GNGTS 2013 - Atti del 32° Convegno Nazionale

The result of dip filtering is an image that shows an approximation of all those events that do not follow the dominant trend of dips. Therefore we can use this result as an estimation of the migrated image of the diffractions. Even in the case of incorrect migration velocity the diffractions can be identified and separated by this methodology because they appear as little “smiles” (in the case of overestimated migration velocity) or “frowns” (in the case of underestimated migration velocity) and they still do not follow the dominant trend of dips. This peculiarity means that, after the separation of diffractions, this domain could be suitable for a velocity analysis based on the focusing of diffraction events. Fomel et al. (2007) use the method of plane-wave destructors (Claerbout, 1992; Fomel, 2002) for dip filtering. In our study we use a different filter based on the gradient squared tensor (GST) as a tool for dip estimation (van Vliet and Verbeek, 1995), because of the easier parametrization, the lower computational complexity, and the presence of a dip coherency output. GST exploits the eigenvectors of the dyadic product of the gradient vector with itself (g•g t ) to estimate the local slopes. The additional feature of dip estimation by the GST method is that it gives the coherency of the local estimate as an auxiliary output, originally called “anisotropy” (van Vliet and Verbeek, 1995). The value of the local dip coherency varies from 0 to 1. A value of 0 corresponds to a perfect isotropy: no dominant dip has been clearly identified, therefore the estimated dip value is not reliable. A value of 1 means that the local neighborhood of the examined point exhibits the same behavior; therefore the estimated dip is very reliable. Local gradients, GST eigenvectors and local dip coherency can be used to build very accurate dip filters (Hale, 2007), which can be used to properly enhance or remove events showing a certain dip, respectively emphasizing coherent events or revealing underlying information (residual image). This methodology works quite well in eliminating reflection events. However, the residual image can also contain noise, effects of uneven illumination, edge effects due to limited migration aperture and other kinds of spurious events besides the desired diffractions. Separation of diffractions in the migrated dip angle domain. The second methodology studied consists in separation of diffractions and reflections in the dip angles domain at the depth point. Among the well-known reflection angle common image gathers (CIGs), it is possible to obtain, as an output of the migration process, the so called dip-angle CIGs which show the image of the events as a function of the imaged reflector’s dip (i.e. the dip of the vector obtained by summing the incident and the reflected slowness vectors). The dip-angle CIGs have been used as a tool for equalization of illumination in depth migrated images, for true amplitude migration (Audebert et al. , 2000), for optimal migration aperture estimation (Bienati et al. , 2009) and for velocity analysis (Reshef and Ruger, 2005) In this domain we are essentially looking at the direction in which the incident energy is sent back. In the case of a reflector the wavefield follows the Snell’s law, therefore it is sent back in a single direction, which is univocally identified by the actual reflector’s dip. In the case of a point diffractor the incident energy is sent back in all directions. In the dip angle domain these directions are identified by the stationarity of the events’ moveout. The stationary points are preserved when summing over the dips according with the stationary phase principle. To be more precise, when migrated with the correct velocity, a diffraction appears as a flat horizontal event if the dip-angle CIG is located exactly above the point diffractor, and as a dipping event if the CIG is relative to an horizontal position near the diffractor. On the contrary the reflections appears as concave events where the apex indicates the actual reflector’s dip. The different behavior of diffractions and reflections in this domain can be exploited for the separation of diffractions e.g. by means of dip filtering of flat horizontal events. The moveouts of reflection and diffractions are different and clearly recognizable even in the case of migration with wrong velocity. In this case the imprint of a reflection is still a 72 GNGTS 2013 S essione 3.1