Earthquake S-P times and a faulted road cut
A seismograph at a school in Tottori records an earthquake. The P wave arrives at 10:00:04 and the S wave at 10:00:10. The school's data table gives P-wave speed 6.0 km/s and S-wave speed 3.5 km/s. A second station, 75 km east, records an S-P time difference of 9.0 s. Near the school, a road cut exposes sandstone, a thin tuff layer, and shale. A fault offsets the tuff layer by 2 m, and a river channel cuts across both the fault and all layers. The teacher asks students to use the seismic data to estimate the distance to the epicenter, to explain why two stations are better than one, and to order the geological events from oldest to youngest.
1. Calculate the distance from the school to the epicenter using the S-P time difference. Show your equation.
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The S-P time difference is 10:00:10 − 10:00:04 = 6.0 s. Let d be the distance in km. The P wave takes d/6.0 seconds and the S wave takes d/3.5 seconds. The difference is d/3.5 − d/6.0 = 6.0. Using a common denominator, (6.0d − 3.5d)/21 = 2.5d/21 = 6.0. Therefore 2.5d = 126, and d = 50.4 km. The school is about 50 km from the epicenter. This is the radius of a circle around the school on which the epicenter must lie.
2. Explain why the second station is needed and how its data are used.
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One station gives only the distance to the epicenter, which defines a circle centered on that station. The epicenter could be anywhere on that circle. The second station's S-P difference of 9.0 s gives a distance of about 75.6 km by the same equation, defining a second circle centered on the second station. The epicenter must lie at an intersection of the two circles. Two circles generally intersect at two points, so a third station is usually needed to choose between them. The second station therefore narrows the location from a whole circle to at most two possible points.
3. Order the geological events from oldest to youngest: deposition of sandstone, deposition of tuff, deposition of shale, faulting, river erosion. Justify using two geological principles.
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From oldest to youngest: sandstone, tuff, shale, faulting, river erosion. The principle of superposition says that in an undisturbed sequence, lower layers are older than higher layers, so the sandstone below the tuff and the tuff below the shale are in order of deposition. The fault offsets the tuff layer, so the fault must have moved after the tuff and the other layers were deposited. This is the principle of cross-cutting relationships: a feature that cuts another is younger than the feature it cuts. The river channel cuts across both the fault and all the layers, so the river erosion is the youngest event.