Time domain viscoelastic full waveform inversion
Time domain viscoelastic full waveform inversion
复制标题
时域粘弹性全波形反演
DOI：
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
B. Giroux
中科院分区：
文献类型：
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作者：
G. Fabien;E. Gloaguen;B. Giroux
粘性衰减对地震波的传播有很大影响，但在全波形反演（FWI）中却很少考虑。在时域FWI中考虑粘弹性问题时，通常采用波动方程的位移公式代替常用的速度-应力公式。然而，反演方案依赖于伴随方程，这是完全不同的速度-应力公式比位移公式。本文将伴随态方法应用于基于广义线性固体流变学的速度-应力方程中的各向同性粘弹性波动方程。通过应用线性变换的波动方程推导出的伴随状态方程，我们得到两组对称的偏微分方程的前向和伴随变量。所得到的方程组仅相差一个符号变化，并且可以通过相同的数值实现来求解。我们还研究了粘弹性方程的参数类（速度和衰减）之间的串扰。更具体地说，我们表明，衰减水平可以用来恢复P波和S波的品质因数，但它们是非常敏感的速度误差。最后，我们提出了一个合成的粘弹性FWI的背景下，监测CO的地质封存的例子。我们表明，FWI的基础上，我们的配方确实可以恢复P波和S波的速度和衰减水平时，衰减是足够高的。FWI恢复的速度和衰减水平的变化都可以用来跟踪注入过程中和注入后的CO2羽流。需要进一步的研究来评估粘弹性FWI在真实的数据上的性能。
Viscous attenuation can have a strong impact on seismic wave propagation, but it is rarely taken into account in full waveform inversion (FWI). When viscoelasticity is considered in time domain FWI, the displacement formulation of the wave equation is usually used instead of the popular velocity–stress formulation. However, inversion schemes rely on the adjoint equations, which are quite different for the velocity–stress formulation than for the displacement formulation. In this paper, we apply the adjoint state method to the isotropic viscoelastic wave equation in the velocity–stress formulation based on the generalized standard linear solid rheology. By applying linear transformations to the wave equation before deriving the adjoint state equations, we obtain two symmetric sets of partial differential equations for the forward and adjoint variables. The resulting sets of equations only differ by a sign change and can be solved by the same numerical implementation. We also investigate the crosstalk between parameter classes (velocity and attenuation) of the viscoelastic equation. More specifically, we show that the attenuation levels can be used to recover the quality factors of P and S waves, but that they are very sensitive to velocity errors. Finally, we present a synthetic example of viscoelastic FWI in the context of monitoring CO₂ geological sequestration. We show that FWI based on our formulation can indeed recover P- and S-wave velocities and their attenuation levels when attenuation is high enough. Both changes in velocity and attenuation levels recovered with FWI can be used to track the CO₂ plume during and after injection. Further studies are required to evaluate the performance of viscoelastic FWI on real data.
影响因子：
3.3
作者：
Mueller, Tobias M.;Gurevich, Boris;Lebedev, Maxim
通讯作者：
Lebedev, Maxim