The similarity transformation to the Christoffel equation preserves the kinematics of the qS-waves,
but inevitably change the phases and amplitudes in their wavefields.
Accordingly, the pseudo-pure-mode wave equations may change the radiation from a point source
(as demonstrated in the examples),
and even distort the amplitude variation with offset (AVO).
In other word, they do not honor the dynamic elasticity of the waves in real media.
In fact, other simplified forms of the elastic wave equation, such as acoustic or pseudo-acoustic wave equations
and the pure-mode approximate wave equations, have similar limitations
(Shang et al., 2015; Operto et al., 2009; Cheng and Kang, 2014; Barnes and Charara, 2009).
For heterogeneous rough media, i.e., when scales for variations in the elastic parameters are small compared with the wavelengths
of the wavefield, the acoustic approximation is no longer reliable (Cance and Capdeville, 2015).
The pseudo-pure-mode wave equations have similar limitations for shear-wave modeling in high-contrast TI media.
However, these limitations are not doomed to be catastrophic, because velocity models
containing high-wavenumber components are rarely involved at most stages of seismic imaging and inversion for real data.
Simulating propagation of separated wave modes in general anisotropic media,
Part II: qS-wave propagators
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