This paper proposes a new deterministic envelope function to define non-stationary stochastic processes modeling seismic ground motion accelerations. The proposed envelope function modulates the amplitude of the time history of a stationary filtered white noise to properly represent the amplitude variations in the time histories of the ground motion accelerations. This function depends on two basic seismological indices: the Peak Ground Acceleration (PGA) and the kind of soil. These indices are widely used in earthquake engineering. Firstly, the envelope function is defined analytically from the Saragoni Hart’s function. Then its parameters are identified for a set of selected real records of earthquake collected in PEER Next Generation Attenuation database. Finally, functions of the parameters depending on the Peak Ground Acceleration and the kind of soil are defined from these identified values of the parameters of the envelope function through a regression analysis.
Cite this paper
G. Marano, M. Morga and S. Sgobba, "Parameters Identification of Stochastic Nonstationary Process Used in Earthquake Modelling," International Journal of Geosciences, Vol. 4 No. 2, 2013, pp. 290-301. doi: 10.4236/ijg.2013.42027.
 K. Beyer and J. J. Bommer, “Selection and Scaling of Real Accelerograms for Bi-Directional Loading: A Review of Current Practice and Code Provisions,” Journal of Earthquake Engineering, Vol. 11, No. S1, 2007, pp. 13-45. doi:10.1080/13632460701280013
 K. Kanai, “Semi-Empirical Formula for the Seismic Characteristics of the Ground Motion,” Bulletin of the Earthquake Research Institute, Vol. 35, No. 2, 1957, pp. 309-325.
 H. Tajimi, “A Statistical Method of Determining the Maximum Response of a Building Structure during an Earthquake,” Proceedings of the 2nd World Conference on Earthquake Engineering, Tokio, 11-18 July 1960, pp. 781-798.
 S. Sgobba, G. C. Marano, P. J. Stafford and R. Greco, “Seismologically Consistent Stochastic Spectra,” New Trends in Seismic Design of Structures, Saxe-Coburg Publisher, Stirling, 2009.
 G. W. Housner and P. C. Jennings, “Generation of Artificial Earthquakes,” ASCE, Journal of the Engineering Mechanics Division, Vol. 90, No. 1, 1964, pp. 113-150.
 V. V. Bolotin, “Statistical Theory of the Aseismic Design of Structures,” Proceedings of the 2nd World Conference on Earthquake Engineering, Tokio, 11-18 July 1960, pp. 1365-1374.
 R. S. Jangid, “Response of SDOF System to Non-Stationary Earthquake Excitation,” Earthquake Engineering & Structural Dynamics, Vol. 33, No. 15, 2004, pp. 1417-1428. doi:10.1002/eqe.409
 K. W. Campbell, “Prediction of Strong Ground Motion Using the Hybrid Empirical Method: Example Application to Eastern North America,” Bulletin of the Seismological Society of America, Vol. 93, No. 3, 2002, pp. 1012-1033. doi:10.1785/0120020002
 G. Cua, “Creating the Virtual Seismologist: Developments in Ground Motion Characterization and Seismic Early Warning,” Ph.D. Thesis, California Institute of Technology, 2005.
 P. J. Stafford, S. Sgobba and G. C. Marano, “An Energy-Based Envelope Function for the Stochastic Simulation of Earthquake Accelerograms,” Soil Dynamics and Earthquake Engineering, Vol. 29, No. 7, 2009, pp.1123-1133.
 J. W. Baker, “Correlation of Ground Motion Intensity Parameters Used for Predicting Structural and Geotechnical Response,” Proceedings of the 10th International Conference on Applications of Statistics and Probability in Civil Engineering, Tokyo, 31 July-3 August 2007.
 G. R. Saragoni and G. C. Hart, “Simulation of Artificial Earthquake,” Earthquake Engineering and Structural Dynamics, Vol. 2, No. 3, 1974, pp. 249-267.
 G. C. Marano, M. Morga and S. Sgobba, “Modelling of Stochastic Process for Earthquake Representation as Alternative Way for Structural Seismic Analysis: Past, Present and Future,” International Conference on Earthquake Analysis and Design of Structures, 1-3 December 2011, Coimbatore, pp. 61-73.
 R. W. Clough and J. Penzien, “Dynamics of Structures,” McGraw-Hill, New York, 1975.
 M. Amin and A. H. S. Ang, “Nonstationary Stochastic Model of Earthquake Motions,” ASCE, Journal of the Engineering Mechanics Division, Vol. 94, No. 2, 1968, pp. 559-583.
 J. P. Conte and B. F. Peng, “Fully Nonstationary Analytical Earthquake Ground-Motion Model,” ASCE, Journal of Engineering Mechanics, Vol. 12, No. 1, 1997, pp. 15-24. doi:10.1061/(ASCE)0733-9399(1997)123:1(15)