Exact Elastic Impedance Tensor for Isotropic Media

Conventional elastic/ray impedance approximations are derived as a scalar to heuristically present seismic reflectivity based on the assumptions of weak impedance, isotropic media, or weak anisotropic media. In this paper, considering the concept of impedance in general physics, we define impedance tensors according to the relation between stress and velocity fields. The impedance tensors have explicit physical meaning and thus each of the derived elastic impedance components represents a unique mechanical property of the medium. Because no assumptions are made in the derivation of the exact expressions of elastic impedances, the expressions have higher accuracy than the approximations of conventional elastic impedance, and can thus potentially be applied in the characterization of unconventional formations having strong impedance contrast. The properties of each of the elastic impedance components are discussed through theoretical analysis. Logs of a turbidite fan reservoir are used to study the interpretation capability of the derived EIs in lithology/facies discrimination. We also discuss a practical workflow of seismic inversion, and thus provide a new method of reservoir characterization.