Frequency-wavenumber implementation for P- and S-wave separation from multi-component seismic data

Abstract

In this paper, we present a frequency-wavenumber domain scheme to separate P- and S-waves from multi-component seismic data at the free surface. Based on the relationship between the P- and S-wave separated elastic equation, and the divergence and curl operators, we modify the equation to make it applicable to surface seismic data. In the modified equation, the P-wavenumber is chosen to reject the P-waves, and the S-wavenumber is chosen to eliminate the S-waves. The changes in the P-S amplitude ratio caused by the wavenumber choice are corrected. For the free surface condition, an up-going wavefield separation filter is introduced into the modified equation, which can remove the free surface effects from the surface seismic data. In the case of a free surface exhibiting lateral heterogeneity, the seismic data are first transformed into the frequency domain using the fast Fourier transform (FFT), and then are transformed into the wavenumber domain using the discrete Fourier transform (DFT). In the second transform using the DFT, the modified equation is used to separate the P- and S-waves. Numerical tests on synthetic data for three models demonstrate the good performance and accuracy of the scheme.