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10 December, 12:13

Earthquake Intensity On the Richter scale, the magnitude R of an earthquake of intensity I is given by

R = (ln I - ln I0) / ln 1o

Where 10 is the minimum intensity used for comparison. Assume 10 = 1.

(a) Find the intensity of the March 11, 2011 earthquake in Japan for which R = 9.0.

(b) Find the intensity of the January 12. 2010 earthquake in Haiti for which R = 7.0.

(c) Fiind the factor by which the intensity is increased when the value of R is doubled.

(d) Find dR/dl.

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Answers (1)
  1. 10 December, 13:12
    0
    (A) 999 734 198.4

    B) 9999043.54

    C) the intensity L is squared when R is doubled

    D) dR/dL = 1 / (Lln10)

    Step-by-step explanation:

    R = (In L - ln Lo) / ln 10

    Since Lo = 1 and ln 1 = 0

    Therefore,

    R = ln L / ln 10

    (A) Since R = 9

    In L = Rln10

    In L = 9 ln10 = 20.723

    L = exp (20.723) = 999 734 198.4

    Therefore, the intensity of earthquake in Japan = 999 734 198.4

    (B) when R = 7

    In L = Rln10

    In L = 7ln10 = 16.118

    L = exp (16.118) = 9999043.54

    Therefore the intensity of earthquake in Haiti = 9999043.54

    (C) when R is doubled, let say R = 14

    L = exp (14ln10) = 99980871640000

    Then the ratio of L (R=14) and L (R=7)

    L (R=14) / L (R=7) = 99980871640000/9999043.54 = 9999043.53

    Since L (R=14) / L (R=7) = L (R=7)

    Therefore, the intensity L is squared when R is doubled

    D) R = lnL/ln10

    dR/dL = 1 / (Lln10)
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