Two Towns, One Fault, One Hospital
Ashville and Benton lie along the same fault system. A school seismograph in Ashville recorded an earthquake with the P wave arriving at 10:00:12 and the S wave at 10:00:24. Benton's station recorded an S–P lag of 5 seconds for the same event. The class reference table gives roughly 8 km of distance for each second of S–P lag, an estimate with real uncertainty.
Benton's council is deciding whether to approve a 60-bed hospital meant to serve the region for the next 50 years. A consultant's report argues, "No damaging earthquake has struck Benton in 80 years, so the hazard is low and standard construction is adequate." The council asks the science class to review the report before the vote. The class must separate what the seismograph data show from what the report assumes.
1. Use the two lag times to decide which town is closer to the epicenter, and show the calculation.
Read the worked answer
The S–P lag grows with distance because S waves travel more slowly than P waves, so the gap between their arrivals widens the farther a station is from the epicenter.
- Ashville: 10:00:24 - 10:00:12 = 12 s lag, so about 12 × 8 = 96 km from the epicenter.
- Benton: 5 s lag, so about 5 × 8 = 40 km from the epicenter.
Benton is closer, roughly 40 km out versus roughly 96 km for Ashville. The numbers should be reported as estimates, because the 8 km per second rule is approximate, and a three-station calculation would locate the epicenter more precisely than two distances alone. This matters for the hospital decision: shaking is generally stronger nearer the epicenter, so Benton's closer position is a reason for more caution, not less.
2. Critique the consultant's reasoning that 80 earthquake-free years mean low hazard.
Read the worked answer
The argument treats a short human record as a long geologic one. Eighty years is a small sample compared with the hundreds or thousands of years a fault may take to complete a cycle. A fault can be locked and storing strain for centuries and then release it suddenly, so a quiet period is not evidence of safety and can even be a warning sign if strain is accumulating.
The claim also confuses the absence of observed damage with the absence of hazard. Benton may simply not have experienced a large rupture in the period people were recording. The scientific approach is to estimate hazard from evidence: mapped fault traces and their slip rates, trenching that exposes older ruptured layers and dates past earthquakes, GPS measurements of ground deformation, records of liquefaction or landslide deposits, and regional historical accounts. That evidence should then shape design standards rather than a single quiet century.
3. Recommend one action for the council and justify it with the available evidence.
Read the worked answer
The council should approve the hospital only with design and siting measures that account for a credible nearby earthquake, and it should fund a proper hazard study before final design. The justification rests on three points: the seismograph data place Benton about 40 km from an active event on the fault system, a distance at which strong shaking is realistic; the fault is the same system that generated the recorded quake, so it is active; and the consultant's 80-year argument is a short record that cannot rule out a longer recurrence interval.
Practical measures include designing to the highest applicable seismic code rather than a generic standard, commissioning fault mapping to avoid building directly across a trace, and choosing a site with low liquefaction risk. Because the building is meant to last 50 years and to function during a regional emergency, the cost of extra design is easier to defend than the cost of losing the only hospital when it is most needed.