1887
Volume 52, Issue 1
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

The modelling technique contributes to understanding noise nature and properties. Prior work has established a primary random noise model in the homogeneous medium, however, this strict assumption of the medium may be not valid under the actual environment so that will reduce the modelling accuracy. Therefore, in this paper, a random noise model is established in the mixed heterogeneous medium to improve the modelling accuracy, so the scattered mechanism is used to describe the random noise field in the heterogeneous medium. Since the perturbation method is always applied to solve the scattering problem, the noise wave field can be regarded as the superposition of the perturbation wave field and the unperturbation wave field. Consequently, the random noise model reveals that the desert random noise is mainly caused by the wind, and it concentrates on 1–20 Hz. A detailed comparison is made between the noise model established in the homogeneous medium and the proposed noise model, the results illustrate that the proposed noise model is more similar to the actual noise. Besides, for embodying the model’s practical application value, the proposed noise model is adopted as the background noise to determine the VMD (variational mode decomposition) denoising parameters. The satisfactory denoising performance supports the usefulness of the proposed noise model for the random noise attenuation.

Loading

Article metrics loading...

/content/journals/10.1080/08123985.2020.1764843
2021-01-02
2026-01-20
Loading full text...

Full text loading...

References

  1. Abassy, T.A., M.A.El-Tawil, and H.K.Saleh. 2004. The solution of KdV and mKdV equations using Adomian Pade approximation. International Journal of Nonlinear Sciences and Numerical Simulation5, no. 4: 327–40. doi: 10.1515/IJNSNS.2004.5.4.327
    https://doi.org/10.1515/IJNSNS.2004.5.4.327 [Google Scholar]
  2. Ahmed, S.M., F.A.E.Eldin, and A.M.Tarek. 2010. Speckle noise reduction in SAR images using adaptive morphological filter. doi:10.1109/ISDA.2010.5687254.
  3. Andić, A.2008. Propagation of high frequency waves in the quiet solar atmosphere. Serbian Astronomical Journal177: 87–99. doi: 10.2298/SAJ0877087A
    https://doi.org/10.2298/SAJ0877087A [Google Scholar]
  4. Asten, M.W.1978. Geological control on the three-component spectra of Rayleigh-wave microseisms. Bulletin of the Seismological Society of America68, no. 6: 1623–36.
    [Google Scholar]
  5. Asten, M.W.2004. Passive seismic methods using the microtremor wave field. ASEG Extended Abstracts2004, no. 1: 1–4.
    [Google Scholar]
  6. Asten, M.W., and J.D.Henstridge. 1984. Array estimators and the use of microseisms for reconnaissance of sedimentary basins. Geophysics49, no. 11: 1828–37. doi: 10.1190/1.1441596
    https://doi.org/10.1190/1.1441596 [Google Scholar]
  7. Badal, J., Y.Chen, M.Chourak, and J.Stankiewicz. 2013. S-wave velocity images of the Dead Sea Basin provided by ambient seismic noise. Journal of Asian Earth Sciences75: 26–35. doi: 10.1016/j.jseaes.2013.06.017
    https://doi.org/10.1016/j.jseaes.2013.06.017 [Google Scholar]
  8. Bonnefoy-Claudet, S., F.Cotton, and P.Bard. 2006. The nature of noise wavefield and its applications for site effects studies. A literature review. Earth-Science Reviews79, no. 3–4: 205–27. doi: 10.1016/j.earscirev.2006.07.004
    https://doi.org/10.1016/j.earscirev.2006.07.004 [Google Scholar]
  9. Bormann, P., and E.Wielandt. 2013. Seismic signals and noise. In New manual of seismological observatory practice, ed. P.Bormann, 1–62. 2nd ed. Posdam, Germany: Deutsches GeoForchungs Zentrum GFZ.
    [Google Scholar]
  10. de Jong, R.M., C.Amsler, and P.Schmidt. 2007. A robust version of the KPSS test based on indicators. Journal of Economics137, no. 2: 311–33. doi: 10.1016/j.jeconom.2006.01.001
