Size vs. strength: Comparing earthquakes

Back-to-back aftershocks — with preliminary magnitudes of 4.8 and 4.1 — jolted Southcentral Alaska around 12:45 p.m. Thursday, in case we weren’t already jumpy enough.

But just how do those stronger aftershocks compare with last week’s magnitude 7.0 earthquake?

Magnitude Collapse of Fourth Avenue near C Street in Anchorage due to a landslide caused by the 9.2 earthquake on March 27, 1964. (U.S. Army/MCT)

Magnitude, according to the U.S. Geological Survey, “is a number that characterizes the relative size of an earthquake ... based on measurement of the maximum motion recorded by a seismograph." Looking at waves on a seismogram — the seismograph’s written record — the magnitude is comparing the amplitude of those waves.

Seems simple enough. But describing how much bigger, and how much stronger, a quake is compared to another requires some math.

Size

Let’s compare the Nov. 30 magnitude 7.0 earthquake with Thursday’s 4.8 aftershock. That’s a difference in magnitude of 2.2. But how much bigger was the 7.0 earthquake?

Magnitude is logarithmic, which means that for every 1.0 increase in magnitude, the shaking is multiplied by 10. (For example, a magnitude 2.0 earthquake is 10 times bigger than a 1.0; a 3.0 earthquake is 10 times bigger than a 2.0; etc.)

To calculate the size difference between a 7.0 and a 4.8, we’d take the difference in magnitude — 2.2 — and raise 10 to that power:

10^2.2 = 158.49

So, the 7.0 earthquake was about 158 times bigger than the 4.8 aftershock.

Strength

Size or amplitude differences are big — but energy (or strength) differences are huge, USGS says.

“One whole unit of magnitude represents approximately 32 times (actually 10^1.5 times) the energy,” USGS says. “This means that a change of 0.1 in magnitude is about 1.4 times the energy release.”

To calculate how much stronger one earthquake is compared to another, you’d take the difference in magnitude, multiply it by 1.5, then raise 10 to that power:

10^(1.5*2.2) = 1995.26

What we get as a result of these calculations: The Nov. 30 quake was about 158 times bigger than the 4.8 aftershock Anchorage felt Thursday — but it was nearly 2,000 times stronger, in terms of energy released.

Want to skip the math? The USGS has created an online calculator that’ll speed up the process.