Vp Vs Ratio Calculator
Free Vp vs ratio Calculator for geology & geophysics. Enter variables to compute results with formulas and detailed steps.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Vp/Vs = sqrt((2-2nu)/(1-2nu)) | nu = ((Vp/Vs)^2 - 2) / (2((Vp/Vs)^2 - 1))
The Vp/Vs ratio relates P-wave and S-wave velocities and is mathematically equivalent to the Poisson ratio. It is a key indicator of lithology and fluid content in geophysics and rock physics.
Worked Examples
Example 1: Gas Sand Identification
Problem:A sandstone has Vp = 2800 m/s and Vs = 1900 m/s. Is it gas-bearing?
Solution:Vp/Vs = 2800/1900 = 1.4737\nPoisson ratio = (1.4737^2 - 2)/(2*(1.4737^2 - 1)) = (2.1718 - 2)/(2*1.1718) = 0.0733\nVp/Vs = 1.47 is well below 1.73, strongly suggesting gas saturation
Result:Vp/Vs = 1.474, nu = 0.073 (likely gas-bearing)
Example 2: Poisson Ratio to Vp/Vs
Problem:Convert a Poisson ratio of 0.30 to Vp/Vs ratio.
Solution:Vp/Vs = sqrt((2 - 2*0.30)/(1 - 2*0.30))\n= sqrt(1.4/0.4) = sqrt(3.5) = 1.8708
Result:Vp/Vs = 1.871 (typical wet sedimentary rock)
Frequently Asked Questions
What does the Vp/Vs ratio tell us about rocks?
The Vp/Vs ratio is a powerful indicator of rock lithology, porosity, fluid content, and consolidation state. For a Poisson solid (nu = 0.25), Vp/Vs equals 1.732. Dry or gas-bearing sandstones typically show low ratios (1.4-1.6) because gas lowers Vp dramatically but barely affects Vs. Water-saturated rocks show higher ratios (1.7-2.0). Unconsolidated sediments can have ratios above 2.0. This makes Vp/Vs a key tool in hydrocarbon exploration and geotechnical site characterization.
How is Vp/Vs related to Poisson ratio?
Vp/Vs and Poisson ratio are mathematically equivalent through the relation: nu = ((Vp/Vs)^2 - 2) / (2*((Vp/Vs)^2 - 1)), or inversely, Vp/Vs = sqrt((2-2*nu)/(1-2*nu)). For nu = 0 (very stiff material), Vp/Vs = sqrt(2) = 1.414. For nu = 0.25 (Poisson solid), Vp/Vs = 1.732. As nu approaches 0.5 (fluid-like), Vp/Vs approaches infinity. Both parameters encode the same elastic information about how a material deforms under stress.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy