Earthquake Magnitude Scales

Magnitude is not the same as intensity

Two different measurements are used to describe an earthquake. Magnitude is a single number for the earthquake as a whole — a measure of the energy released where the fault slipped. Intensity describes how strongly the ground shook at one particular place, and so it has many values for a single earthquake: high near the source, lower with distance, and modified by local soil and rock.

A large, deep earthquake far offshore can have a high magnitude but produce only moderate intensity on land. A smaller, shallow earthquake directly beneath a town can have a lower magnitude but cause severe intensity and damage.

The Richter scale

Charles Richter, working with Beno Gutenberg at Caltech, defined the first magnitude scale in 1935. His local magnitude (M_L, the “Richter scale”) is the base-10 logarithm of the largest wave amplitude recorded on a standard Wood–Anderson seismograph, corrected for the distance to the earthquake.

It was designed for moderate earthquakes in southern California and it works poorly outside that setting. For earthquakes above about magnitude 7 it saturates: the instrument and the wave type it measures stop responding to further increases in the size of the rupture, so a magnitude 8 and a magnitude 9 can come out with nearly the same Richter value. Later scales based on body waves (m_b) and surface waves (M_s) extended the range but saturate too.

Moment magnitude — the modern standard

Since the 1970s, seismologists have reported large earthquakes on the moment magnitude scale (M_w), introduced by Hiroo Kanamori and formalised by Thomas Hanks and Kanamori in 1979. It is derived from the seismic moment, a physical quantity equal to the rigidity of the rock multiplied by the area of the fault that slipped and by the average distance it slipped.

Because it is tied directly to the physical size of the rupture, moment magnitude does not saturate — it works from the smallest recorded microearthquakes to the magnitude 9.5 Chile earthquake of 1960. It is deliberately calibrated to agree with the Richter scale in the range where the Richter scale works, so a “magnitude 5.4” means about the same thing on both. When the news says “Richter,” the figure quoted is almost always moment magnitude (U.S. Geological Survey).

Why the scale is logarithmic

Each whole step on the magnitude scale corresponds to a tenfold increase in the amplitude of ground motion recorded on a seismograph, and roughly a 32-fold increase in the energy released (more precisely, 10^1.5 ≈ 31.6).

The consequences are dramatic and easy to underestimate:

• Magnitude 6 → magnitude 7: about 32 times more energy.
• Magnitude 5 → magnitude 7: about 1,000 times more energy.
• Magnitude 5 → magnitude 9: about one million times more energy.
• The magnitude 9.5 Chile earthquake of 1960 released more energy than all other earthquakes of that decade combined.

How often each size occurs

Smaller earthquakes are vastly more common than large ones. These are long-term global averages from the U.S. Geological Survey:

Intensity: the Modified Mercalli scale

Shaking at a given location is reported on the twelve-level Modified Mercalli Intensity (MMI) scale, written in Roman numerals. It is based on observed effects, not on instruments:

• I–III — not felt to weak; hanging objects may swing.
• IV–V — felt widely indoors; dishes and windows rattle; sleepers wake.
• VI–VII — felt by all; furniture moves; plaster cracks; poorly built structures damaged.
• VIII–IX — considerable damage; walls fall; buildings shift off foundations.
• X–XII — most masonry and frame structures destroyed; ground cracks; rails bent; near-total destruction.

The USGS builds an intensity map (a ShakeMap) for every significant earthquake, combining seismic recordings with public reports collected through its “Did You Feel It?” system.