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NASA NTRS1982

Influence of gravity driven convection on the directional solidification of Bi/MnBi eutectic composites

The role of gravity on Bridgman-Stockharger directional solidification of eutectic Bi/MnBi has been studied in reduced gravity aboard NASA sounding rocket SPAR flight experiments and contrasted with normal gravity investigations. The directional solidification of eutectic Bi/MnBi results in a low volume fraction, faceted/nonfaceted aligned rod eutectic whose MnBi rod size, interrod spacing, thermal and magnetic properties are sensitive functions of solidification processing conditions. The morphology of the low-gravity samples showed striking differences compared with identically processed, normal gravity samples grown in the same apparatus. The MnBi rod diameter and interrod spacing distributions were significantly smaller, approximately 50 percent, for the low gravity samples compared with identically processed one gravity samples. Accompanying the smaller MnBi rod diameters observed in the flight samples, was an increase in permanent magnet properties which reached greater than 97 percent of the theoretical maximum. Gravitationally induced thermal instabilities in one-gravity which result in irregular interface movement and associated difficulty of the faceted MnBi phase to branch are suggested to explain the morphological differences between one and low gravity solidification.

Pirich, R. G.↗

NASA NTRS1987

The behavior of surface tension on steady-state rotating fluids in the low gravity environments

The effect of surface tension on steady-state rotating fluids in a low gravity environment is studied. All the values of the physical parameters used in these calculations, except in the low gravity environments, are based on the measurements carried out by Leslie (1985) in the low gravity environment of a free-falling aircraft. The profile of the interface of two fluids is derived from Laplace's equation relating the pressure drop across an interface to the radii of curvature which has been applied to a low gravity rotating bubble that contacts the container boundary. The interface shape depends on the ratio of gravity to surface tension forces, the ratio of centrifugal to surface tension forces, the contact radius of the interface to the boundary, and the contact angle. The shape of the bubble is symmetric about its equator in a zero-gravity environment. This symmetry disappears and gradually shifts to parabolic profiles as the gravity environment becomes non-zero. The location of the maximum radius of the bubble moves upward from the center of the depth toward the top boundary of the cylinder as gravity increases. The contact radius of interface to the boundary r0 at the top side of cylinder increases and r0 at the bottom side of the cylinder decreases as the gravity environment increases from zero to 1 g.

Hung, R. J.↗

NASA NTRS1987

A study of two-phase flow in a reduced gravity environment

A test loop was designed and fabricated for observing and measuring pressure drops of two-phase flow in reduced gravity. The portable flow test loop was then tested aboard the NASA-JSC KC135 reduced gravity aircraft. The test loop employed the Sundstrand Two-Phase Thermal Management System (TPTMS) concept which was specially fitted with a clear two-phase return line and condenser cover for flow observation. A two-phase (liquid/vapor) mixture was produced by pumping nearly saturated liquid through an evaporator and adding heat via electric heaters. The quality of the two-phase flow was varied by changing the evaporator heat load. The test loop was operated on the ground before and after the KC135 flight tests to create a one-gravity data base. The ground testing included all the test points run during the reduced gravity testing. Two days of reduced gravity tests aboard the KC135 were performed. During the flight tests, reduced-gravity, one-gravity, and nearly two-gravity accelerations were experienced. Data was taken during the entire flight which provided flow regime and pressure drop data for the three operating conditions. The test results show that two-phase pressure drops and flow regimes can be accurately predicted in zero-gravity.

