Deterministic Seismic Hazard Analysis (DSHA)

DSHA fixes one or a few worst-case earthquake scenarios and computes the resulting ground motion, ignoring how often those events occur. PSHA, following Cornell's 1968 formulation, integrates over all possible magnitudes, distances, and recurrence rates to produce the annual frequency with which any ground-motion level is exceeded. DSHA answers 'how bad could it get from a credible event?'; PSHA answers 'how often is a given level exceeded?'. The two are complementary, and modern site studies typically run both, using the deterministic scenario as a transparent, bounding design basis and the probabilistic result for risk-consistent code compliance.

The controlling earthquake is the source scenario that produces the largest ground motion at the site once each source is reduced to its maximum magnitude at its closest credible distance. As Reiter explains, the analyst evaluates every source's worst-case magnitude-distance pair through a ground-motion prediction equation and keeps the one yielding the greatest motion. Importantly, the controlling scenario can differ by spectral period — a large distant rupture may dominate long periods while a nearby moderate event dominates short periods — so practitioners often envelope several scenarios rather than rely on a single one.

Ground-motion prediction equations give the median motion for a magnitude and distance plus a log-normal scatter term with standard deviation sigma. Because DSHA does not encode frequency, it embeds conservatism by choosing a high percentile of this scatter: evaluating at the median (epsilon zero) gives a typical motion, while median-plus-one-sigma (epsilon one) gives roughly the 84th percentile. Critical-facility practice commonly adopts the 84th-percentile level so that the design accounts for the substantial event-to-event variability in shaking, not merely the average expected motion for the controlling scenario.