1st Lamé 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, 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.
In terms of VP and VS
The 'fluid substitution perspective' casts λ in terms of bulk modulus and shear modulus μ:
|Sandstone, 10 pu||1–3|
|Limestone, 10 pu||18–53|
|Shale, 5 pu||3–24|
Analysis and interpretation
This approach—estimating Lamé's parameters indirectly via impedance—is problematic so Gray recommended estimating λ and μ contrasts directly from seismic data. See discussion in Avseth et al.
- 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.
- 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.
- First Lamé parameter — Wikipedia entry