CMG Research: Experiments Aimed at Improving Global Seismic Tomography

0222327 Garnero本研究的目的是采用两种方法，从应用数学领域的地震层析成像，每一个都集中在改善成像的空间数据的目标。 这项工作是一个合作的努力之间的数学家艾德加纳罗和两个应用数学家，安妮盖尔布和罗西雷诺。 这项工作将培养两名研究生在应用数学和地震学领域之间的跨学科方法。虽然在过去的25年里，地球地幔的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，这有效地模糊了结果图像。 研究人员的动机是更好地解决地震速度不均匀性的梯度和形状，因为它们涉及到地球内部的温度和/或成分变化。该项目将采用以下两种方法。 (1)数据再处理和反演方法：反褶积方法将用于智能预处理差分走时计算。反演也可以通过总变分类型惩罚项的正则化来改进。(2)图像重建方法：将Gegenbauer重建方法应用于高分辨率后处理重建，该方法已被证明可有效地去除Gibbs振荡，而不会损害更精细的图像特征，即使在其他应用中（例如磁共振成像）也是如此。这些任务可归纳如下。 (1)反演前处理：旅行时间序列清理评估盲和知识为基础的反卷积，近似从地球内部的结构模型。 (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)反转后处理：通过Gegenbauer重建方法去除伪影来锐化图像。(4)使用数据评估解决方案图像：将分析和建模来自数据覆盖率最高的地理区域的数据，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.