Demonstrating why different magnitude scales become unreliable for large earthquakes and how moment magnitude (Mw) solves this problem
Why Saturation Occurs
Magnitude saturation happens when a scale can no longer distinguish between earthquakes of different sizes above a certain threshold. This occurs because:
- Seismic waves have limited frequency content
- Measurement instruments have finite bandwidth
- Some scales measure only specific wave periods
Real Example: 2004 Sumatra Earthquake
Ms (Surface Wave): 8.5 (saturated)
Mw (Moment): 9.1 (accurate)
Energy difference: ~32 times more!
Body Wave Magnitude (mb)
Measures short-period P-waves (~1 second period)
mb = log(A/T) + Q(h,Δ)
Saturation Point: ~6.8
Short-period waves don't grow proportionally with earthquake size for large events
Used primarily for: Deep earthquakes, nuclear test detection
Surface Wave Magnitude (Ms)
Measures Rayleigh waves with ~20 second periods
Ms = log(A/T) + 1.66log(Δ) + 3.3
Saturation Point: ~8.0
Large earthquakes produce energy at longer periods than 20 seconds
Good for: Shallow earthquakes at teleseismic distances
Moment Magnitude (Mw) - The Solution
Based on total seismic moment, not wave amplitudes
Mw = (2/3)log(M₀) - 6.07
Where M₀ = μ × Area × Displacement
- ✓ No saturation - directly measures fault physics
- ✓ Accurate for all sizes - from tiny to giant earthquakes
- ✓ Physically meaningful - relates to actual energy release