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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
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

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 NTRS1987

Nimbus 7 earth radiation budget wide field of view climate data set improvement. I - The earth albedo from deconvolution of shortwave measurements

A deconvolution method for extracting the top of the atmosphere (TOA) mean, daily albedo field from a set of wide-FOV (WFOV) shortwave radiometer measurements is proposed. The method is based on constructing a synthetic measurement for each satellite observation. The albedo field is represented as a truncated series of spherical harmonic functions, and these linear equations are presented. Simulation studies were conducted to determine the sensitivity of the method. It is observed that a maximum of about 289 pieces of data can be extracted from a set of Nimbus 7 WFOV satellite measurements. The albedos derived using the deconvolution method are compared with albedos derived using the WFOV archival method; the developed albedo field achieved a 20 percent reduction in the global rms regional reflected flux density errors. The deconvolution method is applied to estimate the mean, daily average TOA albedo field for January 1983. A strong and extensive albedo maximum (0.42), which corresponds to the El Nino/Southern Oscillation event of 1982-1983, is detected over the south central Pacific Ocean.

Hucek, Richard R.↗
NASA NTRS1995

JPL Planetary Gravity Efforts and Techniques

The Magellan spacecraft has provided the highest resolution global gravity data set from spacecraft measurements. The X-band Doppler tracking is sensitive to harmonic degree of 120 or greater. We have developed a 75th degree and order global spherical harmonic model using a spatial constraint instead of the usual method. Results are presented for JPL Venus and Mars gravity field determination efforts and efforts are reviewed for developing higher degree models on supercomputers.

gravity fields Doppler tracking Magellan↗
NASA NTRS1979

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Liu, J. J. F.↗
NASA NTRS1981

Information theory lateral density distribution for Earth inferred from global gravity field

Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.

Rubincam, D. P.↗
NASA NTRS1985

The magnetic field at the core-mantle boundary

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.

Bloxham, J.↗
NASA NTRS1983

Testing solar models with global solar oscillations in the 5-minute band

Frequencies of solar oscillation for normal modes described by spherical harmonics with l-values between 0 and 4 are computed. The method of computation is discussed and some of the theoretical uncertainties are examined. It is shown that the standard solar model has eigenfrequencies which do not agree with the frequencies observed for the low l-modes to within the estimated accuracy of either the observed or theoretical frequencies. Four non-standard models are considered: (1) the interior Z abundance is lower than the surface abundance; (2) the interior Z abundance is higher than the surface abundance; (3) the interior Z abundance is altered by mixing; and (4) a large primordial magnetic field remains in the solar core. The effect of all these models on the solar neutrino flux is considered, with the result that the high-Z model is rejected. The conclusions of Bahcall and Ulrich (1971) that a primordial magnetic field increases the neutrino flux are disputed.

Ulrich, R. K.↗
NASA NTRS1990

The development and analysis of geopotential coefficient models to spherical harmonic degree 360

Two new geopotential coefficient models to spherical harmonic degree 360 are developed using recent advances made in theoretical modeling methods, satellite gravitational models, and expanded and improved terrestrial data. The new models are based on the combination of a satellite potential coefficient model (GEM-T2) to degree 50 with 30-arc mean gravity anomalies, yielding an adjusted set of coefficients and gravity anomalies, which were then harmonically analyzed to yield a set of potential coefficients to degree 360. The models were verified in several ways including satellite orbit residual analysis, demonstrating a substantial improvement over previous high-degree expansions.

Rapp, Richard H.↗
NASA NTRS2011

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.

Scott, James R.↗
NASA NTRS1974

Analysis of acoustic radiation in a jet flow environment

The analysis of sound fields from arbitrary source distributions in terms of Legendre and spherical Hankel functions is well known. The purpose of this paper is to extend this classical method of analysis to environments such as jet flows where flow and flow gradients are inherently present. The wave-equation governing the radiation of sound in such an environment is derived. The steady state flow and flow gradients in the axial and transverse directions appear as coefficients in the terms of the wave-equation. A semi-numerical method is used to solve the wave-equation in terms of modified spherical harmonics yielding the phase velocities and the directivities of an infinite set of modes. The directivity of each mode is obtained in terms of modified Legendre functions by numerical integration. Some results of these directivity and phase-velocity calculations are presented for a limited number of frequency and flow parameters. Both convective and shear refraction are shown to be important.

Mungur, P.↗
NASA NTRS1998

An Improved Magnetic Field Model for Jupiter's Inner Magnetosphere Using a Microsignature of Amalthea

Observation of a particle absorption microsignature of the Jovian satellite Amalthea during the Pioneer II close flyby of Jupiter on December 3, 1974, has been described by McKibben et al. The microsignature was also observed by the University of Iowa/Pioneer II instrument in the distribution of protons in the kinetic energy range 0.61 less than T(sub p) less than 3.41 MeV but has not been previously reported. The finer time resolution and superior data quality of the latter observations provide a fresh basis for assessing the accuracy with which various published magnetic field models of Jupiter's magnetic field models describe Jupiter's magnetic field for radial distances of the order of or less than several planetary radii. The expected time of occurrence of the minimum of Amalthea's microsignature was calculated for each model and compared to the time of the observed minimum. The discrepancy between these two times was significant for each of the published models, but it could be reduced to zero by interpolating between two of the closely related models. The spherical harmonic coefficients of this combination model are tabulated. Also included is a novel method for calculating the intensity-time profile of the microsignature. In a later paper, the improved model is utilized to analyze the energetic particle measurements in Jupiter's innermost magnetosphere by the Galileo entry probe in December 1995.

