GMPEs

Ground Motion Prediction Equations (GMPEs) are empirical or semi-empirical models that estimate ground shaking from earthquakes. They predict measures of seismic ground motion, such as peak ground acceleration (PGA) or spectral accelerations at specified periods, as a function of earthquake source characteristics, path effects, and site conditions. GMPEs are used to assess the likely intensity of ground shaking at a given site for a specified earthquake scenario or within probabilistic seismic hazard analysis (PSHA).

GMPEs are derived by regression analyses of strong-motion records collected across many earthquakes. Their functional form typically includes magnitude scaling, distance attenuation, and terms for rupture mechanism, crustal path, and local site amplification. Most models also provide an estimate of dispersion, describing the variability (sigma) around the median prediction, which is essential for hazard calculations. GMPEs can be regional, national, or global in scope and are often updated as more data become available. In practice, multiple GMPEs are used, sometimes combined through a logic-tree approach to reflect epistemic uncertainty.

Inputs commonly required for a GMPE include moment magnitude (Mw), a distance metric such as Rjb or Rrup, style or faulting, and a site-condition proxy like Vs30. Outputs include median ground motion values for PGA or spectral accelerations at various periods, accompanied by standard deviations. In PSHA, the GMPEs are integrated with an earthquake source model and a recurrence model to produce hazard curves indicating annual rates of exceeding specified ground motion levels.

Limitations include regional applicability, extrapolation outside calibration ranges, and the fact that ground motion is affected by factors not always captured in the model. Selecting appropriate GMPEs for a given region and scenario is critical, and organizations may use ensemble or logic-tree approaches to cover uncertainties in model choice, period range, and site conditions.