Bloch–Siegert Effect for Surface Nuclear Magnetic Resonance Sounding Experiments in the Unsaturated Zone

The Bloch–Siegert effect is relevant for NMR experiments where components of the excitation pulse other than the circularly polarized component have an influence on the evolution of the magnetization of the spin system under consideration. For linearly polarized excitation fields this happens at amplitudes higher than roughly one tenth of the magnitude of the static magnetic field. Since surface nuclear magnetic resonance (SNMR) experiments, also called magnetic-resonance-soundings (MRS), are conducted in the relatively low local field of the earth, the Bloch–Siegert effect can quickly become relevant. This is especially the case for SNMR experiments in the unsaturated zone, where due to short relaxation times fast pulses of high intensity must be used. To describe the Bloch–Siegert effect, we use the average Hamiltonian approximation obtained by the Magnus expansion of up to fifth order, as well as the solution of the Bloch equations. The results of these approximations are tested against the Bloch simulations and it is shown that they are only valid for limited ranges of the excitation field amplitude. The influence of the Bloch–Siegert effect on sensitivity kernels is described and verified with experimental data obtained with a small scale SNMR sensor on water containers.