Decoupling approximation of P- and S-wave phase velocities in orthorhombic media

Abstract

Characterizing the kinematics of seismic waves in elastic orthorhombic media involves nine independent parameters. All wave modes, P-, S1-, and S2-waves, are intrinsically coupled. Since the P-wave propagation in orthorhombic media is weakly dependent on the three S-wave velocity parameters, they are set to zero under the acoustic assumption. The number of parameters required for the corresponding acoustic wave equation is thus reduced from nine to six, which is very practical for the inversion algorithm. However, the acoustic wavefields generated by the finite-difference scheme suffer from two types of S-wave artifacts, which may result in noticeable numerical dispersion and even instability issues. Avoiding such artifacts requires a class of spectral methods based on the low-rank decomposition. To implement a six-parameter pure P-wave approximation in orthorhombic media, we develop a novel phase velocity approximation approach from the perspective of decoupling P- and S-waves. In the exact P-wave phase velocity expression, we find that the two algebraic expressions related to the S1- and S2-wave phase velocities play a negligible role. After replacing these two algebraic expressions with the designed constant and variable respectively, the exact P-wave phase velocity expression is greatly simplified and naturally decoupled from the characteristic equation. Similarly, the number of required parameters is reduced from nine to six. We also derive an approximate S-wave phase velocity equation, which supports the coupled S1- and S2-waves and involves nine independent parameters. Error analyses based on several orthorhombic models confirm the reasonable and stable accuracy performance of the proposed phase velocity approximation. We further derive the approximate dispersion relations for the P-wave and the S-wave system in orthorhombic media. Numerical experiments demonstrate that the corresponding P- and S-wavefields are free of artifacts and exhibit good accuracy and stability.

Simulation of improved pure P‐wave equation in transversely isotropic media with a horizontal symmetry axis

“…In this new acoustic approximation, the S‐wave axial phase velocity can be expressed as a function of propagation direction by setting the SV‐wave phase velocity to zero. Thus, the pure P‐wave equations can directly be decoupled with no S‐wave artefacts (Li & Stovas, 2021, 2022; Stovas et al., 2020; Xu, Stovas & Mikada, 2020; Xu, Stovas, Alkhalifah, et al., 2020). However, the form of this new acoustic approximation is quite complicated.…”