2-D Magnetic Resonance Tomography With an Inaccurately Known Larmor Frequency Based on Frequency Cycling

When using magnetic resonance tomography (MRT) for imaging 2-D or 3-D water-bearing structures in a subsurface, the transmitting frequency must be the same as the Larmor frequency. Due to the inhomogeneity and noise interference in a geomagnetic field, it is difficult to determine the precise Larmor frequency using a magnetometer, resulting in unknown frequency offsets and inaccurate estimations of water content and relaxation time (
$T_{2}^{*}$
). To solve the 2-D MRT imaging problem in the case of an unknown frequency offset, a frequency cycling method is proposed in this article. This method takes the estimated Larmor frequency as the center, uses two frequencies with the same offset for transmitting, then combines the acquired MRT signals to obtain frequency-cycled data, and finally uses the off-resonance kernel function for inversion. Based on MRT forward modeling and QT inversion, we conduct synthetic data experiments on a complex model with three water-bearing structures and test the 2-D imaging results of the frequency-cycled data. The results show that the water content and
$T_{2}^{*}$
distribution obtained by the inversion of the frequency-cycled data can accurately reflect the water-bearing structure, which is better than the results of the assumed on-resonance case. In addition, the phase correction method presented in this article significantly improves the accuracy of 2-D MRT estimated aquifer properties under low resistivity conditions. Finally, the validity and accuracy of the frequency cycling method are verified by comparing the inversion results of the data with known drilling data collected in field measurements.