The presently disclosed seismic acquisition technique employs a receiver array and a processing methodology that are designed to attenuate the naturally occurring seismic background noise recorded along with the seismic data during the acquisition. The approach leverages the knowledge that naturally occurring seismic background noise moves with a slower phase velocity than the seismic signals used for imaging and inversion and, in some embodiments, may arrive from particular preferred directions. The disclosed technique comprises two steps: 1) determining from the naturally occurring seismic background noise in the preliminary seismic data a range of phase velocities and amplitudes that contain primarily noise and the degree to which that noise needs to be attenuated, and 2) designing an acquisition and processing method to attenuate that noise relative to the desired signal.