Simulation of Earthquake Motion Phase considering Its Fractal and Auto-covariance Features

다국어 초록 (Multilingual Abstract)

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-affine 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.

참고문헌 (Reference)

1 Meyer, Y., "Wavelets and operators (Vol. 1)" Cambridge University Press 1992

2 Cohen, L., "Time – Frequency analysis, Vol. 778" Prentice Hall 1995

3 Papoulis, A., "The Fourier integral and its applications" McGraw-Hill 1962

4 Yongbo Peng, "Stochastic modeling for starting-time of phase evolution of random seismic ground motions" Elsevier BV 4 (4): 013009-, 2014

5 Zakariya Waezi, "Stochastic Non-Stationary Model for Ground Motion Simulation Based on Higher-Order Crossing of Linear Time Variant Systems" Informa UK Limited 21 (21): 123-150, 2016

6 Biagini, F., "Stochastic Calculusfor Fractional Brownian Motion and Applications" Springer Science & Business Media 2008

7 Sato, T., "Phase spectrum modeling to simulate design earthquake motion" 24 (24): 91-100, 2002

8 N. C. Nigam, "Phase properties of a class of random processes" Wiley 10 (10): 711-717, 1982

9 D. M. Boore, "Phase Derivatives and Simulation of Strong Ground Motions" Seismological Society of America (SSA) 93 (93): 1132-1143, 2003

10 Y. Ohsaki, "On the significance of phase content in earthquake ground motions" Wiley 7 (7): 427-439, 1979

11 Dixiong Yang, "Multifractal characteristic analysis of near-fault earthquake ground motions" Elsevier BV 72 : 12-23, 2015

12 Murono, Y., "Modeling of phase spectra for near-fault earthquake motions" 2002

13 Izumi, M., "Interrelation of fault mechanisms, phase inclinations and nonstationarities of seismic waves" 1 : 89-96, 1980

14 Mandelbrot, B. B., "Fractional Brownian motions, fractional noises and applications" 10 (10): 422-437, 1968

15 Falconer, K., "Fractal geometry: Mathematical foundations and applications" John Wiley and Sons 2014

16 Dixiong Yang, "Fractal characterization and frequency properties of near-fault ground motions" Springer Science and Business Media LLC 12 (12): 503-518, 2013

17 Tanaka, K., "Evaluation of inhomogeneous structures in seismic propagation path in Japan based on the fractal characteristic of observed earthquake motion phase" WCEE 2017

18 Adam A. Abdelrahman, "Definition of Yield Seismic Coefficient Spectrum Considering the Uncertainty of the Earthquake Motion Phase" MDPI AG 9 (9): 2254-, 2019

19 Katukura, H., "A study on the phase properties of seismic waves" Japan Society of Civil Engineers 209-216, 1978

20 Satoh, T., "A study on envelope characteristics of strong motions in a period range of 1 to 15 seconds by using group delay time" WCEE 1996

21 Katukura, K., "A fundamental study on the phase properties of seismic waves" 327 : 20-27, 1983

22 Cong Zhang, "A Phase Model of Earthquake Motions based on Stochastic Differential Equation" 대한토목학회 15 (15): 161-166, 2011