The simulation of acoustic wave propagation in the borehole surrounded by vertical transversely isotropic (VTI) media using staggered-grid high-order finite-difference method

Transversely isotropic(TI) media is a common petrophysical media. It is important to study the propagation characteristics of the acoutic field in the well for sonic logging theory, and it can provide the basis for the sonic log interpretation. This paper derived velocity-stress staggered-grid finite-difference equations of the elastic wave propagation in cylindrical coordinates for vertical transversely isotropic(VTI) media. Furthermore, it numerically simulated acoustic propagation in the VTI media using finite-difference technique with two orders in time and ten orders in space. It gave the snapshots of borehole acoustic wave field in the homogeneous media at different times and calculated the full wave trains with acoustic sources located at the well axis. The calculated results show that if the coefficient of anisotropy of VTI media increases, the change of shear wave propagation has little effect, but the velocity of longitudinal wave propagation has been reduced relatively in the longitudinal direction, and has little change in the radial direction. And if the coefficient of anisotropy of VTI media increases, the first wave slowness of sonic logging will increase, and the acoustic amplitude will be slightly reduced.