  The jet structure of short gamma-ray bursts (GRBs) has been controversial
after the detection of GRB 170817A as the electromagnetic counterparts to the
gravitational wave event GW170817. Different authors use different jet
structures for calculating the afterglow light curves. We formulated a method
to inversely reconstruct a jet structure from a given off-axis GRB afterglow,
without assuming any functional form of the structure. By systematically
applying our inversion method, we find that more diverse jet structures are
consistent with the observed afterglow of GRB 170817A within errors: such as
hollow-cone, spindle, Gaussian, and power-law jet structures. In addition, the
total energy of the reconstructed jet is arbitrary, proportional to the ambient
density $n_0$, with keeping the same jet shape if the parameters satisfy the
degeneracy combination $n_0 \varepsilon_\mathrm{B}^{(p+1)/(p+5)}
\varepsilon_\mathrm{e}^{4(p-1)/(p+5)} = \mathrm{const.}$. Observational
accuracy less than $\sim 6$ per cent is necessary to distinguish the different
shapes, while the degeneracy of the energy scaling would be broken by observing
the spectral breaks and viewing angle. Future events in denser environment with
brighter afterglows and observable spectral breaks are ideal for our inversion
method to pin down the jet structure, providing the key to the jet formation
and propagation.
