A nonstationary random process model for earthquake accelerograms

Though many models for the simulation of earthquake records have been suggested, they are either unrealistic or restricted to a qualitative simulation. If the basic mechanism of earthquakes at different places is similar the underlying mathematical pattern of the different recordings may also be alike. Due to the complexities involved in analyzing the fundamental mechanism, a search for the common pattern must be carried out among the few available ground acceleration records. An attempt has been made in this paper in this direction. An analysis of past records shows that the strength of the oscillations exhibited by the number of zero crossings and extremes in a given interval and the nonstationary random nature revealed by the time-dependent variance function are important characteristics. Using this information a stationary random process modulated by a deterministic function has been developed. Almost all types of known records can be generated from this model by varying its parameters. Approximate methods have also been developed for estimating these parameters in artificial simulation. To test the model, ensembles of a single pulse, a ten-second, a thirty-second and a very long record have been simulated and analyzed for relative velocity and time response spectra. Many quantities realized in the records compare well with the corresponding ones fixed beforehand. Suggestions are made for using the model in aseismic design.

[1]  D. E. Hudson.  Some problems in the application of spectrum techniques to strong-motion earthquake analysis , 1962 .

[2]  C. C. Craig,et al.  Tables of Random Normal Deviates , 1963 .

[3]  Mohammad Amin,et al.  A Nonstationary Stochastic Model for Strong-Motion Earthquakes , 1966 .

[4]  E. Parzen,et al.  Principles and applications of random noise theory , 1959 .

[5]  Emilio Rosenblueth,et al.  Distribution of structural response to earthquakes , 1962 .

[6]  M. Longuet-Higgins,et al.  The statistical distribution of the maxima of a random function , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  D. W. Tufts,et al.  Statistical Communication Theory , 1958 .

[8]  B. Gutenberg,et al.  Effects of ground on earthquake motion , 1957 .

[9]  George W. Housner,et al.  Characteristics of strong-motion earthquakes , 1947 .

[10]  G. N. Bycroft.  White Noise Representation of Earthquakes , 1960 .

[11]  S. Rice.  Mathematical analysis of random noise , 1944 .

[12]  H. J. Stumpf,et al.  Transient Response of a Dynamic System Under Random Excitation , 1961 .

[13]  Arthur Gerald Brady.  Studies of response to earthquake ground motion , 1966 .

[14]  J. Bendat,et al.  Measurement and Analysis of Random Data , 1968 .

[15]  John E. Goldberg,et al.  Response of a simple structure to a random earthquake-type disturbance , 1961 .

[16]  George R. Cooper,et al.  An optimum observation time for estimates of time-varying correlation functions (Corresp.) , 1965, IEEE Trans. Inf. Theory.

[17]  U. S. Coast,et al.  The Parkfield, California, earthquake of June 27, 1966 / , 1966 .

[18]  John E. Goldberg,et al.  The response of simple nonlinear systems to a random disturbance of the earthquake type , 1964 .

[19]  R. H. Battin,et al.  Random Processes in Automatic Control. , 1957 .

[20]  John H. Wiggins,et al.  Effect of Site Conditions on Earthquake Intensity , 1964 .

[21]  P. C. Jennings,et al.  Simulated earthquake motions , 1968 .

[22]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Random Process , 1967 .

[23]  J. Wiggins.  Construction of strong motion response spectra from magnitude and distance data , 1964 .

[24]  George R. Cooper,et al.  Estimates of correlation functions of nonstationary random processes (Corresp.) , 1966, IEEE Trans. Inf. Theory.

[25]  George W. Housner,et al.  Generation of Artificial Earthquakes , 1964 .

[26]  H. Tajimi,et al.  Statistical Method of Determining the Maximum Response of Building Structure During an Earthquake , 1960 .

[27]  George W. Housner,et al.  Integrated velocity and displacement of strong earthquake ground motion , 1961 .

[28]  Nelson M. Blachman.  On Fourier Series for Gaussian Noise , 1957, Inf. Control..

[29]  George W. Housner,et al.  Spectrum analysis of strong-motion earthquakes , 1953 .

[30]  J. Franklin,et al.  Numerical Simulation of Stationary and Non-Stationary Gaussian Random Processes , 1965 .