MHB How are Earthquake Magnitudes Calculated on the Richter Scale?

[arl2267]

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

?

 

[SuperSonic4]

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.