1887
Volume 69, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Magnetotelluric is one of the mainstream exploration geophysical methods, which plays a vital role in studying deep geological structures and finding deep hidden blind ore bodies. The seriousness of human electromagnetic noise causes a large number of abnormal waveforms in the time series of measured magnetotelluric data, and the data can no longer objectively reflect the underground electrical distribution. In this work, we propose a magnetotelluric time series data processing method based on K singular value decomposition dictionary training. First, a training matrix and a to‐be‐processed matrix are built with the pending magnetotelluric signals. Then, let the K singular value decomposition dictionary training process the training matrix to obtain an over‐complete dictionary reflecting the characteristics of the pending signal. Lastly, orthogonal matching pursuit is combined with an over‐complete dictionary updated in real time to sparsely represent the to‐be‐processed matrix and remove human electromagnetic interference in the signal. Experimental results show that the method can update the over‐complete dictionary in real‐time according to the pending magnetotelluric signals, realize the self‐learning signal–noise separation of magnetotelluric signals, and effectively retain low‐frequency information. Compared with method of directions dictionary learning, remote reference method, and orthogonal matching pursuit method, the reconstructed data of the proposed method can more accurately reflect the underground electrical structure information.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13058
2021-01-16
2024-04-29
Loading full text...

Full text loading...

References

  1. Aharon, M., Elad, M. and Bruckstein, A. (2006) K‐SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11), 4311–4322. http://doi.org/10.1109/tsp.2006.881199
    [Google Scholar]
  2. Bryt, O. and Elad, M. (2008) Compression of facial images using the K‐SVD algorithm. Journal of Visual Communication and Image Representation, 19(4), 270–282. http://doi.org/10.1016/j.jvcir.2008.03.001
    [Google Scholar]
  3. Cagniard, L. (1953) Basic theory of the magneto‐telluric method of geophysical prospecting. Geophysics, 18(3), 605–635. http://doi.org/10.1190/1.1437915
    [Google Scholar]
  4. Cai, J. (2014) A combinatorial filtering method for magnetotelluric time‐series based on Hilbert‐Huang transform. Exploration Geophysics, 45(2), 63–73. https://doi.org/10.1071/EG13012
    [Google Scholar]
  5. Cai, T.T. and Wang, L. (2011) Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Transactions on Information Theory, 57(7), 4680–4688. https://doi.org/10.1109/TIT.2011.2146090
    [Google Scholar]
  6. Carbonari, R., D'Auria, L., Di Maio, R. and Petrillo, Z. (2017) Denoising of magnetotelluric signals by polarization analysis in the discrete wavelet domain. Computers & Geosciences, 100, 135–141. https://doi.org/10.1016/j.cageo.2016.12.011
    [Google Scholar]
  7. Carbonari, R., Di Maio, R., Piegari, E., D'Auria, L., Esposito, A. and Petrillo, Z. (2018) Filtering of noisy magnetotelluric signals by SOM neural networks. Physics of the Earth and Planetary Interiors, 285, 12–22. http://doi.org/10.1016/j.pepi.2018.10.004
    [Google Scholar]
  8. Chave, A.D. and Thomson, D.J. (1989) Some comments on magnetotelluric response function estimation. Journal of Geophysical Research: Solid Earth, 94(B10), 14215–14225. http://doi.org/10.1029/jb094ib10p14215
    [Google Scholar]
  9. Chave, A.D. and Thomson, D.J. (2004) Bounded influence magnetotelluric response function estimation. Geophysical Journal International, 157(3), 988–1006. https://doi.org/10.1111/j.1365-246x.2004.02203.x
    [Google Scholar]
