Influences on the resolution of GPR velocity analyses and a Monte Carlo simulation for establishing velocity precision
The precision of ground-penetrating radar velocity models is seldom reported, despite their common use for quantifying subsurface properties. We explore influences on the resolution of ground-penetrating radar velocity analysis and demonstrate a Monte Carlo method for obtaining the implied precision in velocity estimates. A series of synthetic common-midpoint gathers, which assume Ricker wavelets of 50 MHz, 100 MHz and 200 MHz frequencies as source pulses, simulate hyperbolic reflections from the bases of three horizontal layers, each with interval velocity and thickness of 0.1 m/ns and 2 m, respectively. With these, we use coherence analysis to show that the principal influence on stacking velocity (vST) resolution is the traveltime moveout, normalized by the wavelet period, exhibited across some offset range. Where moveout exceeds the period by factors of, e.g., 3 and 6, vST is resolved to [–6.5, +8.2]% to [–3.6, +4.0]%, respectively, at the 50% coherence threshold. The temporal duration of coherence responses is expressed as a one-quarter wavelet period either side of the stacking traveltime. Coherence resolutions are used in Monte Carlo simulations to derive the implied precision in the interval stacking velocity (vIS) and its derivative properties. These analyses are repeated for field common-midpoint data, acquired using 50 MHz antennas, on Quaternary glacio-fluvial media overlying a Cambrian basement (<15 m deep). For three reflections identified in these data, the velocity and temporal resolution of coherence responses vary in a quantitatively similar way to events in the synthetic data. For the corresponding layers, Monte Carlo simulations yield precision estimates for vIS, layer thickness and fractional water content. The procedure predicts a reasonable model of water content decreasing with depth, in accordance with increasing pore compaction and provides a robust error analysis; the uncertainty in estimates of the fractional water content of two (assumed) water-saturated layers is ±2.6% and ±2.1% (shallower and deeper, respectively). Monte Carlo simulations are recommended as an efficient means of establishing the precision in quantitative estimates of subsurface properties derived from ground-penetrating radar velocities, particularly where ground-truth data are unavailable.