Interface Controlled Multiple Elimination by Sparsity Inversion (Communications in Computational Physics, 2020)
Removing internal multiples remains an important but challenging problemin seismic processing. The generalized Estimation of Primaries by Sparsity Inversion(EPSI) method minimizes data residuals between the calculated and observed waveform using the sparse constraint of primary impulse responses to predict multiples andremove them directly, instead of using the conventional adaptive subtraction method.Even though the generalized EPSI method provides a good estimate of the primariesand multiples when they overlap, it is limited by intensive computational cost.In this paper, we introduce two strategies to improve computational efficiency.First, the interface-controlled strategy is introduced by only selecting high-amplitudeprimary responses related to the interfaces with strong impedance contrasts to estimate multiples. The computational time is approximately proportional to the numberof involved reflectors and usually, most of the internal multiple energy in the data isonly related to a few strong reflectors. Therefore the modified method can removemost of the internal multiples in fewer computations than in the generalized EPSI,which loops through all the interfaces. Next, an approximate formula for estimating primary impulse responses is proposed by neglecting a computationally intensiveterm which corresponds to the primary responses estimated from internal multiples.According to our analyses and experiments, in most cases, the contribution of this termis negligible because the internal multiples are weak. Therefore, the computational efficiency can be improved without significantly losing quality when estimating mostprimaries and multiples.In order to demonstrate this, multiple elimination of a two-layered simple data andthe Pluto data are implemented. We find that the modified method can yield reliableresults that require fewer computations. The improvements of the modified methodmay encourage the use of the generalized EPSI method in industry.