空间波法测地物介电常数的反演方法

INVERSE FORMULATIONS FOR PERMITTIVITY MEASUREMENT OF GROUND MATERIALS USING SPACE-WAVE METHOD

空间波法适合于测量大面积目标的介电常数,所以是测量地物微波介电特性的一种较好的方法。这种方法从测量数据反演复介电常数要用菲涅尔公式,如果测量数据包含相位信息,则反演是简单的;但是如果测量数据只是幅度,则反演过程需要求解一个二次非线性方程组,以往都采用近似的数字迭代求解,迭代过程对初值和测量数据本身都太敏感,解的存在性、唯一性和稳定性难以判定。本文给出了严格的解析反演法,并证明了解的唯一性和反演结果对测量误差的敏感性。

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.