Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media
Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media
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DOI：
10.1190/geo2020-0659.1
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发表时间：
2021-07-01
期刊：
影响因子：
3.3
通讯作者：
Leung, Shingyu
中科院分区：
文献类型：
--
作者：
Hu, Jiangtao;Qian, Jianliang;Leung, Shingyu
地震波在地球介质中通常经历衰减，引起能量损失和相位失真。在高频渐近状态下，复值程函是描述衰减介质中波传播的基本成分，其中程函函数的真实的和虚部分别捕获地震波的频散效应和振幅衰减。传统上，这样的复值程函主要通过在复空间中精确地跟踪射线或者通过在真实的空间中近似地跟踪射线来计算，使得所得到的程函在真实的空间中不规则地分布。然而，地震数据处理方法，如叠前深度偏移和层析成像，通常需要均匀分布的复值eikonals。因此，我们已经开发了一个统一的框架来欧拉化几个流行的近似实空间射线追踪方法的复值eikonal，使真实的和虚部的eikonal函数满足经典的实空间eikonal方程和一个新的实空间平流方程，我们称之为欧拉偏微分方程方法。我们进一步发展了高效的高阶方法来解决这两个方程，通过使用因式分解的思想和Lax-Friedrichs加权本质非振荡格式。数值例子表明，我们的方法产生高精度的复值eikonals，类似于射线追踪方法。我们的方法可用于衰减介质中的偏移和层析成像。
Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Conventionally, such a complex-valued eikonal is mainly computed either by tracing rays exactly in complex space or by tracing rays approximately in real space so that the resulting eikonal is distributed irregularly in real space. However, seismic data processing methods, such as prestack depth migration and tomography, usually require uniformly distributed complex-valued eikonals. Therefore, we have developed a unified framework to Eulerianize several popular approximate real-space ray-tracing methods for complex-valued eikonals so that the real and imaginary parts of the eikonal function satisfy the classic real-space eikonal equation and a novel real-space advection equation, respectively, and we dub the resulting method the Eulerian partial-differential equation method. We further develop highly efficient high-order methods to solve these two equations by using the factorization idea and the Lax-Friedrichs weighted essentially nonoscillatory schemes. Numerical examples demonstrate that our method yields highly accurate complex-valued eikonals, analogous to those from ray-tracing methods. Our methods can be useful for migration and tomography in attenuating media.