Ground-Motion Model for Significant Duration Constrained by Seismological Simulations

ABSTRACT A duration ground-motion model for crustal earthquakes based on the normalized Arias intensity (IA) is developed. Two sets of seismological simulations are used to constrain the form and scaling of the duration model. Simulations using a 3D crustal model show that an additive model for the source, path, and site terms captures the physical behavior of duration better than a multiplicative model for the site term. Stochastic finite-fault simulations are used to constrain the saturation of the large-magnitude scaling at short distances. The duration model is developed in two parts: a duration model for the time interval between 5% and 75% of the normalized Arias intensity (D5−75) and a duration model for the ratio of the D5−X/D5−75 duration for X values from 10 to 95. Together, these two models provide a more complete description of the evolution of the seismic energy with time than a single duration metric. A new aspect of the statistical model for duration is the inclusion of a random effect for the path term in addition to random effects for the source and site terms. The source and site random effects are modeled as scale factors on the duration, whereas the path-term random effect is a scale factor on the distance slope. The distribution of the duration residuals has a skewness that is between the skewness of a lognormal distribution and the symmetry of a normal distribution. The final duration aleatory variability is modeled by a power-normal distribution with an exponent of 0.3, which accounts for the amplitude dependence of the aleatory variability of the duration with smaller aleatory variability for large-magnitude events and larger aleatory variability for small-magnitude events as compared to the variability from a lognormal distribution.