A General Anisotropic Effective Medium Model for Laminated Sequence

Abstract

Summary Effective medium rock physics model is the basis for the quantitative petrophysical interpretation of seismic and borehole acoustic measurements, because it links the formation petrophysical parameters with elastic properties, and the latter can be directly inferred from relevant measurements. Many existing works are based on conventional effective medium theories assuming isotropic underground formations, which may lead to erroneous estimates of formation properties. In this work, we extend the existing theories and develop a novel general anisotropic effective medium model to obtain the elastic constants of underground rocks. Three anisotropic effective medium theories are studied: self-consistent approximation (SCA), differential effective medium (DEM), and their combination. A newly extended Kuster-Toksöz (KT) model is also presented for the isotropic effective model. All these effective theories for elastic moduli are verified and validated with independent numerical results and experimental data. Then three workflows are implemented to obtain general stiffness coefficients for different formation models including the shaly sand model, the cracked sand model, and the shaly sand model with cracks. Furthermore, we also study the sensitivity of elastic moduli with respect to variations in pore aspect ratios.