Chapter 15, Problem 39P

(II) Seismic reflection prospecting is commonly used to map deeply buried formations containing oil. In this technique, a seismic wave generated on the Earth’s surface (for example, by an explosion or falling weight) reflects from the subsurface formation and is detected upon its return to ground level. By placing ground-level detectors at a variety of locations relative to the source, and observing the variation in the source-to-detector travel limes, the depth of the subsurface formation can be determined. (a) Assume a ground-level detector is placed a distance x away from a seismic-wave source and that a horizontal boundary between overlying rock and a subsurface formation exists at depth D (Fig. 15–35a). Determine an expression for the time t taken by the reflected wave to travel from source to detector, assuming the seismic wave propagates at constant speed v. (b) Suppose several detectors are placed along a line at different distances x from the source as in Fig. 15–35b. Then, when a seismic wave is generated, the different travel times t for each detector are measured. Starting with your result from part (a), explain how a graph of t² vs. x² can be used to determine D.