Harmonic Noise Cancellation with Varing Fundametal frequency of MRS Signal Using Time-Domain Remote Reference Loop Method

Document Type : Research Article

Authors

1 Department of of Physics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.

2 Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran.

Abstract

Magnetic Resonance Sounding (MRS), as a surface geophysical method, provides good information about the hydro-geophysical parameters (such as water content and hydraulic conductivity) of aquifers. The main advantage of the MRS method compared to other geophysical methods is that the surface measurement of the MRS signal responds directly to the presence of water below the surface. Despite the high efficiency of this method, the recorded signal is strongly affected by electromagnetic noises, including spike noises and harmonic noises. The first generations of MRS instruments were single-channel instruments. In single-channel instruments, both magnetic resonance excitation and signal recording are done with a single loop, and it is necessary to use various forms of filtering to eliminate noise, in particular powerline harmonics.
Then a new generation of multichannel MRS instruments with multiple is was built, so that the main loop is still used for magnetic resonance excitation and signal recording. In addition, a number of reference loops, physically displaced from the main loop, measure only noise. Parts of the noise recorded by the reference loops can correlate with the noise in the main loop. With proper signal processing, the noise in the reference coils can be filtered to obtain a replica of the noise in the main coil and when this replica is subtracted from the signal recorded in the main loop, hence, the MRS signal remains noiseless. One of the current challenges of MRS signal processing is the existence of harmonic noise with the variable fundamental frequency. If the harmonic signal from a specific source has a fundamental frequency that varies with time, most of the proposed algorithms will not perform well in eliminating harmonic noise. Therefore, a new topic that is followed in this paper is to evaluate the performance of the proposed algorithm in cases where the harmonic signal has a fundamental frequency that varies with time.
In this paper, in order to obtain an accurate estimate of the parameters of the magnetic resonance sounding signal, a method for eliminating spike and then harmonic noise in the time domain is presented. Synthetic signals are contaminated with different electromagnetic noises to investigate the effect of different optimal filter parameters for spike and harmonic event elimination methods. Spike noise has a detrimental effect on the performance of the harmonic noise elimination algorithm. Hence, spike signals must be deleted or adjusted before applying the harmonic noise elimination algorithm. First, a statistical processing algorithm based on the signal-dependent rank-order mean (SD-ROM) filter for eliminating spike noise is presented and after deleting spike noise, a method for eliminating harmonic noise is assumed based on the fixed and variable fundamental frequency with time using remote reference loop. Numerical results of applying the proposed processing algorithms in the time domain show that by applying the mentioned methods, a considerable amount of spike and harmonic signals are removed leading to a good estimate of the parameters of the magnetic resonance sounding signal (i.e., initial amplitude, relaxation time, phase and frequency of the signal).

