Influences on the resolution of GPR velocity analyses and a Monte Carlo simulation for establishing velocity precision

Abstract

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.

Constraining variable density of ice shelves using wide-angle radar measurements

“…A complementary approach is to exploit the density dependence of radio-wave propagation speed. The principle underlying the technique involves illuminating a reflector with different ray paths such that both the reflector depth and the radiowave propagation speed may be calculated using methods such as the Dix inversion (Dix, 1955), semblance analysis (e.g., Booth et al, 2010Booth et al, , 2011, interferometry (Arthern et al, 2013), or traveltime inversion based on ray tracing (Zelt and Smith, 1992;Brown et al, 2012).…”

Spectral velocity analysis for the determination of ground‐wave velocities and their uncertainties in multi‐offset GPR data

“…The optimum stacking or root‐mean square (RMS) velocities are then selected by analysing the maxima in the resulting velocity spectrum (i.e., calculated coherency values as a function of tested velocities and traveltime) corresponding to primary reflection events in the analysed CMP gather (e.g., Booth et al . ). In this study, we implement a linear moveout (LMO) model using a spectral velocity analysis approach to describe the linear dependency of direct ground‐wave arrival times t d on antenna offset x in a medium characterized by a constant velocity : …”

“…This observation offers the opportunity to derive velocity uncertainties from the calculated map of CC values and to systematically evaluate different factors (such as frequency content of the data or surveying geometry), which are assumed to affect the reliability of the derived velocity estimate, similar to what has been shown for hyperbolic reflected events (Booth et al . ). In doing so, the velocity step size should be sufficiently small to adequately image the shape and width, respectively, of individual maxima in the resulting map.…”

Active Layer Stratigraphy and Organic Layer Thickness at a Thermokarst Site in Arctic Alaska Identified Using Ground Penetrating Radar

“…For small velocity contrasts, isotropic layers and short-spread conditions (i.e., x is approximately equal to reflector depth z; Taner and Koehler, 1969), V NMO is considered as the root-mean-square velocity (V RMS ), and medium velocity for each layer may be obtained by substituting V RMS into Dix's equation (Dix, 1955). Here we estimate V NMO using the coherence statistics (Sheriff and Geldart, 1995;Booth et al, 2010Booth et al, , 2011. Coherence is a measure of the coherency of energy between radar waveforms.…”

“…Coherence is a measure of the coherency of energy between radar waveforms. We used the methods outlined by Booth et al (2011) to correct a known systematic bias in V NMO caused by the nature of radar waveforms. Uncertainties in GPR measurements of ALT result from uncertainties in constraining the reflector travel times and uncertainties in the radar velocity.…”