Adaptation of prestack migration to multi‐offset ground‐penetrating radar (GPR) data

In adapting the prestack migration technique used in seismic imaging to the inversion of ground-penetrating radar (GPR) from time- to depth-sections, we show that the theoretical integral formulation of the inversion can be applied to electromagnetic problems, albeit with three assumptions. The first two assumptions concern the electromagnetic characteristics of the medium, primarily that the medium must be perfectly resistive and non-dispersive, and the third concerns the antennae radiation pattern, which is taken to be 2D. The application of this adaptation of the inversion method is confirmed by migrating actual GPR measurements acquired on the test site of the Laboratoire Central des Ponts et Chaussees. The results show good agreement with the geometry of the structures in the medium and confirm that the possible departure from the assumption of a purely resistive medium has no visible effect on the information concerning the geometry of scattering and reflecting structures. The field experiments also show that prestack migration processing is sufficiently robust with regard to the assumption of a non-dispersive medium. The assumption of a 2D antennae radiation pattern, however, produces artefacts that could be significant for laterally heterogeneous media. Nevertheless, where the medium is not highly laterally heterogeneous, the migration gives a clear image of the scattering potential due to the geometry of structural contrasts in the medium; the scatterers are well focused from diffraction hyperbolae and well localized. Spatial geometry has limited dimensional accuracy and positions are located with a maximum error equal to the minimum wavelength of the signal bandpass. Objects smaller than one wavelength can nevertheless be detected and well focused if their dielectric contrasts are sufficiently high, as in the case of iron or water in gneiss gravels. Furthermore, the suitability of multi-offset protocols to estimate the electromagnetic propagating velocity and to decrease the non-coherent noise level of measurements is confirmed. Our velocity estimation is based on the semblance calculation of multi-offset migrated images, and we confirmed the relevance of this quantification method using numerical data. The signal-to-noise ratio is improved by summing multi-offset results after the addition of random noise on measurements. Thus the adaptation of prestack migration to multi-offset radar measurements significantly improves the resolution of the scattering potential of the medium. Limitations associated with the methods used here suggest that 3D algorithms should be applied to strongly laterally heterogeneous media and further studies concerning the waveform inversion are necessary to obtain information about the electric nature of the medium.