Iraklis Giannakis

gprMax: open source software to simulate electromagnetic wave propagation for ground penetrating radar

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.

A Realistic FDTD Numerical Modeling Framework of Ground Penetrating Radar for Landmine Detection

A three-dimensional (3-D) finite-difference time-domain (FDTD) algorithm is used in order to simulate ground penetrating radar (GPR) for landmine detection. Two bowtie GPR transducers are chosen for the simulations and two widely employed antipersonnel (AP) landmines, namely PMA-1 and PMN are used. The validity of the modeled antennas and landmines is tested through a comparison between numerical and laboratory measurements. The modeled AP landmines are buried in a realistically simulated soil. The geometrical characteristics of soils inhomogeneity are modeled using fractal correlated noise, which gives rise to Gaussian semivariograms often encountered in the field. Fractals are also employed in order to simulate the roughness of the soils surface. A frequency-dependent complex electrical permittivity model is used for the dielectric properties of the soil, which relates both the velocity and the attenuation of the electromagnetic waves with the soils bulk density, sand particles density, clay fraction, sand fraction, and volumetric water fraction. Debye functions are employed to simulate this complex electrical permittivity. Background features like vegetation and water puddles are also included in the models and it is shown that they can affect the performance of GPR at frequencies used for landmine detection (0.5-3 GHz). It is envisaged that this modeling framework would be useful as a testbed for developing novel GPR signal processing and interpretations procedures and some preliminary results from using it in such a way are presented.

An advanced GPR modelling framework: The next generation of gprMax

gprMax is a freely-available set of electromagnetic wave simulation tools based on the Finite-Difference Time-Domain (FDTD) numerical method. gprMax was originally written in the mid-1990s and has primarily been used to simulate Ground Penetrating Radar (GPR). 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, significant modernisations have been made to gprMax. 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; uniaxially anisotropic materials; dispersive media using multiple Debye, Drude or Lorenz expressions; improved 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.

A Novel Piecewise Linear Recursive Convolution Approach for Dispersive Media Using the Finite-Difference Time-Domain Method

Two novel methods for implementing recursively the convolution between the electric field and a time dependent electric susceptibility function in the finite-difference time domain (FDTD) method are presented. Both resulting algorithms are straightforward to implement and employ an inclusive susceptibility function which holds as special cases the Lorentz, Debye, and Drude media relaxations. The accuracy of the new proposed algorithms is found to be systematically improved when compared to existing standard piecewise linear recursive convolution (PLRC) approaches, it is conjectured that the reason for this improvement is that the new proposed algorithms do not make any assumptions about the time variation of the polarization density in each time interval; no finite difference or semi-implicit schemes are used for the calculation of the polarization density. The only assumption that these two new methods make is that the first time derivative of the electric field is constant within each FDTD time interval.

Time-Synchronized Convolutional Perfectly Matched Layer for Improved Absorbing Performance in FDTD

A performance-enhancing modification to the convolutional perfectly matched layer (CPML) technique for implementing the complex frequency-shifted perfectly matched layer (CFS-PML) absorbing boundary condition is presented. By adopting this modification, an apparent discrepancy in the time synchronization between the CPML and the main finite-difference time-domain (FDTD) algorithm is resolved. This is achieved by employing a semi-implicit approach that synchronizes CPML with the main FDTD algorithm. It is shown through 2-D and 3-D numerical examples that the suggested modification to the CPML algorithm increases its performance without increasing its computational cost.

Incorporating dispersive electrical properties in FDTD GPR models using a general Cole-Cole dispersion function

A new technique based on a hybrid linear-nonlinear optimization is suggested in order to simulate the Cole-Cole dispersion mechanism using a number of Debye functions. A novel method to implement this multi-Debye medium, based on a recursive integration algorithm is also presented. These new techniques are used to simulate the experimental Cole-Cole parameters for dry and moist sand [20].

