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, or lambda ''λ'', is an [[elastic modulus]]. It is used extensively in [[quantitative seismic interpretation]] and [[rock physics]]. It was first described by the French mathematician, [[Wikipedia:Gabriel Lamé|Gabriel Lamé]] (right).
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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).
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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>==
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:<math>\lambda = \rho(V_\mathrm{P}^2 - 2 V_\mathrm{S}^2) </math>
  
 
==Other expressions==
 
==Other expressions==
''&lambda;'' can also be expressed in terms of [[Young's modulus]], ''E'', and [[Poisson's ratio]], ''&nu;'':
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''&lambda;'' can also be expressed in terms of [[Young's modulus]], ''E'', and [[Poisson's ratio]], ''&nu;''. 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 simplest expression casts ''&lambda;'' in terms of bulk modulus and shear modulus ''&mu;'':
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The 'fluid substitution perspective' casts ''&lambda;'' in terms of bulk modulus and shear modulus ''&mu;'':
  
 
:<math>\lambda = K - \frac23 \mu</math>
 
:<math>\lambda = K - \frac23 \mu</math>
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==Typical values==
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{| class="wikitable"
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|-
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! Rock
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! ''&lambda;'', GPa
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|-
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| Quartz || 8
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|-
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| Feldspar || 28
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|-
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| Calcite || 56
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|-
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| Dolomite || 65
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|-
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| Anhydrite || 26
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|-
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| Siderite || 90
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|-
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| Pyrite || 59
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|- style="background: lightgrey"
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| Sandstone, 10 pu ||  1–3
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|- style="background: lightgrey"
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| Limestone, 10 pu ||  18–53
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|- style="background: lightgrey"
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| Shale, 5 pu ||  3–24
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|- style="background: lightblue"
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| Brine || 2.3
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|- style="background: lightblue"
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| Oil, 40&deg;API || 1.6
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|}
  
 
==References==
 
==References==
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<references />
  
 
==External links==
 
==External links==

Revision as of 13:53, 7 September 2011

Gabriel Lamé

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.

In terms of VP and VS

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

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