论文标题
粘弹性TTI介质中2.5-D频域的地震全波反转的位移张量的数值Fréchet衍生物
Numerical Fréchet derivatives of the displacement tensor for 2.5-D frequency-domain seismic full-waveform inversion in viscoelastic TTI media
论文作者
论文摘要
相对于地下的独立模型参数(也称为fréchet衍生物(或灵敏度核)),位移张量的衍生物是通过本地搜索优化算法的地震全波倒置的关键成分。由于给定的调查几何形状的地下模型参数的扰动,它们提供了对地震图的预期变化的定量度量。由于2.5-D波场建模涉及具有3D(球形)波性质的2-D地质模型中的真实点源,因此与常用的2-D Wave模拟相比,它得出的合成数据更接近实际实用场数据,该数据使用不现实的线源,其中波源在该线路上散布了cylindrindrindrindrindrindrindrindrindrindrindrindrindrin。基于我们最近开发的一般2.5-D波场建模方案,我们应用了扰动方法,以获得一般粘弹性各向异性介质中2.5-D/2-D频域的地震全波反转的位移张量的显式分析表达式。然后,我们在两种常见情况下证明了所有这些衍生物的数值计算:(i)粘弹性各向同性和(ii)粘弹性倾斜的横向横向各向同性(TTI)固体。研究了涉及2-D和2.5-D建模的四个不同均匀模型的各种衍生物的不同灵敏度模式的示例。
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.