 |
| |
|
The whole point of numerical modelling is the ability to undertake conceptual design without the need to build and test. The aim is minimisation of development cost and time and the maximisation of system performance. Computational modelling can provide these benefits.
The FDTD method, on which our software is based, is the most popular contemporary method for complex EM analysis tasks. Indeed it is one of very few techniques that can provide solutions for wideband analysis of regions containing inhomogeneous dispersive dielectrics.
Its application in GPR studies comes about from the development of numerical techniques which are able to incorporate both the structure of potentially complex antenna systems together with the frequency dependant and spatially varying material characteristics of the soil within the calculation domain.
Some examples are given in subsequent pages to illustrate the type of study that can be undertaken. In these examples some illustrations are provided that have been produced with the geometry editor of the Celia software. The antennas are rudimentary in nature and present no problem in terms of construction. The difficulty involved in this work is the incorporation of the appropriate material characteristics within the domain, and applying suitable radiation boundary conditions (RBC) to enable a transmissive boundary within the soil medium.
The application of a transmissive boundary condition is a non-trivial task, firstly because the soil has frequency dependent properties and secondly because the return signals are small in magnitude and will be swamped by boundary reflections. The best boundary condition for this work is the perfectly matched layer (PML) RBC. All other types rely on a knowledge of the wave speed to compute the expected scattered wave component arriving at the domain boundary. This is not well defined in a dispersive medium for a time domain solution. The PML method applies a region of matched absorber on the boundary. In this way the characteristics of the PML absorbing layer can be matched with any material, even dispersive materials, to give an effective, low reflection coefficient boundary. This method has been implemented within the Celia software.
Dispersive material characteristics have been incorporated into the Celia code in the form of Debye and Lorentz dispersions applied using the recursive convolution (RC) method of Luebbers[?]. This is a popular method due to its simplicity, and while regarded as less accurate than later formulations, for example the piecewise linear recursive convolution (PLRC), it has been shown (Fan and Liu[?]) that the use of central differencing in its implementation can substantially improve the accuracy of the method.