While fluid percolates through porous media in infinitesimal volume \delta V generates the noise of the power \delta N in a wide frequency range:
| (1) | \delta N = A(f) \cdot {\bf u} \cdot \nabla p \cdot \delta V |
where
{\bf u} | flow velocity |
|---|---|
p | fluid pressure |
A(f) | normalised noise spectrum, \displaystyle \int_0^\infty A(f) \, df = 1 |
f | noise frequency |
While propagating through the rocks the different frequencies will decay at different rate \lambda(f) and if noise sensor is located at {\bf r}_0 = \{0, \, 0, \, 0\} then the it will capture:
| (2) | \delta N_S = int_V A(f) \cdot {\bf u} \cdot \nabla p \cdot \exp[-r/\lambda(f)] \cdot \delta V |