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The use of an average velocity above the refractor permits depth calculations without defining all layers. It can also be useful in accommodating undetected layers, as discussed in the previous chapter. The method described below uses the optimum XY-value, but, unlike the methods of Hawkins [1961, equation (5)] and Woolley et al (1967, p. 279–280), a depth to the refractor is not required. With the substitution of the horizontal-layer approximation, equation (12) becomes

These equations can be combined to form the following expression

For field examples, the calculations of time-depths using equation (10) and refractor velocities using equation (6) present few problems. Therefore, if an optimum XY-value can be determined, then an average velocity can be calculated with equation (27). The total thickness of all layers can then be computed by rearranging equation (25).

An appreciation of the efficacy of equation (27) can be obtained by comparing depths calculated using the average velocity with the actual depths for a fully defined model. The model to be considered (Figure 27) has two layers above the refractor. Although all interfaces are plane and horizontal for ease in computation, the results are considered valid for dips up to 20 degrees, the limit of the GRM horizontal-layer approximations.

The total depth is calculated from equation (25), after an average velocity has been determined by substituting time-depth and XY-values into equation (27). Since there are no field data for this synthetic example, appropriate values of time-depth and XY must first be computed with equations (21) and (23).

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