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A B S T R A C TThe conventional reverse time migration of ground-penetrating radar data is implemented with the two-way wave equation. The cross-correlation result contains low-frequency noise and false images caused by improper wave paths. To eliminate low-frequency noise and improve the quality of the migration image, we propose to separate the left-up-going, left-down-going, right-up-going and right-down-going wavefield components in the forward-and backward-propagated wavefields based on the Hilbert transform. By applying the reverse time migration of ground-penetrating radar data with full wavefield decomposition based on the Hilbert transform, we obtain the reverse time migration images of different wavefield components and combine correct imaging conditions to generate complete migration images. The proposed method is tested on the synthetic ground-penetrating radar data of a tiltinterface model and a complex model. The migration results show that the imaging condition of different wavefield components can highlight the desired structures. We further discuss the reasons for incomplete images by reverse time migration with partial wavefields. Compared with the conventional reverse time migration methods for ground-penetrating radar data, low-frequency noise can be eliminated in images generated by the reverse time migration method with full wavefield decomposition based on the Hilbert transform.

Electrical resistivity tomography employs L 2 norm regularization in many applications. We developed the boundary-sharping inversion method based on the finite element methods and irregular grid approach, in which the contact areas of elements are used to weight the model parameters. Similar approaches have previously only been used for structured grids. We also designed an electrical resistivity tomography system in the laboratory to conduct experimental data tests. Focusing on the imaging of small-scale targets, we further compared the behaviour of various regularization schemes, including L 2 , L 1 and L 0 norm stabilizers. Different control parameters were tested and analysed for approximated L 1 and L 0 norm stabilizers. Three-dimensional conductivity models were reconstructed from synthetic and experimental data. We found that reconstructed images obtained from smooth sparse regularization, such as L 1 , and L 0 norm regularization are superior to L 2 norm regularization for highcontrast aquifer and block models. The synthetic and experimental data show that electrical resistivity tomography with smooth sparse regularization has the potential to improve the imaging of small-scale targets with sharp contours.