An earthquake produces two basic types of waves: surface waves and bulk waves. T

Question

An earthquake produces two basic types of waves: surface waves and bulk waves. The former move along the surface of the earth much like the ripples in the surface of a pond, while the other type propagate through the whole earth forming a hemisphere around the point of origin of the quark assuming that it occurred close to the surface.

One particular earthquake produces bulk and surface waves with identical amplitudes at 1 km from the epicentre. What is the ratio of the amplitude of the surface wave to the bulk wave 134 km from the epicentre of the quake assuming that the earth is a perfect, uniform wave medium?

Explanation / Answer

The surface wave attenuates (reduces itself) in proportion to the circumference of a circle, while the body wave attenuates in proportion to the surface area of the hemisphere, so if the two waves had identical amplitudes when 1 km from the source, the ratio of their amplitudes at 134 km from the source will be (1/134)/(1/134^2) = 134. In other words, the surface wave will have 134 times the amplitude of the body wave.

A certain inaccuracy in my solution arises from the fact that the surface of the earth is not flat. However, 134 km is only a little more than 1 degree of the earth's 360-degree circumference, so it seems reasonable to ignore the curvature in addressing this problem.

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