The 1960 Chilean earthquake measured Ms 8.5 on the surface-wave scale but Mw 9.5 on the moment magnitude scale. What is the best physical explanation for this ~30× energy discrepancy?
AThe two scales use different units, so a direct comparison requires a conversion factor
BThe surface-wave magnitude saturates for very large earthquakes — the specific wave amplitudes it measures stop growing even as the fault keeps rupturing larger areas
CMs 8.5 was a preliminary estimate that was corrected to Mw 9.5 as better seismograph data became available
DThe Chilean earthquake had unusually large slip on a small fault, which Mw captures but Ms does not
Older scales measure amplitudes of specific wave types at specific frequencies. For giant earthquakes, those waves saturate — the seismograph records the maximum amplitude the wave type can carry at that frequency, even as the fault continues to grow. Mw is derived from seismic moment M₀ = μ × A × D, a direct physical measure with no intrinsic upper bound. As fault area and slip grow, M₀ grows proportionally. The factor of ~30 in energy between Ms 8.5 and Mw 9.5 illustrates how severely saturated scales underestimate the largest earthquakes.
Question 2 Multiple Choice
Two earthquakes have identical seismic moment M₀. Earthquake A ruptured a large fault area with small average slip. Earthquake B ruptured a small fault area with large average slip. Which released more energy?
AEarthquake A — larger fault area means more rock displaced and more total energy
BEarthquake B — larger slip means stronger ground shaking and more seismic energy
CThey released equal energy — seismic moment is the product μ × A × D, and identical M₀ means identical total elastic energy released
DCannot be determined without knowing the rock rigidity μ at each fault
Seismic moment M₀ = μ × A × D is the single quantity that physically quantifies earthquake size. Identical M₀ (with similar μ) means the same total elastic energy released, regardless of how area and slip are distributed. Both earthquakes have the same Mw. Their different fault geometries may produce different ground-shaking patterns due to directivity, but the fundamental energy measure is identical.
Question 3 True / False
Moment magnitude Mw was intentionally calibrated to agree with Richter's original local magnitude scale in the magnitude 3–7 range.
TTrue
FFalse
Answer: True
This calibration was deliberate so that historical earthquake catalogs remain comparable. In the range where older scales are reliable (roughly M 3–7), Mw gives equivalent numerical values. Outside this range — especially above M 8 — Mw diverges from saturated scales, correctly capturing the far greater energy release that saturated scales miss.
Question 4 True / False
A larger seismic moment M₀ necessarily implies a larger fault rupture area, since fault area is the dominant physical factor in the equation M₀ = μ × A × D.
TTrue
FFalse
Answer: False
All three factors — rigidity μ, fault area A, and average slip D — contribute multiplicatively. A large slip on a small fault can produce the same M₀ as a small slip on a large fault (with equal μ). For example: A = 10 km², D = 10 m gives the same M₀ as A = 100 km², D = 1 m. Neither area nor slip alone determines earthquake size; only their product (weighted by rigidity) does.
Question 5 Short Answer
Why does moment magnitude Mw not saturate for very large earthquakes, whereas older scales like body-wave magnitude mb and surface-wave magnitude Ms do?
Think about your answer, then reveal below.
Model answer: Older scales measure the amplitude of specific seismic wave types at specific frequency bands. For giant earthquakes, the fault keeps growing in area and releasing energy primarily at very long periods — outside the measurement band of those scales. The wave amplitudes at the measured frequencies stop growing, 'clipping' the scale. Mw is derived from seismic moment M₀ = μ × A × D, which is a direct physical measure of rupture size with no frequency restriction. As fault area and average slip grow, M₀ grows proportionally, and so does Mw, with no upper bound.
The saturation problem is not an instrument deficiency but a fundamental consequence of using narrow-band wave amplitudes as size proxies. Moment magnitude avoids this by being grounded in source physics — the actual forces and displacements on the fault — rather than filtered seismic wave measurements.