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Signal collected from magnetic resonance sounding (MRS) instrument is only a few tens of nano-volt and susceptible to environmental noise, leading to a low signal-to-noise ratio. In addition, the accuracy of characteristic parameter extraction from MRS signal is seriously affected, and the resulting error of the subsequent inversion interpretation increases. In this paper, a fast fixed-point algorithm for independent component analysis (FastICA) is utilized to enhance the performance in the high noisy environment. First, the applicability of FastICA algorithm to noise cancellation of MRS signal is analyzed. Whether the mixed signal can be separated completely depends on the appropriate choice of nonlinear function in FastICA algorithm, moreover, the choice of nonlinear function is closely related to the Gaussian type of signal. Thus, in this process, the kurtoses of noise and full-wave MRS signal are calculated, and then the Gaussian type of signal is determined. Therefore based on the Gaussian type of signal, we can choose the corresponding nonlinear function applied to the FastICA algorithm in order to realize the effective separation of the mixed signals. Secondly, undetermined blind source separation is one of common problems of ICA. To cope with this tough situation, a digital orthogonal method is adopted to construct some extra observed signals combined with the existing observed one as the input signal of this algorithm. Hence, the digital orthogonal method can satisfy the application condition of ICA, i.e., the number of observed signal must be greater than or equal to that of source signal. This means that it is able to remove the application limitation of ICA when there is only one observed signal. Owing to the problem of variable amplitude of separated signals after ICA, it is crucial to recover the initial amplitude of the separated MRS signal, because it represents the amount of water content in the aquifer. Aiming at this problem, a spectrum correcting method is proposed. In frequency domain, the spectrum of separated MRS signal is restored into the original value that is the spectrum of observed signal at Larmor frequency, then transformed into time domain by inversing fast Fourier transform to obtain the desired MRS signal. In the validation of the proposed algorithm, two tests are considered: simulation and field data processing. In the simulation case, the observed signal constructed by full-wave MRS signal and two power-line harmonics with different frequencies is the main processing object, and the proposed algorithm is utilized to realize the observed signal separated into ideal MRS signal and noise effectively. To verify the applicability of this proposed algorithm further, under the condition of different initial amplitudes and relaxation times, the characteristic parameters of separated MRS signal are extracted by this proposed algorithm and the corresponding relative fitting error is determined. The simulation results show that adopting this algorithm can effectively realize the separation of the noisy full-wave MRS signal. In addition, the relative errors of initial amplitude and relaxation time after data fitting are both within 5.00%. When compared with the denoising ability of some other classical algorithms, the performance of this proposed algorithm is superior. Finally, this algorithm is applied to the processing of the field data. The results indicate that power-line harmonics and other single-frequency interference contained in the MRS signal can be removed effectively.
