空間波法測地物介電常數(shù)的反演方法
INVERSE FORMULATIONS FOR PERMITTIVITY MEASUREMENT OF GROUND MATERIALS USING SPACE-WAVE METHOD
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摘要: 空間波法適合于測量大面積目標的介電常數(shù),所以是測量地物微波介電特性的一種較好的方法。這種方法從測量數(shù)據(jù)反演復介電常數(shù)要用菲涅爾公式,如果測量數(shù)據(jù)包含相位信息,則反演是簡單的;但是如果測量數(shù)據(jù)只是幅度,則反演過程需要求解一個二次非線性方程組,以往都采用近似的數(shù)字迭代求解,迭代過程對初值和測量數(shù)據(jù)本身都太敏感,解的存在性、唯一性和穩(wěn)定性難以判定。本文給出了嚴格的解析反演法,并證明了解的唯一性和反演結果對測量誤差的敏感性。Abstract: The space-wave method, suitable for extended surface targets, is a preferable method for permittivity measurement of ground materials at microwave frequencies. The inversion of permittivity from the measured data, which is established on using the Fresnel reflection coefficients, is easy if the measurement includes phase information. However, if the measured quantities are just the amplitudes of the reflected waves, the inversion will be much complicated by solving a quadratic nonlinear equation set, and so far only numerical iterative approaches have been reported in the literature. Unfortunately, the iterative process is highly unstable because of the extremely sensitivity of the inverse algorithms to the measured data and even to the iterative initial values. In the present work, analytical inverse formulations are presented which will give a unique inverse result if it does exist for a set of measured data. Error sensitivity of the inversion to the measurement errors are performed, as well.
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