Reflection coefficients of qP- and qS- incident waves in orthorhombic media can be explicitly expressed by means of impedance matrices. In this paper, we extend previous studies and derive generalized linearized equations of qP-qP and qP-qS waves. Impedance matrices representing complete reflection properties of the medium can be inverted based on the simplified equations. Besides, these equations are reduced for an isotropic medium with a vertical symmetry axis (VTI) or a horizontal axis (HTI). We discuss their accuracy and applicability by means of three models: two models of VTI/VTI interfaces with moderate and strong anisotropy, and a VTI/HTI model. The approximations have sufficient accuracy for relatively strong anisotropy. Therefore they can be applied in the characterization of unconventional resources, for example, shale gas or coalbed methane.


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