Frequency-Domain Wideband Ground Penetrating Radar Modelling
using Finite Elements and Perfectly Matched Layers
C.D. Singh (TU Delft - Civil Engineering & Geosciences)
P. Rulff – Mentor (TU Delft - Applied Geophysics and Petrophysics)
E.C. Slob – Mentor (TU Delft - Applied Geophysics and Petrophysics)
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Abstract
In wideband Ground Penetrating Radar (GPR) forward modelling, a choice can be made between time and frequency domains. With time-domain approach, efficient modelling and testing with real-world cases has been done, especially through gprMax. With frequencydomain approach, however, this level of applicability has not been reached. To take a step in this direction, a 3D wideband-capable GPR forward simulation code has been developed. A wealth of efficient discretization, modelling and inversion strategies exist that exploit the nuances of frequency-domain simulations to enable rapid solutions, that a time-domain approach is inherently not capable of using. Hence, the simulation code developed in this thesis, named elfe3D GPR, aims to provide the means to implement and test these strategies as efficiently as possible. The development of this code is based on another open-source software, elfe3D, which is a 3D electromagnetic fields forward solver using edge-based finite elements developed for Controlled-Source Electromagnetism (CSEM) in Fortran. Its use of the MUMPS direct solver and adaptive refinement makes elfe3D a very strong starting point for the development of GPR simulation. Since CSEM solves for diffusive-field regime of electromagnetism, a few essential changes have been made in the boundary-value problem that elfe3D GPR solves. Since the region of interest in GPR simulations is finite due to physical and computational constraints and due to the wave nature of GPR fields, appropriate absorbing boundary has also been implemented in elfe3D GPR by the means of Perfectly Matched Layers (PML). The specific formulation of PML chosen is a Uniaxial-PML with an exact decay function, due to their excellent absorption performance of outgoing waves. Once these changes were implemented in elfe3D, the new simulation code elfe3D GPR has been extensively tested for synthetic layered and anomalous subsurface models, along with its potential for wide-band simulations. Validation has been performed against analytical solution for layered models, and the results from empymod. The results show promising applicability of elfe3D GPR for generalized GPR forward problems, and should serve as a good basis for implementing the many frequency-domain specific modelling and inversion strategies that exist. As such, elfe3D GPR is kept open-source.