The opinions expressed here are well-reasoned and insightful -- needless to say they are not the opinions of my employers

24 January 2010

How big was that one?

Every semester I spend time explaining the methods of measuring earthquakes to students. I explain magnitude, with a primer on how logarithms work. I talk about the limitations of the Richter scale in measuring larger quakes, as more energy is released at low frequencies, and how the Seismic Moment, though more difficult to calculate, provides a better snapshot of the released energy.

I always emphasize that intensity, as represented by surface wave amplitudes, frequencies and ground acceleration, is a more useful way to describe how earthquakes affect communities. Magnitude has the advantage though, in that it can be reported as a single number. This creates a problem in the way the general public perceives earthquakes, a problem addressed in this post I came across a few days ago.

The earthquake in Haiti, for instance, had a
magnitude of 7.0. Everyone understands that this is bigger than a magnitude 6.7, like Northridge, but few understand that the difference means that the Haiti event released three times the seismic energy of the Northridge earthquake.

And while building codes and construction standards play a big role in determining relative damage and casualties, this is often overplayed. After the 2001 Nisqually earthquake in Washington (Mw=6.8), there were commentaries in the news media suggesting that the lack of serious damage and casualties in Washington reflected poorly on standards in LA, where the Northridge event killed 67 people and caused extensive damage. Of course the primary reason for the difference is that the Nisqually earthquake occurred at a depth of 52 kilometers, versus 19 km in Northridge.

The author of the above post suggests a change in terminology, that when geologists talk to the media about earthquakes they refer to the seismic energy relea
sed by an earthquake (in tons of TNT, rather than joules of course). This would be roughly equivalent to reporting the seismic moment (Mo) rather than the moment magnitude which, is just a way of correlating the seismic moment with the Richter Magnitude.

Of course the 2004 Sumatra earthquake (Mw=9.1) released 1400 times more energy than Haiti, yet the death toll in Haiti has exceeded 100,000 and may approach the quarter million that were lost in 2004 (though most of those deaths were attributable not to the earthquake but to the tsunamis that crossed the Indian ocean as a result). As with the Northridge/Olympia example above, the Haiti earthquake had a focus just 13 km beneath the most densely populated region of Haiti, while the Indian ocean quake was 30 km deep and hundreds of kilometers from the nearest populated area (of course it also displaced the floor of the ocean by approximately 30 meters, generating the tsunami).

My suggestion would be to scale the seismic moment to the distance between the earthquake's focus and the nearest populated area (where energy decreases with distance squared). This does not take into account that a significant portion of energy is released as heat and deformation of materials. It also ignores the complexities of subsurface geology and the unique character of individual focal mechanisms. But I think it would go a long way toward expressing to the general public the relative seriousness of different earthquakes.

Here are a couple of back-of-the-envelope examples. In Haiti, Olympia and Northridge I've scaled only for depth, as the foci were more-or-less directly beneath the affected populations. I begin with the assumption that a magnitude 4 event is the energy equivalent of 1 kiloton of TNT:

Update: Hypocentre contacted me below and pointed out my math errors, which have been corrected in the table.

Though the actual mechanics, geology and secondary effects (such as tsunami and landslides) are different in each situation, these adjusted energies seem to be a reasonable approximation of the casualties and damage for these six earthquakes.

I think this is a relatively easy adjustment to make in reporting events, and conveys much more information to the public than the current method. I'm interested in people's comments...


***Note that the IRS has been instructed to allow tax-deductible donations to Haitian relief made in the current year to be deducted on your 2009 taxes. Give generously.

Red Cross
Oxfam America
Doctors Without Borders


Hypocentre said...

I think you are miscalculating the energy differences. 6.7 to 7.0 is nearly 4 times energy and 7.0 to 9.1 is 1412 times more energy. You need to multiply the magnitude difference by 1.5 before antilogging.

jrepka said...

Thanks for pointing this out. I've adjusted the numbers in the table. They seem to make more sense now...

Anonymous said...

I suppose that not only the character of the focal mechanism is important, but also the rupture. For example, Loma Prieta was a bilateral rupture, propagating out in two directions simultaneously. Had it been a unilateral rupture, I think it's correct to say that the shaking would have been approximately twice the duration. Many structures that can survive 30-second shakes would certainly not survive a minute!

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