The Richter scale was developed by Charles Richter and Beno Gutenberg, in order to measure the magnitude of an earthquake caused by the movement of tectonic plates.
The waves produced by the release of energy from moving plates can cause major disasters.
Charles and Beno's studies resulted in a logarithmic scale called Richter, which scores from 0 to 9 degrees.
The magnitude (degrees) is the logarithm of the measurement of the amplitudes (measured by devices called seismographs) of the waves produced by the release of energy from the earthquake. The formula used is as follows:
M = log A - log A0, where M: magnitude, A: maximum amplitude, A0: reference range.
We can use the formula to compare the magnitudes of two earthquakes. We're going to compare a 6-degree earthquake with an 8-degree earthquake, all on the Richter scale.
M1 – M2 = (log A1 – log A0) – (log A2 – log A0)
6 - 8 = log A1 – log A2
– 2 = log(A1 / A2)
10 -2 = A1 / A2
(1/10)2 = A1 / A2
(1/100) = A1 / A2
THE2 = 100A1
We can note that the waves of the earthquake A
To calculate the energy released by an earthquake, we use the following formula:
I = (2/3)log10(E/E0), where I: ranges from 0 to 9, E: energy released in kW/h
and is0: 7 x 10-3 kW/h.
What is the energy released by an earthquake measuring 6 on the Richter scale?
I = 6
6 = (2/3)log10(E / 7 x 10-3)
9 = log10(E / 7 x 10-3)
109 = E / 7 x 10-3
E = 7 x 10-3 x 109
E = 7 x 106 kW / h
The energy released by an earthquake measuring 6 degrees on the Richter scale is 7 x 106 kW/h.
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by Mark Noah
Graduated in Mathematics
Brazil School Team
Logarithm - Math - Brazil School
Would you like to reference this text in a school or academic work? Look:
SILVA, Marcos Noé Pedro da. "Mathematical Applications in Geology: The Richter Scale"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/aplicacoes-matematicas-na-geologia-escala-richter.htm. Accessed on June 29, 2021.
