Distributed acoustic sensing (DAS) is increasingly used in seismic exploration owing to its wide frequency range, dense sampling and real-time monitoring. DAS radiation patterns help to understand angle response of DAS records and improve the quality of inversion and imaging. In this paper, we solve the 3D vertical transverse isotropic (VTI) Christoffel equation and obtain the analytical, first-order, and zero-order Taylor expansion solutions that represent P-, SV-, and SH-wave phase velocities and polarization vectors. These analytical and approximated solutions are used to build the P/S plane-wave expression identical to the far-field term of seismic wave, from which the strain rate expressions are derived and DAS radiation patterns are thus extracted for anisotropic P/S waves. We observe that the gauge length and phase angle terms control the radiating intensity of DAS records. Additionally, the Bond transformation is adopted to derive the DAS radiation patterns in title transverse isotropic (TTI) media, which exhibits higher complexity than that of VTI media. Several synthetic examples demonstrate the feasibility and effectiveness of our theory.

Common-image gathers are extensively used in amplitude versus angle (AVA) and migration velocity analysis (MVA). The current state of methods for anisotropic angle gathers extraction use slant-stack, local Fourier transform or low-rank approximation, which requires much computation. Based on an anisotropic-Helmholtz P/S wave-mode decomposition method, we propose a novel and efficient approach to produce angle-domain common-image gathers (ADCIGs) in the elastic reverse time migration (ERTM) of VTI media. To start with, we derive an anisotropic-Helmholtz decomposition operator from the Christoffel equation in VTI media, and use this operator to derive the decomposed formulations for anisotropic P/S waves. Second, we employ the first-order Taylor expansion to calculate the normalized term of decomposed formulations and obtain the anisotropic-Helmholtz decomposition method, which generates the separated P/S wavefields with correct amplitudes and phases. Third, we develop a novel way that uses the anisotropic-Helmholtz decomposition operator to define the polarization angles for anisotropic P/S waves and substitute these angles to decomposing formulations. The polarization angles are then calculated directly from the separated vector P- and S-wavefields and converted to the phase angles. The ADCIGs are thusly produced by applying the phase angles to VTI ERTM. In addition, we develop a concise approximate expression of residual moveout (RMO) for PP-reflections of flat reflectors in VTI media, which avoids the complex transformations between the group angles and the phase angles. The approximate RMO curves show a good agreement with the exact solution and can be used as a tool to assess the migration velocity errors. As demonstrated by two selected examples, our ADCIGs not only produce the correct kinematic responses with regards to different velocity pertubatation, but also generate the reliable amplitude responses versus different angle. The final stacking images of ADCIGs data exhibit the identical imaging effect as that of VTI ERTM.