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Keywords:
- magnetic resonance sounding /
- independent component analysis /
- fast fixed-point algorithm /
- noise interference
[1] Schirov M, Legchenko A, Greer G 1991 Explor. Geophys. 22 333
[2] Legchenko A, Baltassat J M, Beauce A, Bernard J 2002 J. Appl. Geophys. 50 21
[3] Lubczynski M, Roy J 2003 J. Hydrol. 283 19
[4] Yaramanci U, Legchenko A, Roy J 2008 J. Appl. Geophys. 66 71
[5] Hao H C 2013 M. S. Dissertation (Changchun: Jilin University) (in Chinese) [郝荟萃 2013 硕士学位论文 (长春: 吉林大学)]
[6] Lin T T, Hui F, Jiang C D, Lin J 2013 Chinese J. Geophys. 56 2849 (in Chinese) [林婷婷, 慧芳, 蒋川东, 林君 2013 地球物理学报 56 2849]
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[8] Chalikakis K, Nielsen M R, Legchenko A 2008 J. Appl. Geophys. 66 176
[9] Legchenko A, Valla P 2002 J. Appl. Geophys. 50 3
[10] Legchenko A 2007 Boletn Geolgicoy Minero 118 489
[11] Legchenko A, Valla P 2003 J. Appl. Geophys. 53 103
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[13] Strehl S 2006 M. S. Dissertation (Berlin: Technical University of Berlin)
[14] Dalgaard E, Auken E, Larsen J J 2012 Geophys. J. Int. 191 88
[15] Mller-Petke M, Costabel S 2014 Near Surf. Geophys. 12 199
[16] Walsh D O 2008 J. Appl. Geophys. 66 140
[17] Walsh D O 2008 US Patent 7 466 128 B2
[18] Jiang C D, Wang Z X, Lin J, Sun S Q, Tian B F, Duan Q M, Rong L L 2009 The 4nd International Workshop on the Magnetic Resonance Sounding Method Applied to Non-invasive Groundwater Investigations Proceedings Grenoble, France, October 20-23, 2009 p101
[19] Jiang C D, Lin J, Duan Q M, Sun S Q, Tian B F 2011 Near Surf. Geophys. 9 459
[20] Tian B F, Lin J, Duan Q M, Jiang C D 2012 Chinese J. Geophys. 55 2462 (in Chinese) [田宝凤, 林君, 段清明, 蒋川东 2012 地球物理学报 55 2462]
[21] Yang J, Chen S S, Huangfu H R, Liang P P, Zhong N 2015 Acta Phys. Sin. 64 058701 (in Chinese) [杨剑, 陈书燊, 皇甫浩然, 梁佩鹏, 钟宁 2015 物理学报 64 058701]
[22] Kulchandani J, Dangarwala K J 2014 Int. J. Computer Sci. Inform. Technol. 5 6739
[23] Xing Y Q, Wang X D, Bi K, Hao X D 2014 Control Decis. 29 411 (in Chinese) [邢雅琼, 王晓丹, 毕凯, 郝新娣 2014 控制与决策 29 411]
[24] An Y W, Wang S 2013 Chin. Phys. C 37 037006
[25] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]
[26] Comon P 1994 Signal Processing 36 287
[27] Hyvarinen A 1999 IEEE Trans. Neural Networks 10 626
[28] Hyvarinen A, Oja E 1997 Neural Comput. 9 1483
[29] Fu W H, Yang X N, Liu N A 2008 J. Electron. Inform. Technol. 30 1853 (in Chinese) [付卫红, 杨小牛, 刘乃安 2008 电子与信息学报 30 1853]
[30] Lin J, Duan Q M, Wang Y J 2011 Theory and Design of Magnetic Resonance Sounding Instrument for Groundwater Detection and Its Applications (Vol. 1) (Beijing: Science Press) p171 (in Chinese) [林君, 段清明, 王应吉 2011 核磁 共振找水仪原理与应用 (北京: 科学出版社) 第171页]
[31] Liu N 2012 Ph. D. Dissertation (Xi'an: Xidian University) (in Chinese) [刘宁 2012 博士学位论文(西安: 西安电子科技大学)]
[32] Chen Y, L S X, Wang M J, Feng J C 2015 Acta Phys. Sin. 64 090501 (in Chinese) [陈越, 吕善翔, 王梦蛟, 冯久超 2015 物理学报 64 090501]
[33] Wu X P, Zhan C A, Zhou H Q, Feng H Q 2000 J. Univ. Sci. Technol. China 30 671 (in Chinese) [吴小培, 詹长安, 周荷琴, 冯焕清 2000 中国科学技术大学学报 30 671]
