Proposing New Methods to Enhance the Low-Resolution Simulated GPR Responses in the Frequency and Wavelet Domains

To date, a number of numerical methods, including the popular Finite-Difference Time Domain (FDTD) technique, have been proposed to simulate Ground-Penetrating Radar (GPR) responses. Despite having a number of advantages, the finite-difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the forward modelling process to be very long lasting, even with modern high-speed computers. In the present study the well-known hyperbolic pattern response of horizontal cylinders, usually found in GPR B-Scan images, is used as a basic model to examine the possibility of reducing the forward modelling execution time. In general, the simulated GPR traces of common reflected objects are time shifted, as with the Normal Moveout (NMO) traces encountered in seismic reflection responses. This suggests the application of Fourier transform to the GPR traces, employing the time-shifting property of the transformation to interpolate the traces between the adjusted traces in the frequency domain (FD). Therefore, in the present study two post-processing algorithms have been adopted to increase the speed of forward modelling while maintaining the required precision. The first approach is based on linear interpolation in the Fourier domain, resulting in increasing lateral trace-to-trace interval of appropriate sampling frequency of the signal, preventing any aliasing. In the second approach, a super-resolution algorithm based on 2D-wavelet transform is developed to increase both vertical and horizontal resolution of the GPR B-Scan images through preserving scale and shape of hidden hyperbola features. Through comparing outputs from both methods with the corresponding actual high-resolution forward response, it is shown that both approaches can perform satisfactorily, although the wavelet-based approach outperforms the frequency-domain approach noticeably, both in amplitude and shape of the outputted hyperbola response.

Keywords:

forward modelling , fourier transform , Ground-Penetrating Radar (GPR) , high resolution , wavelet transform