General theory for accommodating primaries and multiples in internal multiple algorithm: Analysis and numerical tests

Abstract

The inverse scattering series (ISS) predicts internal multiples directly and without subsurface information. This is achieved through a task-specific subseries within the overall ISS. The ISS leading-order attenuator of first-order internal multiple is the leading-order term in the subseries that contributes to the removal of first-order internal multiples. It has shown stand-alone capabilities for internal multiple prediction/attenuation for both marine and on-shore plays. The basic idea behind the leading-order attenuator is that all the events in the data are treated as subevents and combined nonlinearly (three data sets are involved), and among all the combinations first-order internal multiples can be predicted by the combination that has all subevents correspond to primaries. However, the entire data set, consisting of primaries and internal multiples, enters the algorithm. When internal multiples in the data themselves act as subevents, the leading-order attenuator produces not only first-order internal multiples, but also higher-order internal multiples and, at times, spurious events. The latter have been observed in the tests of Fu et al. (2010) and Luo et al. (2011). Weglein et al. (2011) have noted this and suggest that the resolution of the problem would reside in other terms of the ISS. Ma et al. (2012) describes the initial occurrence of the circumstance under which spurious event arises, and explains how to address that issue. This abstract extends the analysis in Ma et al. (2012) to more complex circumstances, and provide a description of the general arrival of spurious events. In this abstract we show how the ISS anticipates the issue due to spurious events and provides the response.