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

Filip P. Adamus

doi:10.1111/1365-2478.12998

E-ISSN: 1365-2478

Orthotropic anisotropy: on contributions of elasticity parameters to a difference in quasi‐P‐wave‐squared velocities resulted from propagation in two orthogonal symmetry planes
By Filip P. Adamus¹
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Affiliations: ¹ Department of Earth Sciences, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada
Source: Geophysical Prospecting, Volume 68, Issue 8, Sep 2020, p. 2361 - 2378
DOI: https://doi.org/10.1111/1365-2478.12998
- Received: 08 Nov 2019
- Accepted: 23 Jun 2020
- Published online: 07 Jul 2020

Abstract

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.

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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

Geophysical Prospecting 68, 2361 (2020); https://doi.org/10.1111/1365-2478.12998

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Article Type: Research Article

Keyword(s): Anisotropy; Elastics; Numerical study; Theory; Velocity analysis

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

Abstract

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