Seismic Wave Velocity Calculator
Calculate seismic wave velocity with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Vp = sqrt((K + 4G/3) / rho) | Vs = sqrt(G / rho)
P-wave velocity depends on bulk modulus K, shear modulus G, and density rho. S-wave velocity depends only on shear modulus and density. These fundamental relationships connect elastic properties of rocks to seismic wave propagation speeds.
Worked Examples
Example 1: Granite P and S-wave Velocity
Problem:Calculate Vp and Vs for granite with K = 50 GPa, G = 30 GPa, density = 2650 kg/m^3.
Solution:Vp = sqrt((50e9 + 4*30e9/3) / 2650)\nVp = sqrt((50e9 + 40e9) / 2650)\nVp = sqrt(3.396e7) = 5828 m/s\nVs = sqrt(30e9 / 2650) = sqrt(1.132e7) = 3365 m/s
Result:Vp = 5828 m/s, Vs = 3365 m/s, Vp/Vs = 1.732
Example 2: Limestone from Young Modulus
Problem:Find velocities for limestone: E = 60 GPa, Poisson ratio = 0.28, density = 2700 kg/m^3.
Solution:K = 60e9 / (3*(1-0.56)) = 45.45 GPa\nG = 60e9 / (2*(1.28)) = 23.44 GPa\nVp = sqrt((45.45e9 + 4*23.44e9/3) / 2700) = 5395 m/s\nVs = sqrt(23.44e9 / 2700) = 2946 m/s
Result:Vp = 5395 m/s, Vs = 2946 m/s
Frequently Asked Questions
What determines seismic wave velocity?
Seismic wave velocity depends on the elastic properties and density of the medium. P-wave velocity Vp depends on the bulk modulus K (resistance to compression), shear modulus G (resistance to shearing), and density: Vp = sqrt((K + 4G/3)/rho). S-wave velocity depends only on shear modulus and density: Vs = sqrt(G/rho). Higher elastic moduli increase velocity, while higher density decreases it. In practice, the modulus effect dominates, so denser rocks generally have higher velocities because they also tend to be stiffer.
What are typical seismic velocities for common rocks?
Common P-wave velocities include: water 1500 m/s, unconsolidated sand 200-800 m/s, sandstone 2000-4500 m/s, limestone 3500-6500 m/s, granite 5000-6500 m/s, basalt 5500-6500 m/s, and the Earth mantle 7800-13700 m/s. S-wave velocities are typically 50-70% of P-wave velocities for solid rocks. Velocities generally increase with depth due to increased confining pressure, which closes cracks and increases stiffness. Fluid saturation increases Vp but has little effect on Vs.
How is Poisson ratio related to wave velocities?
Poisson ratio (nu) is directly calculable from the Vp/Vs ratio: nu = ((Vp/Vs)^2 - 2) / (2*(Vp/Vs)^2 - 2). For most rocks, Poisson ratio ranges from 0.1 to 0.45. A ratio of 0.25 corresponds to Vp/Vs = 1.732. Fluid-saturated rocks tend to have higher Poisson ratios (0.3-0.4) than dry rocks. Gas-bearing sands often show anomalously low Vp/Vs ratios and Poisson ratios, making this measurement valuable for hydrocarbon detection in seismic exploration.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy