摘要:

Inversion theory is a guide for handling inverse problems rather than a set of inversion techniques. The usual ill‐posed character of inverse problems has first to be dealt with by reassessing the concept of solution and by giving a detailed answer to the basic mathematical questions of the solutions existence, uniqueness, construction, stability, and approximation. But this is not sufficient. If the results are to be used by physicists, they should take into account the fact that no physical problem can be given a complete study separately from all others. In other words, investigating mathematical questions, and in particular describing the sets of solutions, must be done in such.a way that physical motivations and physical considerations are always apparent. These remarks are illustrated by several examples taken from scattering theor

ISSN:0048-6604    

DOI:10.1029/RS018i001p00001

年代:1983

数据来源: WILEY

摘要:

An attempt is made to examine critically the basic formulations of current flow in heterogeneous media such as brine‐ saturated rocks with the grains having a regular form. The pore space dependence on the conductivity and permittivity is given special attention. The extension of the small volume loading mixture formulas to large volume loading is carried through explicitly, following the procedure of Bruggeman, Hanai, Cohen, Sen, and others. We indicate that the particle shape plays a major rol

ISSN:0048-6604    

DOI:10.1029/RS018i001p00019

年代:1983

数据来源: WILEY

摘要:

We present a short analysis of the electric transient response when a steady current in a frequency dispersive medium is interrupted. The model is a homogeneous host rock medium with a loading of spheroidally shaped metal ore grains. The latter can have a polarizable interface with the adjacent electrolyte. It is shown that the rate of decay of the electric field is more rapid for the smaller particles. Also, there is an optimum particle size if the area under the decay curve is to be maximized.

ISSN:0048-6604    

DOI:10.1029/RS018i001p00025

年代:1983

数据来源: WILEY

摘要:

In this paper we analyze the numerical aspects of the various methods that have been utilized to analyze thin wire antennas. First, we derive the properties of the operators for Pocklington's and Hallen's integral equation. On the basis of these properties, we discuss the various iterative methods used to find current distribution on thin wire structures. An attempt has been made to resolve the question of numerical stability associated with various entire domain and subdomain expansion functions in Galerkin's method. It has been shown that the sequence of solutions generated by the iterative methods monotonically approaches the exact solution provided the excitations chosen for these problems are in the range of the operator. Such a statement may not hold for Galerkin's methods if the inverse operator is unbounded. Moreover, if the excitation function is not in the range of the operator, then the sequence of solutions forms an asymptotic series. Examples have been presented to illustrate this point.

ISSN:0048-6604    

DOI:10.1029/RS018i001p00029

年代:1983

数据来源: WILEY

摘要:

An integral equation method is proposed for analyzing scattering and mode conversion of guided modes by boundary deformations of a dielectric slab waveguide. Integral equations are derived for the tangential electromagnetic fields on the deformed boundaries only, using the integral expressions of fields and the fundamental properties which the integral over a closed path has. Mode conversion coefficients for guided and radiation modes are easily obtained from the solutions of the integral equations. Using the mode conversion coefficients, physical quantities such as radiation loss, reflected mode power, and total scattered power, are calculated. Numerical examples are presented for the two‐dimensional models of the typical boundary deformations in optical fibers caused by a fusion splic

ISSN:0048-6604    

DOI:10.1029/RS018i001p00039

年代:1983

数据来源: WILEY

摘要:

The kernel of the integrodifferential equations for the excited surface current distribution on a tubular cylinder is expanded in a complete set of orthogonal functions. The expansion coefficients are obtained explicitly as power series of the dimensions of the cylinder. As this kernel is a particular form of the free‐space Green's function, power series representations for the Green's function in other forms are also presented to facilitate direct applications to other problem

ISSN:0048-6604    

DOI:10.1029/RS018i001p00048

年代:1983

数据来源: WILEY

摘要:

Prony's method, a procedure for estimating the parameters of a sum of exponentials, is applied here to linear array pattern synthesis. Unlike most approaches to this problem, Prony's method provides source locations as well as source strengths, so that the synthesized distributions generally involve nonuniformly spaced sources. In this paper, the procedure is developed, its numerical characteristics are discussed, and its application is illustrated for several different radiation patterns. Because the unconstrained procedure discussed here can lead to a requirement for directive sources, paper 2 will treat a version of Prony's method constrained to produce isotropic sources.

ISSN:0048-6604    

DOI:10.1029/RS018i001p00057

年代:1983

数据来源: WILEY

摘要:

This paper derives rigorous results pertaining to the validity of the far‐field approximation for scattering from randomly rough, perfectly conducting surfaces having arbitrary statistics. The methodology employs the stochastic Fourier transform of the current induced on the infinite surface by either a bounded or unbounded incident plane wave. The results are general in that no approximate simplifying forms for the current are employed. Exact expressions are obtained for the mean and variance of the scattered field for unbounded illumination, and they are compared to the far‐field approximations to illustrate how the latter simplifications fail in this limit. Some of the pitfalls of the far‐field approximation in the case of beam illumination are discussed. When the incident plane wave is bounded, the conventional far‐field form for the mean scattered field can be rigorously derived for arbitrary surfaces provided the cross‐sectional area of the incident beam is large in comparison to the square of the electromagnetic wavelength. The conventional far‐field result for the variance of the scattered field is shown to require the additional stipulation that the cross‐sectional area of the incident beam contain many decorrelation intervals of the surface roughness. The results obtained herein are important because they hold for arbitrary surface statistics. Whereas they appear to duplicate previous results, it must be remembered that the earlier results were only valid for a special class of surface statistics, i.e., surfaces for which single scattering

ISSN:0048-6604    

DOI:10.1029/RS018i001p00071

年代:1983

数据来源: WILEY

摘要:

Given the side‐scanned image of a scene characterized by a random, time‐varying reflectivity density, evolving in accordance with a dispersion relation, the linear, minimum mean‐square error estimator of the scene at a given time is found. The data are corrupted by additive, ‘white’ noise. The minimum mean‐square error does not depend on whether the real or the synthetic aperture technique is used or whether in the synthetic case, the ‘signal film’ or ‘complex’ image is the data. The effect of finite scanning velocity υ is to replace the white noise of spectral density ηowith a ‘colored’ noise of spectral density | ‐ υgx(k)/υ|ηowhere υgx(k) is the group velocity directed along υ it is assumed that υgx(k)/υ<1. The anomalous behav

ISSN:0048-6604    

DOI:10.1029/RS018i001p00083

年代:1983

数据来源: WILEY

摘要:

The double‐pulse technique for measuring the Doppler shift of radar auroral echoes contains inherent noise arising from overlapping echoes. By modifying the method of reducing the data, it is possible to reduce this noise so that either greater precision is achieved or less time is require

ISSN:0048-6604    

DOI:10.1029/RS018i001p00093

年代:1983

数据来源: WILEY