Formula & Calculator
Seismic Moment
Calculates the seismic moment of an earthquake, a physical measure of the energy released based on fault properties and slip.
Interpretation
M0 = μ × A × D. The seismic moment: μ is shear modulus, A is fault area, D is average slip. Measures earthquake size independent of distance. Used for moment magnitude.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| M0 | Seismic moment | N*m |
| μ | Shear modulus of rock | Pa |
| A | Rupture area of the fault | m2 |
| D | Average slip (displacement) on the fault | m |
What it means
The seismic moment M0 is the fundamental physical measure of earthquake size. It is the product of the shear modulus of the rock (μ), the area of the fault rupture (A), and the average slip (D) on the fault. Unlike magnitude scales that depend on wave amplitude, M0 is directly related to the physical process. It is used to calculate the Moment Magnitude (Mw), which is more reliable for large earthquakes. This parameter is used in seismology to compare earthquakes, to study fault mechanics, and to assess seismic hazard. Understanding M0 is essential for modern earthquake science.
Worked example
Seismic Moment – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| μ (Pa) | 3.0e10 |
| A (m²) | 1.0e9 |
| D (m) | 2 |
| Parameter | Value |
|---|---|
| μ | 3.0e10 |
| A | 5.0e9 |
| D | 5 |
Common mistakes
- Seismic moment: M₀ = μ·A·D – where μ is shear modulus, A is rupture area, D is average slip.
- μ: Shear modulus of the rock (typical ~3×10¹⁰ Pa for crust).
- A: Fault rupture area – in m².
- D: Average slip over the rupture – in m.
- Units: M₀ in N·m (Joules) – the unit is the same as energy but it is a moment.
Applications
Seismic moment, M₀ = μ·A·D, is the product of shear modulus (μ), rupture area (A), and average slip (D). This is a measure of the total energy released by an earthquake and is directly related to the moment magnitude (Mw). Seismologists use seismic moment to characterise earthquake source parameters, to compare earthquakes of all sizes, and to study the physics of faulting. It is the preferred measure for large earthquakes as it does not saturate. By calculating M₀, scientists can estimate the fault dimensions and slip, aiding in hazard assessment. Understanding seismic moment is fundamental to modern seismology and earthquake engineering.
- Source characterisation and moment tensor inversion
- Calculation of moment magnitude for large earthquakes
- Fault rupture modelling and kinematic studies
- Seismic hazard analysis and earthquake scaling
- Research on earthquake physics and energy budgets
Frequently Asked Questions
M0 = μ × A × D, where μ is the rigidity (shear modulus) of the rock, A is the area of the fault rupture, and D is the average slip (displacement) on the fault. It is a physical measure of earthquake size, directly related to the energy released.
Seismic moment is expressed in Newton‑metres (N·m) or dyne‑cm (1 dyne‑cm = 10⁻⁷ N·m). Typical values for a M6 earthquake are about 10¹⁸ N·m.
Seismic moment (M0) is a physical quantity (energy). Moment magnitude (M_w) is derived from M0 using M_w = (2/3) log₁₀(M0) − 10.7. M_w is a logarithmic scale that is consistent with the Richter scale for moderate events.
From the spatial distribution of aftershocks, geodetic data (InSAR, GPS), or from the length and width of the fault as inferred from seismic wave inversions. The area is typically the product of length and width of the rupture.
μ ranges from about 3×10¹⁰ Pa (30 GPa) for upper crustal rocks to 6×10¹⁰ Pa for deeper rocks. It varies with lithology and depth.
The seismic moment is related to the radiated energy, but there is a difference due to the stress drop. The energy E is approximately E ≈ (1/2) × Δσ × A × D, where Δσ is the stress drop. However, the widely used magnitude‑energy relation is empirical.
Because it does not saturate (unlike the Richter scale), and it is based on the physics of the source, making it a consistent measure for earthquakes of all sizes.
By modelling the low‑frequency spectral amplitudes of P and S waves. The flat level of the displacement spectrum at low frequencies is proportional to M0.
Empirically, M0 ∝ L³ (with width scaling) for many strike‑slip faults. This is the basis for magnitude‑length scaling relations used in paleoseismology.
It is a measure of the total strain energy released and is directly related to the seismic efficiency. It allows comparison of earthquakes across different tectonic settings.