2D wavelet transform‐domain adaptive subtraction for enhancing 3D SRME

Abstract

Surface related multiple elimination (SRME) (Berkhout 1982, Verschuur et al., 1992) is a very popular and effective algorithm for removing surface related multiples. The SRME method includes two steps: multiple modeling or multiple prediction followed by adaptive subtraction. The success of the SRME method depends on how well the predicted multiples match to the actual multiples in the data and on the success of the adaptive subtraction algorithm. This paper deals with the adaptive subtraction algorithm. There are two most common strategies for adaptive subtraction. The first strategy is posed as the least-squares minimization problem that minimizes the energy difference between the original data and the predicted multiples in the x-t domain. The second strategy is based on pattern-based adaptive subtraction (Spitz, 1999, 2000, Soubaras, 1994), which is based on the assumption that the primaries and multiples are predictable in the f-x domain. A detailed comparison study of different adaptive subtraction algorithms is discussed in the paper from Abma et al. (2005). One of the main conclusion from the paper was that the least-squares minimization technique is probably the best available adaptive subtraction algorithm at present, however when multiples strongly interfere with the primaries the technique is not as effective. This conclusion is the main motivation for this paper. The transformation of the data to the 2D stationary wavelet transform domain (SWT) (Nason et al., 1995) provides a potential dip separation to the data and thus gives an opportunity to separate interfering events. In this paper the implementation of the least-squares minimization technique in the 2D SWT domain is discussed.