Far-field radiation patterns of distributed acoustic sensing in anisotropic media with an explosive source and vertically straight fiber

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.