Comparison of global waveform inversions with and without considering cross-branch modal coupling

SUMMARY In this study we present a new approach to inverting long-period seismic waveforms. The effect of lateral heterogeneity is partitioned into two. The first part represents the effect of horizontally averaged structure along the great circle between the source and receiver, and is allowed to remain in non-linear form in the formulation. The second part incorporates any further correction due to cross-branch modal coupling, which has been neglected in the more conventional path average approximation (PAVA). This term is linearized and then treated asymptotically so that the seismogram depends only upon the structure within the great-circle section determined by the source and receiver (Li & Tanimoto 1993a). We refer to this new method as the non-linear asymptotic coupling theory (NACT). The sensitivity kernels predicted by the PAVA and NACT are compared. While the sensitivity kernels are similar for surface waves and shallow-turning body waves, they are very different for body waves that sample the deep mantle. By examining the inversion algorithms for the PAVA and NACT, we demonstrate that the computation time required by the NACT tends to be of the same order of magnitude as that required by the PAVA, as the number of model parameters increases. Based upon a realistically large data set (5041 body-wave seismograms and 1531 mantle-wave seismograms), formal resolution analyses are performed using both PAVA and NACT. We find that the NACT is significantly more powerful in resolving 3-D structure in the deep mantle. We compare the models obtained for the same observed data set using the two approaches. As expected, they differ more in the lower mantle than in the upper mantle. The difference in their amplitude spectra increases with spherical harmonic degree. The model developed using the NACT predicts the observed surface geoid better than that developed using the PAVA, based upon geodynamic flow modelling.

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