### 2.4 Estimating rotation properties directly from coefficients

It is possible to make some inferences about the rotation profile without carrying out a full-scale
inversion. Simple examination of the odd-order coefficients, sorted by the lower turning-point radius of the
modes, reveals the existence of the near-surface shear, the differential rotation within the convection zone,
and a discontinuity in the differential rotation at the base of the convection zone, as shown in Figure 9.
More sophisticated analysis is also possible. For example, Wilson and Burtonclay (1995) gave approximate
expressions for the rotation profile at different latitudes as sensed by a particular multiplet, , as
follows:
These estimates, where the subscripts on the LHS refer to the latitude in degrees, are noisy for individual
multiplets, but Wilson and Burtonclay (1995) were able to build up a picture of the internal rotation from
BBSO data by forming cumulative averages with the input data sorted in ascending order of
.