A way to examine rotational splittings without explicit forward or inverse computations

I derive and demonstrate simple but useful techniques for extracting information about the Sun's internal rotation from the observed frequency splittings of solar acoustic oscillations. The techniques do not require any formal forward or inverse computations and yet are significantly revealing about the radial and latitudinal variations of solar angular velocity reflected by the data. Simple linear combinations of the familiar rotational splitting coefficients, allow one to gain an impression of how any chosen co-latitudinal average of the angular velocity varies with depth, or of the radial variation of angular velocity at any particular co-latitude. The techniques are easy to apply and I illustrate them using the data of Brown and Morrow; they are equally applicable to data published by others. For the Brown and Morrow data, the methods reveal a lack of a substantial radial gradient of angular velocity in the convection zone, and a reversal in the sign of the radial gradient of angular velocity at about 30 degrees latitude at depths near the base of the convection zone. When subject to more detailed forward and inverse analysis, these data have also suggested such characteristics of the solar internal angular velocity. This lends credence to the methods described here