Split-step Fourier migration of GPR data in lossy media

Migration of ground-penetrating radar (GPR) data traditionally has been implemented assuming uniform, nonconductive, and nondispersive media. However, in many real applications, the effects of heterogeneities, conductivity, or dispersion can be important, so it is necessary to consider these effects to image the data correctly. We implement the split-step Fourier technique for migration of GPR data in 2D media transverse-electric (TE) or transverse-magnetic (TM) propagation modes and demonstrate how it takes into account, naturally and efficiently, the effects of dispersion, attenuation, and heterogeneities. Compensation for attenuation during migration implies applying a gain that can make the numerical algorithm unstable. We introduce a homogeneous plane-wave approximation that gives greater stability to the migration technique, allowing a stable and satisfactory migration of the GPR data up to depths equivalent to three times the skin depth computed at the dominant frequency of the radar signal. Multiple slowness references of split-step migration for lossy media are introduced and compared with the single-reference slowness technique. Finally, we propose two limited gain modifications of the migration algorithm and study their usefulness when highly lossy zones are in the media.