A geotechnical report reasons as follows: "The design ground motion for this site has…
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics
The Solid Earth, Ch Faults, the earthquake cycle and seismic hazard
Problem
A geotechnical report reasons as follows: "The design ground motion for this site has a 475yr return period. Therefore an earthquake producing that level of shaking will occur exactly once every 475 years, so a building completed in 2024 is safe from that level of shaking until at least 2499."
((a)) Identify the error in this reasoning.
((b)) Earthquakes producing at least the design shaking occur as a Poisson process with mean rate λ=1/475yr−1. Compute the probability that at least one such earthquake occurs in the next 50yr (the assumed design life of the building).
((c)) Compute the probability that at least one such earthquake occurs within the next 475yr, and the probability that none occurs in 950yr (twice the return period). Comment on what these numbers show about the report's claim.