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NASA NTRS1985

On the geographical correlation of orbit error

The orbit accuracies needed to support the global crustal dynamics project and recent satellite altimeter missions have placed unique demands on the data analysis and orbit analysis systems. These demands include accurate and well distributed observations, improved computational techniques and substantial enhancements in the force models which represent the satellite's motion. For example, the satellite altimeter mission (TOPEX), whose objectives will be: (1) to measure the time variable ocean surface topography, and (2) to demonstrate the ability to map the general ocean circulation, requires that the radial component of the satellite's orbit be known with an rms accuracy of 13 cm for the three year mission lifetime. The primary force model uncertainty which limits the contemporary orbit computation accuracy is the inaccuracy in the values assigned to the spherical harmonic coefficients used to model the Earth's gravity field.

Tapley, B. D.↗

NASA NTRS1983

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

NASA NTRS1984

Ultrasonic wave propagation in two-phase media - Spherical inclusions

Fu, L. S.↗

NASA NTRS1978

Analysis of simulated measurements of earth emitted radiation using geometric shape factors, and some results from analysis of ESSA 7 and Nimbus 6 data

In the reported study, simulated measurements of earth radiation with wide field-of-view (WFOV) radiometers are reduced to earth fluxes through geometric shape factors. Estimates of emitted flux for global and zonal scales and for regions smaller than the detector field-of-view are compared to fluxes derived directly from a model. Geometric shape factors are used to estimate global, zonal, and regional averages of earth-emitted flux from measurements with WFOV detectors on the ESSA 7 satellite and the Nimbus 6 satellite. Zonal and global averages of emitted flux for each of the 3-month periods of ESSA 7 data are shown in a graph. Another graph shows zonal and global averages of emitted flux for August 1975 obtained with the aid of Nimbus 6. The data are compared to values reported by Green and Smith (1977) who used a spherical harmonic solution.

Weaver, W. L.↗

NASA NTRS1973

Nearly spherical constant-power detonation waves as driven by focused radiation

An analysis is made of the flow within a three-dimensional explosion, or spark, created in a gas absorbing energy from a steady conical beam of radiation with nearly spherical symmetry. The radiation, typically from an array of lasers with a common focus, is assumed to be very intense and absorbed immediately behind an outwardly advancing strong shock. Departures of the laser power from spherical uniformity, which would result from practical problems of arrangement, are conveniently represented by an ascending series of Legendre polynomials in the polar angle. For nonuniformities of small amplitude, first-order perturbations of the flow field are analyzed in detail. Self-similarity is shown to be retained for zero counter-pressure and power constant with time. For the first five harmonics in power distortion, the resulting fourth-order system of equations is solved numerically for profiles of velocity components, density, pressure, and shock shape. Results are presented graphically.

George, Y. H.↗

NASA NTRS1990

Ocean tides for satellite geodesy

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Dickman, S. R.↗

NASA NTRS2015

Swarm Flyby Gravimetry

This study describes a new technology for discerning the gravity fields and mass distribution of a solar system small body, without requiring dedicated orbiters or landers. Instead of a lander, a spacecraft releases a collection of small, simple probes during a flyby past an asteroid or comet. By tracking those probes from the host spacecraft, one can estimate the asteroid's gravity field and infer its underlying composition and structure. This approach offers a diverse measurement set,equivalent to planning and executing many independent and unique flyby encounters of a single spacecraft. This report assesses a feasible hardware implementation, derives the underlying models,and analyzes the performance of this concept via simulation.In terms of hardware, a small, low mass, low cost implementation is presented, which consists of a dispenser and probes. The dispenser contains roughly 12 probes in a tube and has a total size commensurate with a 6U P-Pod. The probes are housed in disc shaped sabots. When commanded,the dispenser ejects the top-most probe using a linear motor. The ejected probe separates from its sabots and unfolds using internal springs. There are two types of probes, each designed for a particular tracking modality. The reflective probe type, tracked by a telescope, unfolds to forma diffusely reflective sphere. The retroreflector probe type, tracked by a lidar, unfolds to form a corner-cube retroreflector assembly. Both types are designed to spherical so that their attitude doesn't affect the spacecraft's tracking performance.This analysis indicates that the point-mass term of small bodies larger than roughly 500 m in diameter can be observed from a host spacecraft that tracks locally deployed probes throughout a flyby to an uncertainty of better than 5%. The conditions by which this measurement is possible depends on the characteristics of the asteroid (size, type), the flyby velocity, and the type of tracking available (angles-only or angles+ranging). For most encounters, a few (1-3) well placed probes can be very effective, with marginal improvement for additional probes. Given realistic deployment errors, an encounter may require roughly 10-12 probes to ensure that 1-3 achieve their target. Long duration tracking of probes flying by large asteroids (>5 km diameter) can sometimes provide observability of the gravity field's first spherical harmonic, J( sub 2). In summary, this method offers a feasible, affordable approach to enabling or augmenting flyby science.

