Solid angles and the impact of receiver-array geometry on microseismic moment-tensor inversion
Solid angles and the impact of receiver-array geometry on microseismic moment-tensor inversion
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DOI：
10.1190/geo2011-0077.1
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发表时间：
2011-11
期刊：
影响因子：
3.3
通讯作者：
D. Eaton;Farshid Forouhideh
中科院分区：
文献类型：
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作者：
D. Eaton;Farshid Forouhideh
地震矩张量提供了一个简洁的数学表示的点源，可以用来表征微震震源机制。修正传播效应后，矩张量的六个独立分量可以通过最小二乘反演基于从源的不同方向观察到的P和/或S波形（或频谱）振幅来找到。使用合成波形数据，我们研究了影响这种反演的可靠性的几何因素。我们证明了接收器阵列所对的立体角，从源位置来看，在反演的稳定性中起着根本性的作用。特别地，广义逆的条件数与立体角近似成反比，这意味着对于零立体角（如单个垂直钻孔的情况），反演是病态的。随机噪声的存在对反演结果也有很大的影响，结果表明，随机噪声的存在对反演结果有较大的影响。
Seismic moment tensors provide a concise mathematical representation of point sources that can be used to characterize microseismic focal mechanisms. After correction for propagation effects, the six independent components of a moment tensor can be found by least-squares inversion based on P- and/or S-waveform (or spectral) amplitudes observed at different directions from the source. Using synthetic waveform data, we investigated geometrical factors that affect the reliability of such inversions. We demonstrated that the solid angle subtended by the receiver array, as viewed from the source location, plays a fundamental role in the stability of the inversion. In particular, the condition number of the generalized inverse scales approximately inversely with the solid angle, implying that for a solid angle of zero (as is the case for a single vertical borehole) the inversion is ill-conditioned. The presence of random noise alsohas a significant effect on the inversion results; our results showed that the si...