Abstract: Numerical simulation of acoustic wave is very important for the study of anisotropy characteristics of shale and the study of shale acoustic wave correction in highly inclined well. In order to study the anisotropic characteristics of shale acoustic wave, an equivalent shale model composed of argillaceous and sand layers was established on the basis of equivalent medium theory, the calculation methods of the stiffness coefficient and acoustic wave velocity of the equivalent shale model were derived from the elasticity theory, and the influences of the elastic parameter, thickness, angle and density of the lamina on the stiffness coefficient and the elastic wave velocity of the equivalent shale model were analyzed. The study shows that the thickness ratio of argillaceous layer to sandy layer affected the stiffness coefficient of equivalent medium. The stiffness coefficient of equivalent shale model increased with the increase of parameter ratio. Lamet coefficient of argillaceous layer affected the relationship between P-wave velocity and lamina angle and the extreme value of S-wave velocity, but had no effect on SH wave. The acoustic wave velocity was increased with the increase of shear modulus or parameter ratio of the argillaceous layer, and the shear modulus had a great effect on the relationship between the three wave velocities and the lamina angle. When the lamina density was constant, the P-wave velocity was decreased gradually and stabilized with the increase of lamina angle, the S-wave velocity increased first and then decreased, and the SH wave velocity decreased gradually. When the lamina angle was constant, the three wave velocities were decreased gradually with the increase of lamina density. This study plays a guiding role in the shale acoustic numerical simulation and acoustic logging correction.

Key words: equivalent medium theory, shale model, lamina thickness, lamina elastic parameters, acoustic wave velocity, numerical simulation