Whenever there’s a major earthquake, there’s a chance you’ve heard the Richter scale being mentioned.

The scale is one of the most standard ways to measure the magnitude of earthquakes. Remember the devastating 2021 Haiti earthquake?

That magnitude was 7.2 on the Richter scale. The measurement device was developed by Charles F. Richter in 1935 and records the earthquakes’ amplitude on a seismograph.

This scale measures the amplitude of seismic waves but doesn’t use a linear scale; rather, it uses a logarithmic scale. So, how do logarithms relate to the Richter scale?

Why are logarithms used in the Richter scale?

The Richter scale is logarithmic, meaning the values increase on multiples rather than linearly. The scale used a base-ten log, so a whole number jump in wave magnitude indicates a tenfold increase in the wave amplitude recorded by the seismograph.

For instance, a level 6 earthquake releases ten times the ground shaking effects of a level 5 earthquake and is 100 times greater than a level 4 earthquake. The energy released is 31 times across whole numbers in the magnitude scale.

The energy and the intensity of the earthquakes range greatly, from very faint and undetectable levels to colossal levels that result in billions of dollars in damage.

Microquakes or tremors make up most earthquakes and register amplitudes of 3 and below on the Richter scale.

However, the 7.2 magnitude earthquake that devastated Haiti resulted in more than $1.6 billion in losses.

The largest recorded quake is the 1960 Chile 9.5 earthquake, which accounted for $4 billion in damages when accounting for inflation. 

If we were to use a linear scale, we’d resort to cumbersome and large numbers to represent the energy and intensity of quakes.

To help you get some perspective, a 1 Richter scale quake has the same energy as detonating 6 ounces of TNT.

In contrast, a level 8 quake would be like exploding 6 million tons of TNT. As such, it makes sense to use a logarithmic scale to measure the earthquake’s intensity. 

How are earthquakes and logarithms related?

Logarithms are an easy and convenient way to express large quantities. The energy released by earthquakes and their intensity varies massively, and to represent these huge figures, a log scale comes in handy.

The Richter scale conveniently expresses the amplitude of earthquakes in a base-ten logarithmic magnitude scale. Therefore, large values of the earthquake’s energy can be articulated easily. 

Is the Richter scale linear or logarithmic?

The Richter scale is logarithmic. It uses a base-ten logarithmic scale to indicate the amplitude of seismic waves on a seismograph.

For every whole number in the magnitude, the amplitude of the ground motion effect of an earthquake multiplies by 10. 

How is the Richter scale logarithmic and not exponential?

The Richter magnitude scale is logarithmic and not exponential. In order to analyze the intensity of earthquakes or compare the magnitude of different quakes, a logarithmic function is utilized. 

A logarithm works inversely to an exponential. The magnitude scale is the logarithmic amplitude of waves recorded by seismographs.

So, a whole number increase would represent a tenfold increase in amplitude. For the same increment, the energy would multiply by 31—the energy doubles for every 0.2 increment in the magnitude.

Now, you would require exponential functions when calculating the amplitude from the logarithmic magnitude scale. 

How do you find the magnitude of an earthquake using logarithms?

In the Richter scale, the earthquake’s magnitude is measured from the logarithm of the earthquake’s amplitude as recorded by the seismograph.

The magnitude is expressed as whole numbers and fractions, where an absolute number increase represents a tenfold rise in the amplitude of the earthquake. Also, the same would represent 31 times increase in the energy released by the quake.

Is the magnitude scale logarithmic?

The magnitude scale in a Richter scale is logarithmic and not a linear scale. The scale measures great quantities and ranges of an earthquake’s energy and wave amplitude, thus needing to be logarithmic for ease of display and computation.

The magnitude scale uses a log (base-ten); therefore, for every integer increment in the scale, the amplitude of the seismic waves increases by a factor of 10. For example, a quake of magnitude 7 is ten times greater than a magnitude 6 earthquake.

Take Away

The Richter magnitude scale is logarithmic. Therefore, for every whole number increase in magnitude, the amplitude of the seismic waves multiplies tenfold and the energy released by a factor of 31. The logarithmic scale helps represent large values more conveniently.

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