Three-dimensional seismic survey is widely applied, but 3-D filtering technology has yet to be fully utilized for the analysis of seismic field data. The common approach is to first filter inline and then crossline. However, an effective 3-D filtering method is expected to eliminate coherent noise, such as the ground roll. We propose a 3-D Butterworth filtering method in the time-space domain. Firstly, a Butterworth-type filter in the frequency-wavenumber-domain is designed to suppress the linear noise with a specific apparent velocity. Secondly, transforming this filter to the time and space domain yields 3-D partial differential equations (PDEs), which are applied to suppress the linear noise. Factorizing the finite-difference equations in a different direction other than decreasing the 3-D PDEs to 2-D PDEs produces a highly accurate and efficient algorithm. Designing the 3-D Butterworth filter, selecting the filtering parameters, and showing its application to synthetic data and a 3-D high-density onshore seismic field data from a region in western China are discussed in detail. Numerical experiments with 3-D high-density onshore seismic field data demonstrate that it is more effective than the 3-D frequency-wavenumber-wavenumber (FKK) filtering method.

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