Atchison, Justin↗

NASA NTRS1995

Measurement of high-degree solar oscillation frequencies

We present m-averaged solar p- and f-mode oscillation frequencies over the frequency range nu greater than 1.8 and less than 5.0 mHz and the spherical harmonic degree range l greater than or equal to 100 and less than or equal to 1200 from full-disk, 1000 x 1024 pixel, Ca II intensity images collected 1993 June 22-25 with a temporal cadence of 60 s. We itemize the sources and magnitudes of statistical and systematic uncertainties and of small frequency corrections, and we show that our frequencies represent an improvement in accuracy and coverage over previous measurements. Our frequencies agree at the 2 micro Hz level with Mount Wilson frequencies determined for l less than or equal to 600 from full-disk images, and we find systematic offsets of 10-20 micro Hz with respect to frequencies measured from Big Bear and La Palma observations. We give evidence that these latter offsets are indicative of spatial scaling uncertainties associated with the analysis of partial-disk images. In comparison with theory, our p-mode frequencies agree within 10 micro Hz of frequencies predicted by the Los Alamos model but are as much as 100 micro Hz smaller than frequencies predicted by the Denmark and Yale models at degrees near 1000. We also find systematic differences between our n = 0 frequencies and the frequencies closely agreed upon by all three models.

Bachmann, K. T.↗

NASA NTRS2007

The Local Stellar Velocity Field via Vector Spherical Harmonics

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism.We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) = (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) = (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star...

kinematics↗

NASA NTRS2004

Estimating Antarctic Near-Surface Magnetic Anomalies from Oersted and CHAMP Satellite Magnetometer Observations

Significant improvement in predicting near-surface magnetic anomalies can result from the highly accurate magnetic observations of the CHAMP satellite that is orbiting at about 400 km altitude. In general, regional magnetic signals of the crust are strongly masked by the core field and its secular variations due to wavelength coupling in the spherical harmonic representation and thus are difficult to isolate in the satellite measurements. However, efforts to isolate the regional lithospheric from core field components can exploit the correlations between the CHAMP magnetic anomalies and the pseudo magnetic effects inferred from gravity-derived crustal thickness variations. In addition, we can use spectral correlation theory to filter the static lithospheric field components from the dynamic external field effects. Employing these procedures, we processed the CHAMP magnetic conservations for an improved magnetic anomaly map of the Antarctic crust. Relative to the much higher altitude Oersted and noisier Magsat observations, CHAMP magnetic anomalies at 400 km altitude reveal new details on the effects of intra-crustal magnetic features and crustal thickness variations of the Antarctic. Moreover, these results greatly facilitate predicting magnetic anomalies in the regional coverage gaps of the ADMAP compilation of Antarctic magnetic anomalies from shipborne, airborne and ground surveys. Our analysis suggests that considerable new insights on the magnetic properties of the lithosphere may be revealed by a further order-of-magnitude improvement in the accuracy of the magnetometer.

vonFrese, Ralph R. B.↗

NASA NTRS2004

Time Variable Gravity from Local Mascon Analysis of GRACE Data

We have analyzed GRACE Level 1-B data in 2003 and assessed a new approach for extracting time variable gravity that isolates the gravity signal in both time and space. The Level-1B satellite-to-satellite range rate (KBRR) data and accelerometry are processed in daily arcs using the precise orbit products produced by the GRACE team from GPS to calibrate both the accelerometer and KBRR data. We then adjusted select components of the intersatellite baseline vector for each data segment isolated to the region of interest. Herein, we solved for mass anomalies in 45 deg x 45 deg blocks over the Amazon and the nearby Atlantic Ocean and estimate mass flux in units of cm of water over each block. We show with this approach that we can recover mass anomalies on a submonthly basis with 10 to 15 day temporal resolution. We discuss the important issues related to this solution, including the size of the mascon blocks, the weight given to the temporal and spatial constraint used to stabalize the solutions, as well as the optimal correlation in time and distance. We compare the the mascon results with solutions obtained from the more standard approach using spherical harmonics and with independent hydrology models and lake data. This technique demonstrates that sub-monthly medium wavelength mass flux phenomena are well sensed by the hyper-precise line of sight velocity data produced from GRACE.

