Simulation of Earthquake Motion Phase considering Its Fractal and Auto-covariance Features
- 9 Downloads
The earthquake motion phase (EMP) is decomposed into linear delay and fluctuation parts. In this paper, the peculiar stochastic characteristics of the fluctuation part of the phase (FPP) are discussed. First, we show that the FPP has self-afSne similarity and should be expressed as a fractal stochastic process by using several observed earthquake motion time histories, as well as the FPP has a long term memory in the frequency domain. Moreover, the possibility of simulating FPP using the simple fractional Brownian motion (fBm) is discussed and conclude that this is not possible. To overcome this problem, we develop a new stochastic process, the modified fBm that is able to simulate a stochastically rigorous sample FPP. This newly developed algorithm represents the phase characteristics of the observed EMP well.
Keywordsphase power law of variance auto-covariance modified fractional stochastic process fractional Brownian motion Hurst index
Unable to display preview. Download preview PDF.
The authors would like to acknowledge Japan Meteorological Agency and National Research for Earth and Disaster Resilience, as well as the Peer NGA Strong Motion Database, to provide valuable observed earthquake records. We also acknowledge the supports from JSPS, Grant-in-Aid for Scientific Research #18K04334, the National Natural Science Foundation of China (No.51578140) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD, No. CE02).
- Cohen, L. (1995). Time - Frequency analysis, Vol. 778, Prentice Hall, Upper Saddle River, NJ, USA.Google Scholar
- Izumi, M., Watanabe, T., and Katukura, H. (1980). “Interrelation of fault mechanisms, phase inclinations and nonstationarities of seismic waves.” Proc. 7th World Conference on Earthquake Engineering, Istanbul, Turkey, Vol. 1, pp. 89–96.Google Scholar
- Katukura, H. (1978). “A study on the phase properties of seismic waves.” Proc. 5th Japan Earthquake Engineering Symposium, Japan Society of Civil Engineers, Shinjuku, Tokyo, Japan, pp. 209–216.Google Scholar
- Katukura, K. (1983). “A fundamental study on the phase properties of seismic waves.” Journal of Structural and Construction Engineering, Transactions of AIJ, 327, pp. 20–27.Google Scholar
- Meyer, Y. (1992). Wavelets and operators (Vol. 1), Cambridge University Press, Cambridge, UK.Google Scholar
- Murono, Y, Sato, T., and Murakami, M. (2002). “Modeling of phase spectra for near-fault earthquake motions.” Proc. of 12th European Conf. on Earthquake Eng., Paris, France.Google Scholar
- Sato, T., Murono, Y., and Nishimura, A. (2002). “Phase spectrum modeling to simulate design earthquake motion.” Journal of Natural Disaster Science, Vol. 24, No. 2, pp. 91–100.Google Scholar
- Satoh, T., Uetake, T., and Sugawara, Y. (1996). “A study on envelope characteristics of strong motions in a period range of 1 to 15 seconds by using group delay time.” Proc. 11th World Conference on Earthquake Engineering, WCEE, Acapulco, Mexico.Google Scholar
- Tanaka, K. and Sato, T. (2017). “Evaluation of inhomogeneous structures in seismic propagation path in Japan based on the fractal characteristic of observed earthquake motion phase.” Proc. 16th World Conference on Earthquake Engineering, WCEE, Acapulco, Mexico, Paper No. 1420.Google Scholar