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We can define a minimizing problem that aims at finding by minimizing the following cost function:
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(47) |
The Newton iterative algorithms can be used for solving the minimizing problem. The standard Newton iterative algorithm is
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(48) |
However, the inverse of the Hessian is difficult to calculate. The Quasi-Newton algorithms are used commonly. The inverse of the Hessian matrix can be calculated with the DFP formula:
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(49) |
where , and .
The Quasi-Newton iterative algorithm is
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(50) |
Next: (C) Non-linear waveform inversion
Up: comparison among migration/inversion methods
Previous: (3) Least-squares migration/inversion
Stanford Exploration Project
11/1/2005