GMPE

Ground Motion Prediction Equation (GMPE) is a mathematical model used to estimate the expected ground motion produced by an earthquake at a given site. It expresses the median level of a ground motion measure, such as peak ground acceleration (PGA) or spectral acceleration Sa(T), as a function of factors including earthquake magnitude, source-to-site distance, fault mechanism, and local site conditions (often represented by Vs30 or other site descriptors). GMPEs also specify a dispersion, or sigma, which accounts for variability around the median prediction to represent uncertain influences on ground motion.

GMPEs are central to seismic hazard analysis and engineering design. They are typically derived from observed strong-motion data (empirical) or developed from physical models (physics-based) or hybrids of the two. Most modern GMPEs are regionally calibrated to reflect tectonic settings and ground motion attenuation patterns, and they cover a range of magnitudes, distances, and site conditions. Inputs commonly include magnitude, source-to-site distance, depth, focal mechanism, site class, and the period of interest for spectral measures.

In practice, multiple GMPEs are often used in combination, with weights assigned through logic-tree approaches to capture epistemic uncertainty about existing models. Limitations include extrapolation beyond the range of available data, near-field effects and directivity that some models do not fully capture, and nonlinear site response not always accounted for in all equations. Ongoing development seeks broader regional coverage, improved physical understanding, and more robust quantification of uncertainties for hazard assessment.