Hey,
I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading.
Starting with I = E / (4 * pi * r2) where E = original energy from source, we know that energy falls off as 1/r2, 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 = 4r2 (which is 4x r2).
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
I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading.
Starting with I = E / (4 * pi * r2) where E = original energy from source, we know that energy falls off as 1/r2, 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 = 4r2 (which is 4x r2).
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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