Hill, D.↗

NASA NTRS1989

Modeling of the Earth's gravity field using the New Global Earth Model (NEWGEM)

Traditionally, the global gravity field was described by representations based on the spherical harmonics (SH) expansion of the geopotential. The SH expansion coefficients were determined by fitting the Earth's gravity data as measured by many different methods including the use of artificial satellites. As gravity data have accumulated with increasingly better accuracies, more of the higher order SH expansion coefficients were determined. The SH representation is useful for describing the gravity field exterior to the Earth but is theoretically invalid on the Earth's surface and in the Earth's interior. A new global Earth model (NEWGEM) (KIM, 1987 and 1988a) was recently proposed to provide a unified description of the Earth's gravity field inside, on, and outside the Earth's surface using the Earth's mass density profile as deduced from seismic studies, elevation and bathymetric information, and local and global gravity data. Using NEWGEM, it is possible to determine the constraints on the mass distribution of the Earth imposed by gravity, topography, and seismic data. NEWGEM is useful in investigating a variety of geophysical phenomena. It is currently being utilized to develop a geophysical interpretation of Kaula's rule. The zeroth order NEWGEM is being used to numerically integrate spherical harmonic expansion coefficients and simultaneously determine the contribution of each layer in the model to a given coefficient. The numerically determined SH expansion coefficients are also being used to test the validity of SH expansions at the surface of the Earth by comparing the resulting SH expansion gravity model with exact calculations of the gravity at the Earth's surface.

Kim, Yeong E.↗

NASA NTRS1989

Geodynamics and temporal variations in the gravity field

Just as the Earth's surface deforms tectonically, so too does the gravity field evolve with time. Now that precise geodesy is yielding observations of these deformations it is important that concomitant, temporal changes in the gravity field be monitored. Although these temporal changes are minute they are observable: changes in the J2 component of the gravity field were inferred from satellite (LAGEOS) tracking data; changes in other components of the gravity field would likely be detected by Geopotential Research Mission (GRM), a proposed but unapproved NASA gravity field mission. Satellite gradiometers were also proposed for high-precision gravity field mapping. Using simple models of geodynamic processes such as viscous postglacial rebound of the solid Earth, great subduction zone earthquakes and seasonal glacial mass fluctuations, we predict temporal changes in gravity gradients at spacecraft altitudes. It was found that these proposed gravity gradient satellite missions should have sensitivities equal to or better than 10(exp -4) E in order to reliably detect these changes. It was also found that satellite altimetry yields little promise of useful detection of time variations in gravity.

Mcadoo, D. C.↗

NASA NTRS1989

Refinement of Earth's gravity field with Topex GPS measurements

The NASA Ocean Topography Experiment satellite TOPEX will carry a microwave altimeter accurate to a few centimeters for the measurement of ocean height. The capability can be fully exploited only if TOPEX altitude can be independently determined to 15 cm or better. This in turn requires an accurate gravity model. The gravity will be tuned with selected nine 10-day arcs of laser ranging, which will be the baseline tracking data type, collected in the first six months of TOPEX flight. TOPEX will also carry onboard an experimental Global Positioning System (GPS) flight receiver capable of simultaneously observing six GPS satellites above its horizon to demonstrate the capability of GPS carrier phase and P-code pseudorange for precise determination of the TOPEX orbit. It was found that subdecimeter orbit accuracy can be achieved with a mere two-hour arc of GPS tracking data, provided that simultaneous measurements are also made at six of more ground tracking sites. The precision GPS data from TOPEX are also valuable for refining the gravity model. An efficient technique is presented for gravity tuning using GPS measurements. Unlike conventional global gravity tuning, this technique solves for far fewer gravity parameters in each filter run. These gravity parameters yield local gravity anomalies which can later be combined with the solutions over other parts of the earth to generate a global gravity map. No supercomputing power will be needed for such combining. The approaches used in this study are described and preliminary results of a covariance analysis presented.

