Poisson’s Ratio Calculator: Vp/Vs to Rock Physics Lithology Indicator

Calculate Poisson’s ratio from P-wave and S-wave velocity, compare it across a multi-lithology profile to spot a gas or lithology contrast, or solve backward for the Vp or Vs a target Poisson’s ratio requires. Everything updates live.

The Vp/Vs to Poisson’s Ratio Relationship

Poisson’s ratio equals the Vp to Vs ratio squared minus 2, divided by twice the Vp to Vs ratio squared minus 1. A Vp/Vs ratio of 2.0, common in many shales and brine saturated clastics, gives a Poisson’s ratio of almost exactly one third, a benchmark value worth remembering. As the Vp/Vs ratio drops, Poisson’s ratio drops with it, and as Vp/Vs rises toward higher values typical of some carbonates, Poisson’s ratio climbs toward its upper range.

Because Poisson’s ratio is a ratio of ratios, it carries less absolute scale information than Vp or Vs alone, but it isolates the shape of the rock’s elastic response in a way that is often more diagnostic for lithology and fluid discrimination than either velocity by itself.

Why Poisson’s Ratio Flags Gas

Gas in the pore space lowers Vp substantially through the bulk modulus term while leaving Vs almost unchanged, since shear modulus is fluid independent. That combination pushes the Vp/Vs ratio down and Poisson’s ratio down along with it, often into a distinctly lower range than the same rock would show fully brine saturated. This is why Poisson’s ratio, and closely related quantities like the ratio itself or Lambda-rho over Mu-rho, are central to amplitude versus offset analysis and direct hydrocarbon indicator workups, a gas sand frequently stands out as a low Poisson’s ratio anomaly against a shale or brine sand background.

Comparing Poisson’s Ratio Across a Lithology Profile

Different rock types settle into fairly characteristic Poisson’s ratio ranges, shales and brine saturated clastics often cluster near a third, tight low porosity rocks and many carbonates run higher, and gas sands typically run lower than either. Building a profile across several lithologies or fluid scenarios side by side makes it straightforward to see which zones stand out from the local background trend rather than relying on a single absolute Poisson’s ratio cutoff that may not transfer well between basins.

Solving Backward From a Target Poisson’s Ratio

Since Poisson’s ratio is a direct algebraic function of the Vp/Vs ratio, a target Poisson’s ratio converts back into a target Vp/Vs ratio just as directly, and from there either Vp or Vs solves immediately given the other velocity, no iteration required. This is useful for checking what S-wave velocity a rock physics model would need to match an assumed Poisson’s ratio, or for building synthetic Vs logs from Vp when direct shear velocity measurements are not available.

Common Mistakes

Applying a single universal Poisson’s ratio cutoff to flag gas sands across different basins or depths, when the appropriate cutoff depends heavily on the local background lithology trend and should be calibrated against known wells first.

Treating Poisson’s ratio as carrying the same information as Vp and Vs separately, when in fact it discards the absolute velocity scale and keeps only their ratio, useful for some purposes and a real loss of information for others.

Forgetting that a low Poisson’s ratio can come from a genuinely gas charged rock or simply from an intrinsically stiff, low Poisson’s ratio lithology like some tight sands, and the two require different evidence to tell apart.

Computing Poisson’s ratio from noisy or poorly calibrated shear velocity logs without checking the result against expected ranges for the local lithology, since Poisson’s ratio is quite sensitive to small errors in Vs.

Who Uses This

Rock physicists and geophysicists computing Poisson’s ratio as an input to amplitude versus offset and direct hydrocarbon indicator analysis.

Petrophysicists comparing Poisson’s ratio across a multi-lithology log interval to help distinguish gas sand, brine sand, and shale.

Students and early career geoscientists learning how Vp and Vs combine into Poisson’s ratio and why it responds so strongly to gas.

Analysts building synthetic shear velocity logs by solving backward from an assumed Poisson’s ratio and a measured Vp.

Try It Above

Use the quick convert tab for a single Poisson’s ratio calculation from Vp and Vs, move to the lithology profile tab to compare Poisson’s ratio across several rock types at once, or use the solve target Poisson tab when a target Poisson’s ratio is set and you need the Vp or Vs it requires.

Related Calculators and References

Continue building your workflow with the Gassmann Fluid Substitution Calculator. For background on the formulas used above, see SEG Wiki: Poisson’s ratio.