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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Solar Inverse Theory

Helioseismological inversion, as with the inversion of any other data, is divided into three phases. The first is the solution of the so-called forward problem: namely, the calculation of the eigenfrequencies of a theoretical equilibrium state. The second is an attempt to understand the results, either empirically by determining how those frequencies vary as chosen parameters defining the equilibrium model are varied, or analytically from asymptotic expansions in limiting cases of high order or degree. The third phase is to pose and solve an inverse problem, which seeks to find a plausible equilibrium model of the Sun whose eigenfrequencies are consistent with observation. The three phases are briefly discussed in this review, and the third, which is not yet widely used in helioseismology, is illustrated with some selected inversions of artificial solar data.

Gough, D.↗
NASA NTRS2000

Geoid Recovery using Geophysical Inverse Theory Applied to Satellite to Satellite Tracking Data

This report describes a new method for determination of the geopotential. The analysis is aimed at the GRACE mission. This Satellite-to-Satellite Tracking (SST) mission is viewed as a mapping mission The result will be maps of the geoid. The elements of potential theory, celestial mechanics, and Geophysical Inverse Theory are integrated into a computation architecture, and the results of several simulations presented Centimeter accuracy geoids with 50 to 100 km resolution can be recovered with a 30 to 60 day mission.

Gaposchkin, E. M.↗
NASA NTRS2000

Geoid Recovery Using Geophysical Inverse Theory Applied to Satellite to Satellite Tracking Data

This report describes a new method for determination of the geopotential, or the equivalent geoid. It is based on Satellite-to-Satellite Tracking (SST) of two co-orbiting low earth satellites separated by a few hundred kilometers. The analysis is aimed at the GRACE Mission, though it is generally applicable to any SST data. It is proposed that the SST be viewed as a mapping mission. That is, the result will be maps of the geoid or gravity, as contrasted with determination of spherical harmonics or Fourier coefficients. A method has been developed, based on Geophysical Inverse Theory (GIT), that can provide maps at a prescribed (desired) resolution and the corresponding error map from the SST data. This computation can be done area by area avoiding simultaneous recovery of all the geopotential information. The necessary elements of potential theory, celestial mechanics, and Geophysical Inverse Theory are described, a computation architecture is described, and the results of several simulations presented. Centimeter accuracy geoids with 50 to 100 km resolution can be recovered with a 30 to 60 day mission.

Gaposchkin, E. M.↗
NASA NTRS1991

Contributions from geomagnetic inverse theory to the study of hydromagnetic conditions near the core-mantle boundary

The Final Report on contributions from geomagnetic inverse theory to the study of hydromagnetic conditions near the core-mantle boundary (CMB) is presented. The original proposal was to study five questions concerning what the surface and satellite magnetic data imply about hydromagnetic and electromagnetic conditions near the CMB. The five questions are: (1) what do the surface and satellite data imply about the geomagnetic field B near the surface of the earth; (2) how does one extrapolate B down through the conducting mantle to the CMB; (3) if B on the CMB is visible, how accurately does it satisfy the frozen-flux approximation; (4) if frozen flux is a good approximation on the CMB, what can be inferred about the fluid velocity v in the upper core; and (5) if v at the CMB is visible, does it suggest any dynamical properties of the core, such as vertical advection, Alfven-inertial waves, link instabilities, or mantle effects. A summary of the research is provided.

Backus, George E.↗
DOE OSTI2025

Predictable third harmonic generation in GaAs metasurfaces through group theory inverse design of meta-atoms

Here we report the group theory-based inverse design of meta-atoms for a dielectric metasurface in GaAs with predictable optical linear response and third harmonic generation (THG). Six sharp Fano resonances have been observed with a corresponding polarization dependence as predicted by group theory and the meta-atom’s symmetry in the D2h point group. THG has been observed for two modes under x-polarization excitation and one mode for y-polarization, in agreement with theoretical symmetry predictions. The polarization-dependent THG aspect ratio was observed to reach as high as 108. Through strategic structural or symmetry-preserving perturbations, it was shown that the THG can be enhanced or reduced by a factor of 7. The highest THG conversion efficiency was estimated to be 3.1×10-7 at the pump intensity of 1.51 MW/cm2. This high THG conversion efficiency indicates that our group theory approach to modal engineering opens a new path towards optical nonlinearity tuning in dielectric metasurfaces.

Aoueille, Andrew↗
NASA NTRS1977

Statistical principles of inversion theory

Statistical methods are used to deal with the inverse problem of radiative transfer. All the available information about an unknown profile can be expressed in the form of values of functions of that profile and error estimates of these values. Estimation theory shows how these values are combined to give an estimate of the unknown profile and its error covariance. Many inversion methods are expressed in this form, although the error estimate is not usually carried out. Practical applications are described, both for inversion of individual profiles, and the global analysis of satellite data.

Rodgers, C. D.↗
DOE OSTI2023

Data-assimilated time-lapse visco-acoustic full-waveform inversion: Theory and application for injected CO 2 plume monitoring

