Trade offs between statistical agreement and data reproduction in the generation of synthetic ground motions

Abstract

This paper discusses a method used to generate synthetic time-series, using a set of 3-dimensional recorded ground motions. The Karhunen–Loève expansion is used to represent the stochastic process, taking into account correlation between the three components of the accelerograms. In this way each accelerogram can be decomposed in a linear combination of a finite number of functions, parameterized by a set of d random variables, d being the number of eigenvalues used to estimate the random process, which will be smaller than the number of recorded accelerograms used to perform the KL expansion. A new synthetic accelerogram can be generated by sampling a new set of d random variables. We study more precisely in this paper several sampling methods and in particular the influence of taking into account dependency between those d random variables. We can see that if no dependency is considered, the new set of ground motions will not have the same statistical properties of the recorded set, which could lead to errors if a statistical analysis is performed with this new synthetic set. On the contrary, due to the so-called curse of dimensionality, if the overall joint density function is used to sample new KL parameters, the method will tend to reproduce each single accelerogram from the recorded set. A new method is discussed, where dependence is considered only in a smaller subspace, which enables us to reach a trade-off between those two objectives. The size of the subspace can then be chosen depending on the application and the user's objectives.