粘弹性TTI介质中2.5维频率域地震全波形反演位移张量的数值Fréchet导数
Numerical Fréchet derivatives of the displacement tensor for 2.5-D frequency-domain seismic full-waveform inversion in viscoelastic TTI media
摘要：
位移张量相对于地下的独立模型参数的导数，也称为Fréchet导数（或灵敏度核），是利用局部搜索优化算法进行地震全波形反演的关键成分。它们提供了由于给定勘测几何结构的地下模型参数的扰动而引起的地震图的预期变化的定量测量。由于2.5-D波场模拟涉及具有3D（球面）波特性的2-D地质模型中的真实点源，所以它产生的合成数据比通常使用的2-D波模拟更接近实际的实际场数据，2-D波模拟使用不现实的线源，其中波以圆柱形传播。基于我们最近发展的一般2.5-D波场模拟方案，我们应用摄动方法获得了一般粘弹性各向异性介质中2.5-D/2-D频率域地震全波形反演位移张量导数的显式解析表达式。然后，我们证明了所有这些衍生物在两种常见情况下的数值计算：（i）粘弹性各向同性和（ii）粘弹性倾斜横观各向同性（TTI）固体。不同的敏感性模式的各种衍生物的例子进行了研究，并比较了四个不同的同质模型，涉及2-D和2.5-D建模。
英文摘要：
Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Fréchet derivatives (or sensitivity kernels), are a key ingredient for seismic full-waveform inversion with a local-search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Since 2.5-D wavefield modeling involves a real point source in a 2-D geological model with 3D (spherical) wave properties, it yields synthetic data much closer to the actual practical field data than the commonly used 2-D wave simulation does, which uses an unrealistic line source in which the waves spread cylindrically. Based on our recently developed general 2.5-D wavefield modeling scheme, we apply the perturbation method to obtain explicit analytic expressions for the derivatives of the displacement tensor for 2.5-D/2-D frequency-domain seismic full-waveform inversion in general viscoelastic anisotropic media. We then demonstrate the numerical calculations of all these derivatives in two common cases: (i) viscoelastic isotropic and (ii) viscoelastic tilted transversely isotropic (TTI) solids. Examples of the differing sensitivity patterns for the various derivatives are investigated and compared for four different homogeneous models involving 2-D and 2.5-D modeling.
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