Diffraction traveltime curves

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Problem 6.5a

Show that the slope of the diffraction curve with source in Figure 6.5a(i) approaches for large .

Solution

The diffraction path is in Figure 6.5a(i), so the traveltime curve is

For , the equation of the curve becomes

which is a straight line with slope for , for . The traveltime approaches these asymptotes as

Alternative solution

The slope of the traveltime curve is

For , the slope is as before.

Problem 6.5b

What is the asymptote slope for a coincident source-receiver?

Solution

The traveltime curve for Figure 6.5a(ii) is given by

As increases, . The asymptote has the equation , which is a straight line with slope

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