Decoupled approximation and separate extrapolation of P- and SV-waves in transversely isotropic media

Abstract

Characterizing the kinematics of seismic waves in elastic vertical transversely isotropic (VTI) media involves four independent parameters. To reduce the complexity, the acoustic approximation for P-waves reduces the number of required parameters to three by setting the vertical S-wave velocity to zero. However, since only the SV-wave phase velocities parallel or perpendicular to the symmetry axis are indirectly set to zero, the acoustic approximation leads to coupled P-wave components and SV-wave artifacts. The new acoustic approximation suggests setting the vertical S-wave velocity as a phase angle-dependent variable so that the SV-wave phase velocity is zero at all phase angles. We find that manipulating this parameter is a valid way for P-wave approximation, but doing so inevitably leads to zero- or non-zero-valued spurious SV-wave components. Thus, we have developed a novel approach to efficiently approximate and thoroughly separate the two wave modes in VTI media. First, the exact P- and SV-wave phase velocity expressions are rewritten by introducing an auxiliary function. After confirming the insensitivity of this function, we construct a new expression for it and obtain simplified P- and SV-wave phase velocity expressions, which are three- and four-parameter, respectively. This approximation process leads to the same reasonable error for both wave modes. Accuracy analysis indicates that for the P-wave, the overall accuracy performance of our approach is comparable to that of some existing three-parameter approximations. We then derive the corresponding P- and SV-wave equations in tilted transversely isotropic (TTI) media and provide two available solutions, the hybrid finite-difference/pseudo-spectral scheme and the low-rank approach. Numerical examples illustrate the separability and high accuracy of the proposed P- and SV-wave simulation methods in TTI media.

Two‐dimensional anisotropic acoustic wave modelling using the support operator method

“…It is a fictitious S‐wave that arises in the case of anisotropic acoustic wave modelling and is referred to as S‐wave artefacts in the literature (Alkhalifah, 1998). Several schemes have been proposed (Abedi & Stovas, 2020; B. Li & Stovas, 2021; Stovas et al., 2021; Xu et al., 2020) to suppress these artefacts in the acoustic wave modelling of anisotropic models. The S‐wave artefact is diamond shaped for this model because the anisotropic parameter $$\varepsilon$$ is greater than $$\delta$$, and this behaviour follows the results reported in other studies (Zhou et al., 2006).…”

“…It is a fictitious S-wave that arises in the case of anisotropic acoustic wave modelling and is referred to as S-wave artefacts in the literature (Alkhalifah, 1998). Several schemes have been proposed (Abedi & Stovas, 2020;B. Li & Stovas, 2021;Stovas et al, 2021;Xu et al, 2020) to suppress these artefacts in the acoustic wave modelling of anisotropic models.…”

Method to Measure Radial Thermal Conductivity for Cylindrical Samples

“…Anisotropy is a universal physical property prevailing in common materials or media. Substantial anisotropic differences exist among crystals, various materials used in daily life, and earth media. − The industry is well aware of the importance of thermal conductivity anisotropy in geothermal exploitation. Geophysicists have focused their attention on this anisotropy in rocks.…”

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.…”