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While propagating through the rocks the different frequencies will decay at different rate
and if noise sensor is located at
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| body | --uriencoded--%7B\bf r%7D_0 = \%7B0, \, 0, \, 0\%7D |
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then the it will capture:
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\delta N_S = \int_V A(f) \cdot {\bf u} \cdot \nabla p \cdot \exp[-r/\lambdaalpha(f)r] \cdot \delta V |
The decay decrement
is growing with frequency: | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \frac%7Bd \alpha%7D%7Bdf%7D > 0 |
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.
There is no universal model but it can be approximated by a linear dependance:
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\alpha = \alpha_1 \cdot f |
with
having much slower dependance on frequency than .
See also
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Reservoir Noise
