Use this seismology calculation to reproduce a stated convention, screen observations, or compare scenarios whose units, coordinate conventions, catalog selection, and model assumptions are known.

Ω₀ (N·m·s)

Required number in N·m·s. Low-frequency spectral level.

ρ (kg/m³)

Optional number in kg/m³. Crustal density.

β (km/s)

Optional number in km/s. Shear wave velocity.

S_p

Optional number. Radiation partition factor.

The cited overview of Seismic magnitude scales supplies background for the terminology and domain context used by this tool.^[1]

Compute seismic moment from the low-frequency spectral plateau Ω₀ using the Brune spectral model. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

M₀ (N·m)

Returned number in N·m. Seismic moment.

• Earth structure, source geometry, path effects, site response, instrument response, catalog completeness, uncertainty, and the fitted range can dominate the accuracy of simplified seismic calculations.
• Ω₀ must be at least 0.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

For analysis or hazard decisions, retain uncertainty and provenance and compare the result with waveform processing, calibrated regional models, and guidance from qualified seismologists or the responsible agency.

• Brune Corner Frequency Source Model Calculator

  Compute the Brune (1970) circular-crack corner frequency fc = 4.9e6·β·(Δσ/M₀)^(1/3) with β in km/s, Δσ in bar, and M₀ in dyn·cm.

• Brune Displacement Spectrum Peak Frequency Note

  For the Brune model, displacement amplitude peaks exactly at the corner frequency.

• Corner Frequency Stress Drop Consistency Checker

  Invert the Brune relation fc = 0.49·β·(Δσ/M₀)^(1/3) for stress drop Δσ = M₀·(fc/(0.49·β))³ given the moment and compare with a claimed Δσ; no rigidity term is needed because Δσ/M₀ replaces it.