Modeling the influence of fluid saturation and clay type on variations of Thomsen anisotropy parameters for a clay-rich granular-fractured limestone model

Abstract

Background. Thomsen parameters have become one of the principal tools in modern seismic acoustics for characterizing elastic anisotropy and refining mathematical models of geological media. They enable the quantitative description of anisotropic properties and improve the reliability of seismic data interpretation. However, approximating a geological medium by a transversely isotropic (TI) model in the presence of additional structural and textural heterogeneities may lead to significant systematic errors. Consequently, the determination of elastic anisotropy parameters in complex geological media remains an important challenge in modern geophysics, particularly with regard to numerical modeling of Thomsen parameters for orthorhombic and more complex symmetry systems.
Aim. This study aims to calculate and analyze Thomsen anisotropy parameters for a complex limestone model with different symmetry types based on a previously developed petrophysical model of a clay-bearing granular-fractured limestone from the Volyn-Podillia region.
Methods. The justification for the mathematical modeling framework used is the formulas for the parameters introduced by Thomsen, which are calculated based on the use of the elastic constants of the media. Numerical simulations were performed for transversely isotropic and orthorhombic media with different clay mineral compositions and fluid saturations.
Results. The numerical modeling demonstrated that the type of pore fluid significantly affects Thomsen parameters. Gas saturation increases the anisotropy parameter γ by enhancing the contribution of fractures to shear-wave propagation, whereas water saturation reduces δ owing to an increase in the effective stiffness and elastic homogeneity of the rock. The presence of clay minerals in reservoir rocks increases the ε and γ parameters, while δ exhibits a nonlinear decrease. At clay concentrations exceeding 4%, the behavior of δ becomes considerably more complex. Kaolinite increases all Thomsen parameters, whereas montmorillonite produces the opposite effect, leading to their reduction.
The modeling results further demonstrate that neglecting deviations from transverse isotropy may introduce errors of up to 40% in the estimation of the γ parameter. The δ parameter was found to be highly sensitive to lithological heterogeneity and fracture development. In particular, the orthorhombic parameter δ₁₂ proved to be a direct indicator of lateral fracture systems and therefore provides additional information on the internal structure of fractured reservoirs.
Conclusions. The obtained results improve the understanding of the relationships between rock composition, pore-fluid saturation, and elastic anisotropy in geologically complex reservoir models. The proposed approach demonstrates that Thomsen parameters can be used not only to characterize elastic anisotropy but also as indirect indicators of fluid saturation and reservoir structure. Variations in ε and δ may indicate the migration of fractured zones as well as the position of the oil-water contact, thereby enhancing the interpretation of seismic and well-log data in anisotropic geological environments.