Shear Wave Velocity Calculator

Calculate shear wave velocity from material properties using fundamental wave mechanics.

Determine the velocity of shear waves propagating through materials by inputting shear modulus, density, and other material properties. Essential for geophysical surveys and seismic analysis.

Examples

Click on any example to load it into the calculator.

Granite Rock

granite

Typical properties for granite, a common igneous rock used in construction and geophysical studies.

Shear Modulus: 44.0 GPa

Density: 2650 kg/m³

Poisson's Ratio: 0.25

Young's Modulus: 80.0 GPa

Sandstone Formation

sandstone

Properties for sandstone, a sedimentary rock commonly encountered in oil and gas exploration.

Shear Modulus: 12.0 GPa

Density: 2200 kg/m³

Poisson's Ratio: 0.30

Young's Modulus: 25.0 GPa

Saturated Clay Soil

clay

Soft soil conditions typical of coastal or delta regions, important for foundation design.

Shear Modulus: 0.05 GPa

Density: 1800 kg/m³

Poisson's Ratio: 0.45

Young's Modulus: 0.15 GPa

Reinforced Concrete

concrete

Modern construction material with well-defined elastic properties for structural analysis.

Shear Modulus: 15.0 GPa

Density: 2400 kg/m³

Poisson's Ratio: 0.20

Young's Modulus: 30.0 GPa

Other Titles
Understanding Shear Wave Velocity: A Comprehensive Guide
Explore the fundamental principles of shear wave propagation in materials and learn how to calculate wave velocities for geophysical applications, seismic analysis, and engineering design.

What is Shear Wave Velocity?

  • Wave Types in Solids
  • Shear Wave Characteristics
  • Importance in Geophysics
Shear wave velocity (Vs) is a fundamental property that describes how quickly shear waves propagate through a material. Shear waves, also known as S-waves or secondary waves, are transverse waves that cause particles in the medium to move perpendicular to the direction of wave propagation. Unlike compressional waves (P-waves), shear waves cannot travel through fluids because fluids cannot support shear stress.
The Physics of Shear Wave Propagation
Shear waves are generated when a material is subjected to shear stress, causing adjacent layers to slide past each other. The velocity of these waves depends on the material's shear modulus (G) and density (ρ). The relationship is governed by the fundamental equation: Vs = √(G/ρ). This equation shows that stiffer materials (higher shear modulus) and less dense materials will have faster shear wave velocities.
Why Shear Wave Velocity Matters
Shear wave velocity is crucial in geophysics and engineering for several reasons. It provides information about soil and rock stiffness, which is essential for foundation design and earthquake engineering. In seismic exploration, Vs helps determine subsurface structure and identify potential hydrocarbon reservoirs. For earthquake hazard assessment, Vs values are used to estimate ground motion amplification and liquefaction potential.
Relationship to Other Wave Types
In addition to shear waves, materials can support compressional waves (P-waves) that travel faster than S-waves. The ratio of P-wave to S-wave velocity (Vp/Vs) is an important parameter in geophysics that can indicate rock type, porosity, and fluid content. This ratio typically ranges from 1.4 to 2.0 for most earth materials.

Typical Shear Wave Velocities:

  • Soft Clay: 100-200 m/s
  • Dense Sand: 200-400 m/s
  • Weathered Rock: 500-1000 m/s
  • Hard Rock: 2000-3500 m/s

Step-by-Step Guide to Using the Calculator

  • Gathering Material Properties
  • Input Validation
  • Interpreting Results
Using the shear wave velocity calculator requires accurate material properties. The accuracy of your results depends directly on the quality of your input data.
1. Determine Shear Modulus
The shear modulus (G) is the most critical input. You can obtain this value from laboratory testing, published literature, or field measurements. If you have Young's modulus (E) and Poisson's ratio (ν), you can calculate G using the relationship: G = E/(2(1+ν)). Common values range from 0.01 GPa for very soft soils to 80+ GPa for hard rocks.
2. Measure or Estimate Density
Material density can be measured directly using standard laboratory procedures or estimated from published values for similar materials. Density affects wave velocity inversely - higher density materials generally have slower wave velocities for the same stiffness. Typical values range from 1200 kg/m³ for loose soils to 3000+ kg/m³ for dense rocks.
3. Optional Parameters for Advanced Analysis
Poisson's ratio and Young's modulus are optional but useful for validation and additional calculations. Poisson's ratio typically ranges from 0.1 to 0.5, with 0.25 being common for many rocks. Young's modulus can be used to verify your shear modulus calculation or to calculate additional wave properties.
4. Understanding the Results
The calculator provides shear wave velocity in both m/s and km/s. Higher velocities indicate stiffer, more competent materials. Compare your results with published values for similar materials to validate your calculations. The calculator also provides compressional wave velocity if you input Poisson's ratio.

Validation Guidelines:

  • Compare results with published values for similar materials
  • Check that Vs < Vp (shear waves are always slower than compressional waves)
  • Verify that Vp/Vs ratio is typically between 1.4 and 2.0
  • Consider site-specific conditions that may affect material properties

