2020 Volume 20 Issue 7 Pages 7_46-7_68
We investigated the causes and remedies regarding the Fourier amplitude sags at intermediate frequencies in the source spectra of large earthquakes, which were synthesized from small earthquakes using the stochastic Green's function method. First, we summarized the basic equations and the similarity rules between the large and small earthquakes. And then we summarized the causes of the amplitude sags to (a) the sag at intermediate frequencies caused by the F function (the filtering function of the moment rate from the small to the large earthquake), (b) the sag at the connected frequencies caused by superimposing results based on different phase spectra, which are the coherent phases at lower frequencies and the random phases at higher frequencies, and (c) the sag at intermediate frequencies caused by approximating from the ω-2 model to the ω-3 model, as the number of fault divisions of large earthquakes increases. We investigated the causes of those sags and their improvement method. Furthermore, we theoretically investigated (d) the sag due to the superposition of the element earthquakes, and found that a large sag was caused at transition frequencies by the change in the amplitude of the square of the similarity ratio N at lower frequencies to N at higher frequencies. Finally, as a simple and practical improvement method for the sag, we proposed an amplitude correction method based on the theoretical ω-2 model. We simulated the strong ground motions using the stochastic Green's function method, and compared the results with and without the amplitude correction, and demonstrated that the strong ground motions are greatly underestimated without the correction at the intermediate frequencies.
