Exact Elastic Impedance in Orthorhombic 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, we derive the exact elastic impedance tensors of qP- and qS-waves for orthorhombic media based on the stress-velocity law. They represent the unique mechanical properties of the medium, thus are called elastic mechanical impedance (EMI). The impedance tensor can be reduced for an isotropic medium with a vertical symmetry axis (VTI) or a horizontal axis (HTI). Because no assumptions are made during the derivation, the new impedance shows good accuracy at large angle and can be used to characterize unconventional reservoirs with strong anisotropy, such as shale gas and coal-bed methane reservoirs. An approximation of P-wave EMI is also discussed for a TI medium. It is expressed by vertical velocities and thus is applicable to seismic inversion and interpretation. Application tests on real log data and seismic data show the robust interpretation capability of EMI in lithology characterization compared with conventional impedances.