Improving Ground Penetrating Radar (GPR) forward modeling approach using the numerical finite difference method

The behaviour of Ground Penetrating Radar (GPR) electromagnetic field can be simulated using Maxwell’s equations and associated boundary conditions. So far a number of numerical methods for modeling GPR data have been proposed including the popular Time Domain Finite Difference (TDFD) technique. The popularity of TDFD is mainly due to being relatively simple to implement، its high flexibility and capability to simulate complex subsurface geology. Also، the TDFD approach is not only conceptually accurate for complex geological models but also enables us to design realistic antenna and to study physical electromagnetic phenomena such as dispersion in electrical properties. Despite having these advantages، the finite difference method has pitfalls such as becoming very time consuming in simulating the most common media especially with high dielectric permittivity causing the forward modeling process to become very time consuming even by modern high-speed computers. Synthetic GPR responses are useful for predicting expected GPR data over known geometries such as horizontal cylinders and prisms. The GPR data and subsurface lithological and hydrogeological properties are related through a numerical forward modeling engine. Therefore، the GPR forward modeling engine can transform the subsurface electrical properties into expected GPR responses which in turn can be used for optimizing data acquisition procedures on pre-defined subsurface targets. Since any efficient inversion routine requires a fast forward modeling engine، this study aimed the development of a fast forward modeling algorithm capable of being implemented in any inversion routine. To have efficient numerical forward modeling algorithm، we have adapted a leap-frog، staggered-grid approach introduced by Yee، which incorporates offsetting the electric and magnetic field components in both space and time in such a way that the finite difference approximations of the governing partial derivatives in each equation are centered on the same spatiotemporal location. Obviously 2-D modeling is limited and cannot fully account for antenna behaviour and out-of-plane variations in material properties; however، many important features common to most GPR responses can be identified via employing a computationally cost effective 2D algorithm. In the current study، the patterns of GPR responses that are well known to be hyperbola in shape are used as leading models in order to reduce the execution time. A GPR system collects the reflected pulses coming from different depths in the form of traces which when gathered along with a profile، they make a GPR section called radargram. In general، the simulated GPR traces of common reflected objects are time shifted like the Normal MoveOut (NMO) traces encountered in seismic reflection responses. This property suggests the application of Fourier transform to the GPR traces and the use of time shifting property of such transformation to interpolate traces between the adjusted traces in frequency domain. Therefore، the lateral resolution of GPR traces computed along with any profile is enhanced using a linear interpolation in the Fourier domain resulting in an increased speed of the forward modeling algorithm. Selecting the minimum lateral trace to trace interval with the appropriate sampling frequency of the signal، prevent any aliasing to occur. It is shown that such methodology can significantly decrease the computing time by more than 12. 5 times.