Chile, Haiti, and earthquake moment magnitude vs destructive power: why Matthew Kahn is right and wrong

2010 March 2
by Daniel Lakeland

In a recent blog post, Matthew Kahn suggests his own articles on the importance of development for reducing destruction from natural disaster as an important criteria distinguishing the destruction in Haiti vs Chile. He says: “The richter scale is a base 10 log scale — so the shaking amplitude of the Chile quake was almost 100 times larger than the Haiti quake.

Kahn’s point about the importance of development and economic issues in destruction after disaster is an excellent one, however he misses some physics in the particular example of Haiti vs Chile.

First, the magnitudes of the earthquakes are measured in “moment magnitude” this scale is similar to the Richter scale, but does not saturate at the high end. Basically, you need the moment magnitude scale to measure large earthquakes because the Richter scale is based on shaking of an old school seismometer and after some amount of energy release, the shaking doesn’t really increase. The moment magnitude however increases steadily with total energy radiated.

What this tells us is that moment magnitude is not a good measure of the destructive power of an earthquake. For buildings, a decent measure of the destructive power of an earthquake is the peak ground acceleration, or the spectral acceleration of an oscillator with a similar fundamental frequency as the building. Or even the simple Modified Mercalli Index which is a way to qualitatively assign a number to what people “felt”.

While moment magnitude tells us about the earthquake source, these other measures tell us about the intensity of shaking at the site. For purposes other than buildings, such as soil liquefaction, other parameters may be important, such as peak velocity, peak power, or some time integrated index over the event.

In the Chile earthquake, the source of the power was a deep subduction zone, with hypocenter at 35 km depth. Just the process of traveling to the surface will have attenuated the wave energy density of this earthquake significantly as it spread approximately over an outward expanding sphere. The Haiti earthquake on the other hand was a strike-slip event centered at 13 km depth. The result is that the Modified Mercalli Index which is roughly a measure of “how hard the shaking feels” for Haiti was a full step higher (9) vs the Chilean (8). From the above links you can see the population exposure differences as well.

Furthermore, the Chilean region is a rocky mountainous one where I would expect strong bedrock to provide the foundations, whereas Haiti is an island with significant regions of coastal soft soils. Soft soils cause intensification of the earthquake shaking as wave speed is decreased and the waves pile up on each other.

The physical destructive power of the Haiti earthquake is due to a larger number of people being exposed to a higher intensity of shaking, even though the moment magnitude was lower. In combination with this higher exposure was the higher susceptibility in Haiti, where the people are about an order of magnitude poorer by GDP/capita. So Kahn is right, economics does matter, but it’s not the case that the Chile earthquake involved stronger shaking by a factor of 100.

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