Two hundred years ago, Missouri was rocked by an earthquake so severe it made the Mississippi River flow backward and set off church bells in Boston more than 1,000 miles away.
These details help convey the staggering scale and reach of what was a remarkable geologic event. Today, along with those accounts, we would also get a number: the magnitude of the earthquake. But that number is based on a logarithmic scale, and can be hard to grasp.
Earthquakes aren't measured linearly, but in orders of magnitude. Which means a 6.1 magnitude quake like the one that shook Northern California over the weekend is about twice as big as the 5.8 earthquake that rattled Washington, D.C., in 2011—and nearly three times as strong in terms of the amount of energy it released. Some more context: The 7.0 earthquake that devastated Haiti in 2010 was eight times bigger than the Northern California quake, and released 22 times more energy. None of this jibes with the linear way people use numbers for most measurements in daily life.
Here's how Jesse Singal explained it over at New York magazine earlier this year:
On a linear scale, we know that four is twice as big as two and eight twice as big as four. This is what a casual observer of earthquake magnitude scales would expect: that an earthquake of 6.0 packs twice the punch of a 3.0. But no! In reality, a 6.0 quake releases 31,622.776 times as much energy as a 3.0 quake. And a 7.0 releases 31.622 times as much energy as a 6.0.
So why do geologists talk about earthquakes this way? Why not use a scale that operates more like the ones used to measure weight, or length, or temperature, or any number of other natural phenomena?
The answer, it turns out, begins in outer space. "My amateur interest in astronomy brought out the term 'magnitude,' which is used for the brightness of a star," said Charles Richter—the scientist behind the well-known scale of the same name—in a 1980 interview.
The Richter Magnitude Scale is the method of earthquake measurement widely used in the United States last century. Richter's idea was to track the amount of energy released by a quake the way an astronomer would measure the brightness of a star. Each number on the magnitude scale indicated an earthquake 10 times stronger than the last—which means the quake strength between each increment of one on the scale grows as the numbers climb.
Today, earthquake magnitude is measured using another logarithmic system—usually called Moment Magnitude or just Magnitude—that's calibrated to the Richter Scale but can measure bigger quakes than the Richter Scale could. And while it might not be the most intuitive system, it's a far more useful one than a linear scale would be.
"The logarithmic magnitude scale also allows for comparison of earthquakes on relatively the same terms even though their impacts to society and structures ... can be quite different," Robert Williams, a geologist in the USGS Earthquake Hazards Program, told me in an email. "Compared to a linear scale the logarithmic scale provides an easy and more manageable way to represent this wide range of ground motion amplitude (often many orders of magnitude) and energy release for different quakes within an easily understandable range of numbers."
Richter identified some of the reasons linear alternatives aren't really workable when he and colleagues established the scale in the 1930s. Again Singal: "If you rescaled things to a linear scale—such as how much energy is produced by a given quake—suddenly you’d be dealing with huge numbers for the big quakes. And huge numbers are another thing most people aren’t particularly good at grasping."
Besides, even though Richter apparently acknowledged that "logarithmic plots are a device of the devil," they're actually widely used, as geologist Williams reminded me. "Logarithmic scales are commonly used in other sciences, for example, the decibel scale in sound measurements and the pH scale in chemistry for rating acidity."
For now, at least, it seems we're stuck with charting earthquakes this way. And for those who find thinking logarithmically doesn't come naturally, USGS has a handy online calculator that shows just how different quakes compare with one another.
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