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10544243856
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note
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The travel time data set comprises representative subsets of antipodal PKP(AB)-PKP(DF) data from (10) and of PKP(BC)-PKP(DF) data from (14). The mode data set consists of splitting coefficients C00, C20, and C40, as defined in equation 11 of (25), for 19 inner core-sensitive modes, measured using Bolivia and Kurile data only (23), and corrected for rotation, ellipticity as well as mantle effects, using (20). These coefficients are combined in a spherical harmonic expansion to define the splitting function, and represent integrated effects on the modes of structure from the Earth's center to the surface. Units are in ‰ of degenerate frequency of each mode. The modes considered are given in Table 2. We compared corrections for mantle structure with the use of different mantle models and found that changing the model has no significant effects on our results. Uncertainties on mantle corrections for zonal terms are on the order of 0.1‰. An S to P wave velocity conversion factor of 0.5 was used in the mantle correction computations. This choice has little effect on the inner core models obtained.
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35
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note
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ν; 10 and 15 parameters, respectively); #4, ν = 4, n = 2; (35 parameters); #5, ν = 4, n= 4 (both spatial and depth variations are allowed, and the anisotropy need not be cylindrical; the number of free parameters in this case is 44).
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The determination of the splitting coefficients is a highly nonlinear process. For some inner core-sensitive modes (13S2 and 3S2 in particular), and with the current data set, the solution space exhibits several minima, with significantly different values of the C20 and C40 terms (for example, Megnin and Romanowicz, Eos Fall Suppl. 76, 46 (1995). We have verified that our solutions remain stable when we remove one or both of these modes. This is particularly important for 3S2, whose splitting dominates the mode data set (Fig. 3).
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Previous studies have documented that the top 100 km of the inner core has little anisotropy [(6) and X. Song and D. Helmberger, J. Geophys. Res. 100, 9805 (1995)]. Our limited parameterization with depth does not allow us to resolve this level of detail. Future studies should consider depth parameterizations in terms of layers or other local basis functions, but the price to pay will be the loss of the elegance of the formalism.
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J. Geophys. Res.
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Song, X.1
Helmberger, D.2
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note
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We thank X. Song for making his data available to us and P. Olson for helping us with the computations of streamlines for mode 1 convection, as well as two anonymous reviewers whose comments helped improve the manuscript. This research was partially supported by NSF grant EAR9417862. It is Seismographic Station contribution #9609.
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