Banana-Doughnut Traveltime Tomography

基本上，目前所有的旅行时层析反演法都忽略了衍射波前的恢复，也没有考虑到有限频率的地震波从未受干扰的球面地球射线中“感觉”到3D结构的能力。我们利用NSF Grant EAR-9725496的支持开发了3D香蕉-甜甜圈旅行时间敏感内核，它正确地解释了所有这些有限频率效应。我们打算在Grant EAR-0105387下继续这些研究，将该理论扩展到处理目前公式没有充分模拟的近掠射波和近临界波，并使用我们的3D灵敏度核来反演盖伊·马斯特斯教授及其在斯克里普斯海洋研究所的合作者在过去十年中收集的广泛的全球互相关行时数据集。我们还将开发和应用相速度的2D变化，表示所测量的体波走时对核-地幔边界或410公里或660公里不连续处地形的敏感性的2D核，用于使用地震阵列进行差分走时测量的3D灵敏度核，以及用于其他地震观测的2D和3D灵敏度核，包括体波和面波的到达角和幅度。最后，我们将在伪随机介质和真实的全地幔模型中进行一系列广泛的数值验证和综合反演研究，以确定对长周期地震走时产生显著绕射效应所需的地幔粗糙度。

Essentially all present-day traveltime tomographic inversions ignore diffractive wavefront healing, and fail to account for the ability of a finite-frequency seismic wave to "feel" 3D structure off of the unperturbed spherical-earth ray. We used the support of NSF Grant EAR-9725496 to develop 3D banana-doughnut traveltime sensitivity kernels, which correctly account for all such finite frequency effects. We intend to continue these investigations under Grant EAR-0105387, extending the theory to treat near-grazing and near-critical waves that are not adequately modeled by the present formulation, and using our 3D sensitivity kernels to invert the extensive global cross correlation traveltime dataset collected over the past decade by Professor Guy Masters and his collaborators at the Scripps Institution of Oceanography. We shall also develop and apply 2D variations in the phase velocity, 2D kernels that express the sensitivity of a measured body-wave traveltime to topography on the core-mantle boundary or the 410 km or 660 km discontinuities, 3D sensitivity kernels for differential traveltime measurements made using seismic arrays, and 2D and 3D sensitivity kernels for other seismic observables, including arrival angles and amplitudes of both body and surface waves. Finally, we shall conduct an extensive series of numerical validation and synthetic inversion studies, in both pseudo-random media and realistic whole-mantle models, in order to ascertain the degree of mantle roughness needed to give rise to significant diffraction effects upon long-period seismic traveltimes.