Solution of the inverse problem of the one-dimensional mean field dynamo Parker's model in the thin spherical shell is considered. The method allows to find the spatial distribution of the energy sources in the model: the $\alpha $- and $\Omega $-effects, provided some constraints on the magnetic field are proposed. As an example of such constraint the maximal ratio of the magnetic energies in the northern and southern hemispheres is discussed. The method is a modification of the Monte Carlo method, suitable for application on the parallel computers. The idea is the minimisation of the cost-function, which describes deviation of model solution from the desired one. Calculations demonstrate that the energies ratio can exceed the order of magnitude as for the poloidal, as well as for the toroidal magnetic energies. The ratio depends on the distance between the zones of the maximal generation of the magnetic energies in the hemisphres, and the number of harmonics in the spectrum. The greater the distance, and the greater the number of harmonics the stronger is the equatorial assymetry of the magnetic field.
$^1$The Schmidt Institute of Physics of the Earth RAS