# Measuring the Richter Scale with logarithms

An Earthquake measures 6.1 on the Richter Scale. What is the rating on an earthquake that is twice as powerful?

I = I0 × 10M
I-intensity of earthquake
I0-earthquake with intensity of 0
M-magnitude of earthquake on the Richter Scale

So I figured I'd use I1 = I0 × 106.1 to find the intensity of earthquake 1 (I1)
then, 2I=I2 to find the intensity of earthquake 2 (I2), which is double that of I1
and finally, M=log(I2/I0) to find the resulting magnitude, or rating, of the Richter Scale.

But my problem begins at the very beginning.

If I0 = 0 then I1 = 0 too...
and I'm quite thrown off by this.
Am I taking the totally wrong approach to this?

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Mark44
Mentor
An Earthquake measures 6.1 on the Richter Scale. What is the rating on an earthquake that is twice as powerful?

I = I0 × 10M
I-intensity of earthquake
I0-earthquake with intensity of 0
M-magnitude of earthquake on the Richter Scale

So I figured I'd use I1 = I0 × 106.1 to find the intensity of earthquake 1 (I1)
then, 2I=I2 to find the intensity of earthquake 2 (I2), which is double that of I1
and finally, M=log(I2/I0) to find the resulting magnitude, or rating, of the Richter Scale.

But my problem begins at the very beginning.

If I0 = 0 then I1 = 0 too...
and I'm quite thrown off by this.
Am I taking the totally wrong approach to this?
I0 can't be 0.

I know! :P I don't understand what else it could be though?? No additional info was given in the question and no one else that I have showed this to has a clue of what to do!

Mark44
Mentor

exactly! that would make sense wouldn't it? But no where in the question, or even in the lesson as a matter of fact, did it mention Io being equal to 1.
Quote from the text : "The Richter scale... is based on a comparison of intensities to Io, which is an earthquake of intensity 0."
Did I just understand that incorrectly?

Mark44
Mentor
exactly! that would make sense wouldn't it? But no where in the question, or even in the lesson as a matter of fact, did it mention Io being equal to 1.
Quote from the text : "The Richter scale... is based on a comparison of intensities to Io, which is an earthquake of intensity 0."
Did I just understand that incorrectly?
I don't think it was worded very well. In any case, the definition your book uses in terms of intensities seems unusual. I did a search yesterday when you posted your other question - most of the definitions I saw for Richter calculations involve the shaking amplitude, not the earthquake intensity.

The formula I saw gives the earthquake magnitude as ML = log10(A/A0(δ)), where A is the shaking amplitude of a given earthquake, and A0(δ) is a function of the distance from the epicenter of the quake.