  10. Chen, J., Heincke, B., Jegen, M. and Moorkamp, M. (2012) Using empirical mode decomposition to process marine magnetotelluric data. Geophysical Journal International, 190(1), 293–309. http://doi.org/10.1111/j.1365-246X.2012.05470.x
    [Google Scholar]
  11. Chen, S.S., Donoho, D.L. and Saunders, M.A. (2001) Atomic decomposition by basis pursuit. SIAM Review, 43(1), 129–159. https://doi.org/10.1137/s1064827596304010
    [Google Scholar]
  12. Chen, Y. (2020) Fast dictionary learning for noise attenuation of multidimensional seismic data. Geophysical Journal International, 222(3), 1717–1727. https://doi.org/10.1093/gji/ggaa184
    [Google Scholar]
  13. Chen, Y. and Fomel, S. (2018) EMD‐seislet transform. Geophysics, 83(1), A27–A32. http://doi.org/10.1190/geo2017-0554.1
    [Google Scholar]
  14. Clarke, J., Gamble, T.D., Goubau, W.M., Koch, R.H. and Miracky, R. (1983) Remote‐reference magnetotellurics: Equipment and procedures. Geophysical Prospecting, 31(1), 149–170. http://doi.org/10.1111/j.1365-2478.1983.tb01047.x
    [Google Scholar]
  15. Dong, W., Li, X., Zhang, L. and Shi, G. (2011) Sparsity‐based image denoising via dictionary learning and structural clustering, CVPR 2011. IEEE, pp. 457–464. http://doi.org/10.1109/CVPR.2011.5995478
  16. Donoho, D.L., Tsaig, Y., Drori, I. and Starck, J.L. (2012) Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Information Theory, 58(2), 1094–1121. http://doi.org/10.1109/TIT.2011.2173241
    [Google Scholar]
  17. Egbert, G.D. (1997) Robust multiple‐station magnetotelluric data processing. Geophysical Journal International, 130(2), 475–496. http://doi.org/10.1111/j.1365-246x.1997.tb05663.x
    [Google Scholar]
  18. Egbert, G.D. and Booker, J.R. (1986) Robust estimation of geomagnetic transfer functions. Geophysical Journal International, 87(1), 173–194. http://doi.org/10.1111/j.1365-246x.1986.tb04552.x
    [Google Scholar]
  19. Elad, M. and Aharon, M. (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 15(12), 3736–3745. http://doi.org/10.1109/tip.2006.881969
    [Google Scholar]
  20. Engan, K., Aase, S.O. and Husoy, J.H. (1999) Method of optimal directions for frame design. Proceedings. ICASSP99. IEEE, pp. 2443–2446. http://doi.org/10.1109/icassp.1999.760624
  21. Gamble, T.D., Goubau, W.M. and Clarke, J. (1979) Magnetotellurics with a remote magnetic reference. Geophysics, 44(1), 53–68. https://doi.org/10.1190/1.1440923
    [Google Scholar]
  22. Gangeh, M.J., Ghodsi, A. and Kamel, M.S. (2013) Kernelized supervised dictionary learning. IEEE Transactions on Signal Processing, 61(19), 4753–4767. https://doi.org/10.1109/tsp.2013.2274276
    [Google Scholar]
  23. Garcia, X. and Jones, A.G. (2002) Atmospheric sources for audio‐magnetotelluric (AMT) sounding. Geophysics, 67(2), 448–458. http://doi.org/10.1190/1.1468604
    [Google Scholar]
  24. Goubau, W.M., Gamble, T.D. and Clarke, J. (1978) Magnetotelluric data analysis: Removal of bias. Geophysics, 43(6), 1157–1166. https://doi.org/10.1190/1.1440885
    [Google Scholar]
  25. Griffin, D. and Lim, J. (1984) Signal estimation from modified short‐time Fourier transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(2), 236–243. http://doi.org/10.1109/tassp.1984.1164317
    [Google Scholar]
  26. He, W., Jiang, Z. and Feng, K. (2009) Bearing fault detection based on optimal wavelet filter and sparse code shrinkage. Measurement, 42(7), 1092–1102. http://doi.org/10.1016/j.measurement.2009.04.001
    [Google Scholar]
  27. Jiang, Z., Lin, Z. and Davis, L.S. (2011) Learning a discriminative dictionary for sparse coding via label consistent K‐SVD. IEEE Conference on Computer Vision & Pattern Recognition, http://doi.org/10.1109/cvpr.2011.5995354
    [Google Scholar]
  28. Kao, D.W. and Rankin, D. (1977) Enhancement of signal‐to‐noise ratio in magnetotelluric data. Geophysics, 42(1), 103–110. http://doi.org/10.1190/1.1440703
    [Google Scholar]
  29. Kappler, K.N. (2012) A data variance technique for automated despiking of magnetotelluric data with a remote reference. Geophysical Prospecting, 60(1), 179–191. http://doi.org/10.1111/j.1365-2478.2011.00965.x
