The Fr¿chet derivatives of the fundamental toroidal and poloidal magnetic modes of electromagnetic induction are examined in detail. The response functions for both modes are shown to be Fr¿chet differentiable in an L2 norm for general conductivity structures and arbitrary source frequency-wavenumber morphology. Perturbation forms of the modal Green functions are derived and used to examine the Fr¿chet kernels for a seafloor controlled source and a Kelvin wave model. In both cases, the TM mode possesses superior resolution ability, especially for low relative conductivity contrasts in depth. The results suggest that induction by the ocean tides can see details of the lithospheric structure at depths of at least 50 km.