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Complex velocity in the 5 degree equation

The 5$^\circ$ equation, namely,
      \begin{eqnarray}
{\partial P \over \partial z}&=&{1 \over v }\ {\partial P \over \partial t}
\\ i\,k_z &=& {-i \omega \over v }\end{eqnarray} (2)
(3)
states that a wavefront will take some time to get from one depth to another. With velocity v being a real constant, waves controlled by (2) and (3) propagate without change in form. In practice waveform changes are observed. So v should not be a real constant. An imaginary part of the velocity would cause attenuation. A frequency-dependent velocity would cause frequency dispersion.


previous up next print clean
Next: Absorption Up: COSMETIC ASPECT OF WAVE Previous: Noise, surface waves and
Stanford Exploration Project
10/31/1997