Reconstruction of near offsets based on the multiple and adaptive prediction error filter

In seismic data acquisition, it is usually difficult to obtain the complete seismic wave field due to the restriction of field work conditions and the missing data at near offset are particularly valuable. Currently, many applications of seismic data processing methods depend on the reconstruction of near offset data, and how to reconstruct the missing data at near offset is an important issue of research. In this paper, we generate the pseudoprimaries through the cross correlation of multiples and the primaries and reconstruct the missing near offset data depending on the data itself. Due to the differences between the pseudoprimaries and the ideal primaries in amplitude and phase, we propose using the adaptive prediction-error filter to characterize the energy spectrum of the pseudoprimaries, which is based on nonstationary autoregression, and then using the least-squares inversion to reconstruct the missing near offset data. The adaptive prediction-error filter achieves local adaptive features by solving underdetermined problems with regularization constraints. The test results of Sigsbee2B model data and the field data show that the new method can reasonably reconstruct the complex near offset missing data.