  The article suggests a new approach what is called a consistency method for
the inversion of the spherical Radon transform in 2D with detectors on a line.
It is known that there is not an exact inversion formula in 2D. By means of the
method was proved that the reconstruction has a local description and found a
new iteration formula which give an practical algorithm to recover an unknown
function supported completely on one side of a line $L$ from its spherical
means over circles centered on the line $L$. Such an inversion is required in
problems of thermo- and photo-acoustic tomography.
