The cross-convolution method for interpreting SKS splitting observations, with application to one and two-layer anisotropic earth models
The cross-convolution method for interpreting SKS splitting observations, with application to one and two-layer anisotropic earth models
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DOI：
10.1046/j.1365-246x.2003.01937.x
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发表时间：
2003-08
影响因子：
2.8
通讯作者：
W. Menke;V. Levin
中科院分区：
文献类型：
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作者：
W. Menke;V. Levin
我们提出了一种使用分裂剪切波（例如 SKS）观测来确定各向异性地球模型的新方法。该方法包括首先构建两个时间序列 x(t) 和 y(t)，其中包含有关观测到的地震图和假设的地球模型的信息，然后改变地球模型以尽量减少失配。 e(t) = x(t) - y(t)。时间序列由规则 x(t) = h pre (m, t)* V o b s (t) 和 y(t) = v p re (m, t)*H o b s (t) 定义，其中 V o b s (t) 和 H o b s (t) 分别是观测到的径向水平和切向水平分量地震图， v pre (m, t) 和h p r e (m, t) 分别是由某些地球模型预测的径向水平和切向水平脉冲响应，m 和 * 表示卷积。最拟合的地球模型是相对于 m 最小化 ∥e(t)∥ 2 的模型，其中 ∥.∥ 是幅度归一化的 L 2 范数。这种失配的定义对源小波不敏感，因此从问题中消除了未知量。我们表明，该方法产生的单层分裂参数估计与通过传统方法实现的估计非常相似，但与传统方法不同的是，它可以应用于更复杂的模型（例如多层各向异性），而无需求助于近似“表观分裂”参数。我们将该方法应用于为双层各向异性地球模型生成的合成 SKS 脉冲，并表明它可以成功恢复有关两层的信息。然后，我们将该方法应用于来自加利福尼亚州 Pinon Flat (PFO) 圣安德烈亚斯断层的 SKS 和 PKS 数据。 Ozalaybey 和 Savage、Liu 等人之前已经研究过该站。 Polet 和 Kanamori，他们提供了基于表观分裂参数方位角变化建模的两层解决方案。我们的结果与他们的结果大致一致，但提供了有关两层解决方案的统计显着性的附加信息。通过这种测量，尽管所有已发布的两层解决方案都比最适合的一层解决方案更好地拟合波形数据，但没有一个已发布的两层解决方案明显优于单层解决方案。这一结果与 Ozalaybey 和 Savage 以及 Liu 等人的解释一致，他们对他们的两层解决方案提供了类似的评估。我们的一层和两层解决方案在减少整体失配方面都表现不佳，这一事实强烈表明，除两层各向异性之外的某些过程正在影响 PFO 处的 SKS 和 PKS 波形。
We present a new method for determining anisotropic earth models using observations of split shear waves (such as SKS). The method consists of first constructing two time-series, x(t) and y(t), that contain information concerning both the observed seismograms and a hypothetical earth model, and then varying the earth model so as to minimize the misfit. e(t) = x(t) - y(t). The time-series are defined by the rules, x(t) = h p r e (m, t)* V o b s (t) and y(t) = v p r e (m, t)*H o b s (t), where V o b s (t) and H o b s (t) are the observed radial-horizontal and tangential-horizontal component seismograms, respectively, v p r e (m, t) and h p r e (m, t) are the radial-horizontal and tangential-horizontal impulse responses, respectively, predicted by some earth model, m, and * denotes convolution. The best-fitting earth model is the one that minimizes ∥e(t)∥ 2 with respect to m, where ∥.∥ is an amplitude-normalized L 2 norm. This definition of misfit is insensitive to the source wavelet, and thus eliminates that unknown quantity from the problem. We show that this method yields estimates of one-layer splitting parameters that are very similar to those achieved through traditional means, but that unlike those traditional methods it can be applied to more complicated models (e.g. multilayer anisotropy) without recourse to approximate 'apparent splitting' parameters. We apply the method to synthetic SKS pulses generated for two-layer anisotropic earth models, and show that it can successfully recover information concerning both layers. We then apply the method to SKS and PKS data from Pinon Flat, California (PFO) on the San Andreas fault. This station has been studied previously by Ozalaybey & Savage, Liu et al. and Polet & Kanamori, who provide two-layer solutions based on modelling of the azimuthal variation of apparent splitting parameters. Our results are broadly consistent with theirs, but provide additional information concerning the statistical significance of the two-layer solution. By this measure, none of the published two-layer solutions is significantly better than a one-layer solution, although all fit the waveform data better than the best-fitting one-layer solution. This result is consistent with the interpretations of Ozalaybey & Savage and Liu et al., who provide similar assessments of their two-layer solutions. The fact that neither our one-layer nor two-layer solutions does very well at reducing the overall misfit strongly suggests that some process other than two-layer anisotropy is affecting SKS and PKS waveforms at PFO.