Understanding the limitations of anisotropic of elastic rock physics modeling by Ridzki’s inequalities

The objective of this study is to describe the limitations of anisotropic rock physics modeling using Ridzki inequalities. Anisotropic rock physics modeling provides the link between seismic anisotropy and anisotropic properties of rocks. However, the limitations of anisotropic rock physics modelling are not well described in the literature. We compare isotropic and anisotropic rock physics models to demonstrate the limitations of anisotropic rock physics modeling. We described the limitations of anisotropic rock physics models by the restrictions of anisotropic seismic properties originally reported by the pioneer of seismic anisotropic modeling, Professor Maurice Ridzki. This study shows that difference between isotropic and anisotropic approximations are increased with increasing complexity of pore structure while isotropic and anisotropic approximations are equal when pore structures are assumed to be spherical. Limitations of anisotropic seismic properties suggest that the Self-Consistent Approximation (SCA) is valid for a maximum porosity of 14%, whereas Differential Effective Medium modeling (DEM) is valid for maximum porosity of 17% when the aspect ratio of the pores is 0.2. Furthermore, we introduce an anisotropic elastic constant which can be used to describe the difference between c12 and c13 in transversely isotropic media.