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I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading.

Starting with I = E / (4 * pi * r^{2}) where E = original energy from source, we know that energy falls off as 1/r^{2}, thus amplitude falls off as 1/r.

From wikipedia: "The energy or intensity decreases (divided by 4) as the distance r is doubled;"

This makes sense to me, as when r is doubled we have the energy divided by (2r)^{2}= 4r^{2}(which is 4x r^{2}).

From this same principle, I would expect that the amplitude is divided by 2 when the distance is doubled as we have 1/2r instead of 1/r.

However from a Louisiana State University website:

"Geomteric spreading makes the amplitude of a signal falls off in proportion to the distance traveled by the ray. So that if the path of flight is doubled the amplitude will decrease by a factor of: square root of 2."

I can't see how they got their factor of √2 instead of 2.

Is one a mistake or am I missing something?

Cheers

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# Amplitude decrease with geometrical spreading

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