Moment Magnitude
Modern magnitude from the seismic moment of a quake.
Formula
Variables
Example
A moment of 10²² N·m gives Mw ≈ 8.0
How it works
Moment magnitude converts the physical size of an earthquake source into a logarithmic magnitude scale using the seismic moment, which measures how much rock slipped, over what area, and how rigid the rocks were. The logarithm is used because earthquake energies span enormous ranges, so each unit increase in Mw corresponds to a substantial increase in source size and released energy. This scale was developed to overcome the saturation problem of older magnitude scales, which stop distinguishing very large earthquakes well.
When to use it
Use this formula when you know the seismic moment of an earthquake from seismology or fault modeling and need its moment magnitude. It is especially useful for comparing large earthquakes and for converting physical rupture measurements into the magnitude scale used in geophysics.
Worked example, step by step
Given: M_0 = 5.0 \times 10^{19} \text{ N·m} Step 1: Take the base-10 logarithm: \log_{10}(M_0) = \log_{10}(5.0 \times 10^{19}) = \log_{10}(5.0) + 19 \approx 0.699 + 19 = 19.699 Step 2: Substitute into the formula: M_w = \tfrac{2}{3}(19.699) - 10.7 Step 3: Calculate: M_w \approx 13.133 - 10.7 = 2.433 Final answer: M_w \approx 2.4
Common mistakes to avoid
- Using natural log instead of log base 10
- Forgetting that M_0 must be in N·m before taking the logarithm
- Expecting the result to increase linearly with seismic moment instead of logarithmically
Did You Know?
It replaced the Richter scale for big quakes because Richter "saturates" and can't tell a magnitude 8 from a 9.
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