One possibility in order to obtain a 1D integral relation is to search for the rotation rate at a given latitude only. Since the most constrained zone is the equatorial one, we try to investigate only the equatorial rotation rate. For this purpose we use the approximation
where 
are
radial kernels (e.g. [Cuypers1980])
and Plm(mu) are Legendre functions normalized such that int_{-1}^{1} Plm(mu)dmu=1,
and which satisfy the following property for m=l:
This shows that, for high-degrees l, the major contribution to
sectoral splittings 
comes from the equatorial rotation rate 
.
This leads to the 1D integral approximation:
Nevertheless this approximation is valid only for high degrees l. For lower degrees the sectoral splittings are sensitive not only to the equatorial rotation but also to the rotation rate in a large angular domain around the equator. The extent of this domain and the influence of this approximation on the estimation are discussed in [Corbard1997].
