From removing to using multiples

Abstract In the last decade much progress has been made to remove multiples from seismic data. So far, multiples have been considered as noise and, therefore, after the removal process multiples are thrown away. In this paper, we will show that multiple reflections contain a wealth of information that should be used in seismic imaging. Introduction In the history of multiple removal, algorithms have been based on two differentiating properties: moveout and predictability. If primaries and multiples show different moveout behavior, algorithms are available that allow separation of primaries and multiples in a transform domain. A weak point of moveout algorithms is that they become less effective in the situation of complex wavefields (think of nonhyperbolic wavefronts), or when the moveout of primaries and multiples are alike (e.g. deep data). Predictability has always been important in multiple removal. In the early days of seismic processing (the 1960's), single trace statistical prediction was very successful (Robinson, 1957). In the early 1980â??s prediction-error filtering has been given a wave theoretical base, providing a unified theory for surface-related and internal multiples (Berkhout, 1982). It has increased the effectiveness of multi-channel prediction-error filtering significantly (Verschuur, 1991). Nowadays, multiple removal algorithms are to a large extend presented by wave theory based multi-channel prediction-error filters. Recently, a third direction in the theory of multiple removal was proposed that is inspired by the double focusing process as it occurs in seismic migration (Berkhout, 1997). The new theory is based on the so-called focal transform. Forward focal transformation transforms primary energy into its focal point around zero time. After an imaging step, the result is input to the inverse focal transform leading to the desired multiple-free output. First results indicate that combined prediction and imaging may lead to the next paradigm shift in multiple removal. Figure 1: a) Feedback model for primary reflections (m > 0) and surface-related multiples, the multiple-generating boundary being given by z0=z0(x,y) and the downward reflection operators of this boundary being represented by the columns of the matrix R^(z0). b) One basic element of the weighted convolution process for surface-related multiples, visualized in terms of simple raypaths (m > 0). (Available in full paper) Removal of surface-related multiples, the prediction approach The so-called feedback model shows that prediction of multiples requires a weighted convolution process with the primary response (Berkhout, 1982). If an estimate of the primary response is available, the convolution process becomes iterative. The convergence turns out to be fast, even if one starts with the total dataset as primary estimate (Verschuur and Berkhout, 1997). Let us reconsider the feedback model, using the detail-hiding operator notation (see also Figure 1)