Keywords

Main Subjects


Abreu, E., Lightstone, M., Mitra, S. K., & Arakawa, K. (1996). A new efficient approach for the removal of impulse noise from highly corrupted images. IEEE Transactions on Image Processing, 5, 1012-1025.
Adams, R. K., McIntyre, J. M., & Symonds, F. W. (1982). Characteristics of the eastern interconnection line frequency. IEEE Transactions on Power Apparatus and Systems, (12), 4542-4547.
Aster, R., Borchers B., & Thurber, C. (2005). Parameter Estimation and Inverse Problems. Elsevier Academic Press.
Buttkus, B. (2000). Spectral Analysis and Filter Theory in Applied Geophysics. Springer-Verlag Berlin.
Butler, K. E., & Russell, R. D. (2003). Cancellation of multiple harmonic noise series in geophysical records. Geophysics, 68(3), 1083-1090
Chave, A. D., Thomson, D. J., & Ander, M. E. (1987). On the Robust Estimation of Power Spectra, Coherences, and Transfer Functions. Journal of Geophysical Research, 92(B1), 633–648.
Cohen, M. B., Said, R. K., & Inan, U. S. (2010). Mitigation of 50–60 Hz power line interference in geophysical data. Radio Science, 45, 1-12.
Costabel, S., & Müller-Petke, M. (2014). Despiking of magnetic resonance signals in time and wavelet domain. Near Surface Geophysics, 12, 185-197.
Dalgaard, E., Auken, E., & Larsen, J. (2012). Adaptive noise cancelling of multichannel magnetic resonance sounding signals. Geophysical Journal International, 191(1), 88–100.
Ferahtia, J., Djarfour, N., Baddari, K., & Guérin, R. (2009). Application of signal dependent rank-order mean filter to the removal of noise spikes from 2D electrical resistivity imaging data. Near Surface Geophysics, 7, 159-169.
Ghanati, R., & Hafizi, M. K. (2018). Estimation of harmonic interference parameters of surface-NMR signal using an adaptive method and residual signal power. Iranian Journal of Geophysics, 11(5) 13 – 25.
Ghanati, R., & Hafizi, M. K. (2017). Statistical de-spiking and harmonic interference cancellation from surface-NMR signals via a state-conditioned filter and modified Nyman-Gaiser method. Bollettino Di Geofisica Teorica Ed Applicata, 58(3), 181–204.
Ghanati, R., Hafizi, M. K., Mahmoudvand, R., & Fallahsafari, M. (2016). Filtering and parameter estimation of surface-NMR data using singular spectrum analysis. Journal of Applied Geophysics, 130, 118-130.
Günther, T., & Müller-Petke, M. (2012). Hydraulic properties at the North Sea island of Borkum derived from joint inversion of magnetic resonance and electrical resistivity soundings. Hydrology and Earth System Sciences, 16, 3279–3291.
Hertrich, M. (2005). Magnetic resonance sounding with separated transmitter and receiver loops for the investigation of 2D water content distributions. Ph.D. thesis, School of Civil Engineering and Applied Geosciences, Technical University of Berlin, 125.
Hertrich, M., Green, A. G., Braun, M., & Yaramanci, U. (2009). High-resolution surface-NMR tomography of shallow aquifers based on multi-off set measurements. Geophysics, 74(6), G47–G59.
Jeng, Y., & Chen, C. S. (2011). A nonlinear method of removing harmonic noise in geophysical data. Nonlinear Processes in Geophysics, 18(3), 367-379.
Jiang, C., Lin, J., Duan, Q., Sun, S., & Tian, B. (2011). Statistical stacking and adaptive notch filter to remove high-level electromagnetic noise from MRS measurements. Near Surface Geophysics, 9, 459–468.
Larsen, J. J., Dalgaard, E., & Auken, E. (2014). Noise cancelling of MRS signals combining model-based removal of power-line harmonics and multi-channel Wiener filtering. Geophysical Journal International, 196, 828–836.
Legchenko, A. (2007). MRS measurements and inversion in presence of EM noise. Boletín Geológico y Minero, 118 (3), 489 – 508.
Legchenko, A., & Valla, P. (2003). Removal of power-line harmonics from proton magnetic resonance measurements. Journal of Applied Geophysics, 53, 103-120.
Legchenko, A., & Valla, P. (2002). A review of the basic principles for proton magnetic resonance sounding measurements. Journal of Applied Geophysics, 50 (1–2), 3–19.
Lehmann-Horn, J. A., Hertrich, M., Greenhalgh, S. A., & Green, A. G. (2011). Three-Dimensional Magnetic Field and NMR Sensitivity Computations Incorporating Conductivity Anomalies and Variable- Surface Topography. IEEE Transactions on Geoscience and Remote Sensing, 49, 3878–3891.
Moore, M. S., & Mitra, S. K. (2000). Statistical threshold design for the two-state signal dependent rank order mean filter. In: Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101), 1, 904-907.
Müller-Petke, M., & Costabel, S. (2013). Comparison and optimal parameter setting of reference-based harmonic noise cancellation in time and frequency domain for surface-NMR. Near Surface Geophysics, 12(2), 190–210.
Müller-Petke, M., & Yaramanci, U. (2010). QT inversion - Comprehensive use of the complete surface NMR data set. Geophysics, 75(4), WA199– WA209.
Ross, S. M. (2009). Introduction to probability and statistics for engineers and scientists. Elsevier Academic Press, 664.
Spies, B. R. (1988). Local noise prediction filtering for central induction transient electromagnetic sounding. Geophysics, 53(8), 1068–1079.
Trushkin, D., Shushakov, O., & Legchenko, A. (1994). The potential of a noise-reducing antenna for surface NMR groundwater surveys in the Earth's magnetic field. Geophysical Prospecting, 42, 855 – 862.
Walsh, D. O. (2008). Multi-channel surface NMR instrumentation and software for 1D/2D groundwater investigations. Journal of Applied Geophysics, 66 (3–4), 140–150.