移动线源的Green函数求解及辐射能量分析:高铁地震信号简化建模
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摘要
在基于人工主动源的勘探地震学中,往往采用固定位置和激发时间的点源数学模型来描述爆炸型震源或可控震源,因此就有了描述单点力源作用下的弹性全空间或半空间中弹性波传播的Green函数,成为了勘探地震学的重要理论基础.而如今,行进中的高速列车(高铁)是一种全新的主动源,其接近匀速的运行速度、确定的长度和荷载使其可以被重复利用.本文将行进中的高铁在数学上简化建模为一个移动线源来进行研究,给出了这一震源作用下的弹性半空间和全空间中Green函数的计算方法,并分别讨论了全空间中远场Green函数的频谱特征和空间辐射能量的方向性特点,以及半空间中Green函数与近场观测数据的对比结果,为高铁震源下的地震波传播规律和振动信号的研究与利用提供帮助.
In exploration seismology,a controlled seismic source,such as dynamite or vibroseis,is used to send elastic waves into the Earth,where each medium-discontinuity interface reflects a portion of wave energy back to the surface and allows the rest to transmit through the interface.This physical process can be modelled in mathematics.The controlled seismic source is represented by a body force acting at a particular point of the medium,and Green function describes the propagation of elastic waves induced by this unit impulse body force within a full-space or half space medium.They formed the most important theoretical bases of exploration seismology.Nowadays,the moving high-speed train can also be viewed as another controlled seismic source due to its length,travel speed and weight are fixed and can be measured easily.To use thissource for estimating the properties of the Earth′s subsurface,we need to study the characteristic of elastic waves induced by it.In this paper,we regard the moving high-speed train as a moving line source to simplify the modeling process and present its Green function in the half space and full space,respectively.By analyzing the far-field term of Green function in the full space asymptotically,the characteristics of frequency and radiation directivity for this moving line source are shown.In addition,to evaluate the feasibility of modeling the high-speed train by a moving line source,a comparison between the real data and synthetic data in the near field is also performed,where the synthetic data are obtained by the finite-difference method with the stressfree condition since the proposed half-space Green function is too complex to be calculated analytically.These results will contribute to the study and utilization of seismic signal generated by the high-speed train.
In exploration seismology,a controlled seismic source,such as dynamite or vibroseis,is used to send elastic waves into the Earth,where each medium-discontinuity interface reflects a portion of wave energy back to the surface and allows the rest to transmit through the interface.This physical process can be modelled in mathematics.The controlled seismic source is represented by a body force acting at a particular point of the medium,and Green function describes the propagation of elastic waves induced by this unit impulse body force within a full-space or half space medium.They formed the most important theoretical bases of exploration seismology.Nowadays,the moving high-speed train can also be viewed as another controlled seismic source due to its length,travel speed and weight are fixed and can be measured easily.To use thissource for estimating the properties of the Earth′s subsurface,we need to study the characteristic of elastic waves induced by it.In this paper,we regard the moving high-speed train as a moving line source to simplify the modeling process and present its Green function in the half space and full space,respectively.By analyzing the far-field term of Green function in the full space asymptotically,the characteristics of frequency and radiation directivity for this moving line source are shown.In addition,to evaluate the feasibility of modeling the high-speed train by a moving line source,a comparison between the real data and synthetic data in the near field is also performed,where the synthetic data are obtained by the finite-difference method with the stressfree condition since the proposed half-space Green function is too complex to be calculated analytically.These results will contribute to the study and utilization of seismic signal generated by the high-speed train.
引文
Aki K,Richards P G.2002.Quantitative Seismology.Sausalito,California:University Science Books.
Cao J,Chen J B,Dai M X.2018.An adaptive free-surface expression for three-dimensional finite-difference frequency-domain modelling of elastic wave.Geophysical Prospecting,66(4):707-725.
Johnson L R.1974.Green′s function for Lamb′s problem.Geophysical Journal International,37(1):99-131.
Kristek J,Moczo P,Archuleta R.2002.Efficient methods to simulate planar free surface in the 3D4th-order staggered-grid finite-difference schemes.Studia Geophysica et Geodaetica,46(2):355-381.
Lamb H.1904.On the propagation of tremors over the surface of an elastic solid.Philosophical Transactions of the Royal Society A:Mathematical,Physical and Engineering Sciences,203:1-42.
Lay T,Wallace T C.1995.Modern Global Seismology.San Diego:Academic Press,Inc.
Virieux J.1986.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geophysics,51(4):889-901.
1)骆毅.2018.利用高铁信号对地球内部成像(1):震源时间函数.“高铁地震学”学术讨论会,北京.
Cao J,Chen J B,Dai M X.2018.An adaptive free-surface expression for three-dimensional finite-difference frequency-domain modelling of elastic wave.Geophysical Prospecting,66(4):707-725.
Johnson L R.1974.Green′s function for Lamb′s problem.Geophysical Journal International,37(1):99-131.
Kristek J,Moczo P,Archuleta R.2002.Efficient methods to simulate planar free surface in the 3D4th-order staggered-grid finite-difference schemes.Studia Geophysica et Geodaetica,46(2):355-381.
Lamb H.1904.On the propagation of tremors over the surface of an elastic solid.Philosophical Transactions of the Royal Society A:Mathematical,Physical and Engineering Sciences,203:1-42.
Lay T,Wallace T C.1995.Modern Global Seismology.San Diego:Academic Press,Inc.
Virieux J.1986.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geophysics,51(4):889-901.
1)骆毅.2018.利用高铁信号对地球内部成像(1):震源时间函数.“高铁地震学”学术讨论会,北京.