71 3. Seismic tomography a) Figure 3.8 Constant-depth velocity slices from 3D tomography output, presenting noticeable differences: (a) The depth-slice at 7 m, corresponding to the base of the epikarst, exhibits high-low elongated patterns in 175°N; (b) The depth-slice at 28 m, contrasting with the shallow complexity, is characterized by a very poor resolution (high and homogeneous velocity). Adapted from Galibert et al. (2014). 3.1.5 Conclusions This example showed the successful application of a transmission tomography algorithm to uncover the shallow complex structures at a karst region. A set of elongated furrows incised at the base of the epikarst, along a strike of 175°, were revealed. The limited azimuthal coverage obtained from the surface acquisition data limited the depth of the investigation. To increase the depth of the analysis, a combination of borehole acquisitions is suggested. In general, transmission tomography enables the velocity of subsurface structures to be obtained, containing smooth information on a large scale, which is an essential component for pre or post-stack seismic migrations or inversion techniques. Annex 3-A The limits of spatial resolution can be estimated according to the formula suggested by Sheng and Schuster (2003) ∆x k i f xi p( ) ≈ ( ) π η max , , (3.1) with k s p p r xi xi xi = ∇ ( ) +∇ ( ) [ ] ω τ τ , , , (3.2) where Δxi (p) indicates the resolution limit for the direction i, kxi denotes the horizontal wavenumber at maximum frequency f, ∇xi τ (r1, r2) is the horizontal gradient Slice at depth 7 m (base of epikarst) Slice at depth 28 m, abc
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