Search NASA⌕ Search

SEARCH · Search NASA

Results for “Spherical harmonic analysis”

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.

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

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Comment on "An Analysis of VLF Electric Field Spectra Measured in Titan's Atmosphere by The Huygens Probe" By J. A. Morente et al.

Morente et al. have recently revisited the VLF electric field measurements made with the Permittivity, Wave and Altimetry (PWA) instrument during the descent of the Huygens Probe through the atmosphere of Titan. They assert that they have identified several harmonics of the transverse resonance mode of the surface?]ionosphere cavity, which would prove the existence of an electrical activity in the atmosphere of the largest satellite of Saturn. We refute this finding on the basis that it results from an artifact due to an improper analysis of the data set. [2] The investigators of the Permittivity, Wave and Altimetry (PWA) experiment on the Huygens Probe have reported the extremely low frequency (ELF) and very low frequency (VLF) electric signals recorded during the descent through the atmosphere of Titan. The PWA data are archived in the Planetary Science Archive (PSA) of ESA, and an extensive description of the instrument is at the disposal of the scientific community. Morente and his coworkers have revisited this data set and reported the results of their investigations in two papers. In a first paper, they claim that they have detected in the ELF range (0.100 Hz) several harmonics of a global resonance allegedly generated by lightning activity in the spherical cavity guide formed by the surface of Titan and the inner boundary of the ionosphere, a phenomenon similar to the Schumann resonance observed at EartH In the second paper dedicated to the VLF electric signal recorded by PWA, in the range 0.10 kHz, they argue that they can also bring out the transverse resonance and its harmonics, a more local phenomenon that develops around the excitation source and whose frequency is controlled by the separation between Titan?fs surface and the inner ionospheric boundary. [3] The PWA investigators have analyzed the narrowband ELF signal at about 36 Hz effectively observed during the entire descent. They have not endorsed, however, the alternative approach of Morente et al. that discloses additional ELF narrow-band signals and numerous related harmonics. Hamelin et al. and Beghin et al. have questioned the work of Morente and his coworkers and demonstrated unambiguously that their findings are mere artifacts entirely due to a faulty procedure. Morente et al. refuted this critical analysis of their ELF paper in a rebuttal. The present comment draws a parallelism between the ELF and VLF papers and demonstrates that the VLF signal carries no evidence whatever of any transverse resonance. The analyses of the ELF and VLF signals by Morente and his coworkers are flawed, and their conclusions are shown here to be invalid. A more comprehensive and thorough assessment of the numerical approaches proposed by Morente et al. is given by Berthelin et al..

Grard, Rejean↗
NASA NTRS1984

Continental and oceanic crustal magnetization modelling

Inversion of magnetic data from the MAGSAT satellite, to arrive at intensities of magnetization of the Earth's crust, was performed by two different methods. The first method uses a spherical harmonic model of the magnetic field. The coefficients believed to represent sources in the Earth's crust can then be inverted to arrive at vertical dipole moments per unit area at the Earth's surface. The spherical harmonic models contain coefficients of degrees of harmonics up to 23. The dipole moment per unit area for a surface element can then be determined by summing the contribution for each individual degree of harmonic. The magnetic moments were calculated for continental and oceanic areas separately as well as over certain latitudinal segments. Of primary concern was to determine whether there are any differences between continental and oceanic areas. The second analysis with magnetization intensities was made using narrower ranges of degrees of harmonics, assuming that higher degrees are present in the core field signal.