    https://doi.org/10.1016/j.jeconom.2006.01.001 [Google Scholar]
  11. de Souza, D.B., J.Chanussot, A.C.Favre, and P.Borgnat. 2012. A modified time-frequency method for testing wide-sense stationarity. doi: 10.1109/ICASSP.2012.6288648
    https://doi.org/10.1109/ICASSP.2012.6288648
  12. Drăgănescu, G.E., and V.Căpălnăşăn. 2003. Nonlinear relaxation phenomena in polycrystalline solids. International Journal of Nonlinear Sciences and Numerical Simulation4, no. 3: 219–26. doi: 10.1515/IJNSNS.2003.4.3.219
    https://doi.org/10.1515/IJNSNS.2003.4.3.219 [Google Scholar]
  13. Dragomiretskiy, K., and D.Zosso. 2014. Variational mode decomposition. IEEE Transactions on Signal Process62, no. 3: 531–44. doi: 10.1109/TSP.2013.2288675
    https://doi.org/10.1109/TSP.2013.2288675 [Google Scholar]
  14. Frankel, A., and R.Clayton. 1986. Finite difference simulations of seismic scattering: Implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity. Journal of Geophysical Research91: 6465–89. doi: 10.1029/JB091iB06p06465
    https://doi.org/10.1029/JB091iB06p06465 [Google Scholar]
  15. Gibson, S.B., and R.A.Levander. 1988. Modeling and processing of scattered waves in seismic reflection surveys. Geophysics53: 466–78. doi: 10.1190/1.1442478
    https://doi.org/10.1190/1.1442478 [Google Scholar]
  16. Gomez-Biscarri, J., and J.Hualde. 2015. A residual-based ADF test for stationary cointegration in I (2) settings. Journal of Economics184, no. 2: 280–94. doi: 10.1016/j.jeconom.2014.08.009
    https://doi.org/10.1016/j.jeconom.2014.08.009 [Google Scholar]
  17. He, J.H.1999. Variational iteration method–a kind of non-linear analytical technique: some examples. International Journal of Non-Linear Mechanics34, no. 4: 699–708. doi: 10.1016/S0020‑7462(98)00048‑1
    https://doi.org/10.1016/S0020-7462(98)00048-1 [Google Scholar]
  18. He, J.H.2004. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons & Fractals19, no. 4: 847–51. doi: 10.1016/S0960‑0779(03)00265‑0
    https://doi.org/10.1016/S0960-0779(03)00265-0 [Google Scholar]
  19. Herrera, I., and A.K.Mal. 1965. A perturbation method for elastic wave propagation: 2. Small inhomogeneities. Journal of Geophysical Research70, no. 4: 871–83. doi: 10.1029/JZ070i004p00871
    https://doi.org/10.1029/JZ070i004p00871 [Google Scholar]
  20. KaralJr., F.C., and J.B.Keller. 1964. Elastic, electromagnetic, and other waves in a random medium. Journal of Mathematical Physics5, no. 4: 537–47. doi: 10.1063/1.1704145
    https://doi.org/10.1063/1.1704145 [Google Scholar]
  21. Kishkina, S.B., A.A.Spivak, and J.J.Sweeney. 2009. Short-period seismic noise in Vorkuta, Russia. Seismological Research Letters80, no. 1: 97–101. doi: 10.1785/gssrl.80.1.97
    https://doi.org/10.1785/gssrl.80.1.97 [Google Scholar]
  22. Knopoff, L., and J.A.Hudson. 1964. Scattering of elastic waves by small inhomogeneities. The Journal of the Acoustical Society of America36, no. 2: 338–43. doi: 10.1121/1.1918957
    https://doi.org/10.1121/1.1918957 [Google Scholar]
  23. Li, G., Y.Li, and B.Yang. 2017. Seismic exploration random noise on land: modeling and application to noise suppression. IEEE Transactions on Geoscience and Remote Sensing55, no. 8: 4668–81. doi: 10.1109/TGRS.2017.2697444
    https://doi.org/10.1109/TGRS.2017.2697444 [Google Scholar]
  24. Liu, H.M.2005. Generalized variational principles for ion acoustic plasma waves by He’s semi-inverse method. Chaos, Solitons & Fractals23, no. 2: 573–6. doi: 10.1016/j.chaos.2004.05.005
    https://doi.org/10.1016/j.chaos.2004.05.005 [Google Scholar]
  25. Ministry of Housing and Urban-Rural Development of the People’s Republic of China (MOHURD). 2012. Load code for the design of building structures. Beijing, China: China Building Industry Press.
