Seismic Hazard Assessment for a Regional Town
A town of 18,000 people sits 25 km from an active fault. Historical records, which span only 160 years, show no earthquake above magnitude 4.5 in the region. However, trenching across the fault reveals evidence of three surface-rupturing events in the past 9,000 years, with the most recent about 2,400 years ago. Regional GPS data show the fault is accumulating strain at about 1.5 mm/yr. A proposed hospital must be sited on one of two sites: Site X on deep alluvium 3 km from the fault, or Site Y on bedrock 12 km from the fault. Groundwater bores near Site X show liquefiable sand layers between 4 and 9 m depth.
1. Estimate a recurrence interval from the trench data and explain why the historical record is misleading for hazard assessment.
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Recurrence estimate. Three events in 9,000 years gives an average recurrence interval of 9,000 ÷ 3 = 3,000 years. The elapsed time since the most recent event is about 2,400 years, so on a simple average the fault is roughly 80% of the way through a typical cycle (2,400 ÷ 3,000). This is not a prediction, but it means the fault is not in an early interseismic lull.
Why the historical record misleads. A 160-year record is only about 5% of one recurrence interval. The absence of a magnitude >4.5 event in 160 years is exactly what a fault with a 3,000-year cycle would produce most of the time, so the historical silence carries almost no information about hazard. Using it to conclude the region is aseismic is a sampling error: the observation window is far shorter than the phenomenon's timescale. The trench evidence and GPS strain accumulation are the relevant datasets. The GPS rate of 1.5 mm/yr over 2,400 years implies roughly 3.6 m of accumulated slip, consistent with a large rupture, which reinforces the hazard rather than dismissing it.
2. Recommend a site and justify your choice using site-response and liquefaction reasoning.
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Recommendation: Site Y.
Distance. Site Y is 12 km from the fault versus 3 km for Site X. Shaking intensity attenuates with distance, so Site Y experiences lower peak ground acceleration for the same event.
Site response. Site X sits on deep alluvium, which amplifies ground shaking and lengthens its duration. Soft sediments trap and resonate with seismic waves, so buildings on alluvium generally experience stronger shaking than those on bedrock at comparable distance. Site Y on bedrock avoids this amplification.
Liquefaction. The bore data at Site X show liquefiable sand between 4 and 9 m depth. During strong shaking, saturated loose sand can lose strength and behave as a fluid, causing foundation settlement, lateral spreading and bearing failure. A hospital is a critical facility that must remain functional after an earthquake, so a liquefaction-prone site is unacceptable without costly ground improvement. Site Y on bedrock has no liquefiable material.
Caveat. Site Y is not risk-free: bedrock can transmit high-frequency shaking efficiently, and a hospital still needs seismic-resistant design. But on the evidence given, Site Y reduces both shaking amplification and liquefaction hazard, making it the defensible choice for a critical facility.