Harrison, C. G. A.↗
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.↗
NASA NTRS2014

The Gravity Field, Orientation, and Ephemeris of Mercury from MESSENGER Observations After Three Years in Orbit

We have analyzed three years of radio tracking data from the MESSENGER spacecraft in orbit around Mercury and determined the gravity field, planetary orientation, and ephemeris of the innermost planet. With improvements in spatial coverage, force modeling, and data weighting, we refined an earlier global gravity field both in quality and resolution, and we present here a spherical harmonic solution to degree and order 50. In this field, termed HgM005, uncertainties in low-degree coefficients are reduced by an order of magnitude relative to the earlier global field, and we obtained a preliminary value of the tidal Love number k(sub 2) of 0.451+/-0.014. We also estimated Mercury's pole position, and we obtained an obliquity value of 2.06 +/- 0.16 arcmin, in good agreement with analysis of Earth-based radar observations. From our updated rotation period (58.646146 +/- 0.000011 days) and Mercury ephemeris, we verified experimentally the planet's 3: 2 spin-orbit resonance to greater accuracy than previously possible. We present a detailed analysis of the HgM005 covariance matrix, and we describe some near-circular frozen orbits around Mercury that could be advantageous for future exploration.

MESSENGER↗
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 NTRS1984

Infrared parameterization and simple climate models

The geographical distribution of the annual mean and the annual cycle in surface temperature and satellite-observed IR is examined, and the spherical harmonic representation of the data fields is exploited to demonstrate how variances and covariances are dominated by the largest space and time scales. The geographical distribution of the annual cycle in the T and IR fields is explored; the strong imprint of the continents in both is clearly evident. The influence of the cloudiness of seasonal precipitation regimes on the IR annual cycle is also quite striking, especially over the subtropics. Analysis of the data shows that the simple form IR = A+BT (with A = 204 W/sq m and B = 1.93 W/sq m/K) explains 90 percent of the area-weighted variance in the annual mean and annual cycle of the zonally averaged IR field.

Short, D. A.↗
NASA NTRS1978

Determination of some dominant parameters of the global dynamic sea surface topography from GEOS-3 altimetry

The 1977 altimetry data bank is analyzed for the geometrical shape of the sea surface expressed as surface spherical harmonics after referral to the higher reference model defined by GEM 9. The resulting determination is expressed as quasi-stationary dynamic SST. Solutions are obtained from different sets of long arcs in the GEOS-3 altimeter data bank as well as from sub-sets related to the September 1975 and March 1976 equinoxes assembled with a view to minimizing seasonal effects. The results are compared with equivalent parameters obtained from the hydrostatic analysis of sporadic temperature, pressure and salinity measurements of the oceans and the known major steady state current systems with comparable wavelengths. The most clearly defined parameter (the zonal harmonic of degree 2) is obtained with an uncertainty of + or - 6 cm. The preferred numerical value is smaller than the oceanographic value due to the effect of the correction for the permanent earth tide. Similar precision is achieved for the zonal harmonic of degree 3. The precision obtained for the fourth degree zonal harmonic reflects more closely the accuracy expected from the level of noise in the orbital solutions.

Mather, R. S.↗
NASA NTRS1994

Evidence for active hotspots on Venus from analysis of Magellan gravity data

The 500-Myr average crater retention age for Venus has raised questions about the present-day level of tectonic activity. In this study we examine the relationship between the gravity and topography of four large volcanic swells, Beta, Atla, Bell, and Western Eistla Regiones, for clues about their stage evolution. The Magellan line-of-sight gravity data are inverted using a point mass model of the anomalous mass to solve for the local vertical gravity field. Spectral admittance calculated from both the local gravity inversions and a spherical harmonic model is compared to three models of compensation: local compensation, a 'flexural' model with local and regional compensation of surface and subsurface loads, and a 'hotspot' model of compensation that includes top loading by volcanoes and subsurface loading due to a deep, low density mass anomaly. The coherence is also calculated in each region, but yields an elastic thickness estimate only at Bell Regio. In all models, the long wavelengths are compensated locally. Our results may indicate a relatively old, possibly inactive plume.

