Weak-anisotropy approximation for P-wave reflection coefficient at the boundary between two tilted transversely isotropic media

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Existing and commonly used in industry nowadays, closed-form approximations for a P-wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P-wave reflection amplitudes, a linearised 3D P-wave reflection coefficient at a planar weak-contrast interface separating two weakly anisotropic tilted tranversely isotropic half-spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well-known amplitude-versus-offset “Shuey-type” equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P-wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry-axis orientation angles in both half-spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude-versus-offset attributes converge to well-known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy.

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