Forward modeling method of seismic multiple scattered waves
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摘要: 地震波在穿越地下散射体群时会产生多级散射波，分析其地震响应特征，可推断散射体的分布情况和性质。本文从二维标量波动方程出发，结合地震散射理论和波恩近似理论，推导了多级散射波方程。在此基础上，采用高阶有限差分法对双点散射体模型和复杂散射体模型进行数值模拟，分析了多级散射波的传播规律和波场特征，并通过抽取多级散射记录和各级散射记录的单道记录与参考单道记录的对比，验证了本文推导散射波方程的准确性。Abstract: When seismic waves pass through the underground scatterers, multi-order scattered waves will be generated, and the analysis of their seismic response characteristics is beneficial to infer the distribution and properties of the scatterers. Based on the two-dimensional scalar wave motion equation, combined with the seismic scattering theory and the Born approximation theory, the multi-order scattering wave equation is deduced. The numerical simulation of the two-point scatterer model and the complex scatterer model is carried out by using the high-order finite difference method, and the propagation law and wavefield characteristics of the multi-order scattered wave are analyzed. And then the single track records of multi-order scattering and each scattering are extracted and compared with the reference single track records, which verifies the accuracy of the scattering wave equation derived in this paper.
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Keywords:
- multi-order scattered /
- scalar wave equation /
- finite difference /
- forward modeling
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图 2 多级散射原理示意图
（a） 一级散射；（b） 二级散射；（c） 三级散射
Figure 2. Schematic diagram of multi-order scattering principle
（a） The first-order scattering；（b） The second-order scattering；（c） The third-order scattering
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图 4 不同级数的散射波波场快照
（a） 多级散射波；（b） 一级散射波；（c） 二级散射波；（d） 三级散射波
Figure 4. Snapshots of scattered wavefields at different orders
（a） The multi-order scattering；（b）The first-order scattering；（c） The second-order scatterings；（d） The third-order scattering
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图 5 多级散射记录与参考记录第100道的波形对比
Figure 5. Comparison of the 100th record of the multi-order scattering records with that of the reference records
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图 6 各级散射记录与参考记录第100道的波形对比
Figure 6. Comparison of the 100th record of each scattering records and the reference records
（a） t＝0—1.6 s；（b） t＝0.832—0.960 s；（c） t＝1.240—1.360 s
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图 7 两点弱散射体模型（a）及多级散射记录与参考记录第 100 道的波形对比（b）
Figure 7. A model with two weak scatterers （a） and comparison of the 100th record of the multi-orderscattering records and with that of the reference records （b）
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图 8 各级散射记录与参考记录第100道的波形对比
Figure 8. Comparison of the 100th record of each scattering records and the reference records
（a） t＝0—1.6 s；（b） t＝0.848—0.944 s；（c） t＝1.296—1.318 s
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