一种用于全波形反演的扩展高斯-牛顿方法
An extended Gauss-Newton method for full waveform inversion
AI总结：
本文提出扩展高斯-牛顿方法，将标准GN系统重构为矩阵方程并放宽对角约束，以低计算代价增强全波形反演对初始模型和低频缺失的鲁棒性。
摘要：
全波形反演（FWI）是一个大规模非线性病态问题，对于该问题，计算代价高昂的牛顿型方法可能陷入不理想的局部极小值，尤其是当初始模型缺少低波数分量且记录数据缺少低频内容时。本文提出对高斯-牛顿（GN）方法的一种改进以解决这些问题。针对多震源多接收器FWI的标准GN系统被重新表述为等价的矩阵方程形式，其解变为一个对角矩阵，而不是标准系统中的向量。通过放宽对角性约束，搜索方向从向量变换为矩阵，有效地在地下偏移轴上增加了一个自由度。放宽后的系统可以仅通过求逆两个小矩阵来显式求解，这两个小矩阵沿震源维和接收器维对数据残差矩阵进行解模糊，从而简化了Hessian矩阵的求逆。当用于求解扩展震源FWI目标函数时，扩展GN（EGN）方法融合了模型扩展和震源扩展两者的优点。EGN方法有效地结合了简化FWI方法的计算效率与扩展公式的鲁棒性特征，并为应对FWI的挑战提供了一种有前景的解决方案。它弥合了这些扩展公式与简化FWI方法之间的差距，在保持计算效率的同时增强了反演鲁棒性。通过数值实验证明了EGN算法在波形反演中的鲁棒性和稳定性。
英文摘要：
Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lacks low-frequency content. A modification to the Gauss-Newton (GN) method is proposed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended source FWI objective function, the Extended GN (EGN) method integrates the benefits of both model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
