Reducing Spatial Aliasing in Wave-Equation Multiple Attenuation

Abstract

Abstract Multiples are a major problem in offshore seismic exploration. Wave-equation methods are a popular tool for multiple attenuation, but behave poorly in the presence of spatial aliasing. This paper will propose a method to reduce the effect of spatial aliasing. It does this by first applying a linear transformation to the wave equation. This transformation reduces dips in the data, but does not involve approximations, nor does it change the form of the equation. Wave extrapolation is then performed using an efficient Kirchhoffstyle phase-shift operation. The modeled multiples are adaptively subtracted from the original traces with a multichannel constrained filter. The proposed method has givengood results on a data set from the East Coast of Canada. Introduction The basic model in seismic processing assumes that reflection data consists of primaries only. If multiples are not removed they can be misinterpreted as, or interfere with, primaries. Therefore the attenuation of multiple reflections has been an important research subject and many methods have been developed. The methods can be classified into two types: those that exploit the periodic nature of multiples, and those that exploit the moveout differences between multiple and primary reflections. The first category includes predictive deconvolution in the x-t or ?-? domain. Predictive deconvolution assumes that the multiples are periodic within an application window and that the primary events are not - that is, the multiples can be predicted and thereby subtracted from the seismic records. In the prestack x-t domain, water bottom multiples are periodic only for zero offset traces and flat-water bottoms. To achieve periodicity of multiples for far-offset traces, transforms such as the ?-? transform or the radial trace method must be applied. Still, for shallow water depths (shorter period multiples), periodicity only holds in a limited window. Predictive deconvolution can introduce spurious events and needs to be applied with care. It is more effective for removing "ringing" multiple energy than longer period waterbottom multiples. The second category includes methods in the F-K, K-L and ?-? domains. While these methods are routinely used and can be very effective, there have a number of problems. All of these methods lose effectiveness when the velocity discrimination between primary events and multiples is small. This is the case at near offsets where there is little or no separation of primary and multiple events, and at all offsets when there is little velocity difference. Their effectiveness is further reduced when the seismic events violate the modeling assumptions (non-hyperbolic events for F-K and K-L, or non-parabolic events after NMO for ?-?). Recently there has been interest in techniques based on wave theory, which can be considered extensions of conventional predictive deconvolution. Multiples are predicted by either wavefield extrapolation1,2,3 or wavefield inversion4. They are then subtracted from the original data.