Wu, Sien-Chong↗

NASA NTRS1993

Lunar Scout Two spacecraft gravity experiment

Measurement of the gravity field of the Moon has a high science priority because of its implications for the internal structure and thermal history of the Moon, and it has a high priority for future exploration activities because of the influence of lunar gravity on spacecraft navigation and orbit maintenance. The current state of knowledge in the lunar gravity field (and the uncertainty in the knowledge) is based primarily on data accumulated from the Lunar Orbiter and Apollo programs. Data are sparse and emphasize the equatorial band (+/- 30 deg) on the near side of the Moon. There are no tracking data on the far side and only the Lunar Orbiter 5 provides a small amount of high inclination data. A host of gravity models developed from different combinations of tracking data have large discrepancies in their predictions of spacecraft motion and orbit lifetimes. There are also large disagreements in the Mercator projections of the gravity acceleration from each model, especially on the far side, where the contours tend to have no obvious relationship with the local topography. The science and engineering requirements for global gravity field mapping will be satisfied with continuous radio metric tracking of Lunar Scout 1 in a low polar orbit using the Deep Space Network and Lunar Scout 2 in a high elliptical orbit. The gravity field of the Moon will be mapped during the Scout Program using a two spacecraft concept. In the two spacecraft concept, one spacecraft is placed in a high altitude eccentric orbit while the second spacecraft is in a low altitude polar orbit. The gravity experiment requires a radio frequency that will permit two-way Doppler tracking between the spacecraft and the Deep Space Network (DSN). Both spacecraft carry NASA standard transponder systems for data transmission to Earth as well as for tracking and orbit determination. Data sufficient to produce a gravity field map could be acquired within one month with this system.

Cheng, Andrew F.↗

NASA NTRS1992

Gravity and the geoid in the Nepal Himalaya

Materials within the Himalaya are rising due to convergence between India and Asia. If the rate of erosion is comparable to the rate of uplift the mean surface elevation will remain constant. Any slight imbalance in these two processes will lead to growth or attrition of the Himalaya. The process of uplift of materials within the Himalaya coupled with surface erosion is similar to the advance of a glacier into a region of melting. If the melting rate exceeds the rate of downhill motion of the glacier then the terminus of the glacier will receed up-valley despite the downhill motion of the bulk of the glacier. Thus although buried rocks, minerals and surface control points in the Himalaya are undoubtably rising, the growth or collapse of the Himalaya depends on the erosion rate which is invisible to geodetic measurements. Erosion rates are currently estimated from suspended sediment loads in rivers in the Himalaya. These typically underestimate the real erosion rate since bed-load is not measured during times of heavy flood, and it is difficult to integrate widely varying suspended load measurements over many years. An alternative way to measure erosion rate is to measure the rate of change of gravity in a region of uplift. If a control point moves vertically it should be accompanied by a reduction in gravity as the point moves away from the Earth's center of mass. There is a difference in the change of gravity between uplift with and without erosion corresponding to the difference between the free-air gradient and the gradient in the acceleration due to gravity caused by a corresponding thickness of rock. Essentially gravity should change precisely in accord with a change in elevation of the point in a free-air gradient if erosion equals uplift rate. We were funded by NASA to undertake a measurement of absolute gravity simultaneously with measurements of GPS height within the Himalaya. Since both absolute gravity and time are known in an absolute sense to 1 part in 10(exp 10) it is possible to estimate gravity with a precision of 0.1 mu gal. Known systematic errors reduce the measurement to an absolute uncertainty of 6 mu gal. The free air gradient at the point of measurement is typically about 3 mu gals/cm. At Simikot where our experiment was conducted we determined a vertical gravity gradient of 4.4 mu gals/cm.

Bilham, Roger↗

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 NTRS1994

An Assessment of Wall Effects in Low-Gravity Aerosol Experiments

Low-gravity aerosol experiments are currently being considered for research relating to a variety of science disciplines. One potential difficulty for these low-gravity experiments is the influence of the container on the aerosol's evolution, i.e., wall effects. In an attempt to understand the magnitude of the effects of containment on low-gravity aerosol experiments, this work compares three simulated environments: (1) a ground-based laboratory experiment environment, (2) a zero-gravity experiment environment of an orbiting facility, and (3) a spatially unbounded ideal aerosol environment (also with no gravity). This paper describes the five-dimensional model (three spatial dimensions, plus particle size and time) developed to describe the zero-gravity aerosol experiment environment, and compares the output of this model and the output of a model of an Earth-gravity aerosol experiment environment to a model of particle aggregation alone. The zero-gravity experiment model is found to be a much closer approximation to pure aggregation than the Earth-gravity aerosol experiment model.

