Efficient Deconvolution of Ground-Penetrating Radar Data

The time (vertical) resolution enhancement of ground-penetrating radar (GPR) data by deconvolution is a long-standing problem due to the mixed-phase characteristics of the source wavelet. Several approaches have been proposed, which take the mixed-phase nature of the GPR source wavelet into account. However, most of these schemes are usually laborious and/or computationally intensive and have not yet found widespread use. Here, we propose a simple and fast approach to GPR deconvolution that requires only a minimal user input. First, a trace-by-trace minimum-phase (spiking) deconvolution is applied to remove the minimum-phase part of the mixed-phase GPR wavelet. Then, a global phase rotation is applied to maximize the sparseness (kurtosis) of the minimum-phase deconvolved data to correct for phase distortions that remain after the minimum-phase deconvolution. Applications of this scheme to synthetic and field data demonstrate that a significant improvement in image quality can be achieved, leading to deconvolved data that are a closer representation of the underlying reflectivity structure than the input or minimum-phase deconvolved data. Synthetic-data tests indicate that, because of the temporal and spatial correlation inherent in the GPR data due to the frequency-and wavenumber-bandlimited nature of the GPR source wavelet and the reflectivity structure, a significant number of samples are required for a reliable sparseness (kurtosis) estimate and stable phase rotation. This observation calls into question the blithe application of kurtosis-based methods within short time windows such as that for time-variant deconvolution.