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Markov Envelope를 이용한 지진동의 위상차 확률분포와 전파지연시간의 추정

Inference of the Probability Distribution of Phase Difference and the Path Duration of Ground Motion from Markov Envelope

윤병익|최항
한국지진공학회|2022.09|한국지진공학회논문집 (Jorunal of the Earthquake Engineering Society of Korea)|제26권 제5호|pp. 191-202

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참고문헌

키워드

Phase differenceMarkov envelopeParabolic equationvon Kármán type mediumScattering processPath duration
주제분류토목공학

초록

Markov envelope as a theoretical solution of the parabolic wave equation with Markov approximation for the von Kármán type random medium is studied and approximated with the convolution of two probability density functions (pdf) of normal and gamma distributions considering the previous studies on the applications of Radiative Transfer Theory (RTT) and the analysis results of earthquake records. Through the approximation with gamma pdf, the constant shape parameter of 2 was determined regardless of the source distance ro. This finding means that the scattering process has the property of an inhomogeneous single-scattering Poisson process, unlike the previous studies, which resulted in a homogeneous multiple-scattering Poisson process. Approximated Markov envelope can be treated as the normalized mean square (MS) envelope for ground acceleration because of the flat source Fourier spectrum. Based on such characteristics, the path duration is estimated from the approximated MS envelope and compared to the empirical formula derived by Boore and Thompson. The results clearly show that the path duration increases proportionately to ro1/2-ro2, and the peak value of the RMS envelope is attenuated by exp (-0.0033ro), excluding the geometrical attenuation. The attenuation slope for ro≤100 km is quite similar to that of effective attenuation for shallow crustal earthquakes, and it may be difficult to distinguish the contribution of intrinsic attenuation from effective attenuation. Slowly varying dispersive delay, also called the medium effect, represented by regular pdf, governs the path duration for the source distance shorter than 100 km. Moreover, the diffraction term, also called the distance effect because of scattering, fully controls the path duration beyond the source distance of 300 km and has a steep gradient compared to the medium effect. Source distance 100-300 km is a transition range of the path duration governing effect from random medium to distance. This means that the scattering may not be the prime cause of peak attenuation and envelope broadening for the source distance of less than 200 km. Furthermore, it is also shown that normal distribution is appropriate for the probability distribution of phase difference, as asserted in the previous studies.

Abstract

Markov envelope as a theoretical solution of the parabolic wave equation with Markov approximation for the von Kármán type random medium is studied and approximated with the convolution of two probability density functions (pdf) of normal and gamma distributions considering the previous studies on the applications of Radiative Transfer Theory (RTT) and the analysis results of earthquake records. Through the approximation with gamma pdf, the constant shape parameter of 2 was determined regardless of the source distance ro. This finding means that the scattering process has the property of an inhomogeneous single-scattering Poisson process, unlike the previous studies, which resulted in a homogeneous multiple-scattering Poisson process. Approximated Markov envelope can be treated as the normalized mean square (MS) envelope for ground acceleration because of the flat source Fourier spectrum. Based on such characteristics, the path duration is estimated from the approximated MS envelope and compared to the empirical formula derived by Boore and Thompson. The results clearly show that the path duration increases proportionately to ro1/2-ro2, and the peak value of the RMS envelope is attenuated by exp (-0.0033ro), excluding the geometrical attenuation. The attenuation slope for ro≤100 km is quite similar to that of effective attenuation for shallow crustal earthquakes, and it may be difficult to distinguish the contribution of intrinsic attenuation from effective attenuation. Slowly varying dispersive delay, also called the medium effect, represented by regular pdf, governs the path duration for the source distance shorter than 100 km. Moreover, the diffraction term, also called the distance effect because of scattering, fully controls the path duration beyond the source distance of 300 km and has a steep gradient compared to the medium effect. Source distance 100-300 km is a transition range of the path duration governing effect from random medium to distance. This means that the scattering may not be the prime cause of peak attenuation and envelope broadening for the source distance of less than 200 km. Furthermore, it is also shown that normal distribution is appropriate for the probability distribution of phase difference, as asserted in the previous studies.

참고문헌 (45)

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