A weak-anisotropy approximation to multicomponent induction responses in cross-bedded formations
The multicomponent induction logging response to a cross-bedded formation has been modeled under a weak-anisotropy approximation. With the approximation, a cross-bedded formation can be modeled as a transversely isotropic (TI) medium. The validity of the approximation has been tested for the main (coplanar and coaxial) components of the induction response. The conditions for the weak-anisotropy approximation to be valid depend on the component of the response. For the coplanar components, the approximation is valid for an anisotropy ratio up to 2 if the relative dipping angle between the cross-bedded formation and the borehole axis is below [Formula: see text]. For the coaxial component, the approximation reduces to a previously established result that the apparent resistivity for such a component is the geometric average of the resistivities, parallel and perpendicular to the bedding planes of an anisotropic formation, respectively, if the borehole is ignored. Hence, the approximation holds for the coaxial component regardless of the anisotropy ratio.