Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method
Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method
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DOI：
10.1046/j.1365-246x.2003.01766.x
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发表时间：
2003-02
影响因子：
2.8
通讯作者：
Yaoguo Li;D. Oldenburg
中科院分区：
文献类型：
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作者：
Yaoguo Li;D. Oldenburg
本文将小波变换和对数屏障法应用于大尺度磁测数据的反演，以恢复磁化率的三维分布。使用快速小波变换，沿着阈值化小小波系数，以形成灵敏度矩阵的稀疏表示。结果矩阵的减小的尺寸允许解决否则难以处理的大问题。压缩矩阵用于通过在小波域中执行矩阵向量乘法来进行快速正演建模。CPU时间的减少与矩阵的压缩比成正比。这里使用的算法的第二个重要特征是使用优化的邻域点方法来强制执行正性约束。在这种方法中，积极性被纳入反演的一系列非线性优化近似截断牛顿步骤。算法的核心是求解线性方程组。共轭梯度技术已被用作基本求解器，以利用稀疏矩阵表示所提供的高效正演建模。总体而言，小波变换，内点优化和共轭梯度法的组合很容易使我们能够解决具有几十万个参数和数万个数据的磁逆问题。
SUMMARY In this paper wavelet transforms and a logarithmic barrier method are applied to the inversion of large-scale magnetic data to recover a 3-D distribution of magnetic susceptibility. The fast wavelet transform is used, along with thresholding the small wavelet coefficients, to form a sparse representation of the sensitivity matrix. The reduced size of the resultant matrix allows the solution of large problems that are otherwise intractable. The compressed matrix is used to carry out fast forward modelling by performing matrix-vector multiplications in the wavelet domain. The reduction in CPU time is directly proportional to the compression ratio of the matrix. A second important feature of the algorithm used here is the use of an interior-point method of optimization to enforce positivity constraints. In this approach, the positivity is incorporated into the inversion by a sequence of non-linear optimizations approximated by truncated Newton steps. At the heart of the algorithm, a linear system of equations is solved. The conjugate gradient technique has been used as the basic solver to take the advantage of the efficient forward modelling offered by the sparse matrix representation. Overall, the combination of wavelet transforms, interior point optimization and conjugate gradient solutions readily allows us to solve magnetic inverse problems that have a few hundred thousand parameters and tens of thousands of data.