Urgent mathematics question......?

Question

The Richter Scale is used as a convenient measure for the size of earthquakes and it defines the magnitude of

an earthquake as log10(I/S) where I is the earthquake’s intensity (measured by the amplitude on a seismograph

located 100km from the epicentre of the quake) and S is the intensity of a “standard earthquake”.

The 1989 Loma Prieta earthquake (which destroyed some freeways in San Francisco) had a magnitude of 7.9 on

the Richter Scale.

(a) Given that the 1906 San Francisco quake was 16 times as intense estimate the magnitude on the Richter Scale

for the 1906 quake.

(b) What intensity (compared to the 1989 quake) would be required to generate a Richter Scale magnitude of 9?

[“Massive” quakes with magnitude  9 are fairly rare, e.g. Alaska 1964, Sumatra 2004 ].

Answer 1

Iof 1906 = 16 (I 0f 1989) = 16 (10^(7.9)S)

(I of 1906)/S = 16(10^7.9)

Log(I/S) = (log 1.6) + 7.9...both log to base 10.

Hence the intensity can be calculated.

In general if an earthquake is x time as intense as 1989 E.Q. just add logx to bease 10 to 7.9 and you get it.