Lemoine, Frank G.↗

NASA NTRS1994

On the prediction of velocity fields from redshift space galaxy samples

We present a new method for recovering the underlying velocity field from an observed distribution of galaxies in redshift space. The method is based on a kinematic Zel'dovich relation between the velocity and density fields in redshift space. This relation is expressed in a differential equation slightly modified from the usual Poisson equation and which depends nontrivially on Beta identically equal to Omega(exp 0.6)/b. The linear equation can be readily solved by standard techniques of separation of variables by means of spherical harmonics. One can also include a term describing the 'rocket effect' discussed by Kaiser (1987). From this redshift space information alone, one can generate a prediction of the peculiar velocity field for each harmonic (l, m) as a function of distance. We note that for the quadrupole and higher order moments, the equation is a boundary value problem with solutions dependent on both the interior and exterior mass distribution. However, for a shell at distance r, the dipole, as well as the monopole, of the velocity field in the Local Group frame is fully determined by the interior mass distribution. This implies that the shear of the measured velocity field, when fitted to a dipole distortion, should be aligned and consistent with the gravity field inferred from the well determined local galaxy distribution. As a preliminary application we compute the velocity dipole of distant shells as predicted from the 1.2 Jy IRAS survey compared to the measured velocity dipole on shells, as inferred from a recent POTENT analysis. The coherence between the two fields is good, yielding a best estimate of Beta = 0.6 +/- 0.2.

Nusser, Adi↗

NASA NTRS1992

Tests of a simple data merging algorithm for the GONG project

The GONG (Global Oscillation Network Group) project proposes to reduce the impact of diurnal variations on helioseismic measurements by making long-term observations of solar images from six sites placed around the globe. The sun will be observed nearly constantly for three years, resulting in the acquisition of l+ terabyte of image data. To use the solar network to maximum advantage, the images from the sites must be combined into a single time series to determine mode frequencies, amplitudes, and line widths. Initial versions of combined, i.e., merged, time series were made using a simple weighted average of data from different sites taken simultaneously. In order to accurately assess the impact of the data merge on the helioseismic measurements, a set of artificial solar disk images was made using a standard solar model and containing a well known set of oscillation modes and frequencies. This undegraded data set and data products computed from it were used to judge the relative merits of various data merging schemes. The artificial solar disk images were subjected to various instrumental and atmospheric degradations, dependent on site and time, in order to create a set of images simulating those likely to be taken at the site. The degraded artificial solar disk images for the six observing sites were combined in various ways to form merged time series of images and mode coefficients. Various forms of a weighted average were used, including an equally-weighted average, an average with weights dependent upon air mass and averages with weights dependent on various quality assurance parameters. Both the undegraded solar disk image time series and several time series made up of various combinations of the degraded solar disk images from the six sites were subjected to standard helioseismic measurement processing. This processing consisted of coordinate remapping, detrending, spherical harmonic transformation, computation of power series for the oscillation mode coefficients, and mode frequency identification. Visual and statistical evaluation of the merged data sets themselves and differences between the merged and undegraded data set shows good agreement between the two data sets. Some slight differences in image scale and registration appear between the undegraded data set and the various merged data sets. In the set of power series made from the mode coefficients of the merged data sets, some power leakage is observed into the background and into slightly lower l-value modes, especially at higher l-value mode frequencies. The results of the comparison of time series and mode oscillation frequencies of the undegraded data with those of the data merged using weighted averages indicate that, at least for p-mode solar oscillations, a weighted average of either the detrended remapped images or the mode coefficients gives good determination of the mode frequencies and adequate-to-good determination of the amplitudes and widths of the mode frequency lines. This conclusion is most advantageous to the analysis of the massive amounts of data to be received by the GONG network.

