地震波形伴随层析成像: 1.SEM-FDM混合正演方法

Adjoint seismic waveform tomography:1.A SEM-FDM hybrid forward modeling method

地震波形伴随成像是通过正演波场和伴随波场构建误差泛函关于模型的Fréchet导数. 在波形伴随成像中, 需要数值求解地震波运动方程得到正演波场和伴随波场. 目前, 谱元法(Spectral-element method, SEM)作为地震波场正演模拟方法在地震波形伴随层析成像中得到了广泛应用. SEM具有网格的灵活性, 计算精度高, 且能自然满足自由地表边界条件. 然而, 在复杂模型中SEM能否得到高精度地震波场, 取决于能否构建高质量网格模型. 当模型复杂时较难构建高质量网格模型. 为了实现复杂模型中地震波场高效数值模拟, 本文发展了谱元法和有限差分法(Finite-difference method, FDM)混合方法, 即SEM-FDM混合方法, 其核心思想是避免使用复杂网格模型. SEM-FDM混合方法在近地表处使用SEM模拟地震波场, 利用傅里叶级数近似起伏地表, 根据傅里叶级数和控制参数自动快速生成网格. 在远离起伏地表的区域, 利用FDM模拟地震波场, 采用规则网格刻画模型, 借助非均匀有限差分格式模拟非均匀介质中地震波传播. SEM-FDM混合方法通过设置数据传输层将SEM和FDM耦合. 本文进行了多组数值算例, 用于验证SEM-FDM混合方法模拟复杂模型中地震波传播的高效性. 数值算例说明了复杂模型中使用SEM-FDM混合方法可获得高精度的地震波模拟结果. 本文研究为复杂模型中地震波形伴随层析成像提供了高效正演模拟工具.

In adjoint seismic waveform tomography, the Fréchet derivative of the misfit function is constructed by the forward and adjoint wavefields. Numerical solutions of the seismic wave equation of motion are essential in adjoint seismic waveform tomography. The Spectral-element method (SEM) is widely employed for forward modeling seismic wavefields in adjoint seismic waveform tomography due to its grid flexibility, high numerical accuracy, and natural satisfaction of the free-surface boundary condition. Indeed, high-accuracy seismic wavefields in complex models depend on high-quality grid models for the SEM. However, generating high-quality discrete models can be challenging when dealing with complex models. Here, we present a hybrid method, called the SEM-FDM, to efficiently simulate seismic wavefields in complex models. This hybrid method combines the Spectral-element method (SEM) and Finite-difference method (FDM) to avoid constructing complex grid models. The SEM-FDM hybrid method utilizes the SEM to simulate the seismic wave field near the irregular free surface. For the area near the irregular free surface, the Fourier series is used to approximate the surface. The grid model is automatically generated according to the Fourier series and parameters. The FDM is utilized to simulate seismic wavefields for the area away from the irregular free surface. A regular grid is employed to represent the model, and the propagation of seismic waves is simulated using the finite difference scheme to heterogeneous cases. In the SEM-FDM hybrid method, the SEM is coupled with the FDM by establishing a data exchange layer. We present several numerical examples to demonstrate the computational efficiency, which shows that the SEM-FDM is an efficient forward modeling tool for adjoint seismic waveform tomography in complex models.