The Richter Scale

The Richter Scale Christian Dunn August 8th, 2006

The Richter scale (As written by Christian Dunn compiled from information from 9th grade science class instructed by Mr. J. Evans and basic information about logarithms.) The Richter scale is based on logarithms (which are exponents), and the logarithm that is used to compare one earthquake’s energy to another is the factor which is required that, when multiplied with another factor, the score on the Richter scale of the benchmark earthquake, results in the product of the score on the Richter scale of the other earthquake. The amount of energy that the comparison earthquake releases is equal to the benchmark earthquake raised or lowered to the power expressed in the logarithm found from the comparison factor. This means that: • •

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The factor of energy released compared between 2 magnitudes on the Richter scale is 1000x. The factor of energy released compared between 1 magnitude on the Richter scale is about 31.6228x, or the square root of 1000, which is equal to 10000.5. The number 1000 is lowered to the power of the reciprocal of how the number 2 is compared to one, that is, 2/1. The factor of energy released compared between 0.2 magnitudes on the Richter scale is about 2x. The number 0.2 is 1/10 of the number 2, and therefore the number 1000 is lowered to the power of 0.1, which results with about the number 1.995, which is about equal to the number 2. That is, 10000.1 is about equal to 2. The factor of energy released compared between 0.1 magnitudes on the Richter scale is about equal to 1.41, or about the square root of 2, which is also about equal to 10000.05, for more precise calculation.

Smaller Earthquake Magnitude (Richter scale magnitude)

Larger Earthquake Magnitude (Richter scale magnitude)

5.0

5.1

5.0

5.2

Difference (Richter scale magnitude)

0.1 (2*0.05) 0.2

Theoretical (Left column) / Approximate (Right column) Factor of Difference with the two earthquakes.

10000.05

1.413 [sqrt(2)]

10000.1

1.995 [2]

The Richter Scale Christian Dunn August 8th, 2006

5.0

6.0

(2*0.10) 1.0 (2*0.5)

5.0

7.0

2.0 (2*1.0)

10000.5 10001

31.6228 [32] [sqrt(1000)] 1000

The factor of difference between the number 2 and the difference between the two magnitudes becomes the logarithm of 1000 to determine the factor of difference between the energy released between two such earthquakes.