GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.1 71 (3) We can then express the datumed wave eld as follows: (4) D l (B|A) contains the primary re ections of the interfaces below the datum level as they would have been recorded with the new virtual acquisition geometry. D nl (B|A) contains the additional primary events retrieved by non-linear datuming with sources and receivers placed on the same datum surface. These events contain different information with respect to D l (B|A) because they have interacted with the subsurface discontinuities with different incidence angles. Moreover, the use of D nl (B|A) can increases the overall illumination. The linear component of the Green’s functions can be obtained by using the smooth background velocity model while, in order to compute W nl (A|S) we need the detailed information of the subsurface discontinuities. We can implement the source datuming expressed in Eq. (2) by means of an interferometric procedure using D(A|S) in place of W(A|S) (Schuster, 2010). The following equation relates these two quantities: (5) where F indicates the Fourier spectrum of the seismic source. The eld D(A|S) is what is computed as the source wave eld in RTM by forward propagating the source impulse. The cross-correlation expressed in Eq. (2) can thus be implemented after substituting W(A|S) with D(A|S) , leading to the following formula: (6) The only difference between Eqs. (2) and (6) is a multiplication of the retrieved signal by the source spectrum F . The additional multiplication by F , though, will not affect the kinematics of the reconstructed events. Using the approximation of Eq. (6) we have: (7) being D l (A|S) the wave eld composed of the rst arrivals recorded at A by a source impulse placed at S . D nl (A|S) contains the multiply scattered events generated by the same source in S (see Fig. 1b). Internal multiples imaging. In geological settings characterized by the presence of strong reflective interfaces (salt bodies, carbonates, etc…) we can expect to measure strong internal multiples. They can be generated by the downward bounce occurring, for instance, at the salt edges, either at the bottom of the saline formation or at its top. In a scenario like the one just described we expect to record the types of events that followed the paths drawn in Fig. 1b. If we place our datum level below the salt body and we perform the non-linear datuming procedure explained in the previous section, we reconstruct either up-going and down-going events. The second term in Eq. (4) corresponds to the events composition shown in the panels of Fig 1b. The gures show two examples for the case of, respectively, an intra-salt multiple and an internal multiple event generated by a downward bounce at the bottom of the salt (or more generally at an interface above the datum level). The primary events retrieved as in the left-hand-side panel of Fig. 1b give information about the subsurface region below the datum depth ( D nl below ( B | A )). On the contrary, events of the type of the right-hand-side panel of Fig. 1b, give information about the region above the new virtual acquisition surface ( D nl above ( B | A )). Before applying the interferometric primaries reconstruction shown in Fig. 1b we need to apply a wave elds separa- tion procedure to separate the up-going and down-going components of the wave eld. In order to do so, we rst re-locate the receivers at two different datuming surfaces and then we apply a separation technique similar to the one proposed by Neut et al. (2013).