72 Seismic Imaging of travel time from point r1 to point r2, and η stands for the set of suitable rays selected from all available shots. In the example presented here, only the horizontal resolution is considered and discussed. Our first step was the analysis of the Fresnel zone for a frequency of 120 Hz, with a surface acquisition and velocity gradient model characteristic of the karst region (Figure 3.A.1-a). We noted that: • in the shallow area - wave paths are nearly vertical and provide large horizontal wavenumbers, by combining neighbouring shots, leading to small Δx values => high horizontal resolution (≈ 1.5 m); • in the deeper area - wave paths are nearly horizontal and provide small horizontal wavenumbers for all shots, leading to large Δx values => low horizontal resolution (≈ 10 m). Figure 3.A.1 Horizontal resolution Δx of band limited travel time tomography: (a) for surface acquisition, (b) for borehole acquisition. The contours represent the background velocity gradient. Inside the Fresnel volume, there is no resolution at all along the geometrical ray (white area), according to wave path theory. Resolution increases toward the fringes (dark area). Adapted from Galibert et al. (2014). These very different limits of spatial resolution demonstrate the capacity of the technique, as shown by the surface acquisition data, for investigating the upper epikarst; but its unsuitability for the underlying low-permeability region. To overcome this issue, an additional VSP acquisition was suggested to increase the azimuthal coverage with depth. Under such acquisition conditions, the analysis of the Fresnel zone (Figure 3.A.1- b) illustrates how the wave path is nearly vertical and the horizontal cross width of the low-sensitivity region becomes narrow. Therefore, in situations where it is possible to combine surface and borehole acquisitions, the tomographic resolution should be substantially improved.
RkJQdWJsaXNoZXIy NjA3NzQ=