基于辐射传输理论的高频S波各向异性散射过程研究
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摘要
近年来,全球强震频发,给人类社会带来了不可估量的财产损失和人员伤亡。与历史上其他地震相比,这几次地震的最显著特点之一是：地震发生地点距离城市市区很近。从而,为了更有效的研究这些地震,构建考虑震源破裂机制与传播效应的近场地震动建模理论与方法至关重要。本文针对地震波在复杂介质中传播时遇到的高频地震波散射效应,开展了高频S波的各向异性散射理论研究。
首先,在各向异性散射理论框架内,通过引入表征震源初始脉冲持时的震源特征时间,对地震波能量密度积分方程进行了改进。然后,基于各向异性散射模式,通过离散波数方法求解了改进的S波能量密度积分方程。根据能量密度与速度的对应关系,得到了S波的速度包络。据此,讨论了不同散射模式对S波速度包络的影响。计算结果表明：前散射、各向同性散射、后散射模式均能给出S波速度包络尾波段的衰减一致性；在震源距较小时(小于100km),不同散射模式的结果几乎完全一致,但随着震源距的增加,各向异性散射结果与各向同性散射结果的偏差逐渐增大。其中,基于前散射模式合成的速度包络出现了包络展宽、包络峰值到时延迟现象,从而为定量分析高频S波包络的展宽特性提供了一种新的技术手段。
其次,基于各向异性散射模式,分析了直达波与单次散射组合项,以及多次散射项对S波速度包络的影响。分析结果表明,在震源距较小(小于100km)时,直达波与单次散射组合项几乎与整体速度包络重合。因此,在这种情况下可忽略多次散射项,而用单次散射模型模拟S波的散射过程。随着震源距的增加,多次散射项逐渐占主导地位。其中,前散射模式与后、各向同性散射模式的结果相比,多次散射项的比重上升的较快,当震源距超过200km时即可采用多次散射项的结果近似模拟整个S波速度包络。
最后,将多次前散射模型应用于汶川余震速度记录的拟合,结果表明：与后散射、各向同性散射模式相比,基于前散射模式,合成的速度包络能够体现出S尾波包络的衰减一致性,同时能够描述S波速度包络随震源距的增加而出现的展宽现象。因此,高频S尾波并不是传统意义上的各向同性散射过程、或者后散射过程引起的散射波的叠加,而是源于S波与散射体多次前散射过程中的能量转移。在观测S波速度包络上的表现为：随着传播距离的增加,直达S波峰值降低,尾波段幅值提升。这意味着：S波在传播介质中与散射体的多次前散射作用,抽取了直达波的能量转移至尾波段,从而促成了高频S尾波的形成。高频S尾波形成机制的揭示为S尾波包络的合成提供了理论参考。
Recently, the strong earthquakes stroke the earth frequently and brought human society inestimable loss of possessions and life. In contrast to the historical earthquakes, one of the most remarkable features of these earthquakes is their epicenters are very close to cities. Therefore, in order to study these earthquakes more efficiently, it is the key to build the theory and methodology which consider the rupture mechanism of source and propagation effect of these near fault earthquakes. Focusing on the scattering phenomena of seismic wave which propagated in the complex medium, the anisotropic scattering theory of high frequency S wave is developed in this study.
Firstly, in the framework of anisotropic scattering theory, the seismic wave energy density integral equation is improved by introducing a source characteristic time, which is used to describe the time width of initial impulse of source. Then, based on anisotropic scattering patterns, a discrete wave-number is used to solve the improved S wave energy density integral equation. And the S wave velocity envelope is obtained according to the relationship between energy density and velocity. Based the velocity envelope, the effect of scattering patterns on S wave velocity envelope is discussed. According to the numerical results, forward and backward, as well as isotropic scattering patterns, all of them can model the common decay of S coda wave velocity envelope. When hypocentral distance is small (less than100km), all the S wave velocity envelopes are almost same. However, with the increasing of hypocentral distance, the deviation between isotropic and ansotropic results will be grown. And for the result of forward scattering pattern, the velocity envelope broadening and envelope peak delay will be appeared. Thus, a new quantitative measurement for the S wave envelope broadening is provided.
Secondly, based on anisotropic scattering patterns, the effect of group of direct wave and single scattering term and multiple scattering terms on S wave velocity envelope is investigated. From the analysis result, the result from the group of direct wave and single scattering term match the whole velocity envelope of S wave pretty well at small hypocentral distance (less than100km). Thus, in this case, the multiple scattering terms can be neglected and the single scattering model can be used to simulate the S wave scattering process. With increasing of hypocentral distance, multiple scattering terms will be gradually dominated over the group of direct wave and single scattering term. Compared with results from backward and isotropic scattering pattern, the contribution of multiple scattering terms from forward scattering pattern grew more rapidly. And multiple scattering terms can be used to model the whole S wave velocity envelope when the hypocentral distance is larger than200km.
Finally, the multiple forward scattering pattern is used to fit the velocity record from Wenchuan aftershocks. From the fitting result, in contrast to results from backward and isotropic scattering patterns, the synthesized velocity envelopes from the forward scattering pattern not only describe the common decay of S coda wave, but also represent the envelope broadening which will be appeared when hypocentral distance is increasing. Hence, high frequency S coda wave is not traditional superposition of scattering wave from backward or isotropic scattering process, but is originated from the transfer energy from the multiple forward scattering process between scatters and S wave. This phenomenon appeared on the observed S wave velocity envelope is the attenuation of direct S wave amplitude as well as the rising of S coda wave amplitude. Therefore, the energy of direct wave is pumped by the multiple forward scattering process between S wave and scatters, and the pumped energy is transferred to the coda wave part, which form the high frequency S coda wave. Therefore, a theoretical reference is offered for the synthesis of S coda envelope by a discovery of the mechanism of high frequency S coda wave excitation.
