Summary
The method of spectral representation for uni-variate, one-dimensional, stationary stochastic processes and multi-dimensional, uni-variate (as well as multi-dimensional, multi-variate) homogeneous stochastic fields has been reviewed in detail, particularly from the viewpoint of digitally generating their sample functions. This method of representation has then been extended to the cases of uni-variate, one-dimensional, nonstationary stochastic processes and multi-dimensional, uni-variate nonhomogeneous stochastic fields, again emphasizing sample function generation. Also, a fundamental theory of evolutionary stochastic waves is developed and a technique for digitally generating samples of such waves is introduced as a further extension of the spectral representation method. This is done primarily for the purpose of developing an analytical model of seismic waves that can account for their stochastic characteristics in the time and space domain. From this model, the corresponding sample seismic waves can be digitally generated. The efficacy of this new technique is demonstrated with the aid of a numerical example in which a sample of a spatially two-dimensional stochastic wave consistent with the Lotung, Taiwan dense array data is digitally generated.
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Shinozuka, M., Deodatis, G., Harada, T. (1987). Digital Simulation of Seismic Ground Motion. In: Lin, Y.K., Minai, R. (eds) Stochastic Approaches in Earthquake Engineering. Lecture Notes in Engineering, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83252-9_14
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DOI: https://doi.org/10.1007/978-3-642-83252-9_14
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