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Wideband electromagnetic scattering from multiple objects partially buried beneath rough earth soil surfaces is an important topic during recent years due to its extensive applications in several fields, such as ground remote sensing, ground penetrating radar applications, and target identification. Due to the advantages of finite-difference time-domain (FDTD) method in calculating the wideband electromagnetic scattering from rough surface in the presence of multiple objects, the FDTD method under ultrawideband (UWB) Gaussian pulse wave incidence is utilized in the present study for analyzing the frequency response of rough soil surfaces with periodically distributed multiple rectangular cross-section columns buried partially. In this paper, the dielectric property of the actual land surface is expressed using the four-component model, and the actual rough land surface is simulated utilizing Monte Carlo method with exponential correlation function. The emphasis of the present study is on analyzing the wideband response signatures of composite backscattering coefficient varying with frequency on the basis of extensive numerical simulations, in particular for calculating and discussing in detail the influence of the root-mean-square height and the correlation length of rough soil surface, soil moisture, the length and the width of the rectangular cross-section column, separation distance, burial depth, and tilt angle on the composite backscattering coefficient.

During recent years, more and more attentions are paid to the electromagnetic (EM) wave scattering from rough surface and composite scattering from rough surface with target because of their spread application [

As a numerical method, FDTD can calculate the electromagnetic scattering problems under pulse wave and has superiority of the time-domain numerical algorithm [

In the present study, the actual rough soil surface

Geometry of composite scattering from the rough soil surface and partially buried periodic distributed rectangular cross-section columns.

Suppose that the upper of the coordinate axis

As shown in Figure

FDTD computation in the composite scattering model from the rough surface and partially buried periodic distributed rectangular cross-section columns.

The actual rough land surface is modeled as realizations of a Gaussian random process with exponential correlation function by using Monte Carlo method [

The power spectral density of exponential correlation rough surface is expressed as [

The rough soil surface is simulated by Monte Carlo method, and 1D rough surface realization with length

The dielectric constant of the soil is mainly affected by the incident frequency

Maxwell’s equations are a set of basic equations that govern the macroscopic electromagnetic phenomena. For two-dimensional electromagnetic scattering problems, rectangular components of the electromagnetic field may be classified as independent groups, namely, TM wave and TE wave. In TM wave, as an example, FDTD difference equation has the following form [

FDTD calculation is only in a limited area. Thus, it is necessary to set absorbing boundary in truncated boundary for open domain electromagnetic scattering problem. Anisotropic perfectly matched layer (UPML) absorbing boundary is selected in this work. FDTD iteration order of UPML layers is

Near-field scattering data is obtained by the FDTD calculation. Each time field value on the boundary is recorded, and the far-zone scattered field time response is obtained using extrapolation methods of transient pulse source excitation. Then, the frequency response of scattering coefficient is obtained through substituting the scattering coefficient formula by the Fourier transform.

In this work, the Gaussian pulse electromagnetic wave is given by [

In the following calculations, the emphasis is put on the back composite scattering coefficient which varies with frequency. It should be noted that the incident wave is Gaussian pulse electromagnetic wave of TM polarization, the width of grid is

In order to obtain the characteristics of composite wideband electromagnetic scattering from the rough soil surface with partially buried periodic distributed rectangular cross-section columns, the curves of back composite scattering coefficient which varies with frequency are studied by numerical calculation under different parameters of rough surface and column. In the following, the numerical simulations are performed on the computer with two 2.60 GHz processors (Intel Xeon E5-2650), 16 GB Memory, Microsoft Windows 7 operation system, and the Fortran PowerStation 4.0 compiler. Under the configuration, the computational time and memory size for one realization are approximately 33 min and 47 MB, respectively.

Figure

The influence of

To examine the scattering coefficient difference between single column case and multiple columns case, a comparison of single column case and multiple columns case is made in Figure

A comparison of single column case and multiple columns case.

In Figure

The influence of

The distribution of

The influence of

Figure

The influence of

Figure

The influence of

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The influence of

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The influence of

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The influence of

Hereinbefore, the results from Figures

In this paper, the problems of composite wideband electromagnetic scattering from exponential correlation rough soil surface with partially buried periodic distributed rectangular cross-section columns under Gaussian pulse wave irradiation are investigated using transient FDTD. The influence of the root-mean-square and the correlation length of rough surface fluctuation, soil moisture, the length and the width of the rectangular cross-section column, separation distance, burial depth, and tilt angle on the composite scattering signatures are discussed in detail. The numerical simulations indicate that the variation of composite scattering coefficient versus frequency is oscillatory. It is also showed that the composite scattering coefficient versus frequency increases with the increase of root-mean-square of soil surface, water ratio of soil, the target section height, and the separation distance of target. However, simulation results indicate that the composite scattering coefficient versus frequency decreases with the increase of target section width. In summary, the variation of wideband scattering coefficient is very complicated and is very sensitive to incidence angle of electromagnetic wave. However, the wideband scattering coefficient under Gaussian pulse wave incidence is less sensitive to the correlation length of rough soil surface, the depth of buried objects, and the dielectric constant of target. Although the multiple columns partially buried in a randomly rough surface are a rather simplified model, the present study is potentially valuable for many applications, such as ground remote sensing, ground penetrating radar applications, underground mine detection, tunnel detection, and target identification. In particular, the simplified model of periodically distributed columns represents many realistic objects, such as tree trunks, mine props, telegraph poles. The future investigation on this topic will include electromagnetic scattering from two-dimensional rough land surface with complex multiple targets.

The authors declare that they have no conflicts of interest.

This work was supported in part by the National Natural Science Foundation of China (Grant no. 61379026), in part by the National Science Foundation for Young Scientists of China (Grant no. 61701428), in part by the foundation of construction of high-level university project in Shaanxi Province (Grant no. 2015SXTS02), in part by the open foundation of Fudan University Key Laboratory for Information Science of Electromagnetic Waves (Grant no. EMW201502), in part by the Scientific Research Foundation of Yanan University (Grant nos. YDBK2016-17 and YDY2017-06), and in part by the Natural Science Basic Research Plan in Shaanxi Province of China (Grant no. 2014JM-6113).