GPR modelling by the Fourier method: improvement of the algorithm

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