airborne data are more suitable for these kinds of localized basis functions especially considering the following facts: (1) Unlike the satellite missions that can provide global or near global data coverage, airborne gravity data are usually geographically limited. (2) It is also band limited in the frequency domain. (3) It is straightforward to formulate the RBF observation equations from an airborne gravimetric system. In this study, a set of band-limited RBF is developed to model and downward continue the airborne gravity data for local geoid improvement. First, EIGEN6c4 coefficients are used to simulate a harmonic field to test the performances of RBF on various sampling, noise, and flight height levels, in order to gain certain guidelines for processing the real data. Here, the RBF method not only successfully recovers the harmonic field but also presents filtering properties due to its particular design in the frequency domain. Next, the software was tested for the GSVS14 (Geoid Slope Validation Survey 2014) area in Iowa as well as for the area around Puerto Rico and the US Virgin Islands by use of the real airborne gravity data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project. By fully utilizing the three-dimensional correlation information among the flight tracks, the RBF can also be used as a data cleaning tool for airborne gravity data adjustment and cleaning. This property is further extended to surface gravity data cleaning, where conventional approaches have various limitations. All the related numerical results clearly show the importance and contribution of the use of the RBF for high- resolution local gravity field modeling.

Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions

The application of Tikhonov regularization method for dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation (VCE) and minimum standard deviation (MSTD) approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the first-order Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.

Short note: the experimental geopotential model XGM2016

As a precursor study for the upcoming combined Earth Gravitational Model 2020 (EGM2020), the Experimental Gravity Field Model XGM2016, parameterized as a spherical harmonic series up to degree and order 719, is computed. XGM2016 shares the same combination methodology as its predecessor model GOCO05c (Fecher et al. in Surv Geophys 38(3): 571–590, 2017. doi: 10.1007/s10712-016-9406-y). The main difference between these models is that XGM2016 is supported by an improved terrestrial data set of \(15^\prime \times 15^\prime \) gravity anomaly area-means provided by the United States National Geospatial-Intelligence Agency (NGA), resulting in significant upgrades compared to existing combined gravity field models, especially in continental areas such as South America, Africa, parts of Asia, and Antarctica. A combination strategy of relative regional weighting provides for improved performance in near-coastal ocean regions, including regions where the altimetric data are mostly unchanged from previous models. Comparing cumulative height anomalies, from both EGM2008 and XGM2016 at degree/order 719, yields differences of 26 cm in Africa and 40 cm in South America. These differences result from including additional information of satellite data, as well as from the improved ground data in these regions. XGM2016 also yields a smoother Mean Dynamic Topography with significantly reduced artifacts, which indicates an improved modeling of the ocean areas.

Generalization techniques to reduce the number of volume elements for terrain effect calculations in fully analytical gravitational modelling

Beyond rectangular prism polyhedron, as a discrete volume element, can also be used to model the density distribution inside 3D geological structures. The calculation of the closed formulae given for the gravitational potential and its higher-order derivatives, however, needs twice more runtime than that of the rectangular prism computations. Although the more detailed the better principle is generally accepted it is basically true only for errorless data. As soon as errors are present any forward gravitational calculation from the model is only a possible realization of the true force field on the significance level determined by the errors. So if one really considers the reliability of input data used in the calculations then sometimes the “less” can be equivalent to the “more” in statistical sense. As a consequence the processing time of the related complex formulae can be significantly reduced by the optimization of the number of volume elements based on the accuracy estimates of the input data. New algorithms are proposed to minimize the number of model elements defined both in local and in global coordinate systems. Common gravity field modelling programs generate optimized models for every computation points (dynamic approach), whereas the static approach provides only one optimized model for all. Based on the static approach two different algorithms were developed. The grid-based algorithm starts with the maximum resolution polyhedral model defined by 3–3 points of each grid cell and generates a new polyhedral surface defined by points selected from the grid. The other algorithm is more general; it works also for irregularly distributed data (scattered points) connected by triangulation. Beyond the description of the optimization schemes some applications of these algorithms in regional and local gravity field modelling are presented too. The efficiency of the static approaches may provide even more than 90% reduction in computation time in favourable situation without the loss of reliability of the calculated gravity field parameters.

GOCE Gradiometer Measurements Response to Ionospheric Dynamics

AbstractWith the launch of dedicated satellite gravity missions, starting with CHAllenging Minisatellite Payload (CHAMP) in 2000, with Gravity Recovery and Climate Experiment (GRACE) in 2002, and Gravity field and steady‐state Ocean Circulation Explorer (GOCE) in 2009, the accuracy and spatial resolution of the Earth's global gravity field models have been improved. Highly sensitive accelerometer measurements have not only been useful for gravity field modeling but have also been contributing to the studies of thermospheric dynamics. While improving the sensitivity of the accelerometer measurements, the new instrumentation used on board GOCE brings different challenges in understanding the data and developing sophisticated data processing. Our analyses reveal that the GOCE gravitational gradient measurements were affected by highly variable ionospheric dynamics that did not only degrade the quality of the GOCE Electrostatic Gravity Gradiometer (EGG) measurements but also proved that some characteristics of ionospheric dynamics can be measured by GOCE accelerometers and other Low Earth Orbiters. In this paper, we show how GOCE‐retrieved neutral winds respond to main ionospheric currents and we develop the impulse‐response relation between intense ionospheric dynamics (plasma drift) represented by Poynting energy flux and the gravity gradiometer tensor trace disturbances observed over the north geomagnetic polar region.