Smrekar, Suzanne E.↗
NASA NTRS1986

The onset of time-dependent convection in spherical shells as a clue to chaotic convection in the earth's mantle

This work presents a detailed numerical study of the dynamical behavior of convection in a spherical shell, as applied to mantle convection. From both two-dimensional (120 radial and 360 tangential points) and three-dimensional (60 radial levels and spherical harmonics up to order and degree L = 33, m = 33), it is shown that for a spherical shell (with inner-to-outer radii ratio eta = 0.62) convection becomes time-dependent, with l = 2 dominating, at a Rayleigh number of about 31 times supercritical for a constant-viscosity, base-heated configuration. This secondary instability is characterized by oscillatory time dependence, with higher frequencies involved, at slightly higher Rayleigh numbers. In illustrating the onset of time dependence, the analysis is extended to show that the onset of weak turbulence in spherical-shell convection takes place at about 60 times the critical Rayleigh number via a quasi-periodic mode.

Machetel, Philippe↗
NASA NTRS1993

New Mars free-air and Bouguer gravity: Correlation with topography, geology and large impact basins

Free-air and Bouguer gravity anomalies from a 50x50 field (MGM635), derived at the Goddard Space Flight Center, with global topography, geology, and the distribution of large impact basins was compared. The free-air gravity anomalies were derived from re-analysis of Viking Orbiter and Mariner 9 tracking data and have a spatial resolution of 250-300 km. Bouguer anomalies were calculated using a 50x50 expansion of the current Mars topography and the GSFC degree 50 geoid as the equipotential reference surface. Rotational flattening was removed using a moment of inertia of 0.365 and the corrections from Table B2 of Sleep and Phillips. Crustal density and mean density were assumed to be 2.9 and 3.93 gm/cm(sup 3). The spherical harmonic topography used has zero mean elevation, and differs from the USGS maps by about 2 km. Comparisons with global geology use a simplified map with about 1/3 the number of units on the current maps. For correlation with impact basins, the recent compilation by Schultz and Frey was used.

Frey, Herbert↗
NASA NTRS1996

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We study a novel characterization of errors for numerical weather predictions. In its simplest form we decompose the error into a part attributable to phase errors and a remainder. The phase error is represented in the same fashion as a velocity field and will be required to vary slowly and smoothly with position. A general distortion representation allows for the displacement and a bias correction of forecast anomalies. In brief, the distortion is determined by minimizing the objective function by varying the displacement and bias correction fields. In the present project we use a global or hemispheric domain, and spherical harmonics to represent these fields. In this project we are initially focusing on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically we study the forecast errors of the 500 hPa geopotential height field for forecasts of the short and medium range. The forecasts are those of the Goddard Earth Observing System data assimilation system. Results presented show that the methodology works, that a large part of the total error may be explained by a distortion limited to triangular truncation at wavenumber 10, and that the remaining residual error contains mostly small spatial scales.

Hoffman, Ross N.↗
DOE OSTI2025

Window convolution of the galaxy clustering bispectrum

In galaxy survey analysis, the observed clustering statistics do not directly match theoretical predictions but rather have been processed by a window function that arises from the survey geometry including the sky footprint, redshift-dependent background number density and systematic weights. While window convolution of the power spectrum is well studied, for the bispectrum with a larger number of degrees of freedom, it poses a significant numerical and computational challenge. In this work, we consider the effect of the survey window in the tripolar spherical harmonic decomposition of the bispectrum and lay down a formal procedure for their convolution via a series expansion of configuration-space three-point correlation functions, which was first proposed by Sugiyama et al. (2019). We then provide a linear algebra formulation of the full window convolution, where an unwindowed bispectrum model vector can be directly premultiplied by a window matrix specific to each survey geometry. To validate the pipeline, we focus on the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) luminous red galaxy (LRG) sample in the South Galactic Cap (SGC) in the redshift bin 0.4 ≤ z ≤ 0.6. We first perform convergence checks on the measurement of the window function from discrete random catalogues, and then investigate the convergence of the window convolution series expansion truncated at a finite of number of terms as well as the performance of the window matrix. This work highlights the differences in window convolution between the power spectrum and bispectrum, and provides a streamlined pipeline for the latter for current surveys such as DESI and the Euclid mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2008

