# Fusing Ground-Penetrating Radar Images for Improving Image Characteristics Fidelity
## 3 GPR Principles  
Ground-Penetrating Radar is one of the geophysical methods that revolutionized subsurface exploration. GPR provides high-resolution imaging without any destruction of the target. It is widely used in Archaeology [26], Civil Engineering, Environmental assessment [27], and geology [28]. GPR operates on the concept of the propagation of electromagnetic waves. It sends electromagnetic energy from the surface to the ground in short pulses. These pulses reflect on the surface when they meet the subsurface items of several dielectric elements. Whenever these reflections return, the instrument measures the time taken and the distance and depth to where they reach underground objects. Afterward, the GPR data are processed by means of a complex algorithm as a two- or three-dimensional image. A plane of the EM wave is spread in a rectangular direction to the plane of the oscillation address of both the electric and magnetic fields: \(\mathbf{E}\times\mathbf{H}\). The propagation equation in the frequency field is given by  
\[\frac{\partial^{2}\mathbf{E}}{\partial x^{2}}=i\omega\mu\sigma\mathbf{E}-\omega^{2}\mu \epsilon\mathbf{E} \tag{1}\]  
How effective and how clear GPR data is depends on how the radar waves interact with subsurface materials. This interaction is affected by many key factors, such as diffusion, propagation speed, resistance properties, and dielectric properties. The radar energy is propagated as it travels through the medium, is affected by the electrical conductivity of the ground, and is described by the scattering effect. Propagation refers to the way radar waves travel through a medium, with the speed affected by the material's dielectric properties. The specific conductivity \(i\omega\mu\sigma\), or in other words, the ability of the ground to conduct electricity, affects how quickly the radar signal decays as it travels through the ground. Ground composition with highly conductive materials means that the signal will fade quickly, making it harder for the radar waves to penetrate deeper [29]. In addition, the dielectric constant affects the polarization of the ground by radar waves. Materials that have a high dielectric constant \(\omega^{2}\mu\epsilon\) slow down the radar waves and can provide more detailed images, but they can also cause more signal attenuation. Finally, the wave number is one of the most critical parameters, as it combines the speed of the wave and its attenuation. It is a measure of understanding how fast and how far waves can travel in a particular medium. The wavenumber is affected by both the dielectric constant and the conductivity of the soil and is defined as  
\[k=\sqrt{i\omega\mu\sigma-\omega^{2}\mu\epsilon} \tag{2}\]  
The radar, through the electromagnetic waves reflected by the electromagnetic fields, allows the GPR antenna to detect the structure and composition of the subsoil, as well as to detect changes in its physical parameters. This happens as the interaction between materials and electromagnetic fields causes reflections, which in turn affect the way the field propagates through the medium. This energy returns to the subsurface when coming across similarly sized, localized features, such as objects or boundaries. Objects generate secondary fields that scatter outwards, serving as masks that are energy absorbers or shadow-casters. GPR instruments have numerous performance requirements but must react promptly to signal travel times, whereas others, like airborne and surveillance radars, require reaction times of minutes to hours. Other essential elements of GPR measurements include time delays and bandwidth. Transmitter electronics send signals to excite the environment through a transmitting antenna, and a receiving antenna measures and translates the transmitted fields into electrical signals. The response in GPR data is artifice by the conical shape of the transmitted signal: both forward and transmitted energy traveled reappears toward the group line.