Modeling the effects of pore aspect ratio, porosity, and seismic anisotropy on wave velocity dispersion and attenuation patterns in oil- and brine-saturated carbonates using a dynamic self-consistent anisotropic approach

In this work, numerical modeling was performed using a dynamic self-consistent (SC) anisotropic micromechanics approach. This study examines how porosity, pore aspect ratio, and seismic anisotropy affect the velocity dispersion and attenuation patterns of P-waves and polarized S-waves (SH and SV) traveling through oil- and brine-saturated carbonate rocks (3D body) at seismic, sonic, and ultrasonic frequencies. Here, the carbonate rock was idealized as a mineral carbonate matrix embedded with aligned ellipsoidal fluid inclusions of aspect ratio \(\gamma\) $\gamma$ . These ellipsoidal inclusions represent the porosity \(\phi\) $\varphi$ , which is saturated with fluid. The studied rock was assumed to have a vertical axis of symmetry that is perpendicular to the plane of alignment and therefore will show vertical transverse isotropy (VTI). Wave velocities were modeled considering a variety of porosities ( \(\phi =\) $\varphi =$ 5, 10, 15, and 20%), aspect ratios (ranging from \(\gamma = 0.2\) $\gamma =0.2$ to \(\gamma = 5\) $\gamma =5$ ), and angles of incidence ( \(\theta = 0^\circ ,\) $\theta =0^{\circ },$ \(30^\circ ,\) ${30}^{\circ },$ \(45^\circ\) ${45}^{\circ }$ , \(60^\circ\) ${60}^{\circ }$ , and \(90^\circ\) ${90}^{\circ }$ ), where \(\theta\) $\theta$ is the angle between the symmetry axis and the direction of wave propagation through the rock. Overall, results showed that the largest changes in P- and SH-wave velocities are due to variations in \(\phi\) $\varphi$ (up to 15%), followed by changes in \(\theta\) $\theta$ (up to 6%), and then by changes in \(\gamma\) $\gamma$ (up to 4.3%). By contrast, for SV-wave velocities the order changes in the last two parameters. Finally, the variations in P- and S-wave velocity dispersion and their maximum attenuation are greater for oblate ellipsoids \(\left(\gamma <1\right)\) $\left(\gamma ,<,1\right)$ than for prolate ellipsoids \(\left(\gamma >1\right)\) $\left(\gamma ,>,1\right)$ , regardless of porosity, angle of incidence, and aspect ratio.