Waveforms of long-period body waves in a slightly aspherical earth model

Summary Considering the coupling of normal modes of different dispersion branches, we present a formulation for synthesizing waveforms of long-period body waves in a slightly aspherical Earth model. A general asymptotic result, which is valid when angular degrees of modes are much higher than the maximum harmonic degree of lateral heterogeneity, is derived for arbitrary source mechanisms and receiver components. If we restrict the coupling to the modes along a single dispersion branch, this result reduces to the pre-existing theory for surface waves. For body waves, we demonstrate numerically that cross-branch coupling is important to set up the correspondence between normal mode and ray theories. Actually, the coupling of the modes which interfere constructively in the spherically symmetric reference model represents the largest effects of heterogeneity on the waveform of a body wave packet. This would lead to a significant reduction in computation time. Numerical tests show that the formulation is able to bring out the ray character of body waves: only the structural perturbation in the neighbourhood along the geometrical ray affects the seismogram.

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