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Random field model of sequential ground motions

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Abstract

This paper proposes a random field model of sequential ground motions, which considers the spatial correlation between the mainshock and aftershock from a stochastic view. First, the correlation between the mainshock and aftershock under the physical “source–path–local site” mechanism is explained. Based on the mechanism, the point-source model, and uniform-isotropic-medium model, a random single-point model for sequential ground motion with eight basic parameters is presented. Second, the random field model is developed from the random single-point model. More than 1000 pairs of sequential ground motions are used to identify and analyze statistically the basic parameters in the model. Moreover, the probability distribution of each parameter is presented based on copula functions. The results show that the spatial correlations of sequential ground motions can be effectively simulated based on the proposed random field model. Furthermore, it is possible to realistically reproduce the attenuation and time lag of ground motions at a local site.

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Abbreviations

a(t):

Acceleration time history of single-point ground motion

a(rl,t):

Acceleration time history of ground motion field at a local site

r l :

Distance from the center of the local site along the direction of the wave propagation to any point in the field

A(λ,ω,R):

Fourier amplitude spectrum model of the acceleration time histor

Φ(λ,ω,R):

Fourier phase spectrum model of the acceleration time history

λ :

Random vector of the basic parameters

R :

Epicentral distance

ω :

Circular frequency

A 0 :

Amplitude coefficient that represents the influence of the source intensity

τ :

Source coefficient in Brune’s model

a, b, c, and d :

Empirical parameters

ξ g :

Equivalent damping ratio of the local site

ω g :

Equivalent predominant circular frequency of the local site

α 0 :

Attenuation parameter of the local site

c g :

Apparent seismic wave velocity of the local site

Z :

Basic parameter vector of the sequential ground motion

A0, τ, a, b, c, and d :

Two-dimensional random variables used to describe the correlation of the mainshock and aftershock

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Acknowledgements

The authors thankfully acknowledge the financial support provided by the National Natural Science Foundation of China (U1711264) and Tianshan Scholar Program at Xinjiang University. The constructive discussions with Dr. Jiecheng Xiong and Jinju Tao are highly appreciated.

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Authors and Affiliations

  1. Department of Structural Engineering, College of Civil Engineering, Tongji University, Shanghai, People’s Republic of China

    Jiaxu Shen & Jun Chen

  2. College of Civil Engineering and Architecture, Xinjiang University, Urumqi, People’s Republic of China

    Jun Chen

  3. East China Architectural Design & Research Institute, Shanghai, People’s Republic of China

    Guo Ding

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  1. Jiaxu Shen
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  2. Jun Chen
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Correspondence to Jun Chen.

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Shen, J., Chen, J. & Ding, G. Random field model of sequential ground motions. Bull Earthquake Eng 18, 5119–5141 (2020). https://doi.org/10.1007/s10518-020-00901-4

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