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Tarje Nissen-Meyer, California Institute of Technology (United States)
Alexandre Fournier, Universite Joseph-Fourier (France)
F. A. Dahlen, Princeton University (United States)
Karin Sigloch, Ludwig-Maximilians-Universitaet (Germany)
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We present a computationally light method to incorporate arbitrary seismic observables into linearized tomographic inversion with a specific focus on diffracted waves in the lowermost mantle. The crux of this idea is a spectral-element method to provide all necessary wavefields that underlie Fréchet sensitivity kernels for any desired time-frequency window of a seismogram. Assuming spherical symmetry for the reference background model, these full 3-D wavefields are computed in a 2-D spherical semi-disk by exploiting radiation-pattern symmetries for moment-tensor sources. As such, one can readily construct databases of wavefields up to 1 Hz on conventional PC clusters which is still out of any near reach for alternative 3-D numerical methods or normal-mode summation.
We show several examples of such full-wave based sensitivity kernels at the global scale including their temporal evolution, i.e. waveform sensitivity of an entire seismogram, thereby obtaining a direct view into the interconnection between surface displacements and earth structure. Given a potential target region of interest such as the lowermost mantle, one can immediately extract the associated fractions of a seismogram to which 3-D structure at that location will contribute, thus exploring "optimal" data to incorporate into the inversion without prior knowledge of phases or ray-path coverage. Adhering to the full-wave flexibility, we illustrate several important parameter dependencies of sensitivity kernels such as moment-tensor source type and depth, source-time function, frequency spectrum, epicentral distance, receiver channels, azimuth, and various choices for time windows to extract "static" kernels (e.g. "banana-doughnut" traveltime kernels of direct arrivals). We justify the fundamental limitation to linearized inversions due to spherically symmetric reference models by showing examples that suggest this assumption to be sufficient for most practical cases at the global scale and stressing its immediate- to medium-term value in inverting previously neglected (e.g. non-geometrical) fractions of a seismogram. Finally, we outline the concept of measuring global, broadband traveltime and amplitude data to pave the way for tomographic applications specifically in the context of core-diffracted waves at multiple-frequency bands.
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