  26. Okada, H.2006. Theory of efficient array observations of microtremors with special reference to the SPAC method. Exploration Geophysics37, no. 1: 73–85. doi: 10.1071/EG06073
    https://doi.org/10.1071/EG06073 [Google Scholar]
  27. Pointer, T., E.Liu, and J.Hudson. 1998. Numerical modeling of seismic waves scattered by hydrofractures: application of the indirect boundary element method. Geophysical Journal International135, no. 1: 289–303. doi: 10.1046/j.1365‑246X.1998.00644.x
    https://doi.org/10.1046/j.1365-246X.1998.00644.x [Google Scholar]
  28. Richard, P.2009. Modified fast double sieve bootstraps for ADF tests. Computational Statistics & Data Analysis53, no. 12: 4490–99. doi: 10.1016/j.csda.2009.07.008
    https://doi.org/10.1016/j.csda.2009.07.008 [Google Scholar]
  29. Scales, J.A., and R.Snieder. 1998. What is noise?Geophysics63: 1122–24. doi: 10.1190/1.1444411
    https://doi.org/10.1190/1.1444411 [Google Scholar]
  30. Upadhyay, A., and R.B.Pachori. 2015. Instantaneous voiced/non-voiced detection in speech signals based on variational mode decomposition. Journal of The Franklin Institute-Engineering and Applied Mathematics352, no. 7: 2679–707. doi: 10.1016/j.jfranklin.2015.04.001
    https://doi.org/10.1016/j.jfranklin.2015.04.001 [Google Scholar]
  31. Vakhnenko, V.O., E.J.Parkes, and A.J.Morrison. 2003. A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos, Solitons & Fractals17, no. 4: 683–92. doi: 10.1016/S0960‑0779(02)00483‑6
    https://doi.org/10.1016/S0960-0779(02)00483-6 [Google Scholar]
  32. Wang, D., Y.Li, and P.Nie. 2014. A study on the Gaussianity and stationarity of the random noise in the seismic exploration. Journal of Applied Geophysics109: 210–7. doi: 10.1016/j.jappgeo.2014.08.001
    https://doi.org/10.1016/j.jappgeo.2014.08.001 [Google Scholar]
  33. Yilmaz, Ö. 2001. Seismic data analysis: Processing, inversion, and interpretation of seismic data. In Society of exploration geophysicists, ed. Yilmaz. 1–64. Tulsa, Oklahoma (USA).
    [Google Scholar]
  34. Zhang, W., Z.Zhang, and X.Chen. 2012. Three-dimensional elastic wave numerical modeling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids. Geophysical Journal International190, no. 1: 358–78. doi: 10.1111/j.1365‑246X.2012.05472.x
    https://doi.org/10.1111/j.1365-246X.2012.05472.x [Google Scholar]
  35. Zhong, T., S.Zhang, Y.Li, and B.Yang. 2019. Simulation of seismic-prospecting random noise in the desert by a Brownian-motion-based parametric modeling algorithm. Comptes Rendus Geoscience351, no. 1: 10–16. doi: 10.1016/j.crte.2018.07.003
    https://doi.org/10.1016/j.crte.2018.07.003 [Google Scholar]
  36. Zhong, T., Y.Li, N.Wu, P.Nie, and B.Yang. 2015. A study on the stationarity and Gaussianity of the background noise in land-seismic prospecting. Geophysics80, no. 4: 67–82. doi: 10.1190/geo2014‑0153.1
    https://doi.org/10.1190/geo2014-0153.1 [Google Scholar]
  37. Zhou, J., M.Zhang, S.Piao, K.Iqbal, K.Qu, Y.Liu, and X.Li. 2019. Low frequency ambient noise modeling and comparison with field measurements in the South China Sea. Applied Acoustics148: 34–9. doi: 10.1016/j.apacoust.2018.11.013
    https://doi.org/10.1016/j.apacoust.2018.11.013 [Google Scholar]
  38. Zhou, Y., X.Chen, M.Jiang, and X.Zhou. 2016. Absorption and attenuation of seismic wave by shallow surface layer in Taklimakan desert [j]. Oil Geophysical Prospecting51, no. 02: 218–223+203. (in Chinese).
    [Google Scholar]
/content/journals/10.1080/08123985.2020.1764843
Loading
/content/journals/10.1080/08123985.2020.1764843
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): heterogeneous; image processing; Modelling; noise; random; seismic exploration

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