Introduction of uncertainty of Green's function into waveform inversion for seismic source processes
Introduction of uncertainty of Green's function into waveform inversion for seismic source processes
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DOI：
10.1111/j.1365-246x.2011.05043.x
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发表时间：
2011-08
影响因子：
2.8
通讯作者：
Y. Yagi;Y. Fukahata
中科院分区：
文献类型：
--
作者：
Y. Yagi;Y. Fukahata
原则上，我们永远不可能知道真正的绿色函数，这是地震波形反演中的主要误差源。到目前为止，许多研究都致力于获得尽可能精确的绿色函数。在这项研究中，我们提出了一个新的策略来科普这个问题。也就是说，我们在波形反演分析中引入了绿色函数的不确定性。由于误差的传播规律，绿色函数的不确定性导致具有显著非对角分量的数据协方差矩阵，这自然降低了后期观测数据的权重。由于数据协方差矩阵依赖于表示滑移分布的模型参数，因此要求解的反问题变得非线性。将该方法应用于2006年印尼爪哇海啸地震的P波资料，在不考虑非负滑动约束的情况下，得到了面积的斜率分布和矩率函数。该解与模型参数的初始值无关。如果我们忽略传统公式中由于绿色函数而引起的建模误差，则总滑移分布粗糙得多，具有显著的相反滑移分量，而力矩-速率函数则平滑得多。如果我们使用更强的平滑约束，可以得到更合理的滑移分布，但这样的力矩率函数变得更加平滑。通过比较观测波形和合成波形，我们发现只有新公式才能很好地再现高频分量。建模误差在波形反演分析中是非常重要的，尽管它们通常被忽略。
SUMMARY In principle, we can never know the true Green’s function, which is a major error source in seismic waveform inversion. So far,many studies have devoted their efforts to obtain a Green’s function as precise as possible. In this study, we propose a new strategy to cope with this problem. That is to say, we introduce uncertainty of Green’s function into waveform inversion analyses. Due to the propagation law of errors, the uncertainty of Green’s function results in a data covariance matrix with significant off-diagonal components, which naturally reduce the weight of observed data in later phases. Because the data covariance matrix depends on the model parameters that express slip distribution, the inverse problem to be solved becomes nonlinear. Applying the developed inverse method to the teleseismicP-wave data of the 2006 Java, Indonesia,tsunamiearthquake,weobtainedareasonableslip-ratedistributionandmoment-rate function without the non-negative slip constraint. The solution was independent of the initial values of the model parameters. If we neglect the modelling errors due to Green’s function as in the conventional formulation, the total slip distribution is much rougher with significant opposite slip components, whereas the moment-rate function is much smoother. If we use a stronger smoothing constraint, more plausible slip distribution can be obtained, but then the moment-rate function becomes even smoother. By comparing the observed waveforms with thesyntheticwaveforms,wefoundthathigh-frequencycomponentswerewellreproducedonly by the new formulation. The modelling errors are essentially important in waveform inversion analyses, although they have been commonly neglected.