Publication Date:
2019
Description:
ABSTRACT
We consider a transversely isotropic (TI) medium that is long‐wave equivalent to a stack of thin, parallel, isotropic layers and is obtained using the Backus average. In such media, we analyze the relations among anisotropy parameters; Thomsen parameters, ε, and δ, and a new parameter φ. We discuss the last parameter and show its essential properties; it equals to zero in the case of isotropy of equivalent medium and/or constant Lamé coefficient Λ in layers. The second property occurs to make φ sensitive to variations of Λ in thin‐bedded sequences. According to Gassmann, in isotropic media the variation of fluid content affects only the Lamé coefficient Λ, not μ; thus, the sensitivity to changes of Λ is an essential property in the context of possible detection of fluids. We show algebraically and numerically that φ is more sensitive to these variations than ε or δ.
Nevertheless, each of these parameters is dependent on the changes of μ; to understand this influence, we exhibit comprehensive tables that illustrate the behavior of anisotropy parameters with respect to specific variations of Λ and μ. The changes of μ in layers can be presented by the Thomsen parameter γ that depends on them solely. Hence, knowing the values of elasticity coefficients of equivalent TI medium, we may compute φ and γ, and based on the aforementioned tables, we predict the expected variation of Λ; in this way, we propose a new method of possible fluid detection. Also, we show that the prior approach of possible detection of fluids, proposed by Berryman et al., may be unreliable in specific cases.
To establish our results we use the Monte Carlo (MC) method; for the range and chosen variations of Lamé coefficients Λ and μ—relevant to sandstones—we generate these coefficients in thin layers and, after the averaging process, we obtain an equivalent TI medium. We repeat that process numerous times to get many equivalent TI media, and—for each of them—we compute their anisotropy parameters. We illustrate φ, ε, and δ in the form of cross‐plots that are relevant to the chosen variations of Λ and μ. Additionally, we present a table with the computed ranges of anisotropy parameters that correspond to different variations of Lamé coefficients.
This article is protected by copyright. All rights reserved
Print ISSN:
0016-8025
Electronic ISSN:
1365-2478
Topics:
Geosciences
,
Physics
Permalink