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Modeling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians
Geophysical Prospecting ( IF 1.8 ) Pub Date : 2020-08-06 , DOI: 10.1111/1365-2478.13006
Zhihao Qiao 1, 2 , Chengyu Sun 1, 2 , Jie Tang 1, 2
Affiliation  

ABSTRACT A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant‐Q (i.e. frequency‐independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP‐wave in the constant‐Q viscoelastic anisotropic theory. For numerical simulations, the staggered‐grid pseudo‐spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional‐order Laplacian approximation method is used to cope with spatial variable‐order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant‐Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional‐order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.

中文翻译:

使用解耦分数拉普拉斯算子模拟横向各向同性介质中的粘声波传播

摘要 推导出了一个新的波动方程,用于在声学横向各向同性近似下模拟横向各向同性介质中的粘声波传播。由分数拉普拉斯算子表达的公式可以很好地模拟恒定 Q(即与频率无关的品质因数)衰减、各向异性衰减、解耦幅度损失和速度色散行为。所提出的粘声各向异性方程可以与恒定 Q 粘弹性各向异性理论中的 qP 波保持一致的速度和衰减各向异性效应。对于数值模拟,采用交错网格伪谱方法来求解时域波动方程的速度-应力公式。恒定分数阶拉普拉斯近似方法用于处理空间变阶分数拉普拉斯算子,以便在异质速度和 Q 介质中进行有效建模。齐次模型的模拟结果显示了恒定 Q 方程的速度色散和振幅损失效应的解耦,并说明了各向异性衰减对地震波场的影响。分层模型的建模示例说明了恒定分数阶拉普拉斯近似方法的准确性。最后,使用 Hess 垂直横向各向同性模型验证公式和算法对非均质介质的适用性。齐次模型的模拟结果显示了恒定 Q 方程的速度色散和振幅损失效应的解耦,并说明了各向异性衰减对地震波场的影响。分层模型的建模示例说明了恒定分数阶拉普拉斯近似方法的准确性。最后,使用 Hess 垂直横向各向同性模型验证公式和算法对非均质介质的适用性。齐次模型的模拟结果显示了恒定 Q 方程的速度色散和振幅损失效应的解耦,并说明了各向异性衰减对地震波场的影响。分层模型的建模示例说明了恒定分数阶拉普拉斯近似方法的准确性。最后,使用 Hess 垂直横向各向同性模型验证公式和算法对非均质介质的适用性。
更新日期:2020-08-06
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