3D true-amplitude elastic wave-vector decomposition in heterogeneous anisotropic media

Abstract

Wave-mode separation aims at separating the elastic wavefield into P- and S-wave modes in each subsurface grid. Several wave-mode separation methods require the calculation of polarization vectors of different wave modes. We have developed a wave-mode separation method based on an analytical decomposition operator and a low-rank approximation in the wavenumber domain. When dealing with a general anisotropic medium with low symmetry, the two S-wave modes suffer from the singularity problem, where strong planar artifacts are caused due to the discontinuous polarization vectors at the singularities. A weight function with an adjustable threshold parameter can be designed to mitigate the strong artifacts, thereby obtaining clean S-wave modes. Larger threshold results in a stronger suppression of the artifacts but at the expense of stronger damages to S-wave energy. Here, we provide a new way to deal with the planar artifacts. The S-wave modes separated using a zero threshold containing strong artifacts can be treated as a noisy wavefield. Applying a weighting function can be viewed as a denoising process. Choosing the threshold parameter in the weighting function will inevitably cause an amplitude loss of the signal. Thus, we can apply the local orthogonalization method to compensate for the amplitude loss. Considering the heterogeneity of the wavefield, we apply a nonstationary local orthogonalization method to obtain an accurate wave-mode separation. The final separated wavefields are true amplitude and thus kinematically and dynamically correct, which will benefit a variety of seismic forward and inverse problems. Several 3D synthetic examples demonstrate the performance of the new method.