92 A new concept of karst development based on hydrogeology and geophysics 5.2 3D seismic imaging The processing sequence has been described in detail in several publications (Mari & Porel 2008, 2018, and Mari & Delay, 2011), so it is only briefly explained here. Each shot point was processed independently (both in the cross-line direction and in the in-line direction) to obtain a single-fold section with a sampling interval of 2.5 m (half the distance between two adjacent geophones) in the in-line direction. The processing of an in-line direct and reverse shot gather has made it possible to obtain a single-fold section with an in-line extension of 240 m (indicated by a blue arrow on the seismic line map, Fig. 2a) while a cross-line shot gather has provided a single-fold section with an in-line extension of 120 m (indicated by a red arrow on the seismic lines map, Fig. 2a). A 3D refraction seismic tomography (Mari & Mendes, 2012) was done to map the irregular shape of the top of the karstic reservoir and to obtain static corrections (obtained by inversion tomography after geostatistical analysis, see appendix) and a velocity model of the overburden. To add information to the inversion procedure, we used in-line and cross-line cross shots simultaneously, with an offset of 60 m. The shots were selected to ensure that the refracted wave was the first arrival wave, regardless of the source-receiver distance. The picked times of the first seismic arrivals for all shots (in-line and cross-line shots), and both the depth map of the top of the reservoir and the velocity model obtained by the Plus–Minus (Mari & Mendes, 2019) method were used as input data for the tomographic inversion procedure. The processing sequence (Mari & Porel, 2008, 2018) includes amplitude recovery, deconvolution, wave separation, static corrections (obtained by inversion tomography) and normal move-out (NMO) corrections, using the Vrms velocity log obtained from VSP recorded in borehole C1 (Fig. 3a and 3b). The VSP time versus depth law (Fig. 3b) was also used to convert the time sections into depth sections with a 0.5 m depth sampling interval. The single-fold depth sections were merged to create the 3D block. The width of the block in the in-line direction is 240 m, and 300 m in the cross-line direction. In the in-line direction, the abscissa zero indicates the location of the source line. The abscissa of the reflecting points ranges between -120 m and 120 m in the in-line direction. The distance between the two reflecting points is 2.5 m. In the cross-line direction, the distance between two reflecting points is 5 m. The depth sections were deconvolved to increase the vertical resolution. They were then integrated to transform a 3D amplitude block into a pseudo-velocity block, using velocity functions (filtered sonic logs obtained by full waveform acoustic logging at boreholes C1 (Fig. 3d), MP5, MP6, M08, and M09 as constraints. The pseudo-velocity sections of the 3D block thus obtained were merged with those obtained by refraction tomography to create a 3D extended velocity model from the surface. Figure 4 shows the in-line 31 pseudo-velocity section. The upper part of the figure shows the velocity distribution obtained by refraction tomography. The seismic section clearly shows nearly horizontal stratifications with strong lateral variations of seismic velocities. Figure 5 shows both the 3D seismic velocity model from 35 to 130 m below the ground surface and the
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