The relevance of frequency averaged properties
Relevance of frequency-averaged properties, and differences between radiative heat transfer and temperature inversion problems
Traugott, S. C.↗
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On the optimal angular velocity control of asymmetrical space vehicles
Inverse problem of optimal control for reducing angular velocities of space vehicle to zero
Athans, M.↗
Investigation of the Hylleraas method for determining the potential-energy function from the phase shift
Quantum mechanical inverse problem of elastic scattering theory, discussing Hylleraas solution for determining potential energy function from phase shift
Bernstein, R. B.↗
Vertical resolution of temperature profiles obtained from remote radiation measurements
The Backus-Gilbert theory, originally developed for analysis of inversion problems associated with the physics of the solid earth, was applied to the problem of the vertical sounding of the atmosphere by means of remote radiation measurements. An application was made to spectral intervals 2.8/cm wide in the 667/cm band CO2, and tradeoff curves are presented which quantitatively define the relationship between intrinsic vertical resolution and random error in temperature profile estimates. It is found that for a 1-2 K random error with state-of-the-art instrumentation, the intrinsic vertical resolution ranges from approximately 0.5 locale scale height (l.s.h.) in the lower troposphere to greater than 2 l.s.h. in the upper stratosphere with approximately 1 l.s.h. resolution in the vicinity of the tropopause. These values are somewhat smaller than the widths of the radioactive transfer kernels at similar levels. Increasing the number of spectral intervals from 7 to 16 is found to produce only a marginal improvement in vertical resolution.
Conrath, B. J.↗
Backus-Gilbert inversion of travel time data
Application of the Backus-Gilbert theory for geophysical inverse problems to the seismic body wave travel-time problem is described. In particular, it is shown how to generate earth models that fit travel-time data to within one standard error and having generated such models how to describe their degree of uniqueness. An example is given to illustrate the process.
Johnson, L. E.↗
Culling of redundant data
The inversion of a large data set, with it errors, is demonstrated and the tradeoff curve, or resolving power calculations, are discussed. Consideration is given to inverse problems of the earth, represented in the idealized form of a single scaler function of a single coordinate. The difference between the functional for the real earth and the functional for some model is formulated. A procedure is given for using the linear relationships between the differences in the data and the differences in the model as side conditions. Through a process of diagonalization a model is created that fits the data. The data are culled by accepting only those relative standard errors that are less than 100 percent.
Gilbert, F.↗
Inversion of radiation data in biophysics
Topics in biophysics are summarized in which radiation data inversion problems occur. The topics fall into two main categories. The first relates to information acquired about the distance environment through seeing, hearing, etc. The second relates to the use of electromagnetic, acoustic, or other radiation for diagnostic purposes, either at a bulk or a molecular level.
Twersky, V.↗
Transmission line inversion and synthesis from the point of view of transient response
The transmission line inversion problem is applied to the speech communication process. The problem involves acquiring information necessary for synthesis of speech and for making models of the speech production mechanism. Formulation for the problem is derived from an analysis of the human vocal tract functions. It is known that speech sounds are produced by acoustic excitation of the tract by means of quasi-periodic pulses from the vocal cords during vowel sounds and turbulent air flow at various points along the tract during fricative sounds. By assuming plane wave propagation, differential equations are obtained relating the cross sectional area of the tract, the pressure, and the volume velocity. By replacing the pressure factor with a voltage factor and the volume velocity by current, the problem becomes a transmission line problem.
Sondhi, M. M.↗
Bistatic-radar estimation of surface-slope probability distributions with applications to the moon.
A method for extracting surface-slope frequency distributions from bistatic-radar data has been developed and applied to the lunar surface. Telemetry transmissions from orbiting Apollo spacecraft were received on the earth after reflection from the lunar surface. The echo-frequency spectrum was related analytically to the probability distribution of lunar slopes. Standard regression techniques were used to solve the inverse problem of finding slope distributions from observed echo-frequency spectra. Data taken simultaneously at two wavelengths, 13 and 116 cm, have yielded diverse slope statistics.
