Sensitivity kernels for finite-frequency surface waves
Sensitivity kernels for finite-frequency surface waves
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DOI：
10.1111/j.1365-246x.2005.02707.x
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发表时间：
2002-12
影响因子：
2.8
通讯作者：
K. Yoshizawa;B. Kennett
中科院分区：
文献类型：
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作者：
K. Yoshizawa;B. Kennett
概要基于Born和Rytov近似，利用表面波的势表示，构造了在有限频率下的基模表面波的2-D相速度和3-D剪切波速度的灵敏度核。渐近绿色函数的标量波动方程的使用提供了一种有效的方法来计算玻恩或Rytov核。2-D灵敏度内核使我们能够将表面波的有限频率效应，以及关闭的大圆传播，在层析反演相速结构。我们推导出的2-D的灵敏度内核的例子都为均匀的背景模型（或球对称模型），和横向异质模型。由此产生的失真的形状的灵敏度内核的异质背景模型表明使用适当的内核来考虑在真实的地球的异质性的重要性。通过将一组二维灵敏度核与特定频率范围的一维垂直灵敏度核相结合，并进行逆傅立叶变换，我们可以在时域中导出面波的三维灵敏度核。这样的3-D内核是有用的有效的正演模拟的表面波形，将有限频率的影响，也将使我们能够执行直接反演的表面波形到3-D结构，考虑到有限频率的影响。
SUMMARY Sensitivity kernels for fundamental mode surface waves at finite frequency for 2-D phase speed and 3-D shear wave speed are constructed based on the Born and Rytov approximations working with a potential representation for surface waves. The use of asymptotic Green’s functions for scalar wave equations provides an efficient way to calculate the Born or Rytov kernels. The 2-D sensitivity kernels enable us to incorporate the finite-frequency effects of surface waves, as well as off-great-circle propagation, in tomographic inversions for phasespeed structures. We derive examples of the 2-D sensitivity kernels both for a homogeneous background model (or a spherically symmetric model), and for a laterally heterogeneous model. The resulting distortions of the shape of the sensitivity kernels for a heterogeneous background model indicate the importance of the use of proper kernels to account of the heterogeneity in the real Earth. By combining a set of 2-D sensitivity kernels with 1-D vertical sensitivity kernels for a particular frequency range and taking the inverse Fourier transform, we can derive 3-D sensitivity kernels for surface waves in the time domain. Such 3-D kernels are useful for efficient forward modelling of surface waveforms incorporating finite-frequency effects, and will also enable us to perform direct inversion of surface waveforms into 3-D structure taking account of finite-frequency effects.