Model Misfit Minimization
Model Misfit Minimization
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DOI：
10.1785/0120190079
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发表时间：
2019-10
影响因子：
3
通讯作者：
Yuanyuan Fang;Ying Zhou;Z. Yao
中科院分区：
文献类型：
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作者：
Yuanyuan Fang;Ying Zhou;Z. Yao
在地球物理应用中，不适定反问题的解Ax=b往往是通过分析数据残差‖Ax−b‖2和模型范数‖x‖2之间的权衡得到的。在本研究中，我们证明了传统的L曲线分析并不能得到最接近真实模型的解，因为最大曲率(或L曲线的拐角)取决于数据残差与模型范数之间的相对比例。基于使用训练数据集的经验风险函数最小化的贝叶斯方法可以被设计为找到统计上的最优解，但其成功与否取决于模型的真正实现。为了克服这一局限性，我们使用ATA矩阵的特征向量以及根据观测值和特征向量投影数据之间的相关性计算的谱系数来构建训练模型。这种方法考虑了数据噪声水平，但不需要将其作为先验知识。以全局层析成像为例，我们表明解最接近真实模型。
In geophysical applications, solutions to ill‐posed inverse problems Ax=b are often obtained by analyzing the trade‐off between data residue ‖Ax−b‖2 and model norm ‖x‖2. In this study, we show that the traditional L‐curve analysis does not lead to solutions closest to the true models because the maximum curvature (or the corner of the L‐curve) depends on the relative scaling between data residue and model norm. A Bayes approach based on empirical risk function minimization using training datasets may be designed to find a statistically optimal solution, but its success depends on the true realization of the model. To overcome this limitation, we construct training models using eigenvectors of matrix ATA as well as spectral coefficients calculated from the correlation between observations and eigenvector projected data. This approach accounts for data noise level but does not require it as a priori knowledge. Using global tomography as an example, we show that the solutions are closest to true models.