Resolving Small Objects Using Seismic Traveltime Tomography
Loveday, David Carl
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It is often claimed that the first Fresnel zone associated with the dominant frequency represents the spatial resolution limit of traveltime tomography. We show, however, that the relevant Fresnel limit for tomographic resolution is the maximum, not the dominant frequency in the data. For physically realizable causal wavelets, the maximum frequency is infinite. In practice, noise lowers the effective possible maximum frequency. To demonstrate these points, synthetic seismic data were generated for traveltime picking and inversion for a single, small velocity anomaly embedded in a homogeneous background velocity. A variety of traveltime picking techniques were tested and compared for their ability to detect the presence of objects smaller than that Fresnel zone associated with the dominant frequency. All methods produced accurate ray-theoretical (infinite-frequency) picks from noise-free seismic data for objects smaller than the dominant-frequency Fresnel zone. For the lowest dominant frequencies with Fresnel zones many times larger than the object, picking methods that focus on features along the onset of the first arrival were the most accurate, while cross-correlation with a known wavelet preformed less accurately. First-onset picking methods perform better because they take advantage of the highest frequencies in the data, whereas the correlation wavelet is typically in line with the dominant frequency. All methods successfully detected the presence of objects smaller than a wavelength. The inversion of the traveltime picks from the different picking methods always recovered the position and shape of the object. Random noise at a range of signal-to-noise ratios was then added to the seismic data and the data were repicked. Pick times with different noise realizations are statistically centered on the noise-free pick, not the time that would be recorded in the absence of the object. Trace stacking prior to picking or the averaging of many picks improves the signal-to-noise ratio and can extract signal that is not detected on an individual pick. An averaging of traveltime picks also occurs during tomographic inversion. This inherent signal-to-noise improvement allows tomography to image objects that are undetectable in individual trace picks. The resolution of tomography is limited not by the Fresnel zone associated with the dominant frequency, but by the accuracy of the traveltime picks. Resolution is further improved by dense ray coverage.
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