In this work, a novel gradient descent optimization algorithm based on a dynamic self-consistent SC anisotropic micromechanics approach is implemented to estimate porosity Phi , pore aspect ratio delta , and pore characteristic length a on rocks. The significance of this algorithm is that it can estimate these petro-physical parameters from measured experimental frequency-dependent compressional P and shear wave S velocities travelling through the rock when the rock sample itself is not available. The specimen studied here corresponds to the heavy oil-saturated Uvalde carbonate, which is assumed to be anisotropic and shows a vertical axis of symmetry. Under this assumption, the theoretical anisotropic non-linear SC equations used to model the anisotropic compressional and shear wave velocities are expressed in terms of the heavy oil volume fraction a (rock's porosity Phi), rock pore aspect ratio delta , rock pore characteristic length a , polarization of the shear wave (either vertically or horizontally polarized), and angle of incidence (direction of propagation) h at which the velocity measurements could have been taken with respect to the assumed axis of symmetry. Then, an objective function F is proposed to compare the theoretical velocities to the experimental velocities. Afterwards, for each frequency, a gradient descent algorithm is implemented on F to seek the optimum values alpha(opt) , delta(opt) , a(opt) , and theta(opt) for which the difference between the theoretical and experi-mental velocities is minimal. Results suggest the presence of anisotropy with theta(opt) = 78.3 degrees and Phi = alpha(opt) = 0.224, delta(opt) = 0.27, and a(opt) = 0.00022 m. These values are consistent with experi-mental values reported in the scientific literature: Phi = 0.24, delta = 0.32 and a = 0.00025 m, respectively.
