Earthquake Magnitudes

These days, an earthquake happens and right away it is on the news, including its magnitude. Instant earthquake magnitudes seem as routine an achievement as reporting the temperature, but they're the fruit of generations of scientific work.

Why Earthquakes Are Hard to Measure

Earthquakes are very hard to measure on a standard scale of size. The problem is like finding one number for the quality of a baseball pitcher. You can start with the pitcher's win-loss record, but there are more things to consider: earned-run average, strikeouts and walks, career longevity and so on. Baseball statisticians tinker with indexes that weigh these factors (for more, visit the About Baseball Guide).

Earthquakes are easily as complicated as pitchers. They are fast or slow. Some are gentle, others are violent. They're even right-handed or left-handed. They are oriented different ways—horizontal, vertical, or in between (see Faults in a Nutshell). They occur in different geologic settings, deep within continents or out in the ocean. Yet somehow we want a single meaningful number for ranking the world's earthquakes. The goal has always been to figure out the total amount of energy a quake releases, because that tells us profound things about the dynamics of the Earth's interior.

Richter's First Scale

The pioneering seismologist Charles Richter started in the 1930s by simplifying everything he could think of. He chose one standard instrument, a Wood-Anderson seismograph, used only nearby earthquakes in Southern California, and took only one piece of data—the distance A in millimeters that the seismograph needle moved. He worked up a simple adjustment factor B to allow for near versus distant quakes, and that was the first Richter scale of local magnitude M_L:

M_L = log A + B

A graphical version of his scale is reproduced on the Caltech archives site.

Read More

Measuring Earthquake Intensities Using Seismic Scales

By Andrew Alden

You'll notice that M_L really measures the size of earthquake waves, not an earthquake's total energy, but it was a start. This scale worked fairly well as far as it went, which was for small and moderate earthquakes in Southern California. Over the next 20 years Richter and many other workers extended the scale to newer seismometers, different regions, and different kinds of seismic waves.

Later "Richter Scales"

Soon enough Richter's original scale was abandoned, but the public and the press still use the phrase "Richter magnitude." Seismologists used to mind, but not any more.

Today seismic events may be measured based on body waves or surface waves (these are explained in Earthquakes in a Nutshell). The formulas differ but they yield the same numbers for moderate earthquakes.

Body-wave magnitude is

m_b = log(A/T) + Q(D,h)

where A is the ground motion (in microns), T is the wave's period (in seconds), and Q(D,h) is a correction factor that depends on distance to the quake's epicenter D (in degrees) and focal depth h (in kilometers).

Surface-wave magnitude is

M_s = log(A/T) + 1.66 logD + 3.30

m_b uses relatively short seismic waves with a 1-second period, so to it every quake source that is larger than a few wavelengths looks the same. That corresponds to a magnitude of about 6.5. M_s uses 20-second waves and can handle larger sources, but it too saturates around magnitude 8. That's OK for most purposes because magnitude-8 or great events happen only about once a year on average for the whole planet. But within their limits, these two scales are a reliable gauge of the actual energy that earthquakes release.

The biggest earthquake whose magnitude we know was in 1960, in the Pacific right off central Chile on May 22. Back then, it was said to be magnitude 8.5, but today we say it was 9.5. What happened in the meantime was that Tom Hanks and Hiroo Kanamori came up with a better magnitude scale in 1979.

This moment magnitude, M_w, is not based on seismometer readings at all but on the total energy released in a quake, the seismic moment M_o (in dyne-centimeters):

M_w = 2/3 log(M_o) - 10.7

This scale therefore does not saturate. Moment magnitude can match anything the Earth can throw at us. The formula for M_w is such that below magnitude 8 it matches M_s and below magnitude 6 it matches m_b, which is close enough to Richter's old M_L. So keep calling it the Richter scale if you like—it's the scale Richter would have made if he could.

The U.S. Geological Survey's Henry Spall interviewed Charles Richter in 1980 about "his" scale. It makes lively reading.

PS: Earthquakes on Earth simply can't get bigger than around M_w = 9.5. A piece of rock can store up only so much strain energy before it ruptures, so the size of a quake depends strictly on how much rock—how many kilometers of fault length—can rupture at once. The Chile Trench, where the 1960 quake occurred, is the longest straight fault in the world. The only way to get more energy is with giant landslides or asteroid impacts.