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Stochastic characterization of earthquakes through their response spectrum
Author(s) -
Kaul Maharaj K.
Publication year - 1978
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290060506
Subject(s) - spectral density , response spectrum , stochastic process , spectrum (functional analysis) , representation (politics) , mathematics , function (biology) , basis (linear algebra) , process (computing) , statistical physics , probability density function , mathematical optimization , computer science , physics , statistics , geology , seismology , geometry , quantum mechanics , evolutionary biology , politics , political science , law , biology , operating system
Abstract If earthquakes are modelled by a stochastic process, it is possible to interpret the associated response spectrum in terms of the statistics of extreme values of oscillator response to the process. For a stationary earthquake model this interpretation leads to a relationship between the power spectral density function of the process and the response spectrum. This relationship is examined in this paper and forms the basis for two methods presented to obtain the power spectrum of the earthquake process from its response spectrum. One of these methods is approximate but leads to an explicit representation of the power spectral density function in terms of the response spectrum. The other method is exact wherein an iterative scheme for the solution of the problem is established. An example problem is solved to illustrate the use of the two methods and it is shown that for small values of damping, the approximate derivation yields a fairly accurate solution.