63 2. Well seismic surveying or negative apparent velocities. These wave separation methods can be divided into two categories (Mari and Coppens, 2003; Mari, 2015): • Methods requiring flattening of the well seismic section at the time of the first arrival, before applying the separation algorithm. • Methods that do not require flattening. The methods or filters belonging to the first category include: • Sum and difference filter • Median filter • Wiener filter • Apparent-velocity filter, if the distance between adjacent recording depths is irregular • Filtering by singular value decomposition (SVD). Filters belonging to the second category include: • Filters based on the spectral matrix (SMF) • Parametric methods • Apparent-velocity filter (such as the f-k filter, frequency wave number) if the distance between recording depths is regular. Separation methods that are not based on a criterion of apparent velocity also exist, namely polarization filters to extract P and S-waves. It is often necessary to combine several methods to obtain an optimum wave separation. For instance, for an offset VSP, an apparent-velocity filter is used (f-k filter for example) to separate upgoing and downgoing waves, followed by a polarization filter to separate P and S-waves. An example of f-k filter wave separation and polarization filter is shown in Figure 2.10. The initial data are shown in Figure 2.8. On each component (Z, H), we observe upgoing and downgoing waves which can be separated by an apparent velocity filter. In this case, an f-k filter was applied. After separation, each wave type (upgoing or downgoing) comprises P compression waves and S shear waves, which have similar apparent velocities. The P and S-waves are separated by polarization. Figure 2.10 shows the result of the extraction of downgoing and upgoing P and S-waves. The downgoing P appears throughout the entire recording. The downgoing S-wave only appears after a certain depth, corresponding to the marker on which the conversion phenomenon occurs.
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