Estimating the model resolution matrix for large seismic tomography problems based on Lanczos bidiagonalization with partial reorthogonalization
Estimating the model resolution matrix for large seismic tomography problems based on Lanczos bidiagonalization with partial reorthogonalization
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DOI：
10.1111/j.1365-246x.2007.03418.x
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发表时间：
2007-07
影响因子：
2.8
通讯作者：
Haijiang Zhang;C. Thurber
中科院分区：
文献类型：
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作者：
Haijiang Zhang;C. Thurber
Larsen开发的PROPACK软件包能够基于Lanczos双对角化和部分再正交化有效准确地估计大型矩阵的奇异值和向量。我们将Pavtial Reorthogonalization Package（PROPACK）包到双差地震层析成像代码tomoDD中，并估计大型地震层析成像问题的模型分辨率矩阵。与以前的基于最小二乘QR（LSQR）的方法估计模型分辨率矩阵相比，基于PROPACK的方法计算全分辨率矩阵，从而完整地描述了模型的分辨率。通过对2001年埃特纳火山喷发数据的应用，发现用射线采样密度信息定性表征模式分辨率是合理的，单纯速度反演得到的模式分辨率与同时反演得到的模式分辨率有很好的线性关系，但往往高估了分辨率;并且使用微分时间的反转系统比使用绝对时间的系统具有更大的分辨源极区结构的能力。
SUMMARY The PROPACK package developed by Larsen is able to efficiently and accurately estimate singular values and vectors for large matrices based on the Lanczos bidiagonalization with partial reorthogonalization. We incorporate the Pavtial Reorthogonalization Package (PROPACK) package into the double-difference seismic tomography code tomoDD and estimate the model resolution matrix for large seismic tomography problems. Compared to previous Least Squares QR (LSQR)-based methods for estimating the model resolution matrix the PROPACK-based method calculates the full resolution matrix and thus gives a complete description of how well the model is resolved. Several observations are drawn from the application to data from the 2001 eruption of Mt Etna: for this example, it is reasonable to use ray-sampling density information to characterize the model resolution qualitatively; the model resolution resulting from just velocity inversion bears a close linear relationship to that from simultaneous inversion but always overestimates resolution; and the inversion system using differential times has a greater ability to resolve the source region structure than the system using absolute times.