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首页> 外文期刊>Seismological research letters >Parsimonious Seismic Tomography with Poisson Voronoi Projections: Methodology and Validation
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Parsimonious Seismic Tomography with Poisson Voronoi Projections: Methodology and Validation

机译：与泊松Voronoi预测的帕加隆地震震作：方法论和验证

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摘要

III-posed seismic inverse problems are often solved using Tikhonov-type regularization, that is, incorporation of damping and smoothing to obtain stable results. This typically results in overly smooth models, poor amplitude resolution, and a difficult choice between plausible models. Recognizing that the average of parameters can be better constrained than individual parameters, we propose a seismic tomography method that stabilizes the inverse problem by projecting the original high-dimension model space onto random low-dimension subspaces and then infers the high-dimensional solution from combinations of such subspaces. The subspaces are formed by functions constant in Poisson Voronoi cells, which can be viewed as the mean of parameters near a certain location. The low-dimensional problems are better constrained, and image reconstruction of the subspaces does not require explicit regularization. Moreover, the low-dimension subspaces can be recovered by subsets of the whole dataset, which increases efficiency and offers opportunities to mitigate uneven sampling of the model space. The final (high-dimension) model is then obtained from the low-dimension images in different subspaces either by solving another normal equation or simply by averaging the low-dimension images. Importantly, model uncertainty can be obtained directly from images in different subspaces. Synthetic tests show that our method outperforms conventional methods both in terms of geometry and amplitude recovery. The application to southern California plate boundary region also validates the robustness of our method by imaging geologically consistent features as well as strong along-strike variations of San Jacinto fault that are not clearly seen using conventional methods.
机译：III造成的地震逆问题通常使用Tikhonov型正则化进行解决，即掺入阻尼和平滑以获得稳定的结果。这通常会导致过度平滑的模型，幅度分辨率差，并且在合理的模型之间难度选择。认识到参数的平均值可以比单个参数更好地限制，我们提出了一种地震断层摄影方法，通过将原始的高维模型空间投射到随机的低维子空间，然后从组合中缩小高维解决方案来稳定逆问题这些子空间。子空间由泊松Voronoi小区中的常数常量形成，其可以被视为在某个位置附近的参数的平均值。低维问题是更好的限制，并且子空间的图像重建不需要显式正则化。此外，低维子空间可以通过整个数据集的子集恢复，这增加了效率并提供了减轻模型空间的不均匀采样的机会。然后通过求解另一个正常方程或简单地通过平均低维图像来从不同子空间中的低维图像获得最终（高维）模型。重要的是，可以直接从不同子空间中的图像获得模型不确定性。合成试验表明，我们的方法在几何和幅度恢复方面优于传统方法。南加州板材边界区域的应用还通过成像地质上一致的特征来验证我们的方法的鲁棒性以及使用传统方法清楚地看到的SAN Jacinto故障的强大沿着SAN Jacinto故障的变化。

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