CMG Research: Experiments Aimed at Improving Global Seismic Tomography

这项拟议的研究的目的是将应用数学领域的两种方法应用到地震层析成像；每种方法都集中在改善空间数据成像的目标上。这项工作是地球物理学家埃德·加内罗和两位应用数学家安妮·盖尔布和罗西·雷诺共同努力的结果。这一努力将在应用数学和地震学领域之间以跨学科的方法培训两名研究生。尽管在过去的25年里，地幔的3D图像得到了更清晰的关注，但仍然存在许多挑战，最明显的原因是数据覆盖不完整。地震数据的反演需要平滑和衰减，从而有效地模糊结果图像。研究人员的动机是更好地解决地震速度不均匀的梯度和形状，因为它们与地球内部的温度和/或成分变化有关。该项目将采用以下两种方法。(1)数据后处理和反演方法：将使用反褶积方法对差分走时计算进行智能预处理。通过全变分类型的惩罚项的正则化也可以改善倒置。(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，在其他应用中，如磁共振成像，在不影响更精细的图像特征的情况下，甚至在跳跃附近也能有效地去除Gibbs振荡。这些任务可以概括为以下几点。(1)反演前处理：根据地球内部的结构模型对旅行时间序列的盲反褶积和基于知识的反褶积进行评估。(2)反演实验：确定全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：采用Gegenbauer重建方法去除伪影，实现图像锐化。(4)用数据评估解决方案图像：将对数据覆盖率最高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.