Stratton, David M.↗

NASA NTRS2010

Selecting Tasks for Evaluating Human Performance as a Function of Gravity

A challenge in understanding human performance as a function of gravity is determining which tasks to research. Initial studies began with treadmill walking, which was easy to quantify and control. However, with the development of pressurized rovers, it is less important to optimize human performance for ambulation as rovers will likely perform gross translation for them. Future crews are likely to spend much of their extravehicular activity (EVA) performing geology, construction and maintenance type tasks, for which it is difficult to measure steady-state-workloads. To evaluate human performance in reduced gravity, we have collected metabolic, biomechanical and subjective data for different tasks at varied gravity levels. Methods: Ten subjects completed 5 different tasks including weight transfer, shoveling, treadmill walking, treadmill running and treadmill incline walking. All tasks were performed shirt-sleeved at 1-g, 3/8-g and 1/6-g. Off-loaded conditions were achieved via the Active Response Gravity Offload System. Treadmill tasks were performed for 3 minutes with reported oxygen consumption (VO2) averaged over the last 2 minutes. Shoveling was performed for 3 minutes with metabolic cost reported as ml O2 consumed per kg material shoveled. Weight transfer reports metabolic cost as liters O2 consumed to complete the task. Statistical analysis was performed via repeated measures ANOVA. Results: Statistically significant metabolic differences were noted between all 3 gravity levels for treadmill running and incline walking. For the other 3 tasks, there were significant differences between 1-g and each reduced gravity, but not between 1/6-g and 3/8-g. For weight transfer, significant differences were seen between gravities in both trial-average VO2 and time-to-completion with noted differences in strategy for task completion. Conclusion: To determine if gravity has a metabolic effect on human performance, this research may indicate that tasks should be selected that require the subject to work vertically against the force of gravity.

Norcross, J. R.↗

NASA NTRS2015

Pressure Profiles in a Loop Heat Pipe Under Gravity Influence

During the operation of a loop heat pipe (LHP), the viscous flow induces pressure drops in various elements of the loop. The total pressure drop is equal to the sum of pressure drops in vapor grooves, vapor line, condenser, liquid line and primary wick, and is sustained by menisci at liquid and vapor interfaces on the outer surface of the primary wick in the evaporator. The menisci will curve naturally so that the resulting capillary pressure matches the total pressure drop. In ground testing, an additional gravitational pressure head may be present and must be included in the total pressure drop when LHP components are placed in a non-planar configuration. Under gravity-neutral and anti-gravity conditions, the fluid circulation in the LHP is driven solely by the capillary force. With gravity assist, however, the flow circulation can be driven by the combination of capillary and gravitational forces, or by the gravitational force alone. For a gravity-assist LHP at a given elevation between the horizontal condenser and evaporator, there exists a threshold heat load below which the LHP operation is gravity driven and above which the LHP operation is capillary force and gravity co-driven. The gravitational pressure head can have profound effects on the LHP operation, and such effects depend on the elevation, evaporator heat load, and condenser sink temperature. This paper presents a theoretical study on LHP operations under gravity neutral, anti-gravity, and gravity-assist modes using pressure diagrams to help understand the underlying physical processes. Effects of the condenser configuration on the gravitational pressure head and LHP operation are also discussed.

