Why Earthquake magnitudes are given for 100km from the epicentre

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

29 July 2007

The recent Earth tremors have woken up Denis Warui’s mathematical mind. He says: “you could be right about the 10-power-3 theory. But here comes the question: Since anything raised to the power of zero is [equal to] one, can we ever have a magnitude of zero on a Richter scale? [Secondly] you wrote that we use 100 km from the centre of the quake. Must the quake be 100 km [from the epicentre]? Can there be quakes less than 100 km in area of influence, and if so how are they measured?”

The answer to the first question is yes. An earthquake can have a magnitude of zero on the Richter scale…even though it is too small a movement to be called a “quake”. As explained last week, this corresponds to one micrometer vibrations on the ground 100km from the epicentre of activity.

Denis is correct in saying that anything raised to the power of zero is equal to one. So, if the tremor produces one micrometer vibrations then we proceed as follows:

One micrometer (size of vibration) divided by one micrometer (the reference point of the Richter scale) is one. Then we ask the question: to what power should we raise the number 10, so that the result is one? And the answer to that is zero – remember; anything raised to zero gives one. Therefore, the Richter magnitude is zero – QED.

The answer to the second question (why use 100km?) is simply that 100km is a nice round number and it works very well in calculations. However, this does not mean that earthquakes only affect areas within the 100km radius. No!

The vibrations travel over many hundreds of kilometres, but as they spread, they get weaker. The reason for this weakening is that it is the same energy that was released from the epicentre that is being distributed over larger areas. Thus the greater the distance from the centre, the smaller the energy per unit area.

This effect is similar to what happens to sound waves: The farther you are from the loudspeaker, the softer it sounds. Actually, strictly speaking, earthquakes are sound waves in the ground. But their frequency is too low to be heard by the human ear – even though their amplitude (“loudness”) is very high compared to normal sound.

Because of this reduction of intensity as the waves travel, a problem arises: If we measure a vibration of, say, 0.01mm at Isiolo, can we say whether that was a big or small earthquake? It can be either a small one with an epicentre very near or a big quake that happened very far away. But which is it?

The same problem is found in astronomy – does a star look dim because it is very far away or because it is very small? This is the reason why Richter chose a fixed reference point of 100km (a nice round number) to define the magnitude of an earthquake. In fact, it is said that he was inspired by the astronomical method of measuring star brightness!