Question

The magnitude of an earthquake, measured on the Richter Scale, is M log1o T where / is the amplitude registered on a seismograph 100km away from the seismic center, and lo is a certain very small amplitude. Using the Richter Scale, find the magnitude rating for an earthquake causing an amplitude of 10,000,000 times lo

Answer 1

Answer: The magnitude rating for an earthquake causing an amplitude 10,000,000 times $I_o$ is 7.

Explanation:

Richter scale is defined as the scale which expresses the magnitude of earthquake on the basis of the seismograph oscillations.

The equation used to measure the magnitude of an earthquake on Richter scale is:

$M=log_{10}\frac{I}{I_o}$

where

I = amplitude registered on seismograph 100 km away from seismic center = $10,000,000I_o$

$I_o$ = small amplitude

Putting values in above equation, we get:

$M=\log_{10}(\frac{10000000I_o}{I_o})\\\\M=7$

Hence, the magnitude rating for an earthquake causing an amplitude 10,000,000 times $I_o$ is 7.