# Richter Scale and Earthquake Magnitude

The Richter scale is a logarithmic scale that measures the magnitude of an earthquake, originally developed by Charles F. Richter in 1935. It provides an objective measure of the energy an earthquake releases by quantifying the seismic waves produced. Prior to the invention of the Richter scale, the severity of earthquakes was subjective, often described based on the damage caused or eyewitness accounts, making comparisons across events and over time challenging.

Because the Richter scale is logarithmic, each whole number increase in scale is a 10x increase in the amplitude of the seismic waves.

### Historical Background

Before the development of objective measures of earthquake magnitude, the assessment of earthquakes was largely descriptive. The first systematic approach to quantifying earthquakes was the Rossi-Forel scale, established in the late 19th century. This scale ranged from I (imperceptible) to X (disastrous) and was based on human perception and structural damage.

The Mercalli intensity scale, developed by Italian volcanologist Giuseppe Mercalli in the early 20th century, offered more detailed categories. It improved on the Rossi-Forel scale by incorporating modern engineering understanding into assessments of building damage. However, like its predecessor, the Mercalli scale was subjective and relied heavily on local conditions and the quality of construction in the area affected by the earthquake.

Charles F. Richter and Beno Gutenberg of the California Institute of Technology developed the Richter Scale in the 1930s to provide a more standard and objective measure. The Richter scale uses the measurements of seismic waves as recorded on seismographs. For the first time, earthquake magnitude was defined independently of the effects or damage it caused.

### Calculating Richter Magnitude

Richter derived a formula to calculate the magnitude of an earthquake. It’s expressed as:

ML = log A – log A0

Here:

• ML is the local magnitude (Richter magnitude)
• A is the maximum amplitude (in mm) of a seismic wave as recorded by the Wood-Anderson seismograph
• A0 is the amplitude of a standard wave at 100 km from the earthquake epicenter

The value A0 varies depending on the distance to the earthquake, the depth of the earthquake, and various other factors.

The logarithmic nature of the Richter scale means that each whole number increase in magnitude represents a tenfold increase in the measured amplitude of seismic waves and roughly 31.6 times more energy release.

Note that there are several modern adjustments to this formula, largely based on the distance to the epicenter of the quake. Also, although no earthquakes greater than 10 on the scale have been recorded, there is no upper limit to the Richter scale.

### Magnitude Ranges and their Effects

The Richter scale is open-ended, but most earthquakes fall between magnitudes 2.0 and 9.0. Here is a breakdown of the categories, their descriptions, effects, and estimated annual global frequency:

1. Less than 2.0 (Micro): People don’t feel micro earthquakes, but instruments record them. There are an estimated 1.4 million of these quakes annually worldwide. Basically, they happen all the time.
2. 2.0 – 2.9 (Minor): Minor earthquakes are often felt, but rarely cause damage. There are around 1.3 million occurrences each year.
3. 3.0 – 3.9 (Light): Light earthquakes are often felt, but rarely causes significant damage. Approximately 130,000 of these quakes occur annually.
4. 4.0 – 4.9 (Moderate): A moderate earthquake causes a noticeable shaking of indoor items, accompanied by rattling noises. Significant damage is unlikely. There are about 13,000 occurrences globally each year.
5. 5.0 – 5.9 (Strong): Strong earthquakes potentially cause significant damage to buildings and other structures. There are roughly 1,300 occurrences annually.
6. 6.0 – 6.9 (Major): Major earthquakes cause a lot of damage in populated areas. There are about 100 occurrences each year.
7. 7.0 and higher (Great): These earthquakes cause serious damage. They happen around 10-20 times per year globally. There is usually only one earthquake per year with a magnitude between 8 and 10. No earthquake of 10 or higher has ever been recorded.

Some quakes with a small magnitude on the Richter scale cause more damage than large magnitude quakes. The level of the destruction depends on how deep the earthquake is and whether or not its epicenter is near a populated area. Also, some quake cause tsunamis, which add to the damage.

### The Moment Magnitude Scale

While the Richter scale continues to be well-known among the general public, seismologists mainly use the moment magnitude scale (Mw) for more precise measurements, especially for extremely large earthquakes. The moment magnitude scale is also logarithmic, but it more accurately measures the total energy released by an earthquake.

The moment magnitude scale (Mw) is more complex to calculate than the Richter scale. The basic formula for calculating the moment magnitude is:

Mw = 2/3 log(M0) – 10.7

M0 is the seismic moment, which is measured in dyne-cm (1 dyne-cm = 1×10-7 joules). The seismic moment (M0) is a measure of the total energy released by the earthquake. It is calculated by multiplying the shear modulus of the rocks involved (a measure of the rigidity of the material) by the area of the fault that slipped and the average amount of slip along the fault.

Let’s illustrate this with an example. In the 1906 San Francisco earthquake, the estimated slip along the fault was about 4.5 meters, the area of faulting was about 20,000 km², and the shear modulus of the Earth’s crust is about 3×1011 dyne/cm². Thus, the seismic moment M0 was about 2.7×1027 dyne-cm.

Plug this into the Mw formula:

Mw = 2/3 * log(2.7*1027) – 10.7 ≈ 7.8

The Richter magnitude for the 1906 San Francisco earthquake was approximately 7.9. So, the magnitudes are fairly close for this particular earthquake. However, for very large earthquakes, the Richter scale underestimates the energy release, while the moment magnitude scale remains accurate. This is because the Richter scale is based on the amplitude of seismic waves, which “saturate” or fail to increase in very large earthquakes, whereas the Moment Magnitude scale considers the total energy released by the earthquake. Because the moment magnitude scale considers the area of the fault that slipped, the average amount of slip along the fault, and the rigidity of the rocks involved, it provides a more accurate and consistent measure of large earthquake magnitudes.

### Strongest Earthquake Ever Recorded

The strongest earthquake ever recorded was the Great Chilean Earthquake that struck Chile on May 22, 1960. The earthquake reached a magnitude of 9.5 on the moment magnitude scale. This event released an immense amount of energy, causing widespread damage in Chile and triggering tsunamis that affected coastal regions as far away as Hawaii, Japan, and the Philippines.

The strongest earthquake in the United States was the March 27, 1964 earthquake in the Prince William Sound part of Alaska. Measuring 9.2 on the Richter scale, it is the second-largest quake in the world, following the 1960 earthquake. However, the June 11, 1585 earthquake in the Aleutian Islands (now Alaska) may have surpassed the 1964 quake, with an estimated magnitude of 9.25.

### References

• Abe, Katsuyuki (1982). “Magnitude, seismic moment and apparent stress for major deep earthquakes”. Journal of Physics of the Earth. 30 (4): 321–330. doi:10.4294/jpe1952.30.321
• Boore, D. M. (1989). “The Richter scale: its development and use for determining earthquake source parameter”. Tectonophysics. 166 (1–3): 1–14. doi:10.1016/0040-1951(89)90200-x
• Gutenberg, B.; Richter, C. F. (1936), “Discussion: Magnitude and energy of earthquakes”. Science. 83 (2147): 183–185. doi:10.1126/science.83.2147.183
• Gutenberg, B.; Richter, C. F. (1956). “Earthquake magnitude, intensity, energy, and acceleration”. Bulletin of the Seismological Society of America. 46 (2): 105–145.
• Hutton, L. K.; Boore, David M. (1987). “The ML scale in Southern California”. Nature. 271: 411–414. doi:10.1038/271411a0