A 2.5D Method for Attenuating Free-Surface Multiples Based on Inverse Scattering Series
Authors: Matson Ken H. , Corrigan Dennis 
Published: October 2008

Abstract
This paper describes a simple, practical framework in which wave-equation based methods for attenuating free-surface multiples may be applied to multi-source, multi-receiver marine 3D data sets. The fundamental assumption required to facilitate this approach is that the 3D data are acquired in the dip direction for a subsurface which exhibits little variability in the crossline direction. Given the validity of this assumption, the relevant formulas for multiple prediction are presented and their strengths and weaknesses are illustrated with a number of synthetic data sets as well as a field data example.

Introduction
Conventional multiple attenuation methods typically assume that the earth is one-dimensional, has a simple velocity profile, or that a-priori knowledge of the subsurface is available. As a result, these methods become less effective in situations where the earth becomes complicated. Recently, methods have beendeveloped that do not make any assumptions about the earth model and are thus specifically designed to be effective where conventional methods have problems. These new methods remove all multiples that reflect one or more times from the air-water free-surface and have been demonstrated to be highly effective in numerous applications to 2D data worldwide. Various realizations of the free-surface multiple removal (abbreviated FSMR) algorithm have been developed from inverse scattering series (Ref. 1, Ref. 2), a generalized form of Huygen's principle (Ref. 3, Ref. 4), and reciprocity theory (Ref. 5, Ref. 6). While these theoretical treatments have emphasized the case of a 2D earth, they can be easily extended to accommodate a 3D earth; unfortunately, current 3D data acquisition methods do not provide adequate data coverage for implementation of the full 3D formulation. The growing reliance of the industry on 3D surveys for exploration, development and production dictates the need to expand freesurface multiple attenuation to include geometries commonly used to collect 3D data (see, e.g., Refs. 7 and 8). In the marine environment, this means it is necessary to be able to handle multi-source, multi-streamer configurations with large crossline separation between sources and receivers relative to the spacing in the inline direction.
A great strength of the FSMR approach is that it requires no knowledge of the subsurface below the level of the sources and receivers. An important price to be paid for this model-independence is that the theory requires collection of 'complete' data sets. This means, in principle, that sources and receivers need to occupy all points on the acquisition surface. For 2D marine data applications, modern acquisition often provides a good approximation to this ideal. Missing near offsets can usually be estimated by appropriate extrapolation of the recorded near offset traces (Ref. 9) and when the source spacing exceeds the receiver spacing, the missing sources can be estimated by interpolation.
Unlike the 2D case, the application of FSMR in 3D is compromised from the outset by a large deficit in recorded information.