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When the subsurface can be approximated with plane layers and uniform velocities, the refractor velocity can be obtained from the forward and reverse apparent velocities on the time-distance plot, together with the overlying velocities, using equation (1) of Ewing et al (1939, p. 265).

If these approximations cannot be made, or when the velocities of all layers above the refractor are not known, it is still possible to obtain a reasonable estimate of the refractor velocity by the following approach. Using the symbols of Figure 2, the velocity analysis function tv is defined by the equation

The value of this function is referred to G, which is midway between X and Y.

In routine interpretation, values of tv, calculated using equation (2), are plotted against distance for different XY-values. By a series of tests to be described in chapter 6, an optimum value of XY is selected, and a refractor velocity is taken as the inverse slope of a line fitted to the tv values for the optimum XY.

For the special case of XY equal to zero, equation (2) reduces to equation (7) of Hawkins (1961, p. 809). It is similar to the minus term in the plus-minus method (Hagedoorn, 1959). The velocity analysis formula quoted by Scott (1973, p. 275) is a least-squares fit of data values which are mathematically similar to equation (2), but with XY equal to zero.

One method of testing the efficacy of determining refractor velocities with equation (2) is to apply the equation to a plane-layer case.

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