Parker, M. N.↗
Development of an experiment for visible radiation measurements from a satellite
The inversion problem, I.E., determining the atmospheric turbidity from polarimetry of radiation emerging from the earth's atmosphere, is presented. A major theoretical advance was made by finding a successful approximation for the forward peak scattering of aerosols together with a simplified characterization of particle size distributions. An engineering model of a multibarreled photopolarimeter suitable for operation from a satellite was evaluated in laboratory and high altitude jet aircraft tests. Comparison of the data from flights over the Mexican desert with theoretical curves for a Rayleigh atmosphere with negligible turbidity is in agreement.
Sekera, Z.↗
A macroscopic plasma Lagrangian and its application to wave interactions and resonances
The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.
Peng, Y. K. M.↗
Numerical modelling of instantaneous plate tectonics
Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.
Minster, J. B.↗
The design and performance of axially symmetrical contoured wall diffusers employing suction boundary layer control
This paper presents a procedure for the design and the performance prediction of axially symmetrical contoured wall diffusers employing suction boundary layer control. An inverse problem approach was used in the potential flow design of the diffuser wall contours. The experimentally observed flow characteristics and the stability of flows within the diffuser are also described. Guidelines for the design of low suction (less than 10 percent of the inlet flow) and thus high effectiveness contoured wall diffusers are also provided based on the results of the experimental program.
Nelson, C. D., Jr.↗
Particulate sizes from polarization measurements
Radiation measurements from a ground based polarimeter were used to infer the optical properties of atmospheric particles. The inherent nonunigueness in model calculations is discussed. The inverse problem in atmospheric optics is described, along with incident and emergent beams. Emergent radiation was calculated for all possible particulate distributions, and results were catalogued.
Kuriyan, J. G.↗
Lagrangian density for collisional plasma
For the purpose of deriving appropriate Lagrangians for plasma equations that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first- and second-order quasi-linear partial differential equations. This results in convenient forms of the sufficient conditions under which the given differential equations are Euler-Lagrange equations of a Lagrangian. These conditions are then applied to determine the necessary transformation that converts equations, apparently not already in it, into Euler-Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained, and the Lagrangian is derived for a resistive transmission line.
Peng, Y.-K. M.↗
Dispersion of ensembles of non-interacting particles
The dynamics of an ensemble of noninteracting particles dispersing from a common origin and moving in a common force field with an initial distribution of momenta is analyzed using an approach where the particles are considered as a continuum described by a phase-space distribution function. General solutions are obtained for both the distribution function and the associated spatial density function. The linear case of small departures from circular orbits in an axisymmetric gravitational field is treated along with the specific case of particle dispersion from an object in a circular orbit in the same type of field. Numerical results are presented for the latter case, and consideration is given to the inverse problem of determining the initial time and velocity distribution from knowledge of the ensemble structure at a later time. Explicit results are provided for the case of an ellipsoidal distribution of initial momenta, and a numerical procedure is indicated for treating more general cases.
Heard, W. B.↗
The solar occultation technique for remote sensing of particulates in the earth's atmosphere. I - The inversion of horizon radiances from space
The aerosol scattering coefficient as a function of height can be recovered from a direct inversion of the single-scattering horizon radiance provided the sun is above the horizon and an independent measurement of extinction as a function of height is made. Aerosol detection is effected by means of spacecraft measurements of the horizon radiance made during periods of spacecraft twilight. A solar occultation technique which allows the twilight measurements to be made when the sun is still above the horizon greatly reduces the complexity of the inversion problem. The second part of the paper reports on the use of a coronograph aboard Skylab to photograph the horizon just before spacecraft twilight in order to monitor the aerosol component above the tropopause. The coronograph picture, centered on 26.5 degrees E longitude and 63.0 degrees S latitude, shows that the aerosol layer peaks at a height of 48 plus or minus 1 km.
Schuerman, D. W.↗
Analytic model approach to the inversion of scattering data
An analytic model approach is applied to several simple atmospheric inversion problems. This method gives a sharp determination of aerosol size distribution parameters. It is shown that this analytic approach, together with ground level point sampling data measurements, can be used to infer information on the tropospheric ozone profile.
Green, A. E. S.↗