各向异性介质弹性波多参数全波形反演

各向异性介质弹性波方程全波形反演过程中多参数之间的相互耦合,使得弱参数在反演过程中难得到理想的结果.本文以VTI介质为例,在各参数辐射模式分析的基础上,基于改进的散射积分算法实现目标函数梯度的直接求取,进一步构建高斯牛顿方向,实现Hessian矩阵的有效利用,以考虑Hessian矩阵非主对角线元素包含的各参数间的耦合效应,在不使用任何反演策略的情况下实现高精度的VTI介质弹性波方程多参数同步反演.同时,该方法在计算过程中无需存储庞大的核函数矩阵,且无需传统截断牛顿法中额外的正演计算,因此内存占用小,计算效率高.本文数值试验验证了该方法的有效性,为各向异性多参数全波形反演提供了一种新的解决方案.

Elastic multi-parameter full-waveform inversion for anisotropic media

The trade-off effects between parameters in anisotropic media, which have been studied in radiation patterns analysis, makes it difficult to get acceptable weak parameter results during full-waveform inversion (FWI) based on an elastic wave equation. In this paper, to reduce the trade-off effects between parameters, we apply the truncated Gauss-Newton method to anisotropic FWI, taking VTI media for example. All parameters have been revealed simultaneously without using any strategy. Based on the improved scattering-integral (SI) algorithm, the steepest-descent direction can be directly calculated by vector operations, without storing the huge Fréchet kernels in memory beforehand. The Gauss-Newton descent direction iteration needs just two vector operations without any extra forward computations. Numerical experiments in the final part prove the effectiveness of the proposed method which opens a new approach on simultaneously constructing anisotropic parameters in FWI.