Geophysics · 1998 · 194 citations · 22 references
Determining the depth and geometry of a landfill’s lower boundary is difficult because potential field methods lack depth resolution and seismic reflection data are contaminated by source‑generated noise in the <50 ms time range. The study develops a surface 2‑D tomographic refraction scheme using a fast finite‑difference eikonal solver and damping/smoothing‑constrained inversion to resolve landfill boundaries. The scheme was applied to first‑arrival traveltime data from five profiles across landfills and two natural sediment profiles in northern Switzerland, with high‑quality seismic recordings from multiple shots on closely spaced receivers, and its reliability was assessed through ray diagrams, synthetic‑observed traveltime comparisons, residual analyses, coincident profile comparisons, varied input models, and bootstrap error estimates. The tomographic refraction scheme delineated landfill boundaries by detecting rapid velocity increases from <1000 to >1500 m/s, with near‑surface natural layers 2–6 m thick (occasionally 7 m) and landfill‑associated low velocities extending to 9–11 m, demonstrating efficient, cost‑effective shallow (<20 m) subsurface imaging but requiring additional geological data to distinguish landfill‑from‑natural velocity anomalies.
Determining the depth and geometry of a landfill’s lower boundary is a difficult task. Potential field methods generally lack the necessary depth resolution, and seismic reflection data are usually contaminated by source‐generated noise in the time range of interest (<50 ms). To address this problem, we have developed a surface 2-D tomographic refraction scheme that is based on a fast finite‐difference eikonal solver and an inversion method that incorporates appropriate damping and smoothing constraints. This new scheme has been applied to a first‐arrival traveltime data set collected across adjacent landfills in northern Switzerland. High‐quality seismic data were collected along five profiles that crossed the landfills and two that sampled undisturbed natural sediments. Seismic waves generated from multiple shots were recorded on large numbers of closely spaced receivers during quiet evening periods. Reliability of the resultant velocity tomograms was estimated on the basis of (1) ray diagrams, (2) plots of synthetic and observed traveltimes, (3) traveltime residual analyses, (4) comparisons of coincident velocity‐depth profiles computed from intersecting profiles, (5) inversions with diverse input models, and (6) quantitative error analyses using a bootstrap technique. At our study site, the base of the near‐surface natural layer and the lower boundaries of the landfills were defined by rapid increases in velocity from <1000 m/s to >1500 m/s, with velocities in the upper parts of the models determined to within about ±100 m/s. The thickness of the near‐surface natural layer varied between 2 and 6 m, with occasional thickening to ∼7 m. In contrast, low velocities associated with the landfills could be traced to 9 to 11 m depth. Although our results have demonstrated that the tomographic refraction scheme may be an efficient and cost‐effective means of studying the very shallow subsurface (<20 m depth), complementary geological and other geophysical data were required to discriminate between velocity anomalies attributed to the landfills and those attributed to natural variations in the near‐surface geology.
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Bootstrap Methods: Another Look at the Jackknife
B. Efron · The Annals of Statistics · 1979 · 17.1K citations · Full text