Measuring the Richter Scale with logarithms

[Gregory.gags]

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

I = I₀ × 10^M
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 × 10^6.1 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?

 

[Mark44]

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

I = I₀ × 10^M
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 × 10^6.1 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.

 

[Gregory.gags]

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]

How about I₀ = 1?

 

[Gregory.gags]

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]

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 M_L = 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.