MHB How are Earthquake Magnitudes Calculated on the Richter Scale?

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The Richter scale calculates earthquake magnitudes using the formula R(I) = log(I/I0), where I is the amplitude recorded on a seismograph and I0 is a reference amplitude. For amplitudes of 1,000,000I0 and 1,000,000,000I0, the correct calculations yield positive values, indicating stronger earthquakes. The initial suggestion of negative values was incorrect, as the scale measures relative strength, not absolute amplitude. The 100km distance mentioned is irrelevant for the calculation since I0 cancels out. Understanding the logarithmic nature of the scale is crucial for accurate magnitude assessment.
arl2267
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The magnitude of an earthquake, measured on the Richter scale, is given by

R(I)= log(I/I0)

Where I is the amplitude registered on a seismograph located 100km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale ratings of earthquakes with the following amplitudes:

a) 1,000,000I0

b) 1,000,000,000I0

Okay so would the solution be

log(100/1,000,000)= -4

log(100/1,000,000,000)= -6

?
 
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arl2267 said:
The magnitude of an earthquake, measured on the Richter scale, is given by

R(I)= log(I/I0)

Where I is the amplitude registered on a seismograph located 100km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale ratings of earthquakes with the following amplitudes:

a) 1,000,000I0

b) 1,000,000,000I0

Okay so would the solution be

log(100/1,000,000)= -4

log(100/1,000,000,000)= -6

?

The value of 100km is meaningless in this context - ignore it. The question is giving you values of $I$ in terms of $I_0$ which means the latter will cancel out giving a number.

Your values should be positive. If you consider it logically an earthquake 1 million times stronger than a reference will be larger on the Richter scale than said reference quake.
 
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