gen-define-the-richter-and-moment-magnitude-scales-and-give-one-91b1

Define the Richter and moment magnitude scales and give one short worked example.

# Earthquake Magnitude Scales ## Richter Scale (Local Magnitude, ML) **Definition:** Developed by Charles Richter in 1935, this scale measures earthquake magnitude based on the amplitude of seismic waves recorded on a seismograph, adjusted for distance from the epicenter. **Formula:** ML = log₁₀(A) - log₁₀(A₀) Where: - A = maximum amplitude of seismic waves (in micrometers) - A₀ = reference amplitude at a standard distance (100 km) **Key features:** - Logarithmic scale (each whole number = 10× increase in amplitude) - Most accurate for local earthquakes (< 600 km away) - Saturates around magnitude 6.5-7 (can't accurately measure larger quakes) ## Moment Magnitude Scale (Mw) **Definition:** Modern standard (since 1979) that measures the total energy released by an earthquake based on seismic moment. **Formula:** Mw = (2/3) × log₁₀(M₀) - 10.7 Where M₀ = seismic moment (in dyne-cm) = μ × A × D - μ = shear modulus of rocks (~3 × 10¹¹ dyne/cm²) - A = fault rupture area - D = average slip distance **Key features:** - Doesn't saturate; accurate for all earthquake sizes - Directly relates to physical properties of the fault ## Worked Example (Moment Magnitude) **Given:** An earthquake with: - Fault area: A = 100 km² = 10¹¹ cm² - Average slip: D = 2 m = 200 cm - Shear modulus: μ = 3 × 10¹¹ dyne/cm² **Solution:** M₀ = μ × A × D = (3 × 10¹¹) × (10¹¹) × (200) = 6 × 10²⁴ dyne-cm Mw = (2/3) × log₁₀(6 × 10²⁴) - 10.7 Mw = (2/3) × (24.78) - 10.7 Mw = 16.52 - 10.7 **Mw = 5.8** This represents a moderate earthquake.