Second approximation for dip moveout

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Problem 4.5

The expressions for dip in terms of dip moveout, equation (4.2b), involves the approximation of dropping higher-order terms in the expansion of equation (4.2a). What is the effect on equation (4.2b) if an additional term is carried in this expansion? What is the percentage change in dip?

Solution

In problem 4.2b we obtained the dip equation (4.2b) by taking the first approximation of equation (4.2a), that is, using

where . Expanding and taking the second approximation gives


(4.5a)

If we take two offsets, and , and let , then

Comparing this result with equation (4.2b), we see that the second approximation increases the calculated dip by the fraction , that is, by the approximate percentage

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