CMG Research: Experiments Aimed at Improving Global Seismic Tomography

[0222327]本研究的目的是将应用数学领域的两种方法应用于地震层析成像；每一个都集中在改进空间数据成像的目标上。这项工作是地球物理学家Ed Garnero和两位应用数学家Anne Gelb和Rosie Renaut的合作成果。这项工作将在应用数学和地震学领域之间培养两名跨学科的研究生。虽然在过去的25年里，地幔的3D图像已经变得更加清晰，但仍然存在许多挑战，最明显的是由于数据覆盖不完整。地震数据的反演需要平滑和阻尼，这有效地模糊了得到的图像。研究人员有动力更好地解决地震速度非均质性的梯度和形状，因为它们与地球内部的温度和/或成分变化有关。本项目将采用以下两种方法。(1)数据再处理与反演方法：利用反褶积方法对差分走时计算进行智能预处理。反演也可以通过一个总变异类型惩罚项的正则化来改进。(2)图像重建方法：采用Gegenbauer重建方法进行高分辨率的后处理重建，在磁共振成像等其他应用中，该方法已被证明可以有效地去除吉布斯振荡，而不会影响更精细的图像特征，即使在接近跳变不连续的地方。这些任务可以总结如下。(1)反演前处理：根据地球内部结构模型近似，评估旅行时间序列的盲反褶积和基于知识的反褶积清理。(2)反演实验：确定总变差正则化模型的有效性，特别是结合对反演后处理的影响。(3)反演后处理：利用Gegenbauer重构法去除伪影，锐化图像。(4)用数据评估解决方案图像：将对数据覆盖最好的地理区域的数据进行分析和建模，以测试解决方案结构。

0222327GarneroThe purpose of this proposed research is to employ two methods from the field of applied mathematics to seismic tomography; each is focused on the goal of improved imaging of spatial data. This work is a collaborative effort between geophysicist Ed Garnero and two applied mathematicians, Anne Gelb and Rosie Renaut. This effort will train two graduate students in a cross-disciplinary approach between the fields of applied math and seismology. While 3D images of Earth's mantle have come in clearer focus over the last 25 years, many challenges remain, most notably because of incomplete data coverage. Inversions of seismic data require smoothing and damping that effectively blurs resulting images. The investigators are motivated to better resolve the gradients and shapes of seismic velocity heterogeneity since they relate to temperature and/or compositional changes in Earth's interior. The project will employ the following two methods. (1) Data reprocessing and inversion methods: deconvolution methods will be used to intelligently preprocess differential travel time computations. Inversion may also be improved by regularization through a total variation type penalty term. (2) Image reconstruction methods: apply the Gegenbauer reconstruction method for high resolution post-processing reconstruction, which has proven effective for removing Gibbs oscillations without compromising the finer image features even near jump discontinuities in other applications, such as magnetic resonance imaging. The tasks can be summarized as follows. (1) Pre-inversion processing: travel time series cleanup evaluated for blind and knowledge-based deconvolution, approximated from structural models of the Earth's interior. (2) Inversion experiments: determine effectiveness of a total variation regularization model, particularly in conjunction with the impact on post-inversion processing. (3) Post-inversion processing: sharpen images through removal of artifacts with the Gegenbauer reconstruction method. (4) Assess solution images with data: data from geographical regions with best data coverage will be analyzed and modeled to test solution structures.