Probabilistic Seismic Hazard Analysis (PSHA) is a methodology that estimates the probability of exceeding a given level of ground shaking at a site within a specified time period, accounting for all possible earthquake scenarios and their associated uncertainties. It is the foundation of modern seismic design codes and risk assessment.
Probabilistic Seismic Hazard Analysis (PSHA) is a methodology for estimating the probability that a given level of ground shaking will be exceeded at a site within a specified time period. Unlike deterministic seismic hazard analysis (DSHA), which considers a single "worst-case" earthquake scenario, PSHA integrates over all possible earthquake scenarios β each with its own magnitude, location, and recurrence probability β and accounts for the uncertainty in ground motion prediction. The result is a hazard curve: a plot of the annual probability of exceedance (or its inverse, the return period) against a ground motion intensity measure (typically peak ground acceleration or spectral acceleration at a given period). The methodology was formalized by Cornell in 1968 and has become the foundation of modern seismic design codes, insurance pricing, and risk assessment worldwide.
The PSHA calculation involves four main steps. First, source characterization identifies all seismic sources that could affect the site β faults, areal source zones, and subduction zones β and characterizes their geometry, maximum magnitude, and recurrence behavior. Second, magnitude-frequency relationship defines how often earthquakes of different magnitudes occur on each source, typically using the Gutenberg-Richter relationship or a characteristic earthquake model. Third, ground motion prediction uses GMPEs (Ground Motion Prediction Equations) to compute the distribution of ground motion at the site for each magnitude-distance scenario. Fourth, integration combines all scenarios, weighted by their probability of occurrence, to produce the hazard curve. Modern PSHA uses logic trees to capture epistemic uncertainty in source models, GMPEs, and other inputs β each branch represents a different interpretation, and the final hazard is a weighted combination of all branches.
PSHA is the foundation of modern seismic design practice and has been incorporated into building codes worldwide. In the United States, the USGS National Seismic Hazard Maps β produced through PSHA β form the basis of design ground motions in ASCE 7 and the International Building Code. In Europe, the SHARE project produced a harmonized PSHA for the Eurocode 8 update. In Iran, the BHRC (Building and Housing Research Center) and the International Institute of Earthquake Engineering and Seismology (IIEES) have produced PSHA studies that inform the Iranian seismic design code (Standard 2800). PSHA results are expressed as uniform hazard spectra β response spectra with a constant probability of exceedance across all periods β which are used directly for design. Key challenges in PSHA include: (1) the accuracy of source models, particularly for regions with limited earthquake catalogs; (2) the choice and weighting of GMPEs, which can vary significantly in their predictions; (3) the treatment of aleatory and epistemic uncertainty; (4) the validation of PSHA results against observed ground motions; and (5) the interpretation of hazard curves for decision-making. Modern practice increasingly uses time-dependent PSHA (which accounts for the earthquake cycle), physics-based ground motion simulations (as an alternative to empirical GMPEs), and site-specific PSHA (which accounts for local soil conditions in detail). In Iran, PSHA studies have been conducted for major cities and critical facilities, with ongoing efforts to improve source models, develop region-specific GMPEs, and update the national seismic hazard maps.