Earthquake magnitude scales
Earthquake magnitude is logarithmic. The moment magnitude scale (Mw), now the standard for medium and large earthquakes, is based on the seismic moment: the rigidity of the rock × the fault area × the average slip. It replaced the original Richter scale, which saturates above about magnitude 7 but gives similar values for small, nearby quakes.
What one point of magnitude means
- Ground-motion amplitude on a seismogram is multiplied by 10 for each step of 1.
- Energy released is multiplied by about 32 (10^1.5) for each step of 1, and by 1,000 for each step of 2.
The formulas
- Radiated energy: log₁₀ E = 1.5 M + 4.8, with E in joules.
- Seismic moment: log₁₀ M₀ = 1.5 Mw + 9.1, with M₀ in newton-meters.
- TNT equivalent: one ton of TNT releases 4.184 × 10⁹ joules.
Example
Compare a magnitude 6.0 with a magnitude 7.0:
- amplitude ratio: 10;
- energy ratio: 31.6;
- magnitude 6.0: about 63 TJ, or 15 kilotons of TNT, similar to the Hiroshima bomb;
- magnitude 7.0: about 2,000 TJ, or 480 kilotons.
The 2011 Tōhoku earthquake in Japan (Mw 9.0-9.1) released roughly 1,000 times the energy of a magnitude 7.
Magnitude classes
| Magnitude | Class | Typical effects |
|---|---|---|
| below 3 | micro | rarely felt |
| 3 to 3.9 | minor | often felt, little damage |
| 4 to 4.9 | light | shaking indoors, minor damage |
| 5 to 5.9 | moderate | damage to weak buildings |
| 6 to 6.9 | strong | serious damage in populated areas |
| 7 to 7.9 | major | widespread heavy damage |
| 8 and above | great | destruction over large areas |
Magnitude is not intensity
Magnitude measures the size of the earthquake at its source and has a single value. Intensity, on the Modified Mercalli scale in the US or the EMS-98 scale in Europe, describes the shaking and damage at a given place. It depends on distance, depth, soil and building quality. A moderate shallow quake under a city can do more harm than a great one far offshore.
Energy in perspective
Only a small fraction of an earthquake’s total energy is radiated as seismic waves; the rest goes into fracturing rock and heat. The radiated-energy formula here is the classic Gutenberg–Richter relation, an order-of-magnitude estimate.