0000↗

NASA NTRS2015

Pressure Profiles in a Loop Heat Pipe under Gravity Influence

During the operation of a loop heat pipe (LHP), the viscous flow induces pressure drops in various elements of the loop. The total pressure drop is equal to the sum of pressure drops in vapor grooves, vapor line, condenser, liquid line and primary wick, and is sustained by menisci at liquid and vapor interfaces on the outer surface of the primary wick in the evaporator. The menisci will curve naturally so that the resulting capillary pressure matches the total pressure drop. In ground testing, an additional gravitational pressure head may be present and must be included in the total pressure drop when LHP components are placed in a non-planar configuration. Under gravity-neutral and anti-gravity conditions, the fluid circulation in the LHP is driven solely by the capillary force. With gravity assist, however, the flow circulation can be driven by the combination of capillary and gravitational forces, or by the gravitational force alone. For a gravity-assist LHP at a given elevation between the horizontal condenser and evaporator, there exists a threshold heat load below which the LHP operation is gravity driven and above which the LHP operation is capillary force and gravity co-driven. The gravitational pressure head can have profound effects on the LHP operation, and such effects depend on the elevation, evaporator heat load, and condenser sink temperature. This paper presents a theoretical study on LHP operations under gravity-neutral, anti-gravity, and gravity-assist modes using pressure diagrams to help understand the underlying physical processes. Effects of the condenser configuration on the gravitational pressure head and LHP operation are also discussed.

Thermal Control Systems↗

NASA NTRS2023

Cryogenic Flow Boiling in Microgravity: Effects of Reduced Gravity on Two-Phase Fluid Physics and Heat Transfer

With the growing interest in space exploration, cryogenic technologies involving two-phase flow and heat transfer are in high demand to successfully procure advanced space applications such as fuel depots and nuclear thermal propulsion (NTP) systems for deep space missions. However, the unique and extreme thermal properties of cryogenic fluids introduce distinct flow boiling fluid physics and energy transport phenomena, which differ significantly from those observed with conventional fluids. Understanding the unique two-phase physics in cryogenic flow boiling remains an ongoing challenge. Furthermore, the lack of readily available microgravity cryogenic steady-state heat transfer data hinders the assessment of gravitational effects on cryogenic flow boiling. This study aims to elucidate the gravitational effects on two-phase fluid physics and heat transfer by conducting the first-ever experimental measurement of cryogenic flow boiling performance using a steady-state heated method in a reduced gravity environment. Parabolic flight experiments were performed to acquire both heat transfer measurements and high-speed video of interfacial behaviors, under varying gravity levels (microgravity, hypergravity, Lunar gravity, and Martian gravity). The experiments involved flow boiling of liquid nitrogen (LN 2 ) with a near-saturated inlet along a circular heated tube of dimensions 8.5-mm inner diameter and 680-mm heated length. The operating parameters varied are mass velocity of 398.3 - 1342.8 kg/m2s, inlet quality of -0.08 to -0.01, and inlet pressure of 413.68 - 689.48 kPa. Captured microgravity flow patterns range from bubbly to annular, all having vapor structures that are larger than those under higher gravity levels. Under microgravity, absence of buoyancy yields symmetrical vapor structures without flow stratification, laying a physical foundation for the distinct two-phase heat transfer trends during LN 2 flow boiling in microgravity. Transient data collected during the flight parabolas exhibited decreasing heated wall temperature as the aircraft transitioned from hypergravity to microgravity phases. The temperature variation indicated an enhancement in flow boiling heat transfer with decreasing gravity levels and a reduction with increasing gravity levels. The effect of reduced gravity on cryogenic flow boiling heat transfer coefficient (HTC) is discussed based on steady state heat transfer analysis. Seminal HTC correlations are evaluated against the measured microgravity HTC data, of which one is identified for superior accuracy in predicting microgravity data. Finally, a new HTC correlation is proposed to improve accuracy of microgravity predictions, yet there still exists room for further improvement with future terrestrial flow boiling experiments at different flow orientations relative to Earth gravity.

