3D Surface-Related Multiple Elimination And Interpolation

The need for a true 3D multiple suppression technique becomes evident from many real data examples (e.g. SEG ’97 Multiple Removal workshop, [5]). In these examples the multiples can hardly be suppressed using conventional multiple suppression techniques due to the 3D character of the multiples. The Delft approach to the multiple problem ([1], [10]) can be applied in both 2D and 3D sense and consists of two parts: a multiple prediction part and a least-squares subtraction part. The multiple prediction part can be seen as a Huygens’ source generation ([9]): at every surface position at which a surface multiple reflects a source/receiver pair is needed to predict that multiple. Multiple prediction in a true 3D sense implies that a dense grid of sources and receivers is required that covers all the surface reflection points of the surface multiples. Since such a coverage would never be possible in a 3D marine acquisition geometry, one is forced to interand extrapolate missing source and receiver positions. In this paper 2 types of interpolation techniques are discussed: differential NMO and 3D Prediction Error Filtering (PEF). After accurately interpolating missing source and receiver positions in the sparse 3D dataset, full 3D surface-related multiple elimination can be applied. Introduction The surface-related multiple elimination (SRME) described as a data adaptive procedure by Verschuur et al. [11] has proven to be quite successful over the years. The procedure consists of two steps: in the first step unscaled surface-related multiples are predicted using the data itself as the multiple-prediction operator, and in the second step the unscaled predicted multiples are matched with the true multiples and subtracted from the data in a least-squares sense. The prediction of the surface-multiples can be seen as a Huygens’ source generation ([9]): at every surface position at which a surface multiple reflects a source/receiver pair is needed to predict that multiple. In 3D media these surface reflection points do not always coincide with sources and receivers located on a 2D line (figure 1b), which leads to wrongly predicted multiples ([8]). Extending the subtraction procedure for these wrongly predicted multiples can still achieve a considerable multiple suppression ([4], [5]). However, if the multiple generating boundaries become structurally complex in a 3D sense full 3D SRME is preferred. 3D Surface-related multiple elimination In terms of raypaths, a first order surface multiple raypath can be seen as a combination of two primary raypaths: one from the source to the surface reflection point continued by the path from that point to the receiver (see figure 1a). Prediction of that (raw) surface multiple is accomplished by convolving two traces: one trace from the source at that is measured at the reflection point at the surface at and one trace from a source at the reflection point at measured at the receiver at . Because the reflection points of the surface multiples are unknown, contributions from all possible reflection positions are calculated and stacked, leaving just the contributions from the Fresnel zone, in which the multiple reflection point/region was located. As the seismic data contains many reflections, the