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The requirements for a numerical inversion method to calculate electron density profiles from ionograms are discussed. A systematic investigation about the independence of the two magnetoionic components shows that the extent to which the range of ambiguity can be reduced depends mainly on the magnetic latitude. Error estimates and first-order corrections for less elaborate methods are included.
The inverse scattering problem is introduced in the context of the Schroedinger equation. The emphasis is on the Gelfand Levitan approach to the nonrelativistic problem at fixed angular momentum.
A review of exact techniques for determining the surface of a three-dimensional perfectly conducting body is given, followed by some new results on the uniqueness question concerning the number of measurements that may be required to explicitly determine the surface of the body. It is then shown that the inhomogeneous but spherically symmetric dielectric electromagnetic case is reducible to a scalar inverse problem that can be treated by known techniques.
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.
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.
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.
The direct problem is to compute reflection coefficients for an assumed electron-density profile, using a full-wave solution. The inverse problem is treated numerically, using derivatives of the reflection matrix with respect to model parameters. A technique for the rapid computation of the derivatives is described. An algorithm for determining resolution in the profile is discussed.
The chronological development of multidimensional inversion techniques is reviewed briefly. Some current work in this area is described.
Derivations are presented of the straight-line Abel transform and the seismological Herglotz-Wiechert transform (which takes ray bending into account) that are used in the reconstruction of refractivity profiles from radio-wave phase data. Profile inversion utilizing these approaches, performed in computer-simulated experiments, are compared for cases of positive, zero, and negative ray bending. For thin atmospheres and ionospheres, such as the Martian atmosphere and ionosphere, radio wave signals are shown to be inverted accurately with both methods. For dense media, such as the solar corona or the lower Venus atmosphere, the refractive recovered by the seismological Herglotz-Wiechert transform provide a significant improvement compared with the straight-line Abel transform.
A general expression is given for the derivative of the C sub 4 - inverse of a differentiable matrix A whenever that derivative, as well as the derivative of A, exists.
An analysis is presented that shows the desirability and feasibility of conducting irradiations of large test objects by beams of penetrating radiation, by the method of moving the test object back and forth through the beam, rather than by sweeping the beam across the object. An extension of this method of inverse rastering allows the generation of composite beams with any desired intensity-vs-energy spectrum, obviating the need to determine equivalent damage factors for every energy in the spectrum.
A theoretical study is conducted to investigate the possibility of obtaining inversions in a plasma of metals such as Mg, Ca, Sr, or Ba by charge exchange with inert gas ions. The gases considered include He, Ne, Xe, Ar, or N. The analysis uses rate equations to calculate the density of the various ion levels and an energy equation to calculate the electron temperature. Both charge exchange and electron collisional excitation of the various ion levels are considered.
An alternative method for deriving the generalized inverse of an arbitrary rectangular matrix with real or complex coefficients is described. The method applies a classical minimization procedure without iteration processes and is readily applicable in digital computer programming.
Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
Desired roots are first isolated by Sturm sequence procedure. Then special variant of inverse iteration technique is applied for individual determination of each root along with its vector. Program was written in FORTRAN V for UNIVAC 1100-series computers.
A cross correlation analysis of coronal green line intensity (5303A) and interplanetary magnetic field polarity for the period 1947-1970 shows that the coronal features are organized in a constant pattern with respect to the 4-sector structure through the solar cycle. A sudden inversion of the coronal pattern with respect to the sector structure takes place at the solar minima. The high emission regions of the green corona are located near the solar magnetic sector boundaries having polarities (-,+), (+,-), (-,+) during cycles 18, 19, 20 respectively in the Northern Hemisphere, and (+,-), (-,+), (+,-) in the Southern Hemisphere.
A very detailed greenhouse model derives a methane to hydrogen ratio of unity and a minimum surface pressure of 0.4 atm. Based on a surface gravity g = 140 cm sec/2, the minimum CH4 abundance is 30-40 km-A and the minimum H2 abundance varies from 15 to 85 km-A. A model of the atmosphere of Titan is proposed which seems to be consistent with observations and requires a much smaller CH4 abundance (of the order or 2 km-atm). Although no H2 is required, the presence of some H2 is readily accommodated. In this model, a temperature inversion exists in the atmosphere due to absorption of blue and ultraviolet solar radiation by small particles. The absorbed radiation is re-radiated by the dust and by molecules having long wavelength bands such as CH4 7.7 micrometer and ethane at 12.2 micrometer. The brightness temperature at 20 micrometer is primarily due to re-radiation by the dust.
A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.