Numerical Wavefield Simulation in Deviated Boreholes within Vertical Transversely Isotropic Formations, Part 2: A Dipole Source

The propagation characteristics of acoustic waves in deviated wells within anisotropic formations are analyzed using a three-dimensional finite-difference method accelerated by GPU computing. A coordinate system rotation strategy is employed to efficiently handle anisotropy, significantly improving computational efficiency over traditional finite-difference methods. A 2×2×6m anisotropic wellbore model is used to simulate wave propagation, focusing on shear wave velocity, waveform, and dispersion in formations such as Pierre Shale. Results show that shear wave velocity in the xoz plane increases then decreases with deviation angle, while in the yoz plane, it increases consistently, revealing clear differences between fast and slow shear waves. Velocities extracted via the slowness-time-coherence method align well with theoretical values, confirming the simulation’s reliability. This is particularly evident in the match between simulated shear wave velocities and theoretical group velocities, as well as the phase-group velocity differences observed across waveforms. Increasing well deviation leads to notable changes in elastic moduli, especially in parameters C11 and C33. Sensitivity analysis indicates distinct trends in how P-, SH-, and SV-waves respond to elastic parameter variations. When deviation exceeds 60°, significant differences in amplitude and arrival time between fast and slow shear waves emerge, highlighting the influence of deviation on wave propagation. Real-data analysis further reveals complex acoustic field variations caused by vertical transverse isotropy and azimuthal anisotropy at specific depth intervals. The polarization direction of fast shear waves is strongly associated with borehole azimuth, underscoring wavefield complexity at large deviation angles. These findings deepen the understanding of acoustic wave behavior in anisotropic formations and contribute to improved interpretation and modeling of wave propagation in deviated wells.