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

Abstract

ABSTRACTThe 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 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 m/ns (+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.