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NASA NTRS2021

GRACE Fast Mascons from Spherical Harmonics and a Regularization Design Trade Study

Mass concentration (mascon) solutions have become a prominent medium for investigating time-variable gravity recovered by GRACE and GRACE Follow-On. While GRACE Level-2 spherical harmonic products require various post-processing techniques to eliminate correlated noise, mascon formulations employ spatial regularization strategies during the estimation step to improve signal recovery. However, mascon estimation has traditionally required large computing resources and GRACE Level-1B processing capabilities. In this study, we show that a typical mascon estimation system can be reformulated to allow for the estimation of regularized mascons from Level-2 spherical harmonics. Provided that spherical harmonic solution covariances are available, the computed mascons will be mathematically equivalent to similar mascons estimated from Level-1B observations. This method is computationally efficient, better leverages GRACE spherical harmonics than past methods, and matches the performance of typical mascon solutions without locking scientists into pre-determined regularization designs. We develop a proof-of-concept solution using ITSG-Grace2018 and compare results with traditional mascons from JPL and NASA GSFC. We then assess the effects of spherical harmonic truncation and use of regularization correlations on basin signal recovery. We find that spherical expansions to degree and order 60 provide the minimum expansion necessary to study most basins, while larger expansions help further localize signals. We also find that diagonal regularizations (i.e., regularizations that do not contain inter-mascon correlations) are adversely affected by leakage, especially across boundaries such as coastlines where signals are not highly correlated, whereas including inter-mascon correlations and regional boundaries in the regularization greatly improves signal recovery.

M. J. Croteau↗

NASA NTRS2019

Regularization and Error Characterization of GRACE Mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

B. D. Loomis↗

NASA NTRS2019

Regularization and Error Characterization of GRACE Mascons

Loomis, B. D.↗

NASA NTRS1998

Lunar Basins: New Evidence from Gravity for Impact-Formed Mascons

The prominent gravity highs (mascons) associated with uncompensated mass anomalies in lunar mare basins are a dramatic expression of the present-day rigidity of the lunar lithosphere. First discovered in Lunar Orbiter tracking data, these about 350-mGal gravity highs have been redetermined from the analysis of Clementine and historical tracking. These highs coincide with topographic lows, indicating nonisostatic support. One of the rediscoveries of this analysis is the encirclement of the highs by substantial negative anomalies over topographic highs. Recent gravity fields are providing the increased resolution necessary to determine the causes of this unique mascon signature. The compensation of the basin anomalies remains controversial. The mascon highs have long been interpreted as the result of mare loading, subsequent to the decay of residual stresses resulting from the impact. Substantially more mare fill is required to produce mascon highs than has been inferred on geological grounds, and the amount of near-surface mass deficit required to produce a gravity most exceeds bounds inferred from terrestrial examples. This problem is most acute for the youngest basin, Orientale. Recent gravity fields from Lunar Prospector have suggested mascon highs associated with nonmare basins such as Mendel-Rydberg, or minimally filled basins like Humboldtianum, further calling this explanation into question. We suggest that the mascon gravity signal is produced by a combination of crustal thickness changes, manifested by central mantle uplift, outward displacement of crust, and downward flexure of the lithosphere under mare loading. The mantle uplift is superisostatic, maintained by residual stresses resulting from the process of impact cratering and modification. In particular, the process of crater collapse and mantle rebound terminates abruptly, leaving the mantle plug in a non-equilibrium state, surrounded by a ring of thickened crust. Viscous relaxation over geological timescales has erased some but not all of the signature of the impact process. Mantle uplift inferred from gravity modeling is inversely correlated with age. While the oldest basins such as South Pole Aitken are mainly compensated isotatically, the younger basins appear to have been in a state of superisostatic loading prior to mare emplacement. If this is true, this places an important constraint on the impact process at basin scales. The idea that rebound of the transient crater via acoustic fluidization may freeze substantial stresses imcomplete to this day, may be tested by examining the gravity signatures of major basins on terrestrial bodies. The moon provides the clearest resolved examples to date, but uncertainty in gravity knowledge remains problematic.

