S wave envelope synthesis based on different scattering patterns
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摘要: 为揭示地震波在地壳小尺度非均匀介质中的散射过程，更准确地描述地震波的包络展宽现象，本文基于多次各向异性散射理论，采用离散波数法求解能量密度积分方程，选取高斯型自相关函数表征的散射模式，得到S波能量密度包络。基于此，本文首先分析了单次散射和多次散射在形成S波能量密度包络中的贡献规律；然后探讨了吸收系数和总散射系数对合成S波能量密度包络的影响；最后对比了在不同散射模式下合成的S波能量密度包络的差异。结果显示：① 不同的散射模式下单次散射和多次散射对地震波散射过程的贡献规律是一致的，对于近震（震源距小于100 km），单次散射模型可以近似合成S波能量密度包络；随着震源距增大，多次前散射模型可以更快地接近总能量密度包络；② 吸收系数增大会降低直达S波和尾波幅值，总散射系数增大会降低直达S波幅值，但使得S波尾波幅值升高；③ 前散射模式下S波能量密度包络随震源距的增大会导致峰值延迟，包络展宽，尾波衰减一致性更快等现象产生。Abstract: In order to reveal the scattering process of seismic waves in the small scale inhomogeneous medium of the crust and to describe the envelopment broadening phenomenon of seismic waves more accurately, a discrete wave-number method is used to solve the improved seismic wave energy density integral equation based on the multiple anisotropic scattering theory, and the scattering pattern represented by Gaussian autocorrelation function is selected to obtain the S wave energy density envelope. Firstly, we analyzed the contribution of single scattering and multiple scattering to the energy density envelope of S wave. Then, we discussed the effects of absorption coefficient and total scattering coefficient on the synthesis of S wave energy density envelope. Finally, we compared the differences of the energy density envelope of S wave synthesized in different scattering patterns. The results show that: ① The contribution of single scattering and multiple scattering to the seismic wave scattering process is consistent, and for the near earthquakes （hypocentral distance is less than 100 km）, the single scattering model can be used to match the S-wave energy density envelope. As the hypocentral distance increases, the multiple forward scattering pattern can approach the total energy density envelope more quickly. ② As the absorption coefficient increases, the amplitude of the direct S wave and the coda wave will decrease. And when the total scattering coefficient increases, the amplitude of the direct S wave will decrease, while the coda wave amplitude of the S wave will increase. ③ In the forward scattering pattern, with the increase of hypocentral distance, the energy density envelope of S-wave appears the peak delay, the envelope is widened, and the attenuation consistency of the coda wave is accelerated.
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Keywords:
- anisotropic /
- scattering theory /
- Gaussian medium /
- forward scattering pattern /
- the S wave envelope
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图 6 不同散射模式下吸收系数ηi和总散射系数g0对S波能量密度包络合成的影响
Figure 6. Influence of absorption coefficient and total scattering coefficient on the synthesis of S wave energy density envelope under different scattering patterns
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图 2 引入震源特征时间函数的辐射传输理论示意图
Figure 2. The schematic view of radiative transfer theory with the source characteristic time function
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图 3 直达波 （a）、单次散射波 （b）、多次散射波 （c）的示意图
Figure 3. The schematic view of direct wave， single scattering wave and multiple scattering wave
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图 5 高斯型散射模式表征系数μ取为−2.0 （a），0 （b）和7.0 （c）时不同震源距r的散射结果比较
Figure 5. Comparison of scattering results at different hypocentral distances r when the Gaussian scattering pattern characterization coefficient μ＝−2.0 （a），μ＝0 （b） and μ＝7.0 （c）
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图 7 不同散射模式下合成的S波能量密度包络
（a） 前散射和各向同性散射模式；（b） 各向同性散射和后散射模式。图中纵坐标均为S波能量密度乘震源距系数exp （tS/15）后的结果
Figure 7. The energy density envelope of S wave synthesized in different scattering patterns
（a） The forward scattering and isotropic scattering patterns；（b） The isotropic scattering and back scattering patterns。The ordinates in the figure are the results of S-wave energy density multiplied by hypocentral distance coefficient exp （tS/15）
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图 8 不同散射模式下合成的 S 波能量密度包络衰减一致性
（a） 各向同性散射模式； （b） 后散射模式；（c） 前散射模式
Figure 8. The consistance of the energy density envelope attenuation for the S wave synthesized in different scattering patterns
（a） The isotropic scattering pattern； （b） The back scattering pattern； （c） The forward scattering pattern
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