  The recent gravity field measurements of Jupiter (Juno) and Saturn (Cassini)
confirm the existence of deep zonal flows reaching to a depth of 5\% and 15\%
of the respective radius. Relating the zonal wind induced density perturbations
to the gravity moments has become a major tool to characterise the interior
dynamics of gas giants. Previous studies differ with respect to the assumptions
made on how the wind velocity relates to density anomalies, on the functional
form of its decay with depth, and on the continuity of antisymmetric winds
across the equatorial plane. Most of the suggested vertical structures exhibit
a rather smooth radial decay of the zonal wind, which seems at odds with the
observed secular variation of the magnetic field and the prevailing geostrophy
of the zonal winds. Moreover, the results relied on an artificial equatorial
regularisation or ignored the equatorial discontinuity altogether. We favour an
alternative structure, where the equatorially antisymmetric zonal wind in an
equatorial latitude belt between $\pm 21^\circ$ remains so shallow that it does
not contribute to the gravity signal. The winds at higher latitudes suffice to
convincingly explain the measured gravity moments. Our results indicate that
the winds are geostrophic, i.e. constant along cylinders, in the outer $3000\,$
km and decay rapidly below. The preferred wind structure is 50\% deeper than
previously thought, agrees with the measured gravity moment, is compliant with
the magnetic constraints and the requirement of an adiabatic atmosphere and
unbiased by the treatment of the equatorial discontinuity.
