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 | Kinematics in iterated correlations of a passive acoustic experiment |  |
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Using the forward Fourier transformation equation A-2, the wave equation for pressure in a homogeneous medium with
is written in the frequency-domain as
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(65) |
The frequency-domain Green's function
is defined by introducing an impulsive point source acting at
and
on the right-hand side of equation A-4 as follows:
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(66) |
The Green's function solution for two-dimensional space, under the far field approximation can be obtained as
![$\displaystyle G(\mathbf{x},\mathbf{x}_s,\omega) = \frac{1}{\sqrt{8\pi\omega c_0...
...\left\vert \mathbf{x}-\mathbf{x}_s \right\vert + \frac{\pi}{4} \right] \right).$](img192.png) |
(67) |
A source function is easily included by multiplication with the frequency-domain source function. A measurement,
, at a station located at
of a source at
emitting a source function
is obtained as follows:
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(68) |
The sources in this paper are simulated emitting zero-phase Ricker wavelets with center frequency
. The frequency-domain expression used is
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(69) |
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 | Kinematics in iterated correlations of a passive acoustic experiment |  |
![[pdf]](icons/pdf.png) |
Next: Green's function in the
Up: Wave equation and Green's
Previous: Fourier Transformations
2009-05-05