A novel model and estimation method for the individual random component of earthquake ground-motion relations

In this paper, I introduce a novel approach to modelling the individual random component (also called the intra-event uncertainty) of a ground-motion relation (GMR), as well as a novel approach to estimating the corresponding parameters. In essence, I contend that the individual random component is reproduced adequately by a simple stochastic mechanism of random impulses acting in the horizontal plane, with random directions. The random number of impulses was Poisson distributed. The parameters of the model were estimated according to a proposal by Raschke J Seismol 17(4):1157–1182, (2013a), with the sample of random difference ξ = ln(Y1)-ln(Y2), in which Y1 and Y2 are the horizontal components of local ground-motion intensity. Any GMR element was eliminated by subtraction, except the individual random components. In the estimation procedure, the distribution of difference ξ was approximated by combining a large Monte Carlo simulated sample and Kernel smoothing. The estimated model satisfactorily fitted the difference ξ of the sample of peak ground accelerations, and the variance of the individual random components was considerably smaller than that of conventional GMRs. In addition, the dependence of variance on the epicentre distance was considered; however, a dependence of variance on the magnitude was not detected. Finally, the influence of the novel model and the corresponding approximations on PSHA was researched. The applied approximations of distribution of the individual random component were satisfactory for the researched example of PSHA.