GprMax is open source software that simulates electromagnetic wave propagation, using the Finite-Difference Time-Domain (FDTD) method, for the numerical modelling of Ground Penetrating Radar (GPR). gprMax was originally developed in 1996 when numerical modelling using the FDTD method and, in general, the numerical modelling of GPR were in their infancy. Current computing resources offer the opportunity to build detailed and complex FDTD models of GPR to an extent that was not previously possible. To enable these types of simulations to be more easily realised, and also to facilitate the addition of more advanced features, gprMax has been redeveloped and significantly modernised. The original C-based code has been completely rewritten using a combination of Python and Cython programming languages. Standard and robust file formats have been chosen for geometry and field output files. New advanced modelling features have been added including: an unsplit implementation of higher order Perfectly Matched Layers (PMLs) using a recursive integration approach; diagonally anisotropic materials; dispersive media using multi-pole Debye, Drude or Lorenz expressions; soil modelling using a semi-empirical formulation for dielectric properties and fractals for geometric characteristics; rough surface generation; and the ability to embed complex transducers and targets.Program summaryProgram title: gprMaxCatalogue identifier: AFBG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 627180No. of bytes in distributed program, including test data, etc.: 26762280Distribution format: tar.gzProgramming language: Python.Computer: Any computer with a Python interpreter and a C compiler.Operating system: Microsoft Windows, Mac OS X, and Linux.RAM: Problem dependentClassification: 10.External routines: Cython[1], h5py[2], matplotlib[3], NumPy[4], mpi4py[5]Nature of problem: Classical electrodynamicsSolution method: Finite-Difference Time-Domain (FDTD)Running time: Problem dependentReferences:[1]Cython, http://www.cython.org[2]h5py, http://www.h5py.org[3]matplotlib, http://www.matplotlib.org[4]NumPy, http://www.numpy.org[5]mpi4py, http://mpi4py.scipy.or

Very few researchers have developed numerical models of ground-penetrating radar (GPR) that include realistic descriptions of both the antennas and the subsurface. This is essential to be able to accurately predict responses from near-surface, near-field targets. We have developed a detailed 3D finite-difference time-domain models of two commercial GPR antennas — a Geophysical Survey Systems, Inc. (GSSI) 1.5-GHz antenna and a MALÅ Geoscience 1.2-GHz antenna — using simple analyses of the geometries and the main components of the antennas. Values for unknown parameters in the antenna models (due to commercial sensitivity) were estimated by using Taguchi’s optimization method, resulting in a good match between the real and modeled crosstalk responses in free space. Validation using a series of oil-in-water emulsions to simulate the electrical properties of real materials demonstrated that it was essential to accurately model the permittivity and dispersive conductivity. When accurate descriptions of the emulsions were combined with the antenna models, the simulated responses showed very good agreement with real data. This provides confidence for use of the antenna models in more advanced studies.

The simulation, or forward modeling, of ground penetrating radar (GPR) is becoming a more frequently used approach to facilitate the interpretation of complex real GPR data, and as an essential component of full-waveform inversion (FWI). However, general full-wave 3-D electromagnetic (EM) solvers, such as the ones based on the finite-difference time-domain (FDTD) method, are still computationally demanding for simulating realistic GPR problems. We have developed a novel near-real-time, forward modeling approach for GPR that is based on a machine learning (ML) architecture. The ML framework uses an innovative training method that combines a predictive principal component analysis technique, a detailed model of the GPR transducer, and a large data set of modeled GPR responses from our FDTD simulation software. The ML-based forward solver is parameterized for a specific GPR application, but the framework can be applied to many different classes of GPR problems. To demonstrate the novelty and computational efficiency of our ML-based GPR forward solver, we used it to carry out FWI for a common infrastructure assessment application--determining the location and diameter of reinforcement bars in concrete. We tested our FWI with synthetic and real data and found a good level of accuracy in determining the rebar location, size, and surrounding material properties from both data sets. The combination of the near-real-time computation, which is orders of magnitude less than what is achievable by traditional full-wave 3-D EM solvers, and the accuracy of our ML-based forward model is a significant step toward commercially viable applications of FWI of GPR.

In finite-difference time-domain (FDTD) modeling of elastic waves, absorbing boundary conditions are used to mitigate undesired reflections that can arise at the model's truncation boundaries. The perfectly matched layer (PML) is generally considered to be the best available absorbing boundary condition. An important but rarely addressed limitation of current PML implementations is that their performance is severely reduced when waves are incident on the PML interface at near-grazing angles. In addition, very low frequency waves as well as evanescent waves could cause spurious reflections at the PML interface. In electromagnetic modeling, similar problems are circumvented by using a complex frequency-shifted stretching function in the PML formulas. However, in elastic-wave modeling using the conventional PML formulation — based on splitting the velocityand stressfields — it is difficult to adopt a complex frequency-shifted stretching function. We present an alternative implemen-tation of a PML that is based on recursive integration and does not require splitting of the velocity and stress fields. Modeling re-sults show that the performance of our implementation using a standard stretching function is identical to that of the convention-al split-field PML. Then we show that the new PML can be modi-fied easily to include the complex frequency-shifted stretching function. Results of models with an elongated domain show that this modification can substantially improve the performance of the PML boundary condition. An efficient implementation of the new PML requires less memory than the conventional split-field PML, and, therefore, is a very attractive alternative to the con-ventional PML. By adopting the complex frequency-shifted stretching function, the PML can accommodate a wide variety of model problems, and hence it is more generic.