ABSTRACT
Seismic exploration method is a crucial method to explore oil/gas, coal, and other resources in the underground. Geophones that are arranged at the earth’s surface or in wells can record vibrations of the earth. Data recorded by geophones can be used to extract velocity information from the underground medium after a series of processing flow. In order to reconstruct the structure of the earth correctly, seismic acquisition should satisfy the Nyquist/Shannon sampling theorem not only in the time domain but also in the space domain. Generally, the sampling process in the time domain can fulfill the sampling theorem. However, sampling in the space domain often violates the sampling theorem due to the influence of obstacles, rivers, bad traces, noise, acquisition aperture, topography, and acquisition costs. Seismic data that violate the Nyquist/Shannon sampling theorem may bring harmful aliases and deteriorate the results of migration (Liu and Sacchi 2004), multiple elimination (Naghizadeh 2009), denoising (Soubaras 2004), and amplitude versus offset (AVO) analysis (Liu 2004; Sacchi and Liu 2005; Naghizadeh and Sacchi 2010). In order to remove the influences of subsampled data, the seismic regularization/interpolation/reconstruction/restoration technique is a key step to provide reliable data from the subsampled data. Thus, seismic interpolation is a crucial research direction in exploration seismology (Wang et al. 2011).
