The multiple prediction step, crucial for the success of the whole algorithm, involves one important assumption about the data acquisition geometry, namely, a source/receiver pair is needed wherever a multiple reflects. The Delft approach is quite successful in solving 2-D problems Verschuur and Prein (1999), in which the assumption is relatively easily satisfied. However, in many 3-D surveys, there is a large gap between this assumption and the reality Dragoset and Jericevic (1998).
Two different directions have been taken to solve the problem. One is to interpolate the trace at the missing source and receiver positions massively to attain a dense coverage of the surface van Dedem and Verschuur (1998). However, the computational cost of this method is huge. The other approach is to predict the multiple based on the 2-D theory and then extend the subtraction step to handle incorrectly predicted multiples Ross et al. (1997); Ross (1997). The success of this approach is restricted to simple 3-D cases.
This paper proposes a method designed for multi-streamer geometry. Two distinctive features make it more practical. First, this approach finds the most reasonable proxy from the collected dataset for any missing trace. There is no need to interpolate missing streamers and shotlines. Second, I introduce a concept, the partially-stacked multiple contribution gather (PSMCG). Using the multi-scale prediction-error filter (MSPEF) theory Claerbout (1992), the proposed approach interpolates the PSMCG in the cross-line direction. This gives us a densely sampled multiple contribution from all possible Huygens secondary sources. The following summation step can remove aliasing noise better.
Two numerical examples in this paper demonstrate how the approach works.