Efficient computation of the wavefield in a two media configuration emitted by a GPR system from incident field measurements in the air

For proper imaging and inversion, accurate information on the wavefield that is emitted into the ground is of paramount importance. In case of ground-coupled antennas and without the possibility of time windowing, the wave field in the ground can be best modeled by taking this coupling into account in the model. For air launched antennas, with less ground coupling, or when time windowing is possible, we can obtain the wave field in the ground from wave field extrapolation of the emitted wave field, which is recorded in a certain plane in free space. It is shown that in two media configuration, with homogenous layers, only the down going wave field in the upper half space below the antennas, contributed to the down going wave field in the lower half space. This is generally true for laterally homogenous media. The present state of the art in three-dimensional multi-component GPR imaging is to use analytic expression for Green's functions in canonical configurations that do not sufficiently match the real background. The reason is that full computation of the Sommerfeld-type integrals, which have to be solved for each image plane, are too time consuming for imaging GPR data within reasonable time. We show that approximations to the correct two-media Green's functions leads to a more accurate resolution function than exact formulations of the approximate Green's functions of a single homogenous medium. To achieve this, we use a wave field extrapolation method honoring the spectral bandwidth of the data to be imaged.