Randall, Bruce A.↗
NASA NTRS2011

Investigation of the Crust of the Pannonian Basin, Hungary Using Low-Altitude CHAMP Horizontal Gradient Magnetic Anomalies

The Pannonian Basin is a deep intra-continental basin that formed as part of the Alpine orogeny. It is some 600 by 500 km in area and centered on Hungary. This area was chosen since it has one of the thinnest continental crusts in Europe and is the region of complex tectonic structures. In order to study the nature of the crustal basement we used the long-wavelength magnetic anomalies acquired by the CHAMP satellite. The SWARM constellation, scheduled to be launched next year, will have two lower altitude satellites flying abreast, with a separation of between ca. 150 to 200 km. to record the horizontal magnetic gradient. Since the CHAMP satellite has been in orbit for eight years and has obtained an extensive range of data, both vertically and horizontally there is a large enough data base to compute the horizontal magnetic gradients over the Pannonian Basin region using these many CHAMP orbits. We recomputed a satellite magnetic anomaly map, using the spherical-cap method of Haines (1985), the technique of Alsdorf et al. (1994) and from spherical harmonic coefficients of MF6 (Maus et aI., 2008) employing the latest and lowest altitude CHAMP data. We then computed the horizontal magnetic anomaly gradients (Kis and Puszta, 2006) in order to determine how these component data will improve our interpretation and to preview what the SW ARM mission will reveal with reference to the horizontal gradient anomalies. The gradient amplitude of an 1000 km northeast-southwest profile through our horizontal component anomaly map varied from 0 to 0.025 nT/km with twin positive anomalies (0.025 and 0.023 nT/km) separated by a sharp anomaly negative at o nT/km. Horizontal gradient indicate major magnetization boundaries in the crust (Dole and Jordan, 1978 and Cordell and Grauch, 1985). Our gradient anomaly was modeled with a twodimensional body and the anomaly, of some 200 km, correlates with a 200 km area of crustal thinning in the southwestern Pannonian Basin.

Taylor, Patrick T.↗
NASA NTRS2020

Julia Language 1.1 Ephemeris Reader and Gravitational Modeling Program for Solar System Bodies

This paper analyzes the advancements to the Julia Language 1.1 Ephemeris and Physical constants Reader including the addition of gravitational modeling. Originally written in MATLAB, this Julia Language program is intended to be used in for trajectory design. Written in an open-source coding language, this ephemeris reader can output the state of planetary bodies including asteroids as well as other constants such as gravitational parameters. Two primary methods were chosen to calculate the gravitational potentials which include polyhedral modeling and spherical harmonics.

Gray, Brennan↗
NASA NTRS1995

A new method of presentation the large-scale magnetic field structure on the Sun and solar corona

The large-scale photospheric magnetic field, measured at Stanford, has been analyzed in terms of surface harmonics. Changes of the photospheric field which occur within whole solar rotation period can be resolved by this analysis. For this reason we used daily magnetograms of the line-of-sight magnetic field component observed from Earth over solar disc. We have estimated the period during which day-to-day full disc magnetograms must be collected. An original algorithm was applied to resolve time variations of spherical harmonics that reflect time evolution of large-scale magnetic field within solar rotation period. This method of magnetic field presentation can be useful enough in lack of direct magnetograph observations due to sometimes bad weather conditions. We have used the calculated surface harmonics to reconstruct the large-scale magnetic field structure on the source surface near the sun - the origin of heliospheric current sheet and solar wind streams. The obtained results have been compared with spacecraft in situ observations and geomagnetic activity. We tried to show that proposed technique can trace shon-time variations of heliospheric current sheet and short-lived solar wind streams. We have compared also our results with those obtained traditionally from potential field approximation and extrapolation using synoptic charts as initial boundary conditions.

Ponyavin, D. I.↗
NASA NTRS2004

Magsat to CHAMP: Magnetic Satellite Explorations of Lithospheric Anomalies over Kursk, Bangui and the Antarctic

We compare crustal magnetic anomaly maps over the Kursk (Russia) and Bangui (Central African Republic) isolated anomalies and the Antarctic derived from the Magsat, \Orsted and CHAMP satellite fields. We wish to demonstrate how progress in satellite magnetic missions has improved the recovery of the crustal magnetic field. The 6-month long Magsat mission of 25 years ago generated two major methods of processing satellite magnetic anomaly data for lithospheric studies. The first was a global perspective using spherical harmonics that emphasize the more regional and global lithospheric fields. However, these fields commonly do not resolve local anomaly features in any detail. Therefore a second procedure involved the use of the individual satellite orbit or track data to recover small-scale anomalies on a regional scale. We present results over prominent magnetic anomalies such as Kursk, Bangui and the large Antarctic continent that demonstrate how the various analysis methods affect the recovery of crustal anomalies. The more recent \Orsted and CHAMP missions are successfully recording data with an improved accuracy and with full spatial and temporal coverage. We show and interpret the total magnetic intensity anomaly maps over these areas from all three satellite magnetometer data sets.

Kim, H.↗