Neumann, Gregory A.↗

NASA NTRS2019

Wrinkle Ridges on Mercury and the Moon Within and Outside of Mascons

Found on all terrestrial planets, wrinkle ridges are anticlines formed by thrust faulting and folding resulting from crustal shortening. The MErcury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER) spacecraft's orbital phase returned high resolution images and topographic data of the previously unimaged northern high latitudes of Mercury where there are large expanses of smooth plains deformed by wrinkle ridges. Concurrently, the Lunar Reconnaissance Orbiter (LRO) is obtaining high resolution images and topographic data covering lunar mare wrinkle ridges. These data allow quantitative comparison of the scale of wrinkle ridges in smooth plains volcanic units on Mercury with mare wrinkle ridges. We evaluate the topographic relief of 300 wrinkle ridges within and outside of mascon basins on the Moon and Mercury. Measured wrinkle ridges range from ~112 to 776 m in relief with a mean of ~350 m (median = ~340 m, n = 150) on Mercury and from ~47 to 678 m in relief with a mean of ~198 m (median = ~168 m, n = 150) on the Moon. Wrinkle ridges on Mercury thus are approximately twice as large in mean relief compared to their counterparts on the Moon. The larger scale of Mercury's wrinkle ridges suggests that their formation can be attributed, in part, to global contraction. As global contraction on the Moon is estimated to be an order of magnitude smaller than on Mercury, the smaller scale of lunar wrinkle ridges suggests they most likely form primarily by load induced subsidence of the mare basalt. Wrinkle ridges located in lunar mascon basins and in the Caloris mascon on Mercury are not statistically significantly different in relief than ridges in non-mascon regions, suggesting comparable levels of contractional strain. The fact that mascon basins do not host wrinkle ridges with greater structural relief relative to non-mascon units may indicate the critical role lithospheric thickness plays in controlling subsidence and contraction of thick volcanic sequences on the Moon and Mercury.

Global contraction↗

NASA NTRS2019

Wrinkle ridges on Mercury and the Moon within and outside of mascons

Found on all terrestrial planets, wrinkle ridges are anticlines formed by thrust faulting and folding resulting from crustal shortening. The MErcury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER)spacecraft's orbital phase returned high resolution images and topographic data of the previously unimaged northern high latitudes of Mercury where there are large expanses of smooth plains deformed by wrinkle ridges. Concurrently, the Lunar Reconnaissance Orbiter (LRO) is obtaining high resolution images and topographic data covering lunar mare wrinkle ridges. These data allow quantitative comparison of the scale of wrinkle ridges in smooth plains volcanic units on Mercury with mare wrinkle ridges. We evaluate the topographic relief of 300 wrinkle ridges within and outside of mascon basins on the Moon and Mercury. Measured wrinkle ridges range from ~112 to 776 min relief with a mean of ~350m (median=~340m, n=150) on Mercury and from ~47 to 678 min relief with a mean of ~198 m (median=~168m, n=150) on the Moon. Wrinkle ridges on Mercury thus are approximately twice as large in mean relief compared to their counterparts on the Moon. The larger scale of Mercury's wrinkle ridges suggests that their formation can be attributed, in part, to global contraction. As global contraction on the Moon is estimated to be an order of magnitude smaller than on Mercury, the smaller scale of lunar wrinkle ridges suggests they most likely form primarily by load induced subsidence of the mare basalt. Wrinkle ridges located in lunar mascon basins and in the Caloris mascon on Mercury are not statistically significantly different in relief than ridges in non-mascon regions, suggesting comparable levels of contractional strain. The fact that mascon basins do not host wrinkle ridges with greater structural relief relative to non-mascon units may indicate the critical role lithospheric thickness plays in controlling subsidence and contraction of thick volcanic sequences on the Moon and Mercury.

Lisa S. Schleicher↗

NASA NTRS2006

Recent Mascon Solutions from GRACE

Mascon (mass concentration) solutions computed for entire land area of Earth with several variants from Jul. 2003 through Dec. 2005 Automated scripts developed, "pipeline" now in place. Solutions generally consistent with harmonics for large features but appear able to resolve and localize smaller features more cleanly. Greenland solutions generally consistent with areas of max ice mass loss in South, but mascons seem to clearly identify sub-regions of ice mass growth. May be amplified by mascon sensitivity and ground tracks. Irregular coverage, errors due to tides in Arctic or other leakage from nearby sources? Although mascons are technically 30+ years old, gravity/geodesy community has vastly more experience with harmonics and thus we are still learning the full advantages, limitations, and idiosyncrasies of mascons.

