Removal of internal multiples by iterative construction of virtual primaries

Abstract

Internal multiples are seismic multiple reflections where all of the downward scatterings occur beneath the air-water or air-solid boundary. Removal of internal multiples remains challenging in both onshore and offshore seismic surveys. For onshore seismic data, internal multiples may overwhelm the deep primary reflections when strong velocity inversions exist. So far, a few successful cases on land field internal multiples removal have been reported. Conventional convolution-type internal multiples estimation suffers from inaccuracies in both amplitude and phase estimation, which leads to overdependence on adaptive filtering. To overcome this, we developed a new internal-multiples prediction method for an arbitrary 3-D inhomogeneous lossless acoustic medium, based on wave theory, Rayleigh-Betti reciprocity theorem, and the principle of time-reversal invariance of the two-way acoustic Green's function. The new method developed a newconcept, virtual primaries.Virtual primaries equal an integral of crosscorrelations involving the internal-multiple-free wavefields and the two-way Green's function of primaries. The virtual primaries method employs a similar model with surface-related multiples elimination (SRME). The new method requires the estimates of traveltime of strong primaries or macro velocity. Unlike prevailing convolution-type methods, the virtual primaries method obtains accurate estimation of internal multiples by introducing an amplitude-phase correction term and the two-way Green's function. The correction and the Green's function are derived from wave theory and acoustic reciprocity theorem. We proposed an iterative method to construct virtual primaries and internal multiples, which significantly reduced the dependence of subtraction process on adaptive filtering. We proved that the internal multiples were represented by an integral of convolutions involving the virtual primaries and the muted wavefield. Results on land field data showed that themethod was capable of estimating internal multiples and recovering deep primary energy overwhelmed by multiples.