Are concerned with determining the thickness d of a layer of soil that lies on top of
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Are concerned with determining the thickness d of a layer of soil that lies on top of a rock formation. Geologists send two sound pulses from point A to point D separated by a distance s. The first pulse travels directly from A to D along the surface of the earth. The second pulse travels down to the rock formation, then along its surface, and then back up to D (path ABCD), as in Figure 41. The pulse travels with velocity v1 in the soil and v2 in the rock.
In this exercise, assume that v2/v1 ≥ √1 + 4(d/s)2.
(a) Show that inequality (1) holds if sin θ = v1/v2.
(b) Show that the minimal time for the second pulse is
where k = v1/v2.
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