Pseudo 2D joint elastic waveform inversion for velocities and attenuation in the near surface
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摘要: 利用弹性波的初至波和面波，应用交叉梯度算子，联合反演了近地表的二维纵横波速度和衰减参数，并提出了采用一维弹性波正演模拟，应用二维Tikhonov正则化，同时反演出二维速度模型和衰减模型的方法。理论模型测试和实际数据应用结果均表明本文算法极大地提高了计算效率，同时能够反演出可靠的速度模型和衰减模型。Abstract: In this study, by applying cross-gradient constraints, we joint early arrivals and surface waves to invert the 2D P-wave velocity, S-wave velocity, QP and QS simultaneously for the near-surface area. In order to improve the efficiency of computation, we propose a method that employs 1D elastic forward modeling and applies 2D Tikhonov regularization to invert the 2D velocity structures and attenuation model. Synthetic tests and real data application illustrate that the method can greatly improve the computational efficiency, and is able to invert reliable velocity and attenuation models simultaneously.
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Keywords:
- joint inversion /
- waveform inversion /
- velocity /
- attenuation
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图 2 弹性波对参数vP/vP0 （a），vS/vS0 （b），QP/QP0 （c） 和QS/QS0 （d）的敏感度
Figure 2. Sensitivity of elastic waveform to parameters vP/vP0 （a），vS/vS0 （b），QP/QP0 （c） and QS/QS0 （d）
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图 1 真实理论测试模型
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 1. True models for synthetic tests
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 3 联合反演的初始输入模型
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 3. Initial models for joint inversion
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 4 不同交叉梯度权重下初至波（a）和面波（b）的波形不匹配度随迭代次数的变化
Figure 4. Misfit variation of initial arrival data （a） and surface wave data （b） with iteration number by different cross-gradient weightings
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图 5 交叉梯度权重αt= 0时理论数据的联合反演结果
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 5. The synthetic data inversion results with cross-gradient weighting αt= 0
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 7 理论模型测试的初至波和面波的真实数据（黑线）与模拟数据（红线）的对比
图（a）中红线表示基于初始模型正演计算的数据，图（b）中红线表示基于交叉梯度为αt=10反演模型正演计算的数据，下同
Figure 7. The comparison of true data （black line） and calculated data （red line） for early arrivals and surface waves in the synthetic tests
The red line in Fig.（a） represents the forward calculation date associ-ated with the initial model，the red line in Fig.（b） represents the forward calaulation data resulted from inversion model with cross-gradient weighting αt=10，the same below
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图 6 交叉梯度权重αt=10时理论数据的联合反演结果
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 6. The synthetic data inversion results with cross-gradient weighting αt=10
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 8 ωP取不同值时反演的模型与真实模型之间的差异
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 8. Differences between the true model and the inverted model with different ωp
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 9 实际测试数据的初始输入模型
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 9. Initial models for real data tests
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 11 交叉梯度权重αt= 0时实际数据的联合反演结果
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 11. The real data inversion results with cross-gradient weighting αt= 0
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 12 交叉梯度权重αt=10时实际数据的联合反演结果
（a） vP模型；（b） vS模型；（c） QP模型；（d） QS模型
Figure 12. The real data inversion results with cross-gradient weighting αt=10
（a） vP model；（b） vS model；（c） QP model；（d） QS model
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图 13 实际数据测试的初至波和面波的真实数据（黑线）与基于初始模型（a）和反演模型（b）模拟数据（红线）的对比
Figure 13. The comparison of true data （black line） and calculated data （red line） for early arrivals and surface waves associated with initial models （a） and inversion models （b）
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