**6. Simulation results and discussion**

The operating frequency used in the simulation is 300 MHz, and the free-space wavelength is λ<sup>0</sup> ¼ 1m. The mesh size is approximatively *Δh* ¼ *λ0=40*. The dielectric medium is a rectangular computational domain, the relative permittivity for sandy soil *εrc1* ¼ *4* þ *i0:1*, the relative permittivity for loamy soil *εrc2* ¼ *12* þ *i1:8*, and the relative permittivity for clay soil *<sup>ε</sup>rc3* <sup>¼</sup> *<sup>25</sup>:<sup>3</sup>* <sup>þ</sup> *i5:7*. The angle of incidence is *<sup>0</sup>*o, that is, the incident plane wave travels in the �*y* direction. The wavelength inside the dielectric medium (soil) decreases in terms of the wavelength in free-space and relative permittivity, i.e. *λ* ¼ *λ0=* ffiffiffiffiffi *<sup>ε</sup>rc* <sup>p</sup> , and hence, mesh size *<sup>Δ</sup><sup>h</sup>* <sup>¼</sup> *<sup>λ</sup>0=<sup>40</sup>* resolution corresponds to *λ* ffiffiffiffiffi *εrc* p *=40* resolution inside the dielectric. Therefore, smaller elements are used in dielectric media to preserve the level of accuracy. All simulation results are obtained using MATLAB.

**Figure 5** shows scattering from a dielectric medium for TE mode, with sandy soil characteristics. In (a) and (b), the scattered and total fields are shown respectively. We observe a minimal electric field scattering and an intense total electric field inside the dielectric medium of sandy soil. This is because this medium is porous and allows for better signal propagation.

**Figure 6** shows scattering from a dielectric medium for TM mode, with sandy soil characteristics. In this case, we observe a minimal magnetic field scattering in (a) and an intense total magnetic field in (b) inside the dielectric medium of sandy soil.

**Figure 7** shows scattering from a dielectric medium for TE mode, with loamy soil characteristics. In (a) and (b), the scattered and total fields are shown respectively. We observe an intense electric field scattering and a minimal total electric

**Figure 5.** *Scattering from a dielectric medium (Sandy soil): (a) scattered field (TE) (b) Total field (TE).*

**Figure 6.**

*Scattering from a dielectric medium (Sandy soil): (a) scattered field (TM) (b) Total field (TM).*

*Signal Propagation in Soil Medium: A Two Dimensional Finite Element Procedure DOI: http://dx.doi.org/10.5772/intechopen.99333*

field inside the dielectric medium of loamy soil. This is because this medium is less porous and presents some challenges in signal propagation.

Similarly, **Figure 8** shows scattering from a dielectric medium for TM mode, with loamy soil characteristics. In this case, we observe a high magnetic field scattering in (a) and a low total magnetic field in (b) inside the dielectric medium of loamy soil.

**Figure 9** shows scattering from a dielectric medium for TE mode, with clay soil characteristics. In (a) and (b), the scattered and total fields are shown respectively. We observe very high electric field scattering and a low total electric field inside the dielectric medium of clay soil. This is because this medium is non-porous and presents a very poor signal propagation.

Similarly, **Figure 10** shows scattering from a dielectric medium for TM mode, with clay soil characteristics. In this case, we observe a very high magnetic field

**Figure 7.**

*Scattering from a dielectric medium (loamy soil): (a) scattered field (TE) (b) Total field (TE).*

**Figure 8.**

*Scattering from a dielectric medium (loamy soil): (a) scattered field (TM) (b) Total field (TM).*

**Figure 9.**

*Scattering from a dielectric medium (clay soil): (a) scattered field (TE) (b) Total field (TE).*

scattering in (a) and a low total magnetic field in (b) inside the dielectric medium of clay soil.

**Figures 11**–**13** show the bistatic RCS profiles to describe how scatterers reflect the incident electromagnetic wave in a given direction. This is the area intercepting

**Figure 10.**

*Scattering from a dielectric medium (clay soil): (a) scattered field (TM) (b) Total field (TM).*

**Figure 11.** *Radar cross section in Sandy soil for (a) TE mode and (b) TM mode.*

**Figure 12.** *Radar cross section in loam soil for (a) TE mode and (b) TM mode.*

*Signal Propagation in Soil Medium: A Two Dimensional Finite Element Procedure DOI: http://dx.doi.org/10.5772/intechopen.99333*

**Figure 13.** *Radar cross section in clay soil for (a) TE mode and (b) TM mode.*

that amount of power which, when scattered in the soil medium, produces at the receiver a density which is equal to that scattered by the actual target. The RCS is a function of several parameters, such as operation frequency, polarization, illumination angle, observation angle, geometry, and properties of the soil medium. It is shown in the TE modes (a) and TM modes (b) for sandy soil, loamy soil, and clay soil, respectively.

### **7. Conclusion**

In a two-Dimensional Finite Element Analysis of EM wave Propagation through the soil, a boundary value problem (BVP) used to solve the time-harmonic electromagnetic problem in 2-D, has been expressed in its generic form. In TM and TE cases, the Helmholtz model has considered an infinitely large dielectric object of an arbitrary cross-section for scattering from a dielectric medium and illuminated by an incident wave. Since the domain extends to infinity, an artificial boundary, an absorbing boundary condition (ABC), or a perfectly matched layer (PML), has been used to truncate the computational domain. The incident field, the scattered field, and the total field in terms of the z-component are expressed for the TM and TE modes. The radar cross-section (RCS), a function of several parameters, such as operation frequency, polarization, illumination angle, observation angle, geometry, and material properties of the medium, has been computed to describe how a scatterer reflects an incident electromagnetic wave in a given direction. Simulation results for the scattered field, the total field, have been presented for soil types, and the radar cross-section for different element refinements have also been presented.

*Recent Topics in Electromagnetic Compatibility*
