Advanced Seismic Waves Calculator

Seismic Wave Inputs

Calculation Mode

Wave Type

Propagation Distance (m)

Frequency (Hz)

Initial Amplitude (mm)

Quality Factor Q

Primary Density (kg/m³)

Young’s Modulus (GPa)

Poisson’s Ratio

Direct P-Wave Velocity (m/s)

Direct S-Wave Velocity (m/s)

Love Wave Factor

Second Medium Density (kg/m³)

Second Medium Velocity (m/s)

Elastic mode derives P and S velocities from Young’s modulus, Poisson’s ratio, and density. Direct mode uses measured velocities. Love-wave velocity is approximated using your chosen factor.

Plotly Graph

The graph compares travel time growth for P, S, Rayleigh, and Love waves across distance. It updates using your submitted inputs.

Example Data Table

These example values are approximate engineering references for quick comparison only.

Material	Density (kg/m³)	Young’s Modulus (GPa)	Poisson’s Ratio	Typical P-Wave (m/s)	Typical S-Wave (m/s)
Granite	2700	55	0.25	6000	3460
Sandstone	2300	20	0.23	3500	2100
Saturated Clay	1900	0.15	0.45	1450	180
Concrete	2400	30	0.20	3700	2400

Formula Used

Shear modulus: μ = E / [2(1 + ν)] Lamé constant: λ = Eν / [(1 + ν)(1 - 2ν)] P-wave velocity: Vp = √[(λ + 2μ) / ρ] S-wave velocity: Vs = √[μ / ρ] Rayleigh approximation: Vr ≈ Vs × [(0.862 + 1.14ν) / (1 + ν)] Love approximation: Vl ≈ Vs × love factor Travel time: t = d / V Wavelength: λw = V / f Period: T = 1 / f Angular frequency: ω = 2πf Wavenumber: k = 2π / λw Attenuation model: A(x) = A0 × exp[-πfx / (QV)] Impedance: Z = ρV Reflection coefficient: R = (Z2 - Z1) / (Z2 + Z1) Transmission coefficient: T = 2Z2 / (Z1 + Z2)

Love-wave speed depends on layered media behavior, so this calculator uses an adjustable factor. Reflection and transmission outputs are simplified normal-incidence engineering estimates.

How to Use This Calculator

Choose elastic mode when you know density, modulus, and Poisson’s ratio.
Choose direct mode when field or lab velocities are already available.
Enter propagation distance and dominant frequency for the seismic event.
Add initial amplitude and quality factor to estimate attenuation effects.
Select the wave family you want to inspect most closely.
Optionally enter second-medium properties to estimate interface behavior.
Press the calculate button to show results above the form.
Use the chart and export buttons for reporting or review.

Frequently Asked Questions

1. What does this calculator estimate?

It estimates P, S, Rayleigh, and Love wave behavior. Outputs include velocity, travel time, wavelength, angular frequency, attenuation, impedance, and simplified interface coefficients for preliminary engineering analysis.

2. When should I use elastic mode?

Use elastic mode when material stiffness and density are known, but field wave speeds are not. The tool then derives P-wave and S-wave velocities from standard isotropic elastic relationships.

3. When should I use direct velocities mode?

Use direct mode when measured or published P-wave and S-wave velocities already exist. This is helpful for site investigations, lab tests, borehole surveys, or previous seismic characterization reports.

4. Why are Love-wave results approximate?

Love waves depend strongly on layering, stiffness contrast, and dispersion. This page uses a controllable Love-wave factor for practical estimation, not a full layered-medium dispersion solution.

5. What is seismic impedance used for?

Seismic impedance combines density and velocity. Engineers use it to compare materials, estimate wave transmission at boundaries, and understand reflection strength between adjacent layers or components.

6. How does attenuation change amplitude?

Attenuation reduces amplitude as distance and frequency increase. Higher quality factor values indicate less energy loss, so the wave retains more of its original amplitude over the same path.

7. Can this calculator replace detailed seismic design software?

No. It supports fast engineering screening and education. Final design decisions should still use site-specific investigations, governing standards, and advanced geophysical or structural analysis tools.

8. Why do P waves arrive before S waves?

P waves usually travel faster because they compress and expand the medium along the direction of motion. S waves rely on shear deformation, which is generally slower in solid materials.