Forward and inverse scattering for discrete layered lossy and absorbing media

Frolík, Jeff; Yagle, A.E.

doi:10.1109/82.624998

Cited by 22 publications

(33 citation statements)

References 13 publications

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“…wave propagation in a non-uniform media in a transmission line) in geophysics and electromagnetics, such as the scattering matrix, the transmission matrix, and the ABCD matrix (Proponotarios and Wing, 1967, Claerbout, 1976, Frolik and Yagle, 1997. They are useful when dealing with non-uniform transmission lines.…”

Section: Abcd Matrix Methodsmentioning

confidence: 99%

Real-Time Determination Of Soil Type, Water Content, and Density Using Electromagnetics

Drnevich¹,

Lin²,

Qin³

et al. 2001

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Prepared in cooperation with the Indiana Department of Transportation and Federal Highway Administration. AbstractThe primary objective of this study was to explore the potential use of electromagnetic characteristics of soils using the Time Domain Reflectometry (TDR) technique to identify physical properties of soils. Three fundamental studies in this exploration are the frequencydependent electromagnetic properties of soils, the wave propagation in a TDR system, and the inverse analyses of TDR waveforms. The three-phase model for soils was extended to a four-phase model so as to account for the interface effect and hence the soil fineness. The physical parameters of the four-phase model are related to the frequency-dependent dielectric permitivity of the soil through a semiempirical volumetric mixing model. A spectral analysis method was developed to simulate wave propagation in the TDR system in a realistic way. Inverse analysis based on the material model and the wave propagation model was formulated using Bayesian statistics to calibrate the TDR system and to infer material properties from the measured TDR waveform. A TDR probe system was used to measure the dielectric properties of soils in a compaction mold and in the field. An experimental program was carried out to make TDR measurements of 5 different soils with different water contents and densities. The result of the inverse analysis matched the TDR waveform very well and determined the dielectric spectrum of soils. With the ability to measure the dielectric spectrum of soils, the apparent dielectric constant at a particular frequency can be calculated. Results showed that the apparent dielectric constant at 1 GHz gave much better correlation with soil water content and density than the apparent dielectric constant obtained by measuring the time between reflections from the soil surface and the one from the end of the probe. Additional work was done to assess the effects of temperature of the soil on measured dielectric constant and it showed that temperature effects were relatively small and could be accounted for in a systematic way. The use of the method for soils having large particle sizes was examined and it was found that the method was applicable for particle sizes passing the 19 mm (3/4-in.) sieve as long as the percentage of particles in the larger size range was limited. Finally, the method was examined for use with stabilizing additives for soil. While test results were obtained modified soils, the measured apparent dielectric constant changed with time after compaction whereas the water content by oven drying did not change appreciably. It is conjectured that changes in apparent dielectric constant are sensitive to the hydration caused by these additives. Thus, the use of the TDR method can be a tool to monitor changes in soils containing additives. Detailed study of this phenomenon is continuing. Key WordsTime Domain Reflectometry, electromagnetic wave propagation, soils, gravels, sands, silts, clays, water content, compaction, density, ...

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Section: Abcd Matrix Methodsmentioning

confidence: 99%

Real-Time Determination Of Soil Type, Water Content, and Density Using Electromagnetics

Drnevich¹,

Lin²,

Qin³

et al. 2001

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“…It should also be pointed that the benefits in using this algorithm for recovering weak perturbations are: (i) the formulation makes use of the fact that the network is, by its definition, spatially discrete and not discretized and assembled of lumped elements (unlike [7,8]) and consequently there is an associate inherent frequency dispersion that is accommodated in the inversion; (ii) it renders the inversion, simply, of a direct inverse Fourier transform type without any iterative procedure as in other techniques (see e.g., [7,8,10,14,16]), and without any need for an a-priori knowledge of the size of the network (number of ZY sections); (iii) it recovers the perturbations in both the parallel and series elements (inductance and capacitance and vice versa) over a known background (unlike [15,16]) and for all sections of the network; and (iv) the proposed algorithm can be used for both LC and CL networks without any differences. Recalling that CL networks as propagation environments are interesting in connection with metamaterials where the presented algorithms is among the first to suggests imaging in such structures/networks.…”

Section: Discussionmentioning

confidence: 99%

“…Inversion in discrete types of structures, where cascaded continuos TL sections of finite length are set consecutively is one aspect of discrete inversion (see in [7,8]). Discrete inversion is also applicable to continuous medium that is spatially discretized or, alternatively, in which the spatial domain is set as a grid of lattice points.…”

Section: Introductionmentioning

confidence: 99%

Ultra Wideband Wave-Based Linear Inversion in Lossless Ladder Networks

Shlivinski¹

2012

PIER

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Abstract-A wave-based inversion algorithm for the recovery of deviation in the values of elements of discrete lossless inductancecapacitance and capacitance-inductance ladder networks from their nominal values is formulated. The algorithm uses ultra wideband source excitation over the frequency range where forward and backward voltage and current waves propagate along the network. Employing a weak type scattering formulation renders the voltage wave reflection coefficient to be a Z transform of the sequence of perturbation in the value of the elements. Inversion of the reflected date from the transformed domain to the spatial domain by Fourier type integration yields the element's perturbations and consequently, the actual elements of the network. Demonstrations of the algorithm performance on several test cases show its efficacy as a non-destructive testing tool.

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“…One-dimensional inversion methods can be divided into two categories [1]. The first category includes all direct inversion methods such as the layer stripping method [2]- [4]. The second comprises the so-called model-based inversion methods.…”

Section: Introductionmentioning

confidence: 99%

Application of the multilevel single-linkage method to one-dimensional electromagnetic inverse scattering problem

Nakhkash

Huang

Fang

1999

IEEE Trans. Antennas Propagat.

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An inverse scattering method for the reconstruction of the permittivity and conductivity profiles of a multilayered medium and for that of the impedance profile of a nonuniform transmission line is proposed. The inversion is based on the global minimization of an objective function by the multilevel single-linkage method. The objective function is defined as the mean-square error between the measured data and the data obtained from the solution of the forward problem. An exact formulation for the gradient of the objective function in closed form is derived. The necessary condition for the unique solution of the inverse problem of a nonuniform transmission line is discussed. Reconstruction examples using both experimental and noisy synthetic data are presented.

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Forward and inverse scattering for discrete layered lossy and absorbing media

Cited by 22 publications

References 13 publications

Real-Time Determination Of Soil Type, Water Content, and Density Using Electromagnetics

Real-Time Determination Of Soil Type, Water Content, and Density Using Electromagnetics

Ultra Wideband Wave-Based Linear Inversion in Lossless Ladder Networks

Application of the multilevel single-linkage method to one-dimensional electromagnetic inverse scattering problem

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