SEARCH · Engineering Papers

Results for “spherical harmonics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1977

Onboard magnetic field modeling for Solar Maximum Mission /SMM/

Analysis and simulation results are presented for magnetic field models for use in attitude acquisition onboard Solar Maximum Mission (SMM). A study was made of the degree of the spherical harmonic expansion of the magnetic field required, considering mission requirements, modeling errors, and magnetometer quantization and biases. It is shown that a fifth-degree field is sufficient to provide two-degree roll angle determination accuracy with a residual magnetic bias of 10 milligauss. Also, a spherical harmonic expansion for the McIlwain L-parameter is included for the first time. This parameter will be telemetered to ground with experimental data. The fifth-degree expansion will provide the L-parameter to within two percent of accepted values. The additional onboard computational burden is the storage of 36 coefficients and an increase of about 15% in computation time. Prototype flight code was developed which is anticipated to require about 2000 bytes of core storage and 30 milliseconds of computation time per orbit point on the NSSC-1 computer.

Headrick, R. D.↗

NASA NTRS1982

The inverse problem of constructing a gravimetric geoid

Computation of a single geoidal height from gravity acceleration data formally requires that the latter be known everywhere on the earth. A computational procedure based on linear inverse theory for estimating geoidal heights from incomplete sets of data is presented. The same scheme can be used to estimate gravity accelerations from altimetry-derived geoids. The systematic error owing to lack of data and the choice of a particular inverse operator is described by using resolution functions and their spherical harmonic expansions. An rms value of this error is also estimated by assuming a spectrum for the unknown geoid. The influence of the size of the data region, the spacing between data, the filtering applied to the data, and the model weighting function chosen are all quantified in a spherical geometry. The examples presented show that when low degree spherical harmonic coefficients are available - from satellite orbit analysis - a band-passed version of the geoid can be constructed from local gravity data, even with a relatively restricted data set.

Zlotnicki, V.↗

NASA NTRS1999

The Photospheric Convection Spectrum

Spectra of the photospheric cellular flows are determined from Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) observations. Spherical harmonic decompositions are obtained from the full-disc observations. Fourier decompositions are obtained from the high-resolution observations. The p-mode oscillation signals and instrumental artifacts are reduced by temporal filtering of the Doppler data. The resulting spectra give power (kinetic energy) per wavenumber for effective spherical harmonic degrees from 1 to about 3000. The spectra show distinct peaks representing granules and supergranules but no distinct features at wavenumbers representative of mesogranules or giant cells.

Hathaway, David H.↗

NASA NTRS1999

The Photospheric Convection Spectrum

Spectra of the cellular photospheric flows are determined from observations acquired by the MDI instrument on the SOHO spacecraft. Spherical harmonic spectra are obtained from the full-disk observations. Fourier spectra are obtained from the high-resolution observations. The p-mode oscillation signals and instrumental artifacts are reduced by temporal filtering of the Doppler data. The resulting spectra give power (kinetic energy) per wavenumber for effective spherical harmonic degrees from 1 to over 3000. The spectra show distinct peaks representing granules and supergranules but no distinct features at wavenumbers representative of mesogranu;es or giant cells. The observed cellular patterns and spectra are well represented by a model that only includes granules and supergranules.

Hathaway, D. H.↗

NASA NTRS1977

Gravity-field determination from laser observations

The paper obtains a global representation of the geopotential in spherical harmonics with sufficient detail to determine both a satellite trajectory and the geocentric coordinates of all the tracking stations in a well-defined coordinate system to an accuracy of a few centimeters or better. Laser tracking data on nine satellites are combined with terrestrial gravimetry to obtain a spherical-harmonics representation of the geopotential complete through degree and order 24.

Gaposchkin, E. M.↗

NASA NTRS1979

Southern Hemisphere measurements of the anisotropy in the cosmic microwave background radiation

A recent airborne measurement of the large-angular-scale anisotropy in the cosmic background radiation from the Southern Hemisphere (Lima, Peru) is in essential agreement with previous measurements from the northern hemisphere. The net anisotropy from the combined data can be described by a first-order spherical harmonic (Doppler) anisotropy of amplitude 3.1 plus or minus 0.4 mK with a quadrupole component of less than 1 mK. Additional ground-based measurements of the linear polarization yield an upper limit of l mK, or one part in 3000, at 95% confidence level for the amplitudes of any spherical harmonic through third order.

Smoot, G. F.↗

NASA NTRS2016

Seasonal and static Gravity Field of Mars from MGS, Mars Odyssey and MRO Radio Science

We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k(sub 2) Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k(sub 2) solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k(sub 2) of 0.1697 +/- 0.0027 (3- sigma). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C(sub 30) and, for the first time, C 50. Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C(sub 30) for approximately 1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics ( l = 60-80) than previous solutions.

Genova, Antonio↗

NASA NTRS1981

Electromagnetic deep-probing (100-1000 kms) of the Earth's interior from artificial satellites: Constraints on the regional emplacement of crustal resources

A spherical harmonic analysis program is being tested which takes magnetic data in universal time from a set of arbitrarily space observatories and calculates a value for the instantaneous magnetic field at any point on the globe. The calculation is done as a least mean-squares value fit to a set of spherical harmonics up to any desired order. The program accepts as a set of input the orbit position of a satellite coordinates it with ground-based magnetic data for a given time. The output is a predicted time series for the magnetic field on the Earth's surface at the (r, theta) position directly under the hypothetically orbiting satellite for the duration of the time period of the input data set. By tracking the surface magnetic field beneath the satellite, narrow-band averages crosspowers between the spatially coordinated satellite and the ground-based data sets are computed. These crosspowers are used to calculate field transfer coefficients with minimum noise distortion. The application of this technique to calculating the vector response function W is discussed.

