Difference between revisions of "1st Lamé parameter"
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:<math>\lambda = \frac{E\nu}{(1+\nu)(1-2\nu)}</math> | :<math>\lambda = \frac{E\nu}{(1+\nu)(1-2\nu)}</math> | ||
− | The 'fluid substitution perspective' casts ''λ'' in terms of bulk modulus and shear modulus ''μ'': | + | The '[[fluid substitution perspective]]' casts ''λ'' in terms of [[bulk modulus]] and [[shear modulus]] ''μ'': |
:<math>\lambda = K - \frac23 \mu</math> | :<math>\lambda = K - \frac23 \mu</math> |
Revision as of 15:18, 7 September 2011
The 1st Lamé parameter, sometimes called Lamé's first parameter, but is more usually referred to simply as lambda, λ. It is an elastic modulus and used extensively in quantitative seismic interpretation and rock physics. It was first described by the French mathematician, Gabriel Lamé (right). Lamé's second parameter is equivalent to shear modulus, μ.
It is often said that λ has no physical interpretation, and most people find it hard to visualize.
Contents
In terms of V_{P} and V_{S}
Other expressions
λ can also be expressed in terms of Young's modulus, E, and Poisson's ratio, ν. This could be thought of as 'the engineer's perspective':
The 'fluid substitution perspective' casts λ in terms of bulk modulus and shear modulus μ:
Typical values
Rock | λ, GPa |
---|---|
Quartz | 8 |
Feldspar | 28 |
Calcite | 56 |
Dolomite | 65 |
Anhydrite | 26 |
Siderite | 90 |
Pyrite | 59 |
Sandstone, 10 pu | 1–3 |
Limestone, 10 pu | 18–53 |
Shale, 5 pu | 3–24 |
Brine | 2.3 |
Oil, 40°API | 1.6 |
Analysis and interpretation
Goodway and others^{[1]} have described an alternative to (or augmentation of) classic impedance inversion and interpretation. The parameters are closely related:
This approach—estimating Lamé's parameters indirectly via impedance—is problematic^{[2]} so Gray recommended estimating λ and μ contrasts directly from seismic data^{[3]}. See discussion in Avseth et al^{[2]}.
References
- ↑ Goodway, B, T Chen, and J Downton (1997), Improved AVO fluid detection and lithology discrimination using Lamé's petrophysical parameters, λρ, μρ, and λ/μ fluid stack from P and S inversions. SEG Annual Meeting, Expanded Abstracts, 183–186.
- ↑ ^{2.0} ^{2.1} Avseth, P, T Mukerji and G Mavko (2006), Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk, Cambridge University Press.
- ↑ Gray, D, B Goodway, and T Chen (1999), Bridging the gap: Using AVO to detect changes in fundamental elastic constants, SEG Annual Meeting, Expanded Abstracts, 852–855.
External links
- First Lamé parameter — Wikipedia entry
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