An operator decomposition approach for the separation of signal and coherent noise in seismic wavefields

Extraction of signal from a wavefield corrupted by significant coherent noi se is one of the principal tasks in exploration seismology. Frequently both the signal and coherent noise components exhibit complex characteristics a nd cannot be modelled by popular transforms. In this paper we examine the s eparation of wavefield components by using their respective modelling opera tor as a transform. We form the separation problem as an inverse problem an d study the corresponding invertibility and resolution properties of the re sulting system matrix. We establish a link between the null space of the sy stem matrix and the range overlap of the modelling operators. We introduce model and data regularization and show that these terms help mitigate the r ange overlap. The method is illustrated on a synthetic example for the nonr egularized, model-based and data-based regularization cases.