Jointly Filtering and Regularizing Seismic Data Using Space-Varying FIR Filters

A persistent difficulty with land surveys -- and single sensor surveys in particular -- is that the acquisition grid is often irregular due to obstacles and surface conditions. As a result, in some applications regularizing and filtering may be desirable. The purpose of our work is to develop a filtering method that accounts for nonuniform sampling and that can output traces at regular intervals. The filter output should be stable for different realizations of the receiver locations and it should approximate the output one would get in the ideal case, i.e. if no receiver misplacements had occurred. We formulate a method for jointly filtering and regularizing nonuniformly sampled seismic data as an optimization problem in the space or in the wavenumber domain. Our results show good filtering and regularization accuracy and a high degree of robustness when compared to another similar method. The increase in robustness, however, comes at the price of a higher computational cost. The wavenumber domain formulation of our method does not seem to yield significantly better results, but this may be improved by choosing different relative weights for the stop and pass band in the optimization scheme.