Williams, W. E.↗

NASA NTRS2004

Time Changes of the European Gravity Field from GRACE: A Comparison with Ground Measurements from Superconducting Gravimeters and with Hydrology Model Predictions

We investigate the time-variable gravity changes in Europe retrieved from the initial GRACE monthly solutions spanning a 18 month duration from April 2002 to October 2003. Gravity anomaly maps are retrieved in Central Europe from the monthly satellite solutions we compare the fields according to various truncation levels (typically between degree 10 and 20) of the initial fields (expressed in spherical harmonics to degree 120). For these different degrees, an empirical orthogonal function (EOF) decomposition of the time-variable gravity field leads us to its main spatial and temporal characteristics. We show that the dominant signal is found to be annual with an amplitude and a phase both in agreement with predictions in Europe modeled using snow and soil-moisture variations from recent hydrology models. We compare these GRACE gravity field changes to surface gravity observations from 6 superconducting gravimeters of the GGP (Global Geodynamics Project) European sub-network, with a special attention to loading corrections. Initial results suggest that all 3 data sets (GRACE, hydrology and GGP) are responding to annual changes in near-surface water in Europe of a few microGal (at length scales of approx.1000 km) that show a high value in winter and a summer minimum. We also point out that the GRACE gravity field evolution seems to indicate that there is a trend in gravity between summer 2002 and summer 2003 which can be related to the 2003 heatwave in Europe and its hydrological consequences (drought). Despite the limited time span of our analysis and the uncertainties in retrieving a regional solution from the network of gravimeters, the calibration and validation aspects of the GRACE data processing based on the annual hydrology cycle in Europe are in progress.

Hinderer, J.↗

NASA NTRS1997

A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and other tracking data

A spherical harmonic model of the lunar gravity field complete to degree and order 70 has been developed from S band Doppler tracking data from the Clementine mission, as well as historical tracking data from Lunar Orbiters 1-5 and the Apollo 15 and 16 subsatellites. The model combines 361,000 Doppler observations from Clementine with 347,000 historical observations. The historical data consist of mostly 60-s Doppler with a noise of 0.25 to several mm/s. The Clementine data consist of mostly 10-s Doppler data, with a data noise of 0.25 mm/s for the observations from the Deep Space Network, and 2.5 mm/s for the data from a naval tracking station at Pomonkey, Maryland. Observations provided Clementine, provide the strongest satellite constraint on the Moon's low-degree field. In contrast the historical data, collected by spacecraft that had lower periapsis altitudes, provide distributed regions of high-resolution coverage within +/- 29 deg of the nearside lunar equator. To obtain the solution for a high-degree field in the absence of a uniform distribution of observations, we applied an a priori power law constraint of the form 15 x 10(exp -5)/sq l which had the effect of limiting the gravitational power and noise at short wavelengths. Coefficients through degree and order 18 are not significantly affected by the constraint, and so the model permits geophysical analysis of effects of the major basins at degrees 10-12. The GLGM-2 model confirms major features of the lunar gravity field shown in previous gravitational field models but also reveals significantly more detail, particularly at intermediate wavelengths (10(exp 3) km). Free-air gravity anomaly maps derived from the new model show the nearside and farside highlands to be gravitationally smooth, reflecting a state of isostatic compensation. Mascon basins (including Imbrium, Serenitatis, Crisium, Smythii, and Humorum) are denoted by gravity highs first recognized from Lunar Orbiter tracking. All of the major mascons are bounded by annuli of negative anomalies representing significant subsurface mass deficiencies. Mare Orientale appears as a minor mascon surrounded by a horseshoe-shaped gravity low centered on the Inner and Outer Rook rings that is evidence of significant subsurface structural heterogeneity. Although direct tracking is not available over a significant part of the lunar farside, GLGM-2 resolves negative anomalies that correlate with many farside basins, including South Pole-Aitken, Hertzsprung, Korolev, Moscoviense, Tsiolkovsky, and Freundlich-Sharonov.