Hermance, J. F.↗

NASA NTRS1993

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

Davis, John H.↗

DOE OSTI2022

Terahertz bound state in the continuum in dielectric membrane metasurfaces

Mie-resonant metasurfaces composed of subwavelength dielectric resonators enable an efficient route for electromagnetic wave manipulation. Among these manipulations, a localized mode with a high-quality factor coexisting with a continuous spectrum of radiating waves termed bound state in the continuum (BIC) can arouse many exotic applications in photonics. Here, we demonstrate the terahertz BIC in a dielectric membrane metasurface and analyze its resonant nature based on Mie-resonant multipoles and vector spherical harmonics. The intrinsic splitting of the resonances under oblique incidence is also explored, in which the conversion of multipole radiation patterns versus the oblique angle will drive the resonances from BIC to leaky modes or vice versa. Both Γ and off-Γ point BICs could be identified as the superposition cancellation of vector spherical harmonics for both p-wave and s-wave. Our research not only provides a novel perspective for exploring the essence of BIC metasurfaces in the terahertz regime, but also points new opportunities for achieving terahertz BIC metasurfaces with ultra-high quality factors.

36 MATERIALS SCIENCE↗

NASA NTRS1991

A unified approach to the helioseismic forward and inverse problems of differential rotation

A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion.

Ritzwoller, Michael H.↗

NASA NTRS1982

Data use investigation for the magnetic field satellite (MAGSAT) mission: Geomagnetic field forecasting and fluid dynamics of the core

MAGSAT data were used to construct a variety of spherical harmonic models of the main geomagnetic field emanating from Earth's liquid core at poch 1980. These models were used to: (1) accurately determine the radius of Earth's core by a magnetic method, (2) calculate estimates, of the long-term ange of variation of geomagnetic Gauss coefficients; (3) establish a preferred truncation level for current spherical harmonic models of the main geomagnetic field from the core; (4) evaluate a method for taking account of electrical conduction in the mantle when the magnetic field is downward continued to the core-mantle boundary; and (5) establish that upwelling and downwelling of fluid motion at the top of the core is probably detectable, observationally. A fluid dynamics forecast model was not produced because of insufficient data.

Benton, E. R.↗

NASA NTRS1994

On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Method

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.

Gorski, Krzysztof M.↗

NASA NTRS2016

Determination of Celestial Body Principal Axes via Gravity Field Estimation

The determination of physical parameters of celestial bodies provides critical navigational and scientific information. Determining the mass, rotation state, and density distribution is an important task of the navigation team on an operational mission. One representation of the internal density distribution, spherical harmonics, may be leveraged to compute the orientation of the principal axis frame of the celestial body, which in turn informs the dynamics of the body’s motion. Using data from NASA’s Dawn mission to the massive asteroids (1) Ceres and (4) Vesta, a method is proposed that refines the knowledge of the principal axis frame by utilizing estimated spherical harmonic coefficients. Applying an iterative rotation scheme to the solved-for body-fixed frame leads to convergence on a frame that is very close to the actual dynamical principal axis frame.

Takahashi, Yu↗

NASA NTRS2021

Patched Local Lunar Gravity Solutions using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into twelve regions and two polar caps, with a resolution of 0.15˚ x 0.15˚ (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Sander Goossens↗

NASA NTRS1992

An improved Venus gravity field from Doppler tracking of the Pioneer Venus Orbiter and Magellan spacecraft

A total of 365,000 Pioneer Venus Orbiter (PVO) S-band Doppler data points were fit in arcs ranging from one to four revolutions in length by estimating the spacecraft position and velocity, atmospheric density, and a solar pressure parameter at each arc epoch. The resultant converged PVO orbits were used to produce 194 information arrays for the Venus spherical harmonic coefficients complete to degree and order 21. A similar procedure was used to produce a second set of 72 information arrays for a 21 x 21 gravitational field from a limited, but global, sampling of Magellan S- and X-band data from cycles 1 and 2. The PVO and Magellan information arrays were combined and solved to obtain the 21 x 21 spherical harmonic expansion designated JPL-Venus Gravity Model 6A (VGM6A). The VGM6A harmonic field field produced significant improvements in the Doppler residual statistics obtained from field validation fits to both PVO and Magellan tracking data in comparison with alternative representations of Venus gravity.

Mcnamee, J. B.↗

NASA NTRS1987

Atlas of wide-field-of-view outgoing longwave radiation derived from Nimbus 6 Earth radiation budget data set, July 1975 to June 1978

An atlas of monthly mean outgoing longwave radiation global contour maps and associated spherical harmonic coefficients is presented. The atlas contains 36 months of continuous data from July 1975 to June 1978. The data were derived from the first Earth radiation budget experiment, which was flown on the Nimbus-6 Sun-synchronous satellite in 1975. Only the wide-field-of-view longwave measurements are cataloged in this atlas. The contour maps along with the associated sets of spherical harmonic coefficients form a valuable data set for studying different aspects of our changing climate over monthly, annual, and interannual scales in the time domain, and over regional, zonal, and global scales in the spatial domain.

Bess, T. Dale↗

DOE OSTI2021

encore : an O ( N g2) estimator for galaxy N -point correlation functions

ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.

79 ASTRONOMY AND ASTROPHYSICS↗