Development of a Trans‐Dimensional Fault Slip Inversion for Geodetic Data
Development of a Trans‐Dimensional Fault Slip Inversion for Geodetic Data
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DOI：
10.1029/2020jb020991
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发表时间：
2021-04
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影响因子：
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通讯作者：
F. Tomita;T. Iinuma;R. Agata;T. Hori
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作者：
F. Tomita;T. Iinuma;R. Agata;T. Hori
大地断层滑动反演一般采用具有空间均匀平滑约束的最小二乘法进行。然而，这种传统的方法存在诸多问题：难以严格估计非负解，假设未知数服从高斯分布，不适合表示空间非均匀滑移分布，以及优化许多超参数的计算成本高。在这里，我们开发了一种使用可逆跳跃马尔可夫链蒙特卡罗（rj - MCMC）技术的跨维大地滑动反演方法来克服这些问题。由于子断层位置由Voronoi划分参数化，并且在我们的方法中进行了优化，因此我们可以在不需要空间均匀平滑约束的情况下估计滑动分布。此外，我们还引入了观测误差的标度因子。我们将该方法应用于2011年东北大地震的合成数据和实际大地测量数据，发现该方法成功地再现了包括空间非均匀滑动分布在内的目标滑动分布。该方法提供了带有未知数的后验概率分布，可以表达低概率大滑移等非高斯分布。估计的标度因子适当地调整了初始观测误差，并提供了合理的滑移分布。此外，我们发现棋盘分辨率测试对于考虑rj - MCMC方法观测数据的敏感性是有用的。结果表明，该方法能有效地解决传统反演方法的问题，并能灵活地表达复杂不确定性条件下的断层滑动分布。
Geodetic fault slip inversions have generally been performed by employing a least squares method with a spatially uniform smoothing constraint. However, this conventional method has various problems: difficulty in strictly estimating non‐negative solutions, assumption that unknowns follow the Gaussian distributions, unsuitability for expressing spatially non‐uniform slip distributions, and high calculation cost for optimizing many hyper‐parameters. Here, we have developed a trans‐dimensional geodetic slip inversion method using the reversible‐jump Markov chain Monte Carlo (rj‐MCMC) technique to overcome these problems. Because sub‐fault locations were parameterized by the Voronoi partition and were optimized in our approach, we can estimate a slip distribution without the need for spatially uniform smoothing constraints. Moreover, we introduced scaling factors for observational errors. We applied the method to the synthetic data and the actual geodetic observational data associated with the 2011 Tohoku‐oki earthquake and found that the method successfully reproduced the target slip distributions including a spatially non‐uniform slip distribution. The method provided posterior probability distributions with the unknowns, which can express a non‐Gaussian distribution such as large slip with low probability. The estimated scaling factors properly adjusted the initial observational errors and provided a reasonable slip distribution. Additionally, we found that checkerboard resolution tests were useful to consider sensitivity of the observational data for performing the rj‐MCMC method. It is concluded that the developed method is a powerful technique to solve the problems of the conventional inversion method and to flexibly express fault‐slip distributions considering the complicated uncertainties.