Stochastic Modeling and Simulation of Near- and Far-Field Ground Motions for use in PBEE

Project # NCTRAK

Research Team

  • Armen Der Kiureghian, Professor, UC Berkeley (PI)
  • Sanaz Rezaeian, Graduate Student Researcher (GSR), UC Berkeley

Research Abstract

A fully nonstationary stochastic model for strong earthquake ground motion is developed. The model employs filtering of a discretized white-noise process. Nonstationarity is achieved by varying the filter properties and modulating the intensity of the process in time. Separation of the spectral and temporal nonstationary characteristics of the process allows flexibility and ease in modeling and parameter estimation. The evolving intensity and time-varying frequency content of the process are characterized by a set of statistical measures including the mean-square intensity, the mean zero-level up-crossing rate, and a measure of the bandwidth. Model parameters are identified by matching these measures with those of a target accelerogram. Post-processing of simulated ground motions by a second filter assures zero residual velocity and displacement, and improves the response spectral ordinates for long periods.

By identifying the parameters of the stochastic model for a large sample of recorded accelerograms drawn from the NGA database, predictive equations are developed that empirically re-late the model parameters to a set of earthquake and site characteristics. Using these equations, for specified earthquake and site characteristics, sets of the model parameters are generated that are used in the stochastic model to generate an ensemble of synthetic ground motions. The resulting synthetic accelerations, as well as corresponding velocity and displacement time-histories, capture the main features of real earthquake ground motions, including the evolving intensity, duration, spectral content, natural variability, and peak values. Furthermore, the statistics of their resulting elastic response spectra, i.e., the median and logarithmic standard deviation, closely agree with values predicted by the NGA ground motion prediction equations.

The synthetic motions can be used with or in place of recorded motions in seismic design and analysis, particularly in the context of performance-based earthquake engineering.

The proposed method is extended to simulate the orthogonal horizontal components of ground motion for specified earthquake and site characteristics. This is achieved by taking advantage of the notion of principal axes directions, along which the two components are statistically independent, and by properly accounting for the correlations among the model parameters of the two components.

Research Outcomes

PEER reports:

Archival Journal Papers:

  • Rezaeian, S. and A. Der Kiureghian (2008). A stochastic ground motion model with separable temporal and spectral nonstationarities. Earthquake Engineering & Structural Dynamics, 37:1565-1584.
  • Rezaeian, S. and A. Der Kiureghian (2010). Simulation of synthetic ground motions for specified earthquake and site characteristics. Earthquake Engineering & Structural Dynamics, 39:1155-1180.
  • Rezaeian, S. and A. Der Kiureghian (2011). Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics. Earthquake Engineering & Structural Dynamics, Published online in Wiley Online Library (, doi: 10.1002/eqe.1132

Papers in Conference Proceedings:

  • Der Kiureghian, A., and S. Rezaeian (2007). A stochastic model for earthquake ground motion with separable temporal and spectral nonstationarity. Proc. 10th Int. Conf. On Applications of Statistics and Probability (ICASP10) in Civil Engineering, Kashiwa, Japan, July 31 – August 3, 2007. (CD-ROM)
  • Rezaeian, S., A. Der Kiureghian, and Y. Bozorgnia (2008). Stochastic ground motion model with time-varying intensity, frequency and bandwidth characteristics. CD-ROM Proceedings, 14th World Conf. on Earthquake Engineering (14WCEE), Beijing, China, 12-17 October, Paper No. 03-03-0033.
  • Rezaeian, S.. and Der Kiureghian A. (2010). Synthetic earthquake ground motions for specified seismic design scenario. Proceedings of 9th US National and 10th Canadian Conference on Earthquake Engineering, Toronto, Canada, July 2010. CD-ROM, Paper No. 735.

Research Impact

Performance-based earthquake engineering (PBEE) requires consideration of structural response over a wide range, from linear to grossly nonlinear. For such analysis, there is need for specifica-tion of ensembles of ground motion time histories. Since recorded motions for specified earth-quake and site characteristics are limited in number, there is need for synthetic ground motions that can supplement or supplant recorded motions for PBEE analysis. The results of this research allow generation of synthetic ground motions for a wide spectrum of earthquake and site charac-teristics. The synthetic motions have statistical characteristics that are similar to those of re-corded motions. Thus, the results of this research facilitate and advance the practice of PBEE.