GPR modelling by the Fourier method: improvement of the algorithm

We improve two aspects of the modelling scheme for the simulation of electromagnetic radio waves, based on the Fourier pseudospectral method.
When there are large contrasts in the material properties, use of the standard algorithm (regular grid) causes a series of artefacts, as, for instance, ringing and acausal events. These problems, due to the non-locality of the differential operator, are solved by using the staggered Fourier method (staggered grid).
Realistic radiation patterns can be obtained from simple combinations of magnetic and electric sources. If the directivity pattern of the antenna is known, from either a finite-difference simulation or an analytic evaluation or an experimental characterization, it can then be simulated by a composite-source concept. This effective source is implemented in the modelling algorithm by means of a perturbation technique, which first computes the intensity and directional spectra of the single electromagnetic sources. Their location is optimized to obtain the best fit with a minimum number of sources. The approach is, in principle, valid for the far-field radiation pattern of the antenna.