    [Google Scholar]
  30. Larsen, J.C. (1989) Transfer functions: Smooth robust estimates by least‐squares and remote reference methods. Geophysical Journal International, 99, 645–663. https://doi.org/10.1111/j.1365-246x.1989.tb02048.x
    [Google Scholar]
  31. Larsen, J.C., Mackie, R.L., Manzella, A., Fiordelisi, A. and Rieven, S. (1996) Robust smooth magnetotelluric transfer functions. Geophysical Journal International, 124(3), 801–819. http://doi.org/10.1111/j.1365-246X.1996.tb05639.x
    [Google Scholar]
  32. Li, G., Liu, X., Tang, J., Deng, J., Hu, S., Zhou, C.et al. (2020) Improved shift‐invariant sparse coding for noise attenuation of magnetotelluric data. Earth Planets and Space, 72, 45. http://doi.org/10.1186/s40623-020-01173-7
    [Google Scholar]
  33. Li, J., Yan, H., Tang, J., Zhang, X., Li, G. and Zhu, H. (2018) Magnetotelluric noise suppression based on matching pursuit and genetic algorithm. Chinese Journal of Geophysics, 61(7), 3086–3101. http://doi.org/10.6038/cjg2018L0229
    [Google Scholar]
  34. Li, J., Zhang, X., Tang, J., Cai, J. and Liu, X. (2019) Audio magnetotelluric signal–noise identification and separation based on multifractal spectrum and matching pursuit. Fractals, 27, 1940007. http://doi.org/10.1142/S0218348X19400073
    [Google Scholar]
  35. Li, S. and Fang, L. (2011) Signal denoising with random refined orthogonal matching pursuit. IEEE Transactions on Instrumentation and Measurement, 61(1), 26–34. https://doi.org/10.1109/tim.2011.2157547
    [Google Scholar]
  36. Li, W., Liu, F., Jiao, L., Hao, H. and Yang, S. (2016) A group matching pursuit for image reconstruction. Signal Processing: Image Communication, 49, 47–62. https://doi.org/10.1016/j.image.2016.10.002
    [Google Scholar]
  37. Liu, J., Liu, W., Ma, S., Wang, M., Li, L. and Chen, G. (2018) Image‐set based face recognition using K‐SVD dictionary learning. International Journal of Machine Learning and Cybernetics, 10(5), 1051–1064. http://doi.org/10.1007/s13042-017-0782-5
    [Google Scholar]
  38. Liu, W., Lu, Q., Chen, R., Lin, P., Chen, C., Yang, L. and Cai, H. (2019) A modified empirical mode decomposition method for multiperiod time‐series detrending and the application in full‐waveform induced polarization data. Geophysical Journal International, 217(2), 1058–1079. http://doi.org/10.1093/gji/ggz067
    [Google Scholar]
  39. Mairal, J., Elad, M. and Sapiro, G. (2008) Sparse representation for color image restoration. IEEE Transactions on Image Processing, 17(1), 53–69. http://doi.org/10.1109/tip.2007.911828
    [Google Scholar]
  40. Mallat, S.G. and Zhang, Z. (1993) Matching pursuits with time‐frequency dictionaries. IEEE Transactions on Signal Processing, 41(12), 3397–3415. https://doi.org/10.1109/78.258082
    [Google Scholar]
  41. Platz, A. and Weckmann, U. (2019) An automated new pre‐selection tool for noisy magnetotelluric data using the Mahalanobis distance and magnetic field constraints. Geophysical Journal International, 218, 1853–1872. https://doi.org/10.1093/gji/ggz197
    [Google Scholar]
  42. Protter, M. and Elad, M. (2009) Image sequence denoising via sparse and redundant representations. IEEE Transactions on Image Processing, 18(1), 27–35. http://doi.org/10.1109/tip.2008.2008065
    [Google Scholar]
  43. Qi, J., Zhang, L., Zhang, K., Li, L. and Sun, J. (2020) The application of improved differential evolution algorithm in electromagnetic fracture monitoring. Advances in Geo‐Energy Research, 4(3), 233–246. http://doi.org/10.46690/ager.2020.03.02
    [Google Scholar]
  44. Qin, Y., Zou, J., Tang, B., Wang, Y. and Chen, H. (2019) Transient feature extraction by the improved orthogonal matching pursuit and K‐SVD algorithm with adaptive transient dictionary. IEEE Transactions on Industrial Informatics, 16(1), 215–227. http://doi.org/10.1109/tii.2019.2909305
