Banana-Doughnut Traveltime Tomography

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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.