Применение глобальных моделей гравитационного поля для обработки высокоточного нивелирования

The article studies the properties of the high-degree gravity field model EGM-2008 in the calculation of integral characteristics at large distances several times greater than the spatial resolution of the model. As an example of an indirect evaluation of a high-degree model, a gravimetric correction was computed into the sum of the measured elevations along the line of the high-precision I class leveling of the Krasnovodsk – Chardzhou line located in Turkmenistan. Using the calculator ICGEM, the Bouguer anomalies were calculated at each point of the line, then the attraction of the Bouguer layer (used heights are from catalog) excluded for the transition to free-air anomalies. In parallel, for a direct evaluation of the model, a regular grid of Bouguer anomalies with a step of 2 angular minutes within line area was also obtained, which were then compared with the anomalies from the gravity map J-40 of scale 1

Geosynchronous inclined orbits for high-latitude communications

We present and discuss a solution to the growing demand for satellite telecommunication coverage in the high-latitude geographical regions (beyond 55°N), where the signal from geostationary satellites is limited or unavailable. We focus on the dynamical issues associated to the design, the coverage, the maintenance and the disposal of a set of orbits selected for the purpose. Specifically, we identify a group of highly inclined, moderately eccentric geosynchronous orbits derived from the Tundra orbit (geosynchronous, eccentric and critically inclined). Continuous coverage can be guaranteed by a constellation of three satellites in equally spaced planes and suitably phased. By means of a high-precision model of the terrestrial gravity field and the relevant environmental perturbations, we study the evolution of these orbits. The effects of the different perturbations on the ground track (which is more important for coverage than the orbital elements themselves) are isolated and analyzed. The physical model and the numerical setup are optimized with respect to computing time and accuracy. We show that, in order to maintain the ground track unchanged, the key parameters are the orbital period and the argument of perigee. Furthermore, corrections to the right ascension of the ascending node are needed in order to preserve the relative orientation of the orbital planes. A station-keeping strategy that minimizes propellant consumption is then devised, and comparisons are made between the cost of a solution based on impulsive maneuvers and one with continuous thrust. Finally, the issue of end-of-life disposal is discussed.

THE ADVANCEMENT OF LUNAR GRAVITY MODEL DUE TO THE DEVELOPMENT OF SPACE TRACKING TECHNIQUES

AbstractBased on the three modes of lunar spacecraft tracking techniques: Earth‐based tracking mode, high‐low satellite‐to‐satellite tracking mode and low‐low satellite‐to‐satellite tracking mode, the development of lunar gravity models could be divided into 4 stages. First, we introduce the principle, technical characteristics of the different tracking modes, and the representative gravity models, and then make comments on these models’ precision. Further, through the comparison of gravity anomaly precision, characteristics and orbit determination precision from different stages’ lunar gravity field models, we conclude that: the advancement of space tracking techniques has significantly improved the precision of lunar gravity model and effectively promotes the understanding of lunar interior structure and the reliability of lunar satellite orbit determination. Finally, we analyze the deficiency of current lunar gravity models and give a perspective of future space tracking techniques.

PRECISE ESTABLISHMENT OF THE NEXT‐GENERATION EARTH GRAVITY FIELD MODEL FROM HIP‐3S BASED ON COMBINATION OF INLINE AND PENDULUM SATELLITE FORMATIONS

AbstractBecause the sensitivity of the disturbing intersatellite range measurements to the recovery accuracy of the Earth's gravitational field is superior to that of the intersatellite range measurements, the observation equation of a new Disturbing Intersatellite Range Method (DIRM) is created in this study. Then the orbital stability of the next‐generation Hybrid‐Inline‐Pendulum‐Three‐Satellite (HIP‐3S) formation is efficiently verified. The research results indicate that the HIP‐3S formation is sufficiently steady for further enhancing the accuracy of the future Earth gravity field model. Finally, the Earth's gravitational field complete up to degree and order 120 is precisely recovered by the current GRACE‐2S inline formation and the next‐generation HIP‐3S combined formation based on the new DIRM, and the cumulative geoid height errors are 2.271×10−1 m and 1.923×10−3 m at degree 120, respectively. The study results show that the future HIP‐3S formation is helpful for producing the next‐generation Earth gravity field model with higher accuracy and spatial resolution.

Evidence for a Low Bulk Crustal Density for Mars from Gravity and Topography.

Knowledge of the average density of the crust of a planet is important in determining its interior structure. The combination of high-resolution gravity and topography data has yielded a low density for the Moon's crust, yet for other terrestrial planets the resolution of the gravity field models has hampered reasonable estimates. By using well-chosen constraints derived from topography during gravity field model determination using satellite tracking data, we show that we can robustly and independently determine the average bulk crustal density directly from the tracking data, using the admittance between topography and imperfect gravity. We find a low average bulk crustal density for Mars, 2582 ± 209 kg m-3. This bulk crustal density is lower than that assumed until now. Densities for volcanic complexes are higher, consistent with earlier estimates, implying large lateral variations in crustal density. In addition, we find indications that the crustal density increases with depth.