How to use it
- Compare: enter two magnitudes. The first is compared with the second.
- From fault size: enter the rupture length and width in km, the average slip in metres and the rigidity (30 GPa is a common value for crustal rock).
- Read the ratios, the energies and the TNT equivalent.
Formulas
- Amplitude ratio = 10^(M₁ − M₂)
- Energy log₁₀ E = 1.5 × M + 4.8 (E in J), so the energy ratio = 10^(1.5 × (M₁ − M₂))
- TNT equivalent: 1 tonne of TNT = 4.184 × 10⁹ J
- Seismic moment M₀ = μ × L × W × D (N·m), moment magnitude Mw = ⅔ × (log₁₀ M₀ − 9.1)
| Magnitude step | Amplitude | Energy |
|---|---|---|
| +0.2 | 1.58× | 2× |
| +0.5 | 3.16× | 5.62× |
| +1 | 10× | 31.6× |
| +2 | 100× | 1000× |
Worked example
Magnitude 7 against magnitude 6:
- amplitude ratio 10^1 = 10
- energy ratio 10^1.5 = 31.62
- E₁ = 10^(1.5 × 7 + 4.8) = 10^15.3 J = 1,995.262 TJ, about 476,879.1 t of TNT
- E₂ = 10^13.8 J = 63.096 TJ, about 15,080.2 t of TNT
A rupture 100 km long and 20 km wide that slips 2 m in rock of 30 GPa: M₀ = 3 × 10¹⁰ × 10⁵ × 2 × 10⁴ × 2 = 1.2 × 10²⁰ N·m, so Mw = 7.32.
Tips
- Magnitude is not intensity. Damage depends on depth, distance and ground; intensity scales describe the shaking at a place.
- The energy figure is radiated seismic energy, an estimate; the total energy of the rupture is larger.
- Small and negative magnitudes exist: sensitive networks record quakes below magnitude 0.