A lock-in amplifier modeling recovery method to extract the surface nuclear magnetic resonance signal from residual noise

Abstract

Surface nuclear magnetic resonance (SNMR) could provide direct insights for hydrological investigations but is often limited because of its low signal-to-noise ratio. Many types of residual noise remain after denoising procedures, including despiking, power harmonic noise cancellation, and random noise attenuation. This residual noise prevents the detection of valid signals, especially in strong noise environments, such as cities and industrial areas. In this work, a lock-in amplifier modeling recovery (LIAMR) method is proposed for extracting SNMR signals from high-level residual noise after denoising. The desired SNMR signals can be extracted directly by establishing a model of the SNMR signal passing through the lock-in amplifier and then transforming mathematically the output of the amplifier. The performance of the proposed method is tested on synthetic SNMR signals under varied average relaxation times, simulation noise at different levels, and field noise. Experiment results show that LIAMR can obtain good estimations of SNMR signal parameters with residual noise. Moreover, the proposed method can provide more precise parameters compared with traditional signal extraction methods. LIAMR provides theoretical support for the application of SNMR technology in strong noise environments.