Statistical de-spiking and harmonic interference cancellation from surface-NMR signals via a state-conditioned filter and modified Nyman-Gaiser method

The ability to recover subsurface information from surface-NMR measurements depends upon the signal quality which is adversely affected by ambient electromagnetic interference, i.e., power-line harmonics and impulse noises. We discuss two algorithms to isolate and then subtract these interferences. This study first tackles the use of the signal dependent rank-order mean filter for the detection and mitigation of noise spikes from highly corrupted surface-NMR signals. This algorithm estimates the likelihood the sample under inspection is corrupt relative to a threshold value derived from a statistical procedure and replaces a sample identified as impulse noise with an appropriate value. Then, the removal of power-line harmonics is implemented through a linear adaptive method, called a modified frequency-estimation approach stemming from the estimator proposed by Nyman-Gaiser. To verify the performance of the proposed algorithms to eliminate harmonics and spikes, the methods are tested on synthetic signals embedded in artificial noise and noise-only recordings derived from surface-NMR field measurements and a real data set. The results from the numerical simulations reveal an output signal-to-noise ratio increase with an accompanying enhancement in recovery of the surface-NMR signal parameters. Close agreement is also observed between the results of the field example and a borehole located at the sounding.