    [Google Scholar]
  45. Ren, Z., Kalscheuer, T., Greenhalgh, S. and Maurer, H. (2013) A goal‐oriented adaptive finite‐element approach for plane wave 3‐D electromagnetic modeling. Geophysical Journal International, 194, 700–718. http://doi.org/10.1093/gji/ggt154
    [Google Scholar]
  46. Rosas‐Romero, R. (2014) Remote detection of forest fires from video signals with classifiers based on K‐SVD learned dictionaries. Engineering Applications of Artificial Intelligence, 33, 1–11. http://doi.org/10.1016/j.engappai.2014.03.011
    [Google Scholar]
  47. Sutarno, D. and Vozoff, K. (1991) Phase‐smoothed robust M‐estimation of magnetotelluric impedance functions. Geophysics, 56(12), 1999–2007. http://doi.org/10.1190/1.1443012
    [Google Scholar]
  48. Tang, G., Ma, J. and Yang, H. (2012a) Seismic data denoising based on learning‐type overcomplete dictionaries. Applied Geophysics, 9(1), 27–32. https://doi.org/10.1007/s11770-012-0310-z
    [Google Scholar]
  49. Tang, J., Li, J., Xiao, X., Zhang, L. and Lv, Q. (2012b) Mathematical morphology filtering and noise suppression of magnetotelluric sounding data. Chinese Journal of Geophysics, 55(5), 1784–1793. http://doi.org/10.6038/j.issn.0001-5733.2012.05.036
    [Google Scholar]
  50. Tang, J., Xu, Z., Xiao, X. and Li, J. (2012c) Effect rules of strong noise on magnetotelluric (MT) sounding in the Luzong ore cluster area. Chinese Journal of Geophysics, 55(12), 4147–4159. http://doi.org/10.6038/j.issn.0001-5733.2012.12.027
    [Google Scholar]
  51. Tikhonov, A. (1950) On determining electrical characteristics of the deep layers of the Earth's crust. Proceedings of the USSR Academy of Sciences, 73, 295–297
    [Google Scholar]
  52. Trad, D.O. and Travassos, J.M. (2000) Wavelet filtering of magnetotelluric data. Geophysics, 65(2), 482–491. http://doi.org/10.1190/1.1444742
    [Google Scholar]
  53. Vallianatos, F. (1996) Magnetotelluric response of a randomly layered earth. Geophysical Journal International, 125, 577–583. http://doi.org/10.1111/j.1365-246x.1996.tb00020.x
    [Google Scholar]
  54. Vozoff, K. (1972) The magnetotelluric method in the exploration of sedimentary basins. Geophysics, 37(1), 98–141. http://doi.org/10.1190/1.1440255
    [Google Scholar]
  55. Wang, H., Campanyà, J., Cheng, J., Zhu, G., Wei, W., Jin, S. and Ye, G. (2017) Synthesis of natural electric and magnetic time‐series using inter‐station transfer functions and time‐series from a neighboring site (STIN): Applications for processing MT data. Journal of Geophysical Research: Solid Earth, 122(8), 5835–5851. http://doi.org/10.1002/2017jb014190
    [Google Scholar]
  56. Weckmann, U., Magunia, A. and Ritter, O. (2005) Effective noise separation for magnetotelluric single site data processing using a frequency domain selection scheme. Geophysical Journal International, 161(3), 635–652. http://doi.org/10.1111/j.1365-246x.2005.02621.x
    [Google Scholar]
  57. Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T.S. and Yan, S. (2010) Sparse representation for computer vision and pattern recognition. Proceedings of the IEEE, 98(6), 1031–1044. http://doi.org/10.1109/jproc.2010.2044470
    [Google Scholar]
  58. Yang, J., Wright, J., Huang, T.S. and Ma, Y. (2010) Image super‐resolution via sparse representation. IEEE Transactions on Image Processing, 19(11), 2861–2873. http://doi.org/10.1109/tip.2010.2050625
    [Google Scholar]
  59. Zhang, Q. and Li, B. (2010) Discriminative K‐SVD for dictionary learning in face recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE, pp. 2691–2698. https://doi.org/10.1109/cvpr.2010.5539989
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.13058
Loading
/content/journals/10.1111/1365-2478.13058
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Data processing; Filtering; Magnetotelluric

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error