Phase unwrapping of angle-domain common image gathers |

The following is the outline of the suggested algorithm, (setting for our specific case):

- Set up the initial weights, .
- Set .
- Until has reached the maximum number of iterations, repeat the following steps:
- Solve (to convergence) the Weighted Least Square (WLS) system:

(3) - Compute new weights according to the formula

(4) - Increase by 1.

- Solve (to convergence) the Weighted Least Square (WLS) system:
- End.

is a diagonal matrix with elements , the weights for each equation. The vector is the row of , so that is a scalar and an adequately small value. For efficiency reasons the WLS step is implemented by preconditioned conjugate gradient.

With this iterative mechanism and this particular choice of weights, each equation which is not satisfied at a given iteration is almost ignored for the next iteration, provided that more trusted equations exist that involve the same points.

Thus the choice of the initial weights is critical to yielding good results. We preliminarily used the amplitude information as a measure for the phase reliability: each equation was given a weight proportional to the harmonic average between the amplitudes of the two points involved.

velocity
The velocity used for modeling the seismic data.
Figure 1. |
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Phase unwrapping of angle-domain common image gathers |

2007-09-18