A waveform inversion including tilt: method and simple tests
A waveform inversion including tilt: method and simple tests
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DOI：
10.1111/j.1365-246x.2010.04892.x
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发表时间：
2011-02-01
影响因子：
2.8
通讯作者：
Ohminato, Takao
中科院分区：
文献类型：
--
作者：
Maeda, Yuta;Takeo, Minoru;Ohminato, Takao
P>提出了一种新的波形反演方法来处理受倾斜信号严重污染的水平地震图，无需对倾斜运动进行假设。我们不是将水平地震图分解为平移和倾斜贡献，而是通过计算格林函数来实现此任务，该函数不仅包括地震仪对合成平移运动的响应，还包括对合成倾斜运动的响应。有限差分法 (FDM) 使用交错网格和完美匹配层 (PML) 边界条件来计算格林函数。该方法能够计算波长比计算网格尺寸大 10 倍的波场。尽管来自数值边界的反射波可以忽略不计，但与解析解的比较表明误差高达百分之几个。出现这种情况的原因要么是因为与网格尺寸相比，源到接收器的距离很小，要么是实际自由表面和站位置之间存在半单元差异的结果。此外，在自由表面不平坦的情况下，由于FDM中的地形近似阶梯状，计算倾斜运动时会出现高达60%的误差。通过对沿倾斜分量方向对齐、以目标网格单元为中心的五个相邻单元的倾斜进行平均，可以将后一个误差减少到 10%。通过应用该算法，尽管水平地震图受到倾斜信号的严重污染，但波形反演可以成功地重建日本中部浅间火山超长周期（10-30 s）脉冲的垂直和水平地震图。
P>A new waveform inversion method is proposed to deal with horizontal seismograms strongly contaminated by tilt signals, without assumptions regarding tilt motions. Instead of decomposing the horizontal seismograms into translational and tilt contributions, we realize this task by calculating the Green's functions consisting of not only the seismometer's response to the synthetic translational motions but also to the synthetic tilt motions. A finite difference method (FDM), which uses a staggered grid and a perfect matched layer (PML) boundary condition, is used to calculate the Green's functions. This method enables calculation of wavefields which have wavelengths of up to 10 times larger than the dimension of the computational grid. Although reflected waves from the numerical boundaries are negligible, comparisons with analytical solutions evidence errors of up to several per cent. These occur either because the source-to-receiver distance is small once compared to the grid size, or as a consequence of the half-cell difference between the actual free surface and the station location. In addition, in the case that the free surface is not flat, an error of up to 60 per cent occurs in calculating the tilt motion, due to the stair-like approximation of topography in the FDM. This latter error can be reduced to 10 per cent by averaging the tilts at five adjacent cells aligned in the direction of the tilt component, centred on the target grid cell. By applying this algorithm, a waveform inversion can be used to successfully reconstruct the vertical and horizontal seismograms of very-long-period (10-30 s) pulses at Asama Volcano, central Japan, despite the fact that the horizontal seismograms are strongly contaminated by tilt signals.