Microgravity↗

NASA NTRS2005

Magnetic levitation-based Martian and Lunar gravity simulator

Missions to Mars will subject living specimens to a range of low gravity environments. Deleterious biological effects of prolonged exposure to Martian gravity (0.38 g), Lunar gravity (0.17 g), and microgravity are expected, but the mechanisms involved and potential for remedies are unknown. We are proposing the development of a facility that provides a simulated Martian and Lunar gravity environment for experiments on biological systems in a well controlled laboratory setting. The magnetic adjustable gravity simulator will employ intense, inhomogeneous magnetic fields to exert magnetic body forces on a specimen that oppose the body force of gravity. By adjusting the magnetic field, it is possible to continuously adjust the total body force acting on a specimen. The simulator system considered consists of a superconducting solenoid with a room temperature bore sufficiently large to accommodate small whole organisms, cell cultures, and gravity sensitive bio-molecular solutions. It will have good optical access so that the organisms can be viewed in situ. This facility will be valuable for experimental observations and public demonstrations of systems in simulated reduced gravity. c2005 Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗

NASA NTRS2004

Escherichia coli growth under modeled reduced gravity

Bacteria exhibit varying responses to modeled reduced gravity that can be simulated by clino-rotation. When Escherichia coli was subjected to different rotation speeds during clino-rotation, significant differences between modeled reduced gravity and normal gravity controls were observed only at higher speeds (30-50 rpm). There was no apparent affect of removing samples on the results obtained. When E. coli was grown in minimal medium (at 40 rpm), cell size was not affected by modeled reduced gravity and there were few differences in cell numbers. However, in higher nutrient conditions (i.e., dilute nutrient broth), total cell numbers were higher and cells were smaller under reduced gravity compared to normal gravity controls. Overall, the responses to modeled reduced gravity varied with nutrient conditions; larger surface to volume ratios may help compensate for the zone of nutrient depletion around the cells under modeled reduced gravity.

Non-NASA Center↗

NASA NTRS2013

A Comparison Between Gravity Wave Momentum Fluxes in Observations and Climate Models

For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations,MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.

mathematical models↗

NASA NTRS2013

Source Parameter Inversion for Recent Great Earthquakes from a Decade-long Observation of Global Gravity Fields

We quantify gravity changes after great earthquakes present within the 10 year long time series of monthly Gravity Recovery and Climate Experiment (GRACE) gravity fields. Using spherical harmonic normal-mode formulation, the respective source parameters of moment tensor and double-couple were estimated. For the 2004 Sumatra-Andaman earthquake, the gravity data indicate a composite moment of 1.2x10(exp 23)Nm with a dip of 10deg, in agreement with the estimate obtained at ultralong seismic periods. For the 2010 Maule earthquake, the GRACE solutions range from 2.0 to 2.7x10(exp 22)Nm for dips of 12deg-24deg and centroid depths within the lower crust. For the 2011 Tohoku-Oki earthquake, the estimated scalar moments range from 4.1 to 6.1x10(exp 22)Nm, with dips of 9deg-19deg and centroid depths within the lower crust. For the 2012 Indian Ocean strike-slip earthquakes, the gravity data delineate a composite moment of 1.9x10(exp 22)Nm regardless of the centroid depth, comparing favorably with the total moment of the main ruptures and aftershocks. The smallest event we successfully analyzed with GRACE was the 2007 Bengkulu earthquake with M(sub 0) approx. 5.0x10(exp 21)Nm. We found that the gravity data constrain the focal mechanism with the centroid only within the upper and lower crustal layers for thrust events. Deeper sources (i.e., in the upper mantle) could not reproduce the gravity observation as the larger rigidity and bulk modulus at mantle depths inhibit the interior from changing its volume, thus reducing the negative gravity component. Focal mechanisms and seismic moments obtained in this study represent the behavior of the sources on temporal and spatial scales exceeding the seismic and geodetic spectrum.

Parameter Inversion↗