Orthotropic anisotropy: on contributions of elasticity parameters to a difference in quasi-P-wave-squared velocities resulted from propagation in two orthogonal symmetry planes

We investigate the dependence of quasi P-wave phase velocity propagating in orthotropic media on particular elasticity parameters. Specifically, due to mathematical facilitation, we consider the squared-velocity difference, , resulted from propagation in two mutually perpendicular symmetry planes. In the context of the effective medium theory, may be viewed as a parameter evaluating the influence of cracks – embedded in the background medium – parallel to one or both aforementioned planes. Our investigation is both theoretical and numerical. Based on Christoffel's equations, we propose two accurate approximations of . Due to them, we interpret the aforementioned squared-velocity difference as being twice more dependent on , than on . To describe the magnitude of the dependence, we consider the proportions between the partial derivatives of . Further, it occurs that is influenced by the ratio of vertically propagating quasi P-wave to vertically propagating quasi S-wave. Anomalously high might be caused by the low P/S ratio, which in turn can be an indicator of the presence of gas in natural fractures or aligned porosity. Also, we carry out numerical sensitivity study, according to which is approximately twice more dependent on than on , twice more sensitive to than to , and equally dependent on as on . The dependence on and can be neglected, especially for small phase angles. We verify the approximations and perform the sensitivity study, using eight examples of the elasticity tensors.