Another old paper is added to the collection of reproducible documents:
Multiple suppression using prediction-error filter

I present an approach to multiple suppression, that is based on the moveout between primary and multiple events in the CMP gather. After normal moveout correction, primary events will be horizontal, whereas multiple events will not be. For each NMOed CMP gather, I reorder the offset in random order. Ideally, this process has little influence on the primaries, but it destroys the shape of the multiples. In other words, after randomization of the offset order, the multiples appear as random noise. This “man-made” random noise can be removed using prediction-error filter (PEF). The randomization of the offset order can be regarded as a random process, so we can apply it to the CMP gather many times and get many different samples. All the samples can be arranged into a 3-D cube, which is further divided into many small subcubes. A 3-D PEF can then be estimated from each subcube and re-applied to it to remove the multiple energy. After that, all the samples are averaged back into one CMP gather, which is supposed to be free of multiple events. In order to improve the efficiency of the algorithm of estimating the PEF for each subcube, except for the first subcube which starts with a zero-valued initial guess, all the subsequent subcubes take the last estimated PEF as an initial guess. Therefore, the iteration count can be reduced to one step for all the subsequent subcubes with little loss of accuracy. Three examples demonstrate the performance of this new approach, especially in removing the near-offset multiples.