GRACE↗

NASA NTRS2013

Antarctica, Greenland and Gulf of Alaska Land-ice Evolution from an Iterated GRACE Global Mascon Solution

We have determined the ice mass evolution of the Antarctica and Greenland ice sheets (AIS and GIS) and Gulf of Alaska (GOA) glaciers from a new GRACE global solution of equal-area surface mass concentration parcels (mascons) in equivalent height of water. The mascons were estimated directly from the reduction of the inter-satellite K-band range-rate (KBRR) observations, taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons were estimated with 10 day and 1 arc degree equal-area sampling, applying anisotropic constraints. An ensemble empirical mode decomposition adaptive filter was applied to the mascon time series to compute annual mass balances. The details and causes of the spatial and temporal variability of the land-ice regions studied are discussed. The estimated mass trend over the total GIS, AIS and GOA glaciers for the time period 1 December 2003 to 1 December 2010 is -380 plus or minus 31 Gt a(exp -1), equivalent to -1.05 plus or minus 0.09 mma(exp -1) sea-level rise. Over the same time period we estimate the mass acceleration to be -41 plus or minus 27 Gt a(exp -2), equivalent to a 0.11 plus or minus 0.08 mm a(exp -2) rate of change in sea level. The trends and accelerations are dependent on significant seasonal and annual balance anomalies.

MASCON↗

NASA NTRS1974

On the origin of mascons and moonquakes

Hypotheses are proposed for the origin of mascons and moonquakes. It is noted that a horizontal transfer of magma is required to explain the mascons and that a basin which can fill with lava to a depth of about 20 km is necessary before mascon formation is possible. It is shown that hydrostatic equilibrium theories can account for the excess filling of lava in circular maria and that mascons will result when this process occurs in the presence of a thick rigid lithosphere. It is postulated that a cylindrical fault system extends through the lithosphere and surrounds the circular maria. In this case, the release of potential energy through the fault system would be adequate to explain moonquakes, their properties, and the clustering of the locations of lunar transient events around the circular maria.

Runcorn, S. K.↗

NASA NTRS2020

Development of a Daily GRACE Mascon Solution for Terrestrial Water Storage

The Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow On missions have provided a global history of terrestrial water storage changes since 2002. Traditional GRACE products resolve monthly time-variable gravity at spatial resolutions of 300-500 km, with many recent efforts focusing on regularized mass concentration (mascon) solutions to better resolve signals spatially. However, monthly resolution inhibits the applicability of GRACE to investigations of sub-monthly signals. This study presents a new daily mass change solution estimated as deviations from the NASA Goddard Space Flight Center (GSFC) converged monthly mascon product and quantifies the fundamental trade-off between temporal and spatial resolution in GRACE-only solutions. As an iteration of the GSFC product, this daily solution represents a mixing of monthly information at higher relative spatial resolution with daily information at lower relative spatial resolution, resolving each temporal scale at the best resolution achievable without requiring hydrological model dependencies in the estimation. The resolution of the daily mascons is 300-400 km at high latitudes and 600-1,000 km lower, depending on each daily orbital track and the proximity of each mascon to constraint region boundaries (e.g., coastlines). Through simulations and model comparisons, we demonstrate that daily signals over areas larger than 400,000 km(2) are recoverable, with basins larger than 800,000 km(2) exhibiting strong signal recovery relative to leakage. This analysis establishes baselines for daily signal recovery from GRACE in the context of longer time scale solutions, characterizes leakage inherent in daily GRACE information, and creates new opportunities for applying GRACE to investigations of sub-monthly signals.

M. J. Croteau↗

NASA NTRS2022

Mascon Basins

Large basins across the lunar surface have observable positive gravity anomalies within the interiors, referred to as mass concentrations, or “mascons.” Some near-side mascons can be explained by flexural support of the mare basalts within the basins, like Orientale, that have excessive mascons. There are also some basins that exhibit masons but lack mare basalts. Lunar gravity and topography data are most often used to determine the morphology and gravity anomalies of the mascons.

Caitlin Ahrens↗

NASA NTRS1973

On the formation of the lunar mascons

A new mascon hypothesis is proposed which accounts for: (1) the existence of lunar mascons for more than 3 b.y., (2) the evidence for extensive volcanic activity from 3.7 to 3.2 b.y. ago, (3) the existence of negative gravity anomaly rings, (4) insufficient mare material in Mare Orientale, and (5) the lack of mascons associated with craters smaller than 200 km diameter. Moreover, it provides a simple mechanism for mass transfer into the basins. The hypothesis is based on the perturbations introduced into a spherically symmetric thermal evolution model of the moon by a giant impact.

