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Measuring the Richter Scale with logarithms

  1. Aug 2, 2012 #1
    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?
     
  2. jcsd
  3. Aug 2, 2012 #2

    Mark44

    Staff: Mentor

    I0 can't be 0.
     
  4. Aug 2, 2012 #3
    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!
     
  5. Aug 2, 2012 #4

    Mark44

    Staff: Mentor

    How about I0 = 1?
     
  6. Aug 2, 2012 #5
    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?
     
  7. Aug 2, 2012 #6

    Mark44

    Staff: Mentor

    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.
     
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