基于非精确单调与非单调线搜索的全波形反演

A Full Waveform Inversion Based on Inexact Monotone and Non-Monotone Line Search

摘要: 在数学物理反问题中，全波形反演是一种高分辨率地震成像方法。然而，全波形反演目标函数的高度非线性和不适定性使其易陷入局部极值难题。针对全波形反演多局部极值问题，对非精确单调与非单调线搜索全局化策略进行对比研究，并基于线搜索全局化策略和牛顿算法建立全波形反演算法。针对牛顿法中需要求解大规模线性方程组难题，基于Lanczos对角化方法构建共轭梯度法近似求解牛顿方程，建立免矩阵计算的截断牛顿反演算法。为了进一步提高截断牛顿反演方法的计算效率，基于伴随法导出了一种快速计算矩阵与向量乘积的高效方法。基于Sigsbee标准测试模型进行数值模拟，数值结果表明，在不增加计算量的情况下，基于非单调线搜索的截断牛顿反演算法在收敛速度和计算效率方面优于基于单调线搜索的截断牛顿反演算法。

Abstract: In the mathematical physics inverse problem, full waveform inversion is a seismic imaging method with high resolution. However, its highly nonlinearity and ill-posedness of the misfit functional make it easy to fall into the local minima. For the multiple local minima problem of the full-waveform inversion, a comprehensive comparison is made based on the globalization strategy of approximate monotone and non-monotone line search, and a full-waveform inversion algorithm is established based on the non-monotone line search globalization strategy and Newton method. To efficiently solve the large-scale linear equations of Newton method, a conjugate gradient method is constructed based on the Lanczos diagonalization method to approximately solve Newton equation, and a matrixfree truncated Newton inversion algorithm is established. In order to further improve the computational efficiency of the truncated Newton inversion method, an efficient method to efficiently calculate matrix vector products is derived based on the adjoint method. The numerical simulation is carried out based on Sigsbee model. The numerical results show that, without increasing compu- tational loads, the performance of the truncated Newton inversion method based on the non-monotone line search is better than that of the method based on the monotone line search in terms of convergent speed and computational efficiency.