Earthquake Magnitude Scales

Why This Matters

Earthquake magnitude scales quantify how "big" an earthquake is, but different scales measure fundamentally different things: wave amplitude, fault rupture mechanics, or radiated energy. Knowing which scale measures what is central to geophysics because it determines how you interpret seismic data, assess hazard, and understand the limitations of any reported magnitude value.

These scales also illustrate core geophysics principles: logarithmic relationships, wave mechanics, fault rupture physics, and energy quantification. Don't just memorize which scientist developed which scale. Focus on what physical quantity each scale captures, when it works well, and when it breaks down. If you see a magnitude value on a seismic hazard map, you need to know exactly what it represents.

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Amplitude-Based Scales

These scales measure the size of seismic waves as recorded on seismographs. The key principle: wave amplitude correlates with ground shaking, but amplitude alone doesn't capture the full physics of fault rupture.

Richter Scale (Local Magnitude)

The original Richter Scale, developed in 1935 by Charles F. Richter, was designed specifically for Southern California earthquakes recorded on Wood-Anderson seismographs. It's logarithmic: each whole-number increase represents a tenfold increase in wave amplitude and roughly 31.6 times more energy released.

The critical limitation is saturation above about magnitude 7. The scale effectively "maxes out" because very large earthquakes produce long-period waves that the original methodology doesn't capture well. This makes it unreliable for the biggest, most consequential events.

Local Magnitude ($M_L$)

$M_L$ is the modern adaptation of the Richter approach, using the same logarithmic amplitude framework but calibrated for contemporary digital seismographs rather than the original Wood-Anderson instruments.

• Limited to about 600 km from the epicenter, which is why it's called "local"
• Provides quick preliminary estimates for regional seismic networks
• Still saturates for large earthquakes, so $M_w$ values should be used for any serious hazard assessment

In practice, when news outlets say "Richter scale," they usually mean $M_L$ or even $M_w$. The original Richter Scale is rarely used in its pure form anymore.

Surface Wave Magnitude ($M_s$)

$M_s$ specifically measures Rayleigh wave amplitude at periods around 20 seconds. Rayleigh waves are surface waves that travel along Earth's outer layer, so this scale works best for shallow, teleseismic events (distant earthquakes, typically greater than magnitude 5.0).

• Local geology and crustal structure can distort surface wave amplitudes, reducing reliability
• Like other amplitude-based scales, $M_s$ saturates for the very largest earthquakes (around magnitude 8.3)

Body Wave Magnitude ($m_b$)

$m_b$ measures the amplitude of P-waves (compressional waves that travel through Earth's interior). Because P-waves arrive before surface waves, $m_b$ allows rapid magnitude estimation within minutes of an event.

• Best suited for deep earthquakes, where surface waves are weak or absent
• Saturates around magnitude 6.5, making it unreliable for large events
• Typically measured at periods around 1 second

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Physics-Based Scales

These scales go beyond amplitude to capture the actual mechanics of fault rupture. The key principle: true earthquake size depends on how much rock moved, over what area, and against what resistance.

Moment Magnitude Scale ($M_w$)

$M_w$ is derived from the seismic moment ($M_0$), which is calculated from three physical quantities of the fault rupture:

$M_0 = \mu A D$

• $\mu$ = shear modulus (rigidity of the rock)
• $A$ = rupture area on the fault plane
• $D$ = average slip (displacement) across the fault

The magnitude is then:

$M_w = \frac{2}{3} \log_{10}(M_0) - 10.7$

(where $M_0$ is in dyne-cm; if using SI units in N·m, the constant is 6.07)

Because $M_w$ is tied to the geometry and mechanics of the rupture itself, it does not saturate at high magnitudes. This is the main reason it has become the standard for seismology and engineering. Building codes, ground motion prediction equations, and seismic hazard maps all reference $M_w$.

Energy Magnitude ($M_e$)

$M_e$ quantifies the total seismic energy radiated by an earthquake, using the Gutenberg-Richter energy-magnitude relation:

$\log_{10} E = 1.5M + 4.8$

where $E$ is in joules.

• Energy release correlates more directly with damage potential than amplitude alone
• Particularly useful for earthquakes with complex or prolonged ruptures, where $M_w$ and $M_e$ can diverge
• For most earthquakes, $M_w$ and $M_e$ are similar, but they can differ significantly for slow rupture events (like tsunami earthquakes, where $M_e$ may be lower than $M_w$)

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Duration-Based Scales

This approach uses the length of shaking rather than peak amplitude. The key principle: longer shaking duration often indicates larger fault rupture and greater total energy release.

Duration Magnitude ($M_d$)

$M_d$ is calculated from the coda wave duration, which is how long seismic waves remain detectable above background noise after the main arrivals. The "coda" refers to the tail end of the seismogram, consisting of scattered waves bouncing through the crust.

• Useful when amplitude clips: during strong nearby earthquakes, seismograph recordings can go off-scale, making amplitude-based magnitudes impossible to calculate. $M_d$ still works because you only need to measure how long the signal lasts.
• More common in seismic network operations and research than in engineering practice
• Requires empirical calibration for each region, since coda duration depends on local crustal scattering properties

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Quick Reference Table

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Self-Check Questions

1. Why has $M_w$ replaced the Richter Scale as the standard, and what physical quantities does $M_w$ incorporate that amplitude-based scales miss?

2. Compare $m_b$ and $M_s$: which would provide more reliable estimates for a deep-focus earthquake, and why?

3. If a seismograph's amplitude recording clips during a nearby large earthquake, which magnitude scale could still provide a useful estimate, and what does it measure instead of amplitude?

4. Explain the seismic moment equation $M_0 = \mu A D$ and why this makes $M_w$ more physically meaningful than amplitude-based scales for characterizing fault rupture.

5. Two earthquakes both have $M_w = 7.0$, but one has a much lower $M_e$ than the other. What might this tell you about the nature of the rupture?