Envelope Extraction Algorithm for Magnetic Resonance Sounding Signals Based on Adaptive Gaussian Filters

Magnetic resonance sounding is a geophysical method for quantitatively determining the state for groundwater storage that has gained international attention in recent years. However, the practical acquisition of magnetic resonance sounding signals, which are on the nanovolt scale, is susceptible to various types of interference, such as power-line harmonics, random noise, and spike noise. Such interference can degrade the quality of magnetic resonance sounding signals and, in severe cases, be completely drowned out by noise. This paper introduces an adaptive Gaussian filtering algorithm that is well-suited for handling intricate noise signals due to its adaptive solving characteristics and iterative sifting approach. Notably, the algorithm can process signals without relying on prior knowledge. The adaptive Gaussian filtering algorithm is applied for the envelope extraction of noisy magnetic resonance sounding signals, and the reliability and effectiveness of the method are rigorously validated. The simulation results reveal that, even under strong noise interference (with original signal-to-noise ratios ranging from −7 dB to −25 dB), the magnetic resonance sounding signal obtained after algorithmic processing is compared to the ideal signal, with 16 sets of data statistics, and the algorithm ensures an initial amplitude uncertainty within 4nV and restricts the uncertainty of the relaxation time within a 6 ms range. The signal-to-noise ratio can be boosted by up to 53 dB. The comparative assessments with classical algorithms such as empirical mode decomposition and the harmonic modeling method confirm the superior performance of the adaptive Gaussian filtering algorithm. The processing of the field data also fully proved the practical application effects of the algorithm.