Inversion of the same target models as in Fig. 12, but with the difference in oscillation frequencies calculated from the difference in structure and the oscillation kernels. This essentially performs the inversion as if there were no nonlinear dependencies on the structure. All inversion parameters were kept the same. The quality of the fit is significantly better and the inferred profiles match the actual difference between the models much better. The corrected period-spacing patterns show how strong the nonlinear dependency on the structure is, deviating significantly from the actual period-spacing patterns of the target models shown in Fig. 12. In the case of target model #2 this even causes the oscillation modes to cross in frequency.