Triangulating an Epicenter with One Doubtful Station
Three school seismograph stations record the same earthquake. Station A reports a P-wave arrival at 10:12:04 and an S-wave arrival at 10:12:28. Station B reports P at 10:12:10 and S at 10:12:46. Station C reports P at 10:12:18 and S at 10:12:39. The class uses the standard S-minus-P distance relation: 21 s corresponds to about 180 km, 24 s to about 210 km, and 36 s to about 330 km. Students draw circles on a map. The three circles do not meet at one point: A and B intersect near a mapped fault, but C's circle passes 80 km south of that intersection. Station C's clock was reset by a substitute the previous day, and its record has a 5 s gap just before the P arrival. The class must decide whether to report the A-B intersection as the epicenter.
1. Using the S-minus-P intervals, determine the approximate distance for each station and explain why the three circles fail to meet.
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Station A: S minus P = 28 - 4 = 24 s, so distance is about 210 km. Station B: 46 - 10 = 36 s, so distance is about 330 km. Station C: 39 - 18 = 21 s, so distance is about 180 km. In principle, three circles should intersect at one epicenter. They fail because at least one distance is wrong. Station C has two red flags: an unexplained clock reset the day before and a 5 s gap just before the P arrival. A constant clock offset changes both arrivals but not the S-minus-P interval; however, the gap could cause a mispick of P or S, and a reset clock may not be synchronized. The A-B intersection is therefore better supported, but two circles alone give two possible intersections.
2. Recommend how the class should report the epicenter and what uncertainty statement is appropriate. Justify whether to use all three stations, only A and B, or a different method.
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The class should not report a single precise point. It can report an epicenter near the A-B intersection on the mapped fault, with an uncertainty of at least 30 to 50 km, and state that Station C was excluded because its timing is suspect. Two circles intersect at two points; the fault trace and the pattern of first motions or felt reports can choose between them. A better report says 'approximate epicenter near the fault, based on Stations A and B; Station C needs rechecking.' The class should re-read C's record, check its clock against a time standard, and ask a regional network for a third reliable station before publishing a final location.
3. What should students do to prevent this problem in future recordings, and how does the clock issue illustrate a difference between precision and accuracy?
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Students should log clock checks at the start and end of each recording day, use GPS or network time, and keep a maintenance log so a substitute's reset is documented. They should flag gaps automatically and not use an arrival within a gap for location. The episode distinguishes precision from accuracy: the arrival times are recorded to the second, which is precise, but a clock offset or mispick makes them inaccurate. S-minus-P is partly self-correcting for a constant clock offset, but not for a changed offset or a wrong pick. Redundancy and metadata are what make the precise numbers trustworthy.