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The conjugate gradient vector has two parts. The first part is related to the traveltime residuals, and the second part
is related to the constraints. The computation of is simple
because matrix is known. We want to compute with a
finite difference method. The components of are as follows:

| |
(14) |

It is shown in Appendix A that if we solve the first-order linear PDE
| |
(15) |

with the initial condition that *q*_{i}(*x*,*z*) is equal to zero at the source
location, then *h*^{(1)}_{i}(*r*) is equal to *q*_{i}(*x*,*z*) at the receiver
locations. Equation (15) has a form similar to the eikonal equation;
hence we can use the algorithm for the traveltime calculation,
after being slightly modified, to solve it.

** Next:** CONCLUSIONS
** Up:** FINITE DIFFERENCE METHODS
** Previous:** Computation of the gradient
Stanford Exploration Project

12/18/1997