[34] Yan H W, Huang X L, Zhao Y, Si J F, Liu T B, Liu H X 2014 Chin. Phys. B 23 118702
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[1] Schirov M, Legchenko A, Greer G 1991 Explor. Geophys. 22 333
[2] Legchenko A, Baltassat J M, Beauce A, Bernard J 2002 J. Appl. Geophys. 50 21
[3] Lubczynski M, Roy J 2003 J. Hydrol. 283 19
[4] Yaramanci U, Legchenko A, Roy J 2008 J. Appl. Geophys. 66 71
[5] Hao H C 2013 M. S. Dissertation (Changchun: Jilin University) (in Chinese) [郝荟萃 2013 硕士学位论文 (长春: 吉林大学)]
[6] Lin T T, Hui F, Jiang C D, Lin J 2013 Chinese J. Geophys. 56 2849 (in Chinese) [林婷婷, 慧芳, 蒋川东, 林君 2013 地球物理学报 56 2849]
[7] Juan P, Felix R 2002 J. Appl. Geophys. 50 83
[8] Chalikakis K, Nielsen M R, Legchenko A 2008 J. Appl. Geophys. 66 176
[9] Legchenko A, Valla P 2002 J. Appl. Geophys. 50 3
[10] Legchenko A 2007 Boletn Geolgicoy Minero 118 489
[11] Legchenko A, Valla P 2003 J. Appl. Geophys. 53 103
[12] Strehl S, Rommel I, Hertrich M, Yaramanci U 2006 Proceedings of the 3rd Magnetic Resonance Sounding International Workshop Madrid, Spain, October 25-27, 2006 p65
[13] Strehl S 2006 M. S. Dissertation (Berlin: Technical University of Berlin)
[14] Dalgaard E, Auken E, Larsen J J 2012 Geophys. J. Int. 191 88
[15] Mller-Petke M, Costabel S 2014 Near Surf. Geophys. 12 199
[16] Walsh D O 2008 J. Appl. Geophys. 66 140
[17] Walsh D O 2008 US Patent 7 466 128 B2
[18] Jiang C D, Wang Z X, Lin J, Sun S Q, Tian B F, Duan Q M, Rong L L 2009 The 4nd International Workshop on the Magnetic Resonance Sounding Method Applied to Non-invasive Groundwater Investigations Proceedings Grenoble, France, October 20-23, 2009 p101
[19] Jiang C D, Lin J, Duan Q M, Sun S Q, Tian B F 2011 Near Surf. Geophys. 9 459
[20] Tian B F, Lin J, Duan Q M, Jiang C D 2012 Chinese J. Geophys. 55 2462 (in Chinese) [田宝凤, 林君, 段清明, 蒋川东 2012 地球物理学报 55 2462]
[21] Yang J, Chen S S, Huangfu H R, Liang P P, Zhong N 2015 Acta Phys. Sin. 64 058701 (in Chinese) [杨剑, 陈书燊, 皇甫浩然, 梁佩鹏, 钟宁 2015 物理学报 64 058701]
[22] Kulchandani J, Dangarwala K J 2014 Int. J. Computer Sci. Inform. Technol. 5 6739
[23] Xing Y Q, Wang X D, Bi K, Hao X D 2014 Control Decis. 29 411 (in Chinese) [邢雅琼, 王晓丹, 毕凯, 郝新娣 2014 控制与决策 29 411]
[24] An Y W, Wang S 2013 Chin. Phys. C 37 037006
[25] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]
[26] Comon P 1994 Signal Processing 36 287
[27] Hyvarinen A 1999 IEEE Trans. Neural Networks 10 626
[28] Hyvarinen A, Oja E 1997 Neural Comput. 9 1483
[29] Fu W H, Yang X N, Liu N A 2008 J. Electron. Inform. Technol. 30 1853 (in Chinese) [付卫红, 杨小牛, 刘乃安 2008 电子与信息学报 30 1853]
[30] Lin J, Duan Q M, Wang Y J 2011 Theory and Design of Magnetic Resonance Sounding Instrument for Groundwater Detection and Its Applications (Vol. 1) (Beijing: Science Press) p171 (in Chinese) [林君, 段清明, 王应吉 2011 核磁 共振找水仪原理与应用 (北京: 科学出版社) 第171页]
[31] Liu N 2012 Ph. D. Dissertation (Xi'an: Xidian University) (in Chinese) [刘宁 2012 博士学位论文(西安: 西安电子科技大学)]
[32] Chen Y, L S X, Wang M J, Feng J C 2015 Acta Phys. Sin. 64 090501 (in Chinese) [陈越, 吕善翔, 王梦蛟, 冯久超 2015 物理学报 64 090501]
[33] Wu X P, Zhan C A, Zhou H Q, Feng H Q 2000 J. Univ. Sci. Technol. China 30 671 (in Chinese) [吴小培, 詹长安, 周荷琴, 冯焕清 2000 中国科学技术大学学报 30 671]
[34] Yan H W, Huang X L, Zhao Y, Si J F, Liu T B, Liu H X 2014 Chin. Phys. B 23 118702
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