Earthquake Magnitude Scales

Why This Matters

In earthquake engineering, understanding magnitude scales isn't just academic—it directly affects how you design structures, assess seismic hazard, and communicate risk. You're being tested on your ability to distinguish between scales that measure wave amplitude, seismic moment, and energy release, and to recognize when each scale is appropriate for engineering applications. The PE exam and graduate coursework expect you to know why the Moment Magnitude Scale has become the industry standard and where older scales like Richter still appear in practice.

These scales demonstrate fundamental principles of logarithmic relationships, wave mechanics, fault rupture physics, and energy quantification. Don't just memorize which scientist developed which scale—understand what physical quantity each scale measures and why that matters for structural design, building codes, and ground motion prediction. When you see a magnitude value in a design specification, 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 intensity, but amplitude alone doesn't capture the full physics of fault rupture.

Richter Scale (Local Magnitude)

• Logarithmic amplitude measurement—each whole number increase represents a tenfold increase in wave amplitude and roughly 31.6 times more energy released
• Developed in 1935 by Charles F. Richter specifically for Southern California earthquakes using Wood-Anderson seismographs
• Saturates above magnitude ~7—cannot accurately measure very large earthquakes because the scale "maxes out," making it inadequate for major engineering events

Local Magnitude (ML)

• Modern adaptation of Richter—uses the same logarithmic amplitude approach but calibrated for contemporary digital seismographs
• Limited range of 600 km—only valid for earthquakes recorded relatively close to the epicenter, hence the name "local"
• Quick preliminary estimates—provides rapid magnitude values for regional seismic networks, though engineers should wait for $M_w$ values for design decisions

Surface Wave Magnitude (Ms)

• Measures Rayleigh wave amplitude—specifically targets surface waves with periods around 20 seconds traveling along Earth's surface
• Best for shallow, distant events—effective for earthquakes greater than magnitude 5.0 occurring far from recording stations
• Geological distortion possible—local soil conditions and crustal structure can affect readings, reducing reliability for engineering applications

Body Wave Magnitude (mb)

• Measures P-wave amplitude—focuses on compressional waves traveling through Earth's interior rather than along the surface
• Effective for deep earthquakes—provides better estimates for events occurring at significant depth where surface waves are less prominent
• Rapid first estimates—P-waves arrive first, allowing quick magnitude calculation within minutes of an event

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Physics-Based Scales

These scales move beyond simple amplitude measurements 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 (Mw)

• Based on seismic moment—calculated from fault rupture area, average slip distance, and rock rigidity using $M_0 = \mu A D$ where $\mu$ is shear modulus, $A$ is fault area, and $D$ is displacement
• No saturation at high magnitudes—accurately measures the largest earthquakes, making it essential for engineering design and seismic hazard analysis
• Current engineering standard—building codes, ground motion prediction equations, and seismic hazard maps all reference $M_w$ values

Energy Magnitude (Me)

• Quantifies total radiated energy—estimates the seismic energy released using the relationship $\log_{10} E = 1.5M + 4.8$ (in joules)
• Captures earthquake impact potential—energy release correlates more directly with damage potential than amplitude alone
• Complements $M_w$ for large events—particularly valuable when assessing earthquakes that release energy over extended rupture durations

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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 (Md)

• Measures coda wave duration—calculates magnitude from how long seismic waves remain detectable above background noise, called the "coda" of the seismogram
• Useful when amplitude clips—provides magnitude estimates even when seismograph recordings are saturated or off-scale during strong shaking
• Research and monitoring applications—less common in engineering practice but valuable for seismic network operations and studying prolonged rupture events

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Quick Reference Table

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Self-Check Questions

1. Why has the Moment Magnitude Scale ($M_w$) replaced the Richter Scale as the standard for engineering applications, and what physical quantities does $M_w$ incorporate that amplitude-based scales miss?

2. Compare Body Wave Magnitude ($m_b$) and Surface Wave Magnitude ($M_s$): 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 relationship between 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. When reviewing seismic hazard maps or building code provisions, why is it critical to confirm that magnitude values are reported in $M_w$ rather than $M_L$ or $m_b$?