Fast Plasma Instrument for MMS: Simulation Results

Magnetospheric Multiscale (MMS) mission will study small-scale reconnection structures and their rapid motions from closely spaced platforms using instruments capable of high angular, energy, and time resolution measurements. The Dual Electron Spectrometer (DES) of the Fast Plasma Instrument (FPI) for MMS meets these demanding requirements by acquiring the electron velocity distribution functions (VDFs) for the full sky with high-resolution angular measurements every 30 ms. This will provide unprecedented access to electron scale dynamics within the reconnection diffusion region. The DES consists of eight half-top-hat energy analyzers. Each analyzer has a 6 deg. x 11.25 deg. Full-sky coverage is achieved by electrostatically stepping the FOV of each of the eight sensors through four discrete deflection look directions. Data compression and burst memory management will provide approximately 30 minutes of high time resolution data during each orbit of the four MMS spacecraft. Each spacecraft will intelligently downlink the data sequences that contain the greatest amount of temporal structure. Here we present the results of a simulation of the DES analyzer measurements, data compression and decompression, as well as ground-based analysis using as a seed re-processed Cluster/PEACE electron measurements. The Cluster/PEACE electron measurements have been reprocessed through virtual DES analyzers with their proper geometrical, energy, and timing scale factors and re-mapped via interpolation to the DES angular and energy phase-space sampling measurements. The results of the simulated DES measurements are analyzed and the full moments of the simulated VDFs are compared with those obtained from the Cluster/PEACE spectrometer using a standard quadrature moment, a newly implemented spectral spherical harmonic method, and a singular value decomposition method. Our preliminary moment calculations show a remarkable agreement within the uncertainties of the measurements, with the results obtained by the Cluster/PEACE electron spectrometers. The data analyzed was selected because it represented a potential reconnection event as currently published.

Figueroa-Vinas, Adolfo↗
NASA NTRS1990

Geodetic and oceanographic results from the analysis of 1 year of Geosat data

The radial error model of Engelis (1987) is extended using the altimeter data obtained by the Geosat Exact Repeat Mission for simultaneous measurements of the stationary sea surface topography and geopotential coefficients. It is shown that the proper utilization of the Geosat altimeter data significantly improved the quality of field modeling at wave numbers by providing, simultaneously, the solution for improved orbits and the oceanographic information on the global scale. A new set of Geosat geophysical data records with the improved orbits was created, which also contains the values of the geoid undulation computed from a recent spherical harmonic expansion to degree 360.

Denker, Heiner↗
NASA NTRS1974

Lunar gravity analysis results from Explorer-49

An analysis of the lunar gravity field utilizing 234 days of Explorer-49 mean Keplerian elements is presented. A third-degree and third-order gravity model developed at the Goddard Space Flight Center (GSFC) for mission operations is compared with published models derived from Lunar Orbiter data. Improved predictions of e and Omega using the GSFC model are observed. The results suggest that use of Explorer-49 orbital data in a multisatellite solution would lead to improved global estimates of low-order spherical harmonic coefficients of the lunar gravitational potential.

Bryant, W. C., Jr.↗
NASA NTRS1981

Geopotential resonance in a Landsat orbit

A Landsat 1 resonance analysis was conducted on the basis of almost continuous range-rate observations provided by the S-Band station at Greenbelt, MD for a twenty-four day period in September 1976. Constraints on the resonance effects of Landsat 1, determined directly from radar tracking data could be summarized in a number of equations for fully normalized geopotential coefficients. The coefficient values for the dominant resonance terms can be directly determined through the estimation scheme, as the resonance constraints are implicit in the spherical harmonic representation chosen for the geopotential. The degree of the constraint equation series may be arbitrarily increased with analytical expressions for the along-track orbital component in terms of Keplerian elements.

Dunn, P.↗
NASA NTRS2013

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Boussalis, Dhemetrios↗