Shear Wave Velocity Calculator

About the Shear Wave Velocity Calculator

The **Shear Wave Velocity Calculator** computes the speed of shear (S) waves through a material using v_s = √(G/ρ), where G is the shear modulus and ρ is the density. It also calculates P-wave velocity, Rayleigh wave velocity, and travel times over a specified distance. Shear wave velocity is one of the most important parameters in geotechnical engineering and seismology.

S-waves travel through the Earth at speeds ranging from about 100 m/s in soft soil to over 3,000 m/s in steel. Their velocity directly reveals the stiffness and composition of subsurface materials. In seismology, the difference in arrival times of P-waves and S-waves at seismograph stations determines earthquake location and depth. The v_p/v_s ratio helps identify rock and soil types.

The calculator includes a library of 13 materials spanning metals, rocks, and soils, plus wavelength tables at various frequencies and a comprehensive material comparison. This covers applications from geotechnical site characterization (NEHRP soil classification uses v_s,30) to non-destructive testing and ultrasonic inspection.

When This Page Helps

Geotechnical engineers use shear wave velocity for earthquake site classification (NEHRP categories A-F), soil liquefaction assessment, ground response analysis, and foundation design. Seismologists use S-wave and P-wave velocities to image Earth's interior — the fact that S-waves cannot travel through liquids proved the outer core is molten.

Non-destructive testing uses ultrasonic shear waves to detect internal flaws in materials. The wavelength table helps select appropriate frequencies: shorter wavelengths detect smaller defects but attenuate faster. Medical ultrasound elastography uses shear wave speed to map tissue stiffness for tumor detection.

How to Use the Inputs

1. Select a material from the dropdown or enter custom shear modulus and density values.
2. Enter a travel distance to compute wave arrival times.
3. Review S-wave, P-wave, and Rayleigh wave velocities.
4. Check the v_p/v_s ratio for material identification.
5. Use the wavelength table to determine resolution at different frequencies.
6. Compare velocities across materials using the reference table.

Example Calculation

Tips & Best Practices

• S-waves cannot propagate through liquids or gases — shear modulus is zero for fluids.
• v_p is always faster than v_s. For ν = 0.25, v_p/v_s = √3 ≈ 1.73.
• NEHRP site class is based on average v_s in the top 30 m (v_s,30): Class A > 1500 m/s, E < 180 m/s.
• Rayleigh waves travel along surfaces at about 90-95% of the S-wave velocity.
• The S-P time difference (Δt) × 8 km/s gives approximate earthquake distance in km.
• For soils, v_s increases with depth due to increasing confining pressure.

Seismic Wave Types

Elastic waves in solids come in two body wave types: P-waves (primary, compressional, longitudinal) and S-waves (secondary, shear, transverse). P-waves arrive first at a seismograph because they travel faster. S-waves arrive later but typically carry more energy and cause more damage. Surface waves (Rayleigh and Love waves) travel along the surface and dominate ground motion at distances greater than a few wavelengths from the source.

The v_p/v_s ratio is a powerful diagnostic tool in geophysics. For rocks and consolidated soils, v_p/v_s typically ranges from 1.5 to 2.0. Saturated loose soils have very high ratios (approaching infinity as G → 0 while K remains finite from water incompressibility). Gas-bearing formations have anomalously low v_p/v_s ratios.

Site Response and Ground Amplification

Soft soil deposits amplify seismic waves because of the impedance contrast between soft surface layers and stiff bedrock. The amplification factor depends on the velocity ratio: a site with v_s = 200 m/s over bedrock at v_s = 1500 m/s will amplify significantly. The fundamental site period is approximately T = 4H/v_s (H = soil thickness), and structures with natural periods near this value experience resonance.

Non-Destructive Testing Applications

Ultrasonic shear wave testing detects cracks, voids, and inclusions in metals, welds, and concrete. Angle beam techniques use mode-converted shear waves to inspect welds from the surface. Time-of-flight diffraction (TOFD) uses both P and S waves for accurate crack sizing. Phased array ultrasonics combine multiple elements to steer and focus shear wave beams for detailed defect characterization.

Frequently Asked Questions

• Why are shear waves slower than P-waves?

  P-waves involve compression/extension (volumetric change), which mobilizes both bulk and shear stiffness. S-waves involve only shearing (no volume change), mobilizing only shear stiffness. Since M = K + 4G/3 > G always, P-waves are always faster: v_p > v_s.

• Why can S-waves not travel through liquids?

  Liquids have zero shear modulus — they cannot resist shear deformation. Since v_s = √(G/ρ) and G = 0 for liquids, v_s = 0. This is how seismologists discovered that Earth outer core is liquid — S-waves from earthquakes on the far side of the Earth are blocked by it.

• What is v_s,30 and why does it matter?

  v_s,30 is the time-averaged shear wave velocity in the top 30 meters of soil. It is the primary parameter for seismic site classification in building codes worldwide (NEHRP, Eurocode 8, IBC). Sites with low v_s,30 amplify seismic waves more, requiring stronger structures.

• How is shear wave velocity measured in the field?

  Common methods: downhole surveys (sensor lowered into a borehole), crosshole surveys (source in one borehole, receiver in another), SASW/MASW (surface wave methods using geophones), and seismic CPT (combined cone penetration and wave velocity). MASW is the most cost-effective for shallow profiles.

• How does shear wave velocity relate to soil stiffness?

  Shear modulus G = ρ × v_s². This gives the small-strain (elastic) stiffness of the soil, which is the starting point for dynamic soil analysis. G_max (from v_s) is the upper bound on soil stiffness — it decreases with increasing shear strain during strong shaking.

• What frequencies are used in ultrasonic testing?

  Typical ranges: geophysics 0.1-50 Hz, geotechnical surveys 1-100 Hz, structural NDT 0.5-25 MHz, medical ultrasound 1-20 MHz. Higher frequencies give better resolution but attenuate faster. The wavelength must be smaller than the feature to detect it.