What I learned about earthquakes from Nate Silver’s “Signal and the Noise”

I felt both earthquakes this past week in Palm Springs which is about 170 miles from the epicenter in Ridgecrest. It compelled me to review the chapter from Nate Silver’s Signal and the Noise discussing our inability to forecast earthquakes despite a long history of seers and scientists trying. What do we know?

• While we are confident in the statistical nature of aftershocks, when a large earthquake hits we still don’t know if it is the main event or a foreshock.
Earthquakes result from a buildup of stress along fault lines. It might follow that the stress builds up until it is discharged, like a geyser erupting with boiling water, relieving the stress and resetting the process. The fault system is complex: regions like California are associated with multiple faults, and each fault has its own branches and tributaries. When an earthquake does strike, it may relieve the stress on one portion of a fault, but it can transfer it along to neighboring faults, or even to some faraway portion of the same fault.
• We do not understand geological processes that cause earthquakes enough to construct models which can predict earthquakes. Without such bottoms-up simulations, we are left to rely purely on statistics of past earthquakes to predict them.
You can create a statistical variable called “stress” in your model. But since there’s no way to measure it directly, that variable is still just expressed as a mathematical function of past earthquakes
• We are able to approximate long-term averages. Enter the Gutenberg-Richter law.
There is a relatively simple relationship between the magnitude of an earthquake and how often one occurs. If you compare the frequencies of earthquakes with their magnitudes, you’ll find that the number drops off exponentially as the magnitude increases. While there are very few catastrophic earthquakes, there are literally millions of smaller ones.

If you graph earthquakes on a log scale with the Y-axis as frequency and X-axis as magnitude we see a “stunning regularity”.

Credit: Signal and the Noise
A power-law distribution emerges!

Something that obeys this distribution has a highly useful property: you can forecast the number of large-scale events from the number of small-scale ones, or vice versa. In the case of earthquakes, it turns out that for every increase of one point in magnitude, an earthquake becomes about ten times less frequent. So, for example, magnitude 6 earthquakes occur ten times more frequently than magnitude 7’s, and one hundred times more often than magnitude 8’s.

But now I must let you down. Even though we can approximate the frequency of earthquakes we can’t predict when and where they might occur.

• The official position of the USGS is even more emphatic: earthquakes cannot be predicted. “Neither the USGS nor Caltech nor any other scientists have ever predicted a major earthquake,” the organization’s Web site asserts. “They do not know how, and they do not expect to know how any time in the foreseeable future.”
Find your city and remember — these are long-term averages. There is no concept of “we are due for one”. And conversely, if we just had a big one, that does not mean we are due for a break.

credit: Signal and the Noise