Vp Vs Ratio Calculator

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.

Can I use Vp Vs Ratio Calculator on a mobile device?

Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.

Is Vp Vs Ratio Calculator free to use?

Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.

How accurate are the results from Vp Vs Ratio Calculator?

All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.

How do I get the most accurate result?

Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.