Difference between revisions of "1st Lamé parameter"
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[[File:Gabriel-Lamé.jpg|thumb|Gabriel Lamé]] | [[File:Gabriel-Lamé.jpg|thumb|Gabriel Lamé]] | ||
− | The '''1st Lamé parameter''', sometimes called Lamé's first parameter, | + | 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, [[Wikipedia:Gabriel Lamé|Gabriel Lamé]] (right). |
+ | |||
+ | It is often said that ''λ'' has no physical interpretation, and most people find it hard to visualize. | ||
==In terms of ''V''<sub>P</sub> and ''V''<sub>S</sub>== | ==In terms of ''V''<sub>P</sub> and ''V''<sub>S</sub>== | ||
+ | |||
+ | :<math>\lambda = \rho(V_\mathrm{P}^2 - 2 V_\mathrm{S}^2) </math> | ||
==Other expressions== | ==Other expressions== | ||
− | ''λ'' can also be expressed in terms of [[Young's modulus]], ''E'', and [[Poisson's ratio]], ''ν'': | + | ''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': |
:<math>\lambda = \frac{E\nu}{(1+\nu)(1-2\nu)}</math> | :<math>\lambda = \frac{E\nu}{(1+\nu)(1-2\nu)}</math> | ||
− | The | + | 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> | ||
+ | |||
+ | ==Typical values== | ||
+ | |||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! Rock | ||
+ | ! ''λ'', GPa | ||
+ | |- | ||
+ | | Quartz || 8 | ||
+ | |- | ||
+ | | Feldspar || 28 | ||
+ | |- | ||
+ | | Calcite || 56 | ||
+ | |- | ||
+ | | Dolomite || 65 | ||
+ | |- | ||
+ | | Anhydrite || 26 | ||
+ | |- | ||
+ | | Siderite || 90 | ||
+ | |- | ||
+ | | Pyrite || 59 | ||
+ | |- style="background: lightgrey" | ||
+ | | Sandstone, 10 pu || 1–3 | ||
+ | |- style="background: lightgrey" | ||
+ | | Limestone, 10 pu || 18–53 | ||
+ | |- style="background: lightgrey" | ||
+ | | Shale, 5 pu || 3–24 | ||
+ | |- style="background: lightblue" | ||
+ | | Brine || 2.3 | ||
+ | |- style="background: lightblue" | ||
+ | | Oil, 40°API || 1.6 | ||
+ | |} | ||
==References== | ==References== | ||
+ | <references /> | ||
==External links== | ==External links== |
Revision as of 13:53, 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).
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 |
References
External links
- First Lamé parameter — Wikipedia entry
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