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Equations (6) and (7) usually contain an enormous number
of variables and, as will be shown later, are extremely ill-conditioned.
However,
good results may be obtained in a small number of iterations if a conjugate gradient
method is used.
To solve the equation
| |
(8) |

we can minimize the function
| |
(9) |

or for stochastic inversion,
| |
(10) |

where and are the variances of the data and
the model spaces respectively.
When a velocity analysis panel is obtained by the solution of equation (6) or
equation (7), an inversion is easily done by application of
the operator or on the velocity analysis
panel .

We can also consider solving the equation

| |
(11) |

where was obtained by the application of on (*t*,*x*)-space, and
| |
(12) |

where was obtained by the application of on
(*t*,*x*)-space.

** Next:** COMPUTATION OF ADJOINT OPERATORS
** Up:** VELOCITY ANALYSIS
** Previous:** VELOCITY ANALYSIS
Stanford Exploration Project

1/13/1998