Abstract
SUMMARY In the waveform inversion for global 3-D heterogeneous mantle structure, it is critical to accurately compute the perturbation of synthetic seismograms caused by the crustal heterogeneities. In actual applications, to reduce the required CPU time, a weak form equation of motion in terms of global trial functions is widely used. For those trial functions, the principal difficulty is how to compute the effect of the perturbation in the location of boundaries (such as Moho and the surface). In previous studies, the formulation has been based on the first-order perturbation theory of the free oscillation. However, this method holds only for weakly heterogeneous media and for lower frequencies. In this study, we derive the exact weak form elastic equation of motion for finite boundary perturbations. Our method can be applied to arbitrary strongly heterogeneous media and to arbitrary frequencies, and should facilitates accurate crustal correction.
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