Velocity and attenuation (Q) anisotropy are widely distributed in the Earth’s interior, significantly affecting the kinematic and dynamic characteristics of seismic‐wave propagations. Previous studies developed to simulate these effects are mainly restricted to the constant‐Q assumption. However, seismic attenuation in high‐temperature and high‐pressure regions is demonstrated to be frequency‐dependent and usually follows a power‐law formulation. To simulate this Q effect in transversely isotropic (TI) attenuating media, we derive a new pure‐viscoacoustic wave equation with decoupled fractional Laplacians, which can simultaneously simulate amplitude dissipation and velocity dispersion effects. Based on the wavenumber relationship between the observation and physical coordinate systems, the tilted TI (TTI) wave equation is further derived. Compared with the pseudoviscoacoustic wave equation, the proposed pure‐viscoacoustic equation can simulate stable P wavefields in complex geological structures without S‐wave artifacts. To solve this new equation, two low‐rank decompositions are introduced to approximate the real and imaginary parts and avoid the separation of wavenumbers and dip angles, making it much simpler in programming and implementation. We further use this equation to perform Q‐compensated reverse‐time migration to generate high‐resolution migration images in anisotropic attenuating media. Numerical examples demonstrate the effectiveness of the proposed method for pure‐viscoacoustic wavefield simulations and migrations in TTI attenuating media with power‐law frequency‐dependent Q effects.

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