Real-World Applications and Engineering Significance

  • Seismic Hazard Assessment
  • Foundation Design
  • Geophysical Exploration
Shear wave velocity has numerous practical applications in engineering and geophysics, making it an essential parameter for various projects and analyses.
Earthquake Engineering and Seismic Design
In earthquake-prone regions, shear wave velocity is critical for assessing site response and designing earthquake-resistant structures. Building codes often require Vs30 measurements (average Vs over the top 30 meters) to determine site classification. Sites with low Vs values (soft soils) typically experience stronger ground shaking and require more robust structural design.
Foundation and Geotechnical Engineering
Shear wave velocity provides direct information about soil and rock stiffness, which is essential for foundation design. High Vs values indicate competent materials suitable for shallow foundations, while low values may require deep foundations or ground improvement. Vs measurements are also used to estimate soil liquefaction potential during earthquakes.
Oil and Gas Exploration
In petroleum exploration, shear wave velocity helps characterize reservoir rocks and identify potential hydrocarbon-bearing formations. The Vp/Vs ratio is particularly useful for distinguishing between different rock types and detecting fluid content. Shear wave data from seismic surveys provides crucial information for reservoir modeling and production planning.
Environmental and Engineering Geophysics
Shear wave velocity measurements are used in environmental studies to assess soil contamination, monitor groundwater levels, and evaluate waste disposal sites. In mining and tunneling projects, Vs helps determine rock quality and stability, guiding excavation methods and support design.

Site Classification by Vs30 (Building Codes):

  • Site Class A (Hard Rock): Vs30 > 1500 m/s
  • Site Class B (Rock): 760 < Vs30 ≤ 1500 m/s
  • Site Class C (Very Dense Soil): 360 < Vs30 ≤ 760 m/s
  • Site Class D (Stiff Soil): 180 < Vs30 ≤ 360 m/s
  • Site Class E (Soft Soil): Vs30 ≤ 180 m/s

Common Misconceptions and Measurement Challenges

  • Laboratory vs. Field Measurements
  • Scale Effects
  • Anisotropy Considerations
Understanding shear wave velocity involves recognizing common misconceptions and the challenges associated with its measurement and interpretation.
Laboratory vs. Field Scale Effects
A common misconception is that laboratory-measured Vs values directly represent field conditions. Laboratory tests typically use small, intact samples that may not represent the in-situ conditions, including fractures, weathering, and stress state. Field measurements using seismic methods provide more representative values but may have lower resolution and accuracy.
Frequency Dependence and Dispersion
Shear wave velocity can be frequency-dependent, especially in soils and soft rocks. This phenomenon, called dispersion, means that Vs measured at different frequencies may yield different results. High-frequency measurements (ultrasonic) typically give higher Vs values than low-frequency measurements (seismic). Understanding the frequency range of your application is crucial for selecting appropriate measurement methods.
Anisotropy and Directional Dependence
Many earth materials are anisotropic, meaning their properties vary with direction. Shear wave velocity may be different in different directions due to bedding planes, fractures, or stress anisotropy. This is particularly important in sedimentary rocks and layered soils. Single Vs measurements may not capture the full complexity of the material's behavior.
Temperature and Pressure Effects
Shear wave velocity is affected by temperature and pressure conditions. In deep boreholes or high-temperature environments, these effects can be significant. Pressure increases typically increase Vs, while temperature increases may decrease Vs. These effects are particularly important in geothermal and deep petroleum applications.

Measurement Method Comparison:

  • Crosshole Seismic: High resolution, limited depth
  • Downhole Seismic: Good depth coverage, moderate resolution
  • Surface Wave Methods: Non-invasive, depth-averaged results
  • Laboratory Ultrasonic: High accuracy, small sample size

Mathematical Derivation and Advanced Relationships

  • Wave Equation Derivation
  • Elastic Moduli Relationships
  • Anisotropic Media
The mathematical foundation of shear wave velocity calculation is based on the theory of elastic wave propagation in solids. Understanding these relationships helps in interpreting results and extending calculations to more complex scenarios.
Derivation of the Shear Wave Velocity Formula
The shear wave velocity formula Vs = √(G/ρ) is derived from the wave equation for elastic media. Starting with the equation of motion for a shear wave: ρ∂²u/∂t² = G∇²u, where u is the displacement, ρ is density, and G is shear modulus. Assuming a plane wave solution u = Aei(kx-ωt), we substitute and solve for the phase velocity v = ω/k, which gives us v = √(G/ρ). This is the shear wave velocity.
Relationships Between Elastic Moduli
In isotropic elastic materials, the elastic moduli are interrelated. The shear modulus G can be calculated from Young's modulus E and Poisson's ratio ν: G = E/(2(1+ν)). The bulk modulus K is related by: K = E/(3(1-2ν)). These relationships allow calculation of all elastic moduli if any two are known. The compressional wave velocity Vp is given by: Vp = √((K + 4G/3)/ρ) = √((E(1-ν))/(ρ(1+ν)(1-2ν))).
Vp/Vs Ratio and Its Significance
The ratio of compressional to shear wave velocity (Vp/Vs) is a crucial parameter in geophysics. For most earth materials, this ratio ranges from 1.4 to 2.0. The ratio can be expressed in terms of Poisson's ratio: Vp/Vs = √(2(1-ν)/(1-2ν)). This relationship allows estimation of Poisson's ratio from seismic measurements. Values of Vp/Vs > 2.0 may indicate the presence of fluids or highly fractured rock.
Anisotropic Media and Directional Dependence
In anisotropic materials, shear wave velocity depends on propagation direction and polarization. For transversely isotropic media (common in sedimentary rocks), there are typically two shear wave velocities: one for waves polarized parallel to the symmetry axis and another for waves polarized perpendicular to it. This shear wave splitting or birefringence is used to determine anisotropy parameters and stress directions.

Important Mathematical Notes:

  • Vs is always less than Vp in the same material
  • The Vp/Vs ratio is related to Poisson's ratio by: Vp/Vs = √(2(1-ν)/(1-2ν))
  • For ν = 0.25, Vp/Vs ≈ 1.73 (common for many rocks)
  • The relationship between moduli: E = 2G(1+ν) = 3K(1-2ν)