Semblance response to a ground-penetrating radar wavelet and resulting errors in velocity analysis

The propagation velocity of a ground-penetrating radar (GPR) wavelet may be used to derive physical subsurface properties, including layer thickness, porosity and water content. We describe a systematic error in semblance analysis of GPR common-midpoint (CMP) data, arising from the response of the statistic to the waveform of the GPR pulse. Only the first-breaks of GPR wavelets express true velocities and traveltimes but these cannot deliver a semblance response since they have zero amplitude; instead, this response derives from subsequent wavelet half-cycles, delayed from the first-break. This delay causes semblance picks to express slower velocity and later traveltime with respect to true quantities, even for simple cases of reflectivity. For a two-layer synthetic CMP data set, in which the GPR source pulse via a 500 MHz Berlage wavelet, semblance picks underestimate interval velocities of 0.135 m/ns and 0.060 m/ns by 10.0% and 2.0%, respectively. Velocity biases are corrected using the coherence statistic to simulate first-break traveltimes from a set of velocity picks, in a process termed 'backshifting'. A t(2)-x(2) linear regression of simulated first-breaks yields smaller errors in the same interval velocities of 2.2% and -1.0%. A first real-data example considers a reflection from the base of a 3.39 m thick air-gap. Semblance analysis estimates the air-wave velocity as 0.289 m/ns (-3.6% error) and the air-gap thickness as 3.59 m (+6.1% error); backshifting yields equivalent estimates of 0.302 mins (+0.9% error) and 3.35 m (-1.2% error). In a second example, semblance- and backshifting-derived velocity models overestimate the thickness of clay-rich archaeological deposits by 19.0% and 3.1%, respectively. Backshifting is a simple modification to conventional practice and is recommended for any analysis where physical subsurface properties are to be derived from the output GPR velocity.