Accelerating full waveform inversion via source stacking and cross-correlations
Accelerating full waveform inversion via source stacking and cross-correlations
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DOI：
10.1093/gji/ggz437
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发表时间：
2019-10
影响因子：
2.8
通讯作者：
B. Romanowicz;Li-Wei Chen;S. French
中科院分区：
文献类型：
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作者：
B. Romanowicz;Li-Wei Chen;S. French
现在可以使用谱元法（SEM）在三维地球模型中计算精确的合成地震波场，这有助于提高全波形全球层析成像的分辨率。然而，计算成本仍然是一个挑战。这些成本可以通过实施震源叠加方法来降低，在该方法中，多个震源在仅一次地震SEM模拟中同时触发。这种方法的一个缺点是在深度处的分辨率的感知损失，特别是因为高振幅基模表面波支配求和波形，而没有如在常规波形层析成像中那样的开窗和加权的可能性。这可以通过重新定义成本函数和在每次反演迭代之前计算成对站之间的互相关波场来解决。虽然两个站之间的绿色函数没有像在环境噪声层析成像的情况下那样被重建，其中源更均匀地分布在地球仪周围，但是这不是缺点，因为相同的处理被应用于3-D合成和数据，并且源参数已知为良好的近似。通过这样做，我们可以分离出与基模表面波对应的大能量到达的时间窗口。这开启了设计加权方案以显示泛音和体波的贡献的可能性。它还可以平衡频繁采样路径与很少采样路径的贡献，如在更传统的断层扫描中。在这里，我们提出了这样一种方法的合成3分量长周期波形数据集（周期长于60秒），计算273个全球分布的事件在一个简单的玩具3-D径向各向异性上地幔模型，其中包含剪切波异常在不同尺度的概念测试的证明结果。我们比较了10 000 s长的堆叠时间序列的反演结果，从1-D模型开始，使用源堆叠波形和这些堆叠波形的站对互相关的成本函数的定义。我们计算梯度和海森使用正常模式微扰理论，这避免了使用伴随方法形成梯度时遇到的串扰问题。我们在添加和不添加真实噪音的情况下进行了反演，并表明使用一种或另一种成本函数可以同样好地恢复模型。所提出的方法在计算上非常有效。虽然应用到更现实的合成数据集超出了本文的范围，以及真实的数据，因为这需要额外的步骤来解决丢失数据等问题，我们说明了这种方法如何帮助通知一阶问题，如模型分辨率在噪声的存在下，以及不同的物理参数（各向异性，衰减，地壳结构等）之间的权衡。当使用基于单事件波场计算的常规全波形层析成像时，这在计算上是非常昂贵的。
Accurate synthetic seismic wavefields can now be computed in 3-D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because high-amplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography. This can be addressed by redefining the cost-function and computing the cross-correlation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3-D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility of designing a weighting scheme to bring out the contribution of overtones and body waves. It also makes it possible to balance the contributions of frequently sampled paths versus rarely sampled ones, as in more conventional tomography. Here we present the results of proof of concept testing of such an approach for a synthetic 3-component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3-D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked time-series, starting from a 1-D model, using source stacked waveforms and station-pair cross-correlations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of cross-talk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function. The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and trade-offs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on single-event wavefield computations.