Relationship for a dipping bed

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Problem 4.3

Show that, for a dipping reflector and constant velocity, equation (4.2a) becomes (see Gardner, 1947)


(4.3a)

where in equation (4.2a) is replaced by , the slant depth at the midpoint between source and receiver , and in Figure 4.3a.

Solution

Equation (4.2a) is based on Figure 4.2a where the receiver is down dip from the source, the offset being ; in Figure 4.3a the up-dip receiver is offset from source , so that the dip is negative; thus equation (4.2a) becomes

Replacing with where , we obtain

Figure 4.3a.  Geometry for dipping bed.

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