Pseudo-Helmholtz decomposition for an elastic VTI wavefield based on wavefront phase direction

Abstract

P and S waves are coupled when propagating in anisotropic elastic media. The separation of P and S waves helps to study the characteristics of different types of seismic waves as well as mitigating crosstalk artifacts in elastic reverse time migration and elastic full-waveform inversion. At present, the methods of seismic wave mode separation in anisotropic media are mainly built on divergence- and curl-like operations, pseudo-Helmholtz decomposition, and low-rank approximation. We develop a new pseudo-Helmholtz decomposition operator based on eigenform analysis and the wavefront phase direction to decompose vertically transversely isotropic elastic wavefields. The corresponding P-/S-wave decoupling formulas are also derived in detail. Compared with the divergence- and curl-like methods, the new method does not change the phase of P and S waves. Compared with existing pseudo-Helmholtz decomposition methods based on eigenform analysis, our method achieves more accurate wavefield separation than the zero-order pseudo-Helmholtz decomposition operator. Our method requires solving one vector Poisson equation only, resulting in much less computational cost than the existing first-order pseudo-Helmholtz decomposition methods. In addition, the accuracy of our method is analyzed by providing homogeneous media with different parameter settings. Finally, the numerical examples demonstrate that the new pseudo-Helmholtz decomposition method is effective, efficient, and robust against random noise.