Effects due to aliasing on surface-wave extraction and suppression in frequency-velocity domain

Surface waves are treated as a kind of strong noise in petroleum seismic exploration. We can suppress surface waves by extracting them because of the different distribution features of surface waves and body waves in the frequency-velocity (f-v) domain. The accuracy of surface-wave extraction and suppression relies on high-resolution and high-accuracy imaging, however, while spatial aliasing will inevitably smear energy images in the f-v domain due to sparse sampling. It is crucial to analyze the effects due to spatial aliasing on surface-wave extraction and suppression. We use the reversible linear operator, high-resolution linear Radon transform, to extract and analyze the energy caused by spatial aliasing. Real-world and theoretical examples demonstrate that the retrieved surface-wave fields will be polluted by spurious body waves once the spatial aliasing energy in the f-v domain gets involved in surface-wave extraction, which will subsequently affect the quality of surface-wave suppression. We suggest that the surface-wave extraction range should be kept within Nyquist spatial sampling limits as much as possible. In addition, the results of synthetic data show that the spatial aliasing could cause mode misidentification since it is easy to be recognized as the higher modes of the surface waves in the f-v domain. In order to distinguish higher modes from spatial aliasing, we proposed using the asymptotic velocity of high modes at high frequencies and derived formulas to calculate the location of the energy due to spatial aliasing to correctly identify the high modes.