Continuous seismic monitoring for quantifying CO 2 plume migration and detection of any potential leakages in the subsurface is essential for the security of long-term anthropogenic carbon dioxide geologic storage. Traditional time-lapse full-waveform inversion (TLFWI) methods aim to map the CO 2 distribution by estimating seismic velocity changes, but recent studies find that CO 2 -induced attenuation is an important complement to seismic velocity for tracking the CO 2 plumes and even quantifying the CO 2 saturation. We have developed a novel data-assimilated TLFWI method to construct high-resolution time-lapse velocity and attenuation changes from dense time-lapse monitoring data. This method consists of two theoretical developments: visco-acoustic full-waveform inversion (QFWI) and multiparameter hierarchical matrix-powered extended Kalman filter (mHiEKF). The method is capable of (1) posing temporal constraints to retrieve time-lapse information from dense monitoring data by using mHiEKF, (2) accurately recovering high-spatial-resolution velocity and attenuation perturbations using first-order equation system-based QFWI, and (3) providing the model uncertainty by estimating their model standard deviation. With numerical examples, we first find the effectiveness of the new QFWI on estimating accurate velocity and attenuation models simultaneously. Then, a CO 2 leakage case and a realistic Frio-II CO 2 monitoring case are presented to find the advantages and applicability of our data-assimilated QFWI method for estimating time-lapse changes using dense time-lapse monitoring surveys. Here, by assimilating time-lapse seismic monitoring data over time, our data-assimilated QFWI method can improve the resolution of velocity and attenuation changes and decrease their model uncertainties.

58 GEOSCIENCES↗
NASA NTRS1999

Main Geomagnetic Field Models from Oersted and Magsat Data Via a Rigorous General Inverse Theory with Error Bounds

The purpose of the grant was to study how prior information about the geomagnetic field can be used to interpret surface and satellite magnetic measurements, to generate quantitative descriptions of prior information that might be so used, and to use this prior information to obtain from satellite data a model of the core field with statistically justifiable error estimates. The need for prior information in geophysical inversion has long been recognized. Data sets are finite, and faithful descriptions of aspects of the earth almost always require infinite-dimensional model spaces. By themselves, the data can confine the correct earth model only to an infinite-dimensional subset of the model space. Earth properties other than direct functions of the observed data cannot be estimated from those data without prior information about the earth. Prior information is based on what the observer already knows before the data become available. Such information can be "hard" or "soft". Hard information is a belief that the real earth must lie in some known region of model space. For example, the total ohmic dissipation in the core is probably less that the total observed geothermal heat flow out of the earth's surface. (In principle, ohmic heat in the core can be recaptured to help drive the dynamo, but this effect is probably small.) "Soft" information is a probability distribution on the model space, a distribution that the observer accepts as a quantitative description of her/his beliefs about the earth. The probability distribution can be a subjective prior in the sense of Bayes or the objective result of a statistical study of previous data or relevant theories.

Backus, George E.↗
NASA NTRS1983

Computation of Jupiter interior models from gravitational inversion theory

Spacecraft measurements of Jupiter have provided the mass, standard pressure level radius, rotation law, internal mass distribution multipole moments, and internal composition and temperature distribution constraints, for the present implementation of a method for deriving planetary interior models that exactly satisfy a set of N gravitational constraints by means of appropriate iteration. The models are not forced to fit the more indirectly derived constraints, which are instead used as conistency checks. In the case of an He mass fraction in the envelope Y of 0.2, the inferred pressure at a mass density of about 0.2 g/cu cm is about a factor of 2 higher than would be indicated by experimental H compression data in the relevant pressure range of 100,000 to one million bar. The inferred pressure distribution is in better agreement with the shock data for a nominal Y value of 0.3 + or - 0.05.

Hubbard, W. B.↗
NASA NTRS1976

Adequacy of classical inverse bremsstrahlung theory for low-temperature plasmas

The authors examine those plasma heating conditions under which a theory more accurate than the classical inverse bremsstrahlung theory should be used to predict absorption coefficients when laser energy is injected into the plasma. A correlation plot for measured absorption coefficients at three laser wavelengths versus those calculated by quantum mechanical theory yields a correlation coefficient for the least-squares fit of 0.994. A plot of the ratio of the quantum-mechanically corrected electron ion inverse bremsstrahlung absorption coefficient to that calculated by classical methods versus plasma temperature shows that at around 20 eV and above the differences between classical and quantum predictions are negligible, but significant errors could arise from application of classical theories to lower-temperature plasmas. Some recent experiments in the literature are shown to be worthy of reinterpretation in this light.

Billman, K. W.↗
NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗
NASA NTRS1979

Applications of estimation theory to inverse problems in meteorology

The paper applies iterated and non-iterated extended Kalman filters to solve two practical meteorological inversion problems. Passive microwave satellite soundings are used to infer vertical temperature profiles and cloud parameters. In both cases it is shown that improvements can be obtained over presently used techniques. Finally, the results suggest that modern multivariate nonlinear recursive estimation techniques based in a Bayesian methodology can be a valuable tool in the area of remote sounding of atmospheric parameters.

Gustafson, D. E.↗
NASA NTRS1979

Modular theory of inverse systems

The relationship between multivariable zeros and inverse systems was explored. A definition of zero module is given in such a way that it is basis independent. The existence of essential right and left inverses were established. The way in which the abstract zero module captured previous definitions of multivariable zeros is explained and examples are presented.

Source record↗
NASA NTRS1990

A physical model of the bidirectional reflectance of vegetation canopies. I - Theory. II - Inversion and validation

A new physically based analytical model of the bidirectional reflectance of vegetation canopies is derived. The model expresses the bidirectional reflectance field of a semiinfinite canopy as a combination of functions describing (1) the optical properties of the leaves through their single-scattering albedo and their phase function, (2) the average distribution of leaf orientations, and (3) the architecture of the canopy. The model is validated against laboratory and ground-based measurements in the visible and IR spectral regions, taken over two vegetation covers. The intrinsic optical properties of leaves and the information on the geometrical canopy arrangements in space were obtained using an inversion procedure based on a nonlinear optimization technique. Model predictions of bidirectional reflectances obtained using the inversion procedure compare well with actual observations.

Verstraete, Michel M.↗
NASA NTRS1992

Effective equations and the inverse cascade theory for Kolmogorov flows

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Weinan, E.↗