Wave separation > Wave separation in borehole seismics by the SVD method

The example shows:

Above, from left to right:
-the wavelets (vectors u, Filtering by singular value decomposition SVD) of the first 10 eigensections (numbered from 0 to 9),
-the eigenvalues of the first 10 eigensections (numbered from 0 to 9).

Below, from left to right:

  • the amplitudes (vectors v, Filtering by singular value decomposition SVD) of the first N eigensections,
  • the initial data,
  • the down-going waves obtained from the sum of the first N eigensections,
  • the up-going waves obtained from the difference between the initial data and the down-going waves.

It is possible to choose N (Number of stacked eigensections).

The sections which show changes of sign of the amplitude are not physically interpretable.
The signal part associated with the down-going wavefield is the first eigensection only if these waves were previously perfectly aligned. The complimentary part (the noise section) contains the up-going waves and the noise.