🔹 1. Local Magnitude (ML or Richter Magnitude)
Developed by Charles Richter for Southern California.
Formula:
Where:
-
A: Maximum amplitude of seismic waves (in micrometers) on a Wood-Anderson seismograph
-
A_0(\Delta): Empirical calibration curve depending on epicentral distance \Delta
Used for: Small to moderate local earthquakes (M < 6)
🔹 2. Moment Magnitude (Mw)
Now the most commonly used physically meaningful magnitude scale.
Formula:
Where:
-
M_0: Seismic moment in dyne-cm (or N·m in SI units)
-
\log_{10} is base-10 logarithm
Seismic Moment Formula:
-
\mu: Shear modulus (about 3 \times 10^{10} Pa for crust)
-
A: Rupture area
-
D: Average slip on the fault
🔹 3. Body Wave Magnitude (Mb)
Used for deep or teleseismic events.
Formula:
Where:
-
A: Amplitude of body waves
-
T: Period
-
Q(\Delta, h): Empirical function of distance and depth
🔹 4. Surface Wave Magnitude (Ms)
Based on 20-second surface wave amplitudes.
Formula:
Where:
-
A: Ground motion amplitude in microns
-
T: Period (~20 s)
-
\Delta: Epicentral distance (degrees)
✅ Most Reliable: Moment Magnitude (Mw)
Modern seismic catalogs (e.g., USGS, GCMT) primarily use Mw because:
-
It does not saturate for large events
-
Directly tied to fault physics and energy release