首先,在各向异性散射理论框架内,通过引入表征震源初始脉冲持时的震源特征时间,对地震波能量密度积分方程进行了改进。然后,基于各向异性散射模式,通过离散波数方法求解了改进的S波能量密度积分方程。根据能量密度与速度的对应关系,得到了S波的速度包络。据此,讨论了不同散射模式对S波速度包络的影响。计算结果表明：前散射、各向同性散射、后散射模式均能给出S波速度包络尾波段的衰减一致性；在震源距较小时(小于100km),不同散射模式的结果几乎完全一致,但随着震源距的增加,各向异性散射结果与各向同性散射结果的偏差逐渐增大。其中,基于前散射模式合成的速度包络出现了包络展宽、包络峰值到时延迟现象,从而为定量分析高频S波包络的展宽特性提供了一种新的技术手段。
其次,基于各向异性散射模式,分析了直达波与单次散射组合项,以及多次散射项对S波速度包络的影响。分析结果表明,在震源距较小(小于100km)时,直达波与单次散射组合项几乎与整体速度包络重合。因此,在这种情况下可忽略多次散射项,而用单次散射模型模拟S波的散射过程。随着震源距的增加,多次散射项逐渐占主导地位。其中,前散射模式与后、各向同性散射模式的结果相比,多次散射项的比重上升的较快,当震源距超过200km时即可采用多次散射项的结果近似模拟整个S波速度包络。
最后,将多次前散射模型应用于汶川余震速度记录的拟合,结果表明：与后散射、各向同性散射模式相比,基于前散射模式,合成的速度包络能够体现出S尾波包络的衰减一致性,同时能够描述S波速度包络随震源距的增加而出现的展宽现象。因此,高频S尾波并不是传统意义上的各向同性散射过程、或者后散射过程引起的散射波的叠加,而是源于S波与散射体多次前散射过程中的能量转移。在观测S波速度包络上的表现为：随着传播距离的增加,直达S波峰值降低,尾波段幅值提升。这意味着：S波在传播介质中与散射体的多次前散射作用,抽取了直达波的能量转移至尾波段,从而促成了高频S尾波的形成。高频S尾波形成机制的揭示为S尾波包络的合成提供了理论参考。
Recently, the strong earthquakes stroke the earth frequently and brought human society inestimable loss of possessions and life. In contrast to the historical earthquakes, one of the most remarkable features of these earthquakes is their epicenters are very close to cities. Therefore, in order to study these earthquakes more efficiently, it is the key to build the theory and methodology which consider the rupture mechanism of source and propagation effect of these near fault earthquakes. Focusing on the scattering phenomena of seismic wave which propagated in the complex medium, the anisotropic scattering theory of high frequency S wave is developed in this study.
Firstly, in the framework of anisotropic scattering theory, the seismic wave energy density integral equation is improved by introducing a source characteristic time, which is used to describe the time width of initial impulse of source. Then, based on anisotropic scattering patterns, a discrete wave-number is used to solve the improved S wave energy density integral equation. And the S wave velocity envelope is obtained according to the relationship between energy density and velocity. Based the velocity envelope, the effect of scattering patterns on S wave velocity envelope is discussed. According to the numerical results, forward and backward, as well as isotropic scattering patterns, all of them can model the common decay of S coda wave velocity envelope. When hypocentral distance is small (less than100km), all the S wave velocity envelopes are almost same. However, with the increasing of hypocentral distance, the deviation between isotropic and ansotropic results will be grown. And for the result of forward scattering pattern, the velocity envelope broadening and envelope peak delay will be appeared. Thus, a new quantitative measurement for the S wave envelope broadening is provided.
Secondly, based on anisotropic scattering patterns, the effect of group of direct wave and single scattering term and multiple scattering terms on S wave velocity envelope is investigated. From the analysis result, the result from the group of direct wave and single scattering term match the whole velocity envelope of S wave pretty well at small hypocentral distance (less than100km). Thus, in this case, the multiple scattering terms can be neglected and the single scattering model can be used to simulate the S wave scattering process. With increasing of hypocentral distance, multiple scattering terms will be gradually dominated over the group of direct wave and single scattering term. Compared with results from backward and isotropic scattering pattern, the contribution of multiple scattering terms from forward scattering pattern grew more rapidly. And multiple scattering terms can be used to model the whole S wave velocity envelope when the hypocentral distance is larger than200km.
Finally, the multiple forward scattering pattern is used to fit the velocity record from Wenchuan aftershocks. From the fitting result, in contrast to results from backward and isotropic scattering patterns, the synthesized velocity envelopes from the forward scattering pattern not only describe the common decay of S coda wave, but also represent the envelope broadening which will be appeared when hypocentral distance is increasing. Hence, high frequency S coda wave is not traditional superposition of scattering wave from backward or isotropic scattering process, but is originated from the transfer energy from the multiple forward scattering process between scatters and S wave. This phenomenon appeared on the observed S wave velocity envelope is the attenuation of direct S wave amplitude as well as the rising of S coda wave amplitude. Therefore, the energy of direct wave is pumped by the multiple forward scattering process between S wave and scatters, and the pumped energy is transferred to the coda wave part, which form the high frequency S coda wave. Therefore, a theoretical reference is offered for the synthesis of S coda envelope by a discovery of the mechanism of high frequency S coda wave excitation.
引文
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