The semi-empirical method, in which small-event records are used as Green's functions to synthesize strong ground motions from a large earthquake, has become one of the most practical methods for generating the input ground motion for earthquake-resistant design of structures. The stability of the synthesized ground motions was examined in the applicability for engineering purposes. The accelerograms from the 1980 Izu-Hanto-Toho-Oki, Japan, earthquake with a magnitude of 6.7 were simulated by using the records from 17 foreshocks and aftershocks with magnitudes of 3.4 to 4.9. The syntheses were carried out for each small-event record and 17 results are obtained. The coefficients of variation (percentages of the standard deviations to the mean values) of the ratios of the synthesized PGA, PGV and SI to the observed ones were found to be 40 to 80 per cent, which consisted of 20 to 30 per cent caused by our synthesis procedure itself, 30 to 40 per cent caused by the approximation of the source spectrum for each small event by the ω-square model, and 0 to 70 per cent caused by the similarity relations used to obtain the source parameters (L, W, D, and σe from the magnitude. Consequently, in order to minimize the variation caused by the modeling of the source spectrum and the similarity relations, we proposed a new synthesis procedure, in which the small-event records were normalized with regard to the source size and then chosen randomly as Green's functions for each element of the fault plane of the main shock. The coefficients of variation of the results by the present new procedure became 15 to 25 per cent much more stable.

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