Third-Order Cumulants Based on Quadratic Frequency Coupling Constraints for Parameter Extraction of Magnetic Resonance Sounding Signals

In this article, a novel third-order cumulant (TOC) method based on quadratic frequency coupling (QFC) constraints is proposed to enhance the accuracy of parameter extraction for magnetic resonance sounding (MRS) signals. As a geophysical exploration technology, MRS signals are often affected by environmental noise and human interference, leading to reduced signal-to-noise ratio (SNR) and increased difficulty in parameter extraction. To address this issue, a new signal processing technique is introduced in this study. By combining the third-order accumulated main diagonal slices with the QFC, it is possible to identify and suppress random and harmonic noise in an effective manner. This method is not only suitable for traditional harmonic noise processing but also capable of handling complex noise environments with multiple fundamental frequencies and time-varying fundamental frequencies. The simulation results show that for the noisy signal with an initial SNR of about −20 dB, the SNR can be increased to more than 20 dB after processing by the QFC, with an increase of at least 40–50 dB, and the fitting error of the characteristic parameter extraction is less than ±5%. Compared with the traditional HMC and SSA algorithms, the QFC algorithm obtains the minimum root mean square error of 0.72 nV; besides, the computational efficiency of the QFC has obvious advantages, which is 3.3 times that of the HMC and 9.4 times that of the SSA. Therefore, the QFC has higher accuracy in parameter extraction and computational efficiency. The successful application of this method will provide strong technical support for hydrogeological exploration, environmental monitoring, and underground engineering detection.