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Orthotropic anisotropy: on contributions of elasticity parameters to a difference in quasi‐P‐wave‐squared velocities resulted from propagation in two orthogonal symmetry planes
- Source :
- Geophysical Prospecting. 68:2361-2378
- Publication Year :
- 2020
- Publisher :
- Wiley, 2020.
-
Abstract
- 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, s2, resulted from propagation in two mutually perpendicular symmetry planes. In the context of the effective medium theory, s2 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 s2. Due to them, we interpret the aforementioned squared‐velocity difference as being twice more dependent on C55−C44, than on C13−C23. To describe the magnitude of the dependence, we consider the proportions between the partial derivatives of s2. Further, it occurs that s2 is influenced by the ratio of vertically propagating quasi P‐wave to vertically propagating quasi S‐wave. Anomalously high s2 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 s2 is approximately twice more dependent on C55 than on C13, twice more sensitive to C44 than to C23, and equally dependent on −C33 as on C13+C23. The dependence on C11 and C22 can be neglected, especially for small phase angles. We verify the approximations and perform the sensitivity study, using eight examples of the elasticity tensors.
- Subjects :
- Physics
Christoffel symbols
010504 meteorology & atmospheric sciences
Mathematical analysis
010502 geochemistry & geophysics
Orthotropic material
01 natural sciences
Geophysics
Geochemistry and Petrology
Perpendicular
Partial derivative
Phase velocity
Elasticity (economics)
Porosity
Anisotropy
0105 earth and related environmental sciences
Subjects
Details
- ISSN :
- 13652478 and 00168025
- Volume :
- 68
- Database :
- OpenAIRE
- Journal :
- Geophysical Prospecting
- Accession number :
- edsair.doi...........1a055e6e373c0832317e564a8ad98186