Adaptive subtraction remains a critical part of today’s seismic data processing. Many existing adaptive subtraction methods can be formulated as a parameter estimation problem, and all of them, although fundamentally different, have a common restriction that the dimension of the unknown parameters must be determined in advance. We have developed an adaptive subtraction framework called multimodel adaptive subtraction (MMAS) that aims to relax this restriction as well as regularize the estimation of the parameters through a generalized information criterion combined with a nonconcave penalized likelihood function. MMAS is a fully general framework that can be applied to many existing adaptive subtraction methods. As an example, we determined how MMAS can be applied to the popular least-squares adaptive subtraction (LSAS) method, and we call the resulting algorithm the multimodelLSAS (MMASLS); furthermore, we studied its computational complexity and developed an efficient implementation for MMASLS. We applied our proposed MMASLS method in the context of multiple attenuation, and we used computer simulations to demonstrate the advantages of our method over the traditional LSAS method, which included the capabilities to be more aggressive (use longer filters) in regions in which multiples occurred, to be less aggressive (use smaller filters) in regions dominated by primary reflections, and to be passive and take no effect (no filters used) in regions in which multiples were absent from the data.

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