3.7 Limitations

It is important to bear in mind the limitations of the inversion process when considering the results. The deepest and shallowest depths that can be resolved, for example, are limited by the deepest and shallowest turning-point radii of the available modes. The rotational splitting at a given m is to first order proportional to the rotation rate multiplied by |m |; since the only mode whose latitudinal kernel reaches the pole is the m = 0 mode, which has no longitudinal structure and so can convey no rotational information, and the modes of small |m |∕l have only a few nodes around the equator and hence have low sensitivity to the rotation, the 2d inversion becomes progressively less reliable at high latitudes. Furthermore, since only modes of relatively low degree (l ≤ 20) penetrate into the radiative interior, the latitudinal resolution in this region is quite poor and becomes progressively worse with depth; radial resolution also becomes coarser in the interior. The practical effects of such limitations can be assessed by careful inspection of the averaging kernels, or by performing forward-calculation tests in which the averaging kernels are convolved with known test profiles.

Another point to bear in mind when considering inversion results is that the inversion can measure only the north – south symmetric part of the profile; any asymmetry between the hemispheres is averaged out. The inversions are also insensitive to meridional motions. Some information on hemispheric differences can be obtained using the techniques of local helioseismology, as reviewed by Birch and Gizon (2005), but these techniques, using high-degree modes, are mostly sensitive only to the outer layers of the Sun.

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