A Ground Motion Prediction Equation (GMPE) is an empirical model that estimates ground motion intensity — such as PGA, PGV, or spectral acceleration — as a function of earthquake magnitude, source-to-site distance, and site conditions. GMPEs are the fundamental building blocks of probabilistic seismic hazard analysis and modern ground motion selection.
A Ground Motion Prediction Equation (GMPE), also called an attenuation relationship or ground motion model, is an empirical or semi-empirical equation that predicts a ground motion intensity measure (IM) at a site given the earthquake source, path, and site characteristics. Standard inputs include magnitude (typically moment magnitude M_w), source-to-site distance (R_rup, R_jb, R_epi, or R_hypo depending on the model), site condition (Vs30 or site class), and sometimes additional parameters such as faulting style, hanging-wall effects, and directivity.
GMPEs are the cornerstone of probabilistic seismic hazard analysis (PSHA). A PSHA integrates over all possible earthquake scenarios and computes the probability that a given IM is exceeded at a site within a specified time window. This requires a GMPE — or a logic tree of multiple GMPEs — to convert each scenario's magnitude and distance into a distribution of ground motion values. Modern practice uses multiple GMPEs weighted by expert judgment, following frameworks such as the NGA-West2 project for shallow crustal earthquakes and the NGA-Sub project for subduction zones. In Iran, several region-specific GMPEs have been developed, including those by Zare, Soghrat, and others.
GMPEs are empirical models with inherent uncertainty. Every GMPE includes a median prediction and a standard deviation (sigma) that captures aleatory variability — the natural randomness of ground motion given a scenario. Some also distinguish between inter-event (between earthquakes) and intra-event (within an earthquake) variability. The choice of GMPE can significantly affect hazard estimates, especially at long return periods. Epistemic uncertainty — our incomplete knowledge of the correct model — is handled through logic trees and model weighting. GMPEs are region-specific: a model developed for California may not apply to Iran, and using an inappropriate GMPE is one of the most common errors in seismic hazard studies.