10.3 Earthquake measurement and intensity scales

Earthquakes pack a punch, and scientists have clever ways to measure their power. From the Richter scale to the moment magnitude scale, these tools help us understand just how much energy quakes release. But it's not all about numbers—the Modified Mercalli scale tells us how earthquakes affect people and places.

Pinpointing where earthquakes start is crucial for understanding their impact. Scientists use seismograms to track seismic waves and triangulate epicenters. By analyzing wave arrival times and patterns, they can map out the earthquake's origin and help communities prepare for future shakes.

Earthquake Measurement and Intensity Scales

Earthquake magnitude measurement

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• Quantifies the amount of energy released by an earthquake based on the amplitude of seismic waves recorded on a seismogram
• Richter scale is a logarithmic scale developed by Charles Richter in 1935 to measure earthquake magnitude
  • Each whole number increase represents a tenfold increase in wave amplitude (e.g., magnitude 5 vs. magnitude 4)
  • One unit increase corresponds to a 32-fold increase in energy released (e.g., magnitude 6 vs. magnitude 5)
• Richter magnitude calculated using the formula: $M_L = \log_{10}(A) - \log_{10}(A_0)$
  • $M_L$: Richter magnitude
  • $A$: Maximum amplitude of seismic waves recorded by a seismograph (in millimeters)
  • $A_0$: Standard amplitude for a reference earthquake at a distance of 100 km (in millimeters)

Limitations of Richter scale

• Saturates for large earthquakes with magnitudes greater than 6.5, underestimating their true energy release
• Based on measurements from a specific type of seismograph (Wood-Anderson torsion seismograph), limiting its applicability
• Inaccurate for measuring earthquakes at great distances from the seismograph due to attenuation of seismic waves
• Moment magnitude scale (Mw) developed to overcome these limitations
  • Based on seismic moment, a measure of the energy released by an earthquake considering fault area, average slip, and rock rigidity
  • More accurate for larger earthquakes (Mw > 7) and those at greater distances
  • Calculated using the formula: $M_w = \frac{2}{3}\log_{10}(M_0) - 10.7$, where $M_0$ is the seismic moment in dyne-cm

Modified Mercalli Intensity scale

• Qualitative scale that measures the intensity of an earthquake based on its effects on people, structures, and the environment
• Ranges from I (not felt) to XII (total destruction) and is assigned based on observations and reports from the affected area
• Simplified levels:
  1. I-III: Not felt to weak shaking, no damage
  2. IV-VI: Light to strong shaking, slight to moderate damage (e.g., cracked plaster, fallen chimneys)
  3. VII-IX: Very strong to violent shaking, considerable to heavy damage (e.g., collapsed buildings, ground fissures)
  4. X-XII: Extreme shaking, destruction, and total damage (e.g., landslides, bridges destroyed, objects thrown into the air)
• Provides a qualitative assessment of earthquake effects, helping emergency responders prioritize relief efforts and compare relative impacts across different locations

Interpreting seismograms for epicenters

• Seismograms record ground motion detected by a seismograph, displaying P-waves (primary) and S-waves (secondary) arrivals
• Epicenter is the point on the Earth's surface directly above the hypocenter (origin of the earthquake)
• Locating the epicenter using triangulation method:
  1. Use arrival times of P- and S-waves at three or more seismic stations
  2. Calculate distance between each station and epicenter using seismic wave velocities
  3. Plot circles with radii equal to calculated distances around each station
  4. Epicenter is estimated at the point where circles intersect
• S-P time method for a single seismic station:
  1. Measure time difference between P- and S-wave arrivals
  2. Use travel-time curve or table to determine distance to epicenter
  3. Plot circle with calculated distance as radius around the station
  4. Repeat for two more stations to triangulate epicenter location