Numerical modelling and neural networks for landmine detection using ground penetrating radar

A numerical modelling case study is presented aiming to investigate aspects of the applicability of artificial neural networks (ANN) to the problem of landmine detection using ground penetrating radar (GPR). An essential requirement of ANN and machine learning in general, is an extensive training set. A good training set should include data from as many scenarios as possible. Therefore, a training set consisting of simulated data from a diverse range of models with varying: topography, soil inhomogeneity, landmines, false alarm targets, height of the antenna, depth of the landmines, has been produced and used. Previous approaches, have employed limited training sets and as a result they often have underestimated the capabilities of ANN. In this preliminary study, a 2D Finite-Difference Time-Domain (FDTD) model has been used as the training platform for ANN. Although a 2D approach is clearly a simplification that cannot directly translate to a practical application, it is a computationally efficient approach to examine the performance of ANN subject to an extensive training set. The results are promising and provide a good basis to further expand this approach in the future by employing even more realistic, but computationally expensive, 3D models and well-characterised, real data sets.

Realistic modelling of ground penetrating radar for landmine detection using FDTD

A finite-difference time-domain (FDTD) algorithm is used to model and study the performance of ground penetrating radar (GPR) for anti-personnel (AP) landmine detection. A novel algorithm is proposed which creates the geometry of the vegetation for both grass and roots. Soils inhomogeneities as well as the rough surface are simulated using fractal correlated noise. Debye functions are used in order to simulate the frequency dependent dielectric properties of both the soil and of the vegetation. The antenna unit that has been employed in the model is based on a previously developed detailed antenna model approximating a well known commercial GPR antenna, and the target is the anti-personnel (AP) landmine PMA-1. Surface water puddles have been included into the models and their effects on the performance of GPR are investigated. Simulation results are realistic and provide a useful testbed for evaluating GPR processing approaches for landline detection.

A Method to Detect Displacements of Borehole Electrodes through Electrical Resistivity Tomography

In this work a new geophysical methodology is presented which is able to detect any displacements of buried electrodes that are permanently installed in boreholes. These displacements can seriously affect the quality of the measurements and the subsequent resistivity inversion image. The exact knowledge of the electrode displacements will either help in correcting the electrode coordinates and the geometric factors of the measurements associated with these electrodes or just to reject all corresponding erroneous measurements. During this method pole-pole type measurements are conducted, where the current is injected in every buried electrode in the borehole and the potential is measured on a number of electrodes that are spread out along a line on the ground surface. A finite-difference least-squares non-linear inversion algorithm with damping constraints has been developed in an effort to recover the accurate coordinates of the borehole electrodes. Although a priori resistivity model resulted by a surface ERT or by any other geological and geophysical information can be used to constrain the optimization algorithm it is also shown that that the lack of this knowledge does not affect the resulting electrode positioning. The validity and effectiveness of the approach was tested through synthetic modeling and real data.

Performance of a Ground Penetrating Radar Antenna in Heterogeneous Environments

Understanding how energy is transmitted and received by Ground Penetrating Radar antennas is crucial to many areas of the industry: antenna design, data processing and inversion algorithms, usage of antennas in GPR surveys, and interpretation of GPR responses. The radiation characteristics of antennas are usually investigated by studying the radiation patterns and directivity. For GPR antennas it is important to study these characteristics when the antenna is in environments that would typically be encountered in GPR surveys. Physically measuring antenna radiation patterns in such environments presents many practical difficulties, and there have been very limited numerical studies that combine real GPR antenna models with realistic environments. This paper presents a numerical investigation of the radiation characteristics of a high-frequency GPR antenna in a realistic environment. An advanced modelling toolset has been developed that enables detailed models of GPR antennas to be used with realistic heterogeneous soil models. In this initial investigation small differences in directivity have been observed between a lossless dielectric environment and a more realistic environment featuring a heterogeneous soil model. These findings are part of an on-going full parametric study incorporating a range of different soils, fractal weightings and also the inclusion of rough surface modelling.