Arkani-Hamed, J.↗

NASA NTRS1980

Lunar mascon basins - Lava filling, tectonics, and evolution of the lithosphere

The paper extends the study of the relationships among lunar mare filling, mare basin tectonics, and global thermal evolution to the major mascon maria: Imbrium, Crisium, Orientale, Humorum, Nectaris, Smythii, Grimaldi, and Serenitatis. For each of the eight major mascon mare basins on the moon, the paper describes the distribution and history of major mare units, the characteristics and geometry of basin-related tectonic features, the temporal relations between tectonic features and geologic units, the response of the lunar lithosphere to basalt loading as a function of space and time, and the relationship between loading stress and global thermal stress in controlling lunar tectonic history. The principal features of the volcanic, tectonic, and thermal history of the mascon maria are summarized.

Solomon, S. C.↗

NASA NTRS1991

Modelled and measured strain in mascon basins on the moon

The close association of wrinkle ridges and grabens with mascon basins on the Moon has suggested that the responsible compression and extension resulted from basin subsidence and peripheral flexing of the lithosphere. The distribution of grabens and wrinkle ridges associated with mascon basins has been further used along with elastic plate bending models to constrain the thickness of the lithosphere at the time of their formation. Kinematic models for basin subsidence have also been developed and compared with strains inferred from grabens and wrinkle ridges. Note that kinematic models may be preferable to dynamic models because the strain associated with tectonic features can be compared directly with model predictions and because fewer assumptions are required for their calculations, such as perfect elasticity and specific values of the elastic moduli. Also, if the results from kinematic models compare favorably with the strain estimated across the tectonic features on the Moon, then a global strain field may not be necessary. Herein, the strain inferred for wrinkle ridges and grabens was compared to that calculated from a simple kinematic subsidence model for mascon basins on the Moon.

Golombek, M. P.↗

NASA NTRS1992

An analytical evaluation of mascon effects in a semi-analytic theory

A semianalytic method to predict the orbit of a spacecraft orbiting a planet and perturbed by oblateness and a gravity anomaly (mascon) is presented. The Hamiltonian is first expressed in closed form in terms of the nonsingular canonical set of Poincare elements where the mascon is represented by a point-mass. The planet global potential is limited to the second and third harmonics. The mascon potential in harmonics is limited to second degree and first order. The original Lie-Hori method is then applied to transform the canonical equations of motion from the osculating element space to the mean element space. Numerical integration of the new equations is used.

Salama, Ahmed H.↗

NASA NTRS2012

An Iterated Global Mascon Solution with Focus on Land Ice Mass Evolution

Land ice mass evolution is determined from a new GRACE global mascon solution. The solution is estimated directly from the reduction of the inter-satellite K-band range rate observations taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons are estimated with 10-day and 1-arc-degree equal area sampling, applying anisotropic constraints for enhanced temporal and spatial resolution of the recovered land ice signal. The details of the solution are presented including error and resolution analysis. An Ensemble Empirical Mode Decomposition (EEMD) adaptive filter is applied to the mascon solution time series to compute timing of balance seasons and annual mass balances. The details and causes of the spatial and temporal variability of the land ice regions studied are discussed.

Luthcke, S. B.↗

DOE OSTI2022

Mascon distribution techniques for asteroids and comets

The mass-concentration model is an approach that has been used to model the gravitational fields of irregularly shaped bodies such as asteroids and comets. By this approach, the body is treated as a collection of point masses. The method is conceptually simple, easy to program, valid down to the surface, and capable of modeling arbitrary density heterogeneities. How the mass concentrations are distributed as well as how mass is assigned to these concentrations is, however, nontrivial. These aspects significantly affect the accuracy and efficiency of the gravitational model. In this paper, we frame the distribution process in terms of numerical integration applied to finite volume meshes. We describe a new method using unstructured, curvilinear, finite volume meshes to significantly improve the accuracy of the mass-concentration model. We then compare the accuracy and efficiency of several variations of our distribution technique to those from literature using Asteroid Eros and Bennu as example bodies. Our results show that the mascon model can be as accurate as the analytic polyhedral model at the surface using an equivalent number of computational elements—i.e., mascon to surface facets. We report the improvement in the model’s performance can be mainly attributed to the volume mesh topology while mesh curving can provide modest case-dependent improvements.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Mascon distribution on the moon

Results concerning the distribution of mascons on the moon have been obtained from an analysis of Apollo 8, 10, 11, and 12 lunar orbit missions. It was concluded that the tugging and pulling by the moon on the orbit plane of the Apollo spacecraft yields qualitative information concerning the distribution of the mascons.

Murphy, J.↗