We propose a set of local operators to deal with internal discontinuities that do not coincide with collocated Cartesian grids in 2D transversely isotropic media. We use globally optimally accurate operators in order to obtain high accuracy. We derive modified operators by extrapolating wavefields from nearby grid points to the discontinuous point, introducing boundary conditions; we then distribute those conditions to the nearby grid points. Numerical examples suggest that the operators improve the coherency of the wavefront. We would like to optimise the local operators to control all the error propagation during the modelling.