Lemonie, Frank G. R.↗

NASA NTRS1993

Geophysical models of Western Aphrodite-Niobe region: Venus

The new topography and gravitational field data for Venus expressed in spherical harmonics of degree and order up to 50 allow us to analyze the crust-mantle boundary relief and stress state of the Venusian lithosphere. In these models, we consider models in which convection is confined beneath a thick, buoyant lithosphere. We divide the convection regime into an upper mantle and lower mantle component. The lateral scales are smaller than on Earth. In these models, relative to Earth, convection is reflected in higher order terms of the gravitational field. On Venus geoid height and topography are highly correlated, although the topography appears to be largely compensated. We hypothesize that Venus topography for those wavelengths that correlate well with the geoid is partly compensated at the crust-mantle boundary, while for the others compensation may be distributed over the whole mantle. In turn the strong sensitivity of the stresses to parameters of the models of the external layers of Venus together with geological mapping allows us to begin investigations of the tectonics and geodynamics of the planet. For stress calculations we use a new technique of space- and time-dependent Green's response functions using Venus models with rheologically stratified lithosphere and mantle and a ductile lower crust. In the basic model of Venus the mean crust is 50-70 km thick, the density contrast across the crust-mantle boundary is in the range from 0.3 to 0.4 g/cm(exp -3). The thickness of a weak mantle zone may be from 350 to 1000 km. Strong sensitivity of calculated stress to various parameters of the layered model of Venus together with geological mapping and analysis of surface tectonic patterns allow us to investigate the tectonics and geodynamics of the planet. The results are presented in the form of maps of compression-extension and maximum shear stresses in the lithosphere and maps of crust-mantle boundary relief, which can be presented as a function of time. We have modeled the region of Western Aphrodite and the Niobe plains to get reasonable depths of compensation. Crust mantle boundary relief is calculated for Western Aphrodite-Niobe relative to a mean crustal thickness of 50 km. The calculations include the consequences of simple crust models and more complicated models with a weak, ductile lower crust, a strong upper mantle and a weak lower mantle layer.

Marchenkov, K. I.↗

NASA NTRS1997

Modeling of the Coupled Magnetospheric and Neutral Wind Dynamos

Over the past four years of funding, SRI, in collaboration with the University of Texas at Dallas, has been involved in assessing the influence of thermospheric neutral winds on the electric field and current systems at high latitudes. The initial direction of the project was to perform a set of numerical experiments concerning the contribution of the magnetospheric and neutral wind dynamo processes, under specific boundary conditions, to the polarization electric field and/or the field-aligned current distribution at high latitudes. To facilitate these numerical experiments we developed a numerical scheme that relied on using output from the NCAR Thermosphere-Ionosphere General Circulation Model (NCAR-TIGCM), expanding them in the form of spherical harmonics and solving the dynamo equations spectrally. Once initial calculations were completed, it was recognized that the neutral wind contribution could be significant but its actual contribution to the electric field or currents depended strongly on the generator properties of the magnetosphere. Solutions to this problem are not unique because of the unknown characteristics of the magnetospheric generator, therefore the focus was on two limiting cases. One limiting case was to consider the magnetosphere as a voltage generator delivering a fixed voltage to the high-latitude ionosphere and allowing for the neutral wind dynamo to contribute only to the current system. The second limiting case was to consider the magnetosphere as a current generator and allowing for the neutral wind dynamo to contribute only to the generation of polarization electric fields. This work was completed and presented at the l994 Fall AGU meeting. The direction of the project then shifted to applying the Poynting flux concept to the high-latitude ionosphere. This concept was more attractive as it evaluated the influence of neutral winds on the high-latitude electrodynamics without actually having to determine the generator characteristics of the magnetosphere. The influence of the neutral wind was then determined not by estimating how much electric potential or current density it provides, but by determining the contribution of the neutral wind to the net electromagnetic energy transferred between the ionosphere and magnetosphere. The estimate of the net electromagnetic energy transfer and the role of the neutral winds proves to be a more fundamental quantity in studies of magnetosphere- ionosphere coupling also showed that by using electric and magnetic field measurements from the HILAT satellite, the Poynting flux could be a measurable quantity from polar-orbiting, low- altitude spacecraft. Through collaboration with Dr. Heelis and others at UTD and their expertise of the electric field measurements on the DE-B satellite, an extensive analysis was planned to determine the Poynting flux from the DE-B measurements in combination with a modeling effort to help interpret the observations taking into account the coupled magnetosphere-ionosphere.

Thayer, Jeffrey P.↗