Skip to main content
SpringerLink
Log in

Introduction to Denoising and Data Gap Filling of Seismic Reflection Data

  • Chapter
  • First Online:
Modern Singular Spectral-Based Denoising and Filtering Techniques for 2D and 3D Reflection Seismic Data

  • 378 Accesses

Abstract

Seismic data is a mixture of several wanted (reflections, refractions) and unwanted (ground roll, diffractions, airwave etc.) signals. Different wave fields recorded by the seismic receiver can be seen from Fig. 1.1. Separation of wanted signal from such unwanted noises is therefore fundamental in geophysical signal processing. Especially, it is very difficult for a visual inspection to completely distinguish primary reflections and noise in the raw data of active seismic experiment for the interpretation of subsurface layers and their discontinuities. The primary reflections in the raw seismic data are always hindered by the wave fields arising from several unwanted sources such as: diffractions, ground roll, airwave etc. and unknown random signals. Separation of signal from the noise is an important task in geophysical signal processing industry. The accuracy of seismic data interpretation mainly depends on the quality of the data i.e., Signal-to-Noise Ratio (S/N). Therefore, separation of unwanted signals from the seismic field data is almost essential and a challenging task in seismic industry for accurate and geologically consistent physical interpretation of primary reflections for understanding the study area. In the following section, we begin with the basic classification of different kinds of noises based on their statistical and spectral characteristics before proceeding to discuss about denoising techniques used in seismic industry.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abma, R. and Claerbout, J. (1995). Lateral prediction for noise attenuation by t-x and F-X techniques. Geophysics, 60(6), 1887–1896.

    Article  ADS  Google Scholar 

  • Al-Dossary, S. and Marfurt, K.J. (2006). 3D volumetric multispectral estimates of reflector curvature and rotation. Geophysics, 71(5), 41–51.

    Article  ADS  Google Scholar 

  • Allen, M.R. and Smith, L.A. (1997). Optimal filtering in singular spectrum analysis. Physics Letters A, 234(6), 419–428.

    Article  ADS  Google Scholar 

  • Alexandrov, T. (2009). A method of trend extraction using singular spectrum analysis. Revstat–Statistical Journal, 7(1), 1–22.

    MathSciNet  MATH  Google Scholar 

  • Barnett, T.P. and Hasselmann, K. (1979). Techniques of linear prediction, with application to oceanic and atmospheric fields in the tropical Pacific. Reviews of Geophysics, 17(5), 949–968.

    Article  ADS  Google Scholar 

  • Bekara, M. and Van der Baan, M. (2007). Local singular value decomposition for signal enhancement of seismic data. Geophysics, 72(2), V59–V65.

    Article  Google Scholar 

  • Bednar, J.B. (1983). Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data. Geophysics, 48(12), 1598–1610.

    Article  ADS  Google Scholar 

  • Broomhead, D.S. and King, G.P. (1986a). Extracting qualitative dynamics from experimental data. Physica D, 20, 217–236.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Broomhead, D.S. and King, G.P. (1986b). On the qualitative analysis of experimental dynamical systems: Nonlinear Phenomena and Chaos. Sarkar S. (Ed.), Adam Hilger, Bristol.

    Google Scholar 

  • Canales, L.L. (1984). Random noise reduction. In 1984 SEG Annual Meeting. Society of Exploration Geophysicists.

    Google Scholar 

  • Chopra, S. and Marfurt, K.J. (2007). Volumetric curvature attributes add value to 3D seismic data interpretation. The Leading Edge, 26(7), 856–867.

    Article  Google Scholar 

  • Claerbout, J.F. (1976). Fundamentals of geophysical data processing. Blackwell Scientific Publications.

    Google Scholar 

  • Colebrook, J.M. (1978) Continuous plankton records: Zooplankton and environment, north-east Atlantic and North Sea, 1948–1975 Oceanol. Acta, 1, 9–23.

    Google Scholar 

  • Danilov, D. and Zhigljavsky, A. (1997). Principal components of time series: The ‘Caterpillar’ method. St. Petersburg: University of St. Petersburg.

    Google Scholar 

  • Darche, G. (1990). Spatial interpolation using a fast parabolic transform. 60th Annual International Meeting, SEG, Expanded Abstracts, 1647–1650.

    Google Scholar 

  • Djarfour, N., Ferahtia, J., Babaia, F., Baddari, K., Said, E.A. and Farfour, M. (2014). Seismic noise filtering based on Generalized Regression Neural Networks. Computers & Geosciences, 69, 1–9.

    Article  ADS  Google Scholar 

  • Duijndam, A.J.W., Schonewille, M.A. and Hindriks, C.O.H. (1999). Reconstruction of band-limited signals, irregularly sampled along one spatial direction. Geophysics, 64(2), 524–538.

    Article  ADS  Google Scholar 

  • Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. and Picard, D. (1996). Density estimation by wavelet thresholding. The Annals of Statistics, 24, 508–539.

    Article  MathSciNet  MATH  Google Scholar 

  • Elsner, J.B. and Tsonis, A.A. (Eds.) (1996). Singular spectrum analysis: A new tool in time series analysis. Springer Science & Business Media.

    Google Scholar 

  • Foster, D.J., Mosher, C.C. and Hassanzadeh, S. (1994). Wavelet transform methods for geophysical applications. 1994 SEG Annual Meeting. Society of Exploration Geophysicists.

    Google Scholar 

  • Fraedrich, K. (1986). Estimating dimensions of weather and climate attractors. J. Atmos. Sci., 43, 419–432.

    Article  ADS  MathSciNet  Google Scholar 

  • Ghil, M., Allen, M.R., Dettinger, M.D., Ide, K., Kondrashov, D., Mann, M.E., Robertson, A.W., Saunders, A., Tian, Y., Varadi, F. and Yiou, P. (2002). Advanced spectral methods for climatic time series. Review of Geophysics, 40(1), 1003–1044.

    Article  ADS  Google Scholar 

  • Golyandina, N., Nekrutkin, V. and Zhigljavsky, A.A. (2001). Analysis of Time Series Structure: SSA and Related Techniques. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Taylor & Francis.

    Google Scholar 

  • Golyandina, N. and Stepanov, D. (2005). SSA-based approaches to analysis and forecast of multidimensional time series. In: Proceedings of the 5th St. Petersburg Workshop on Simulation (Vol. 293, p. 298).

    Google Scholar 

  • Golyandina, N. and Zhigljavsky, A. (2013). Basic SSA. In: Singular Spectrum Analysis for Time Series. Springer, Berlin, Heidelberg.

    Google Scholar 

  • Hamza, A.B. and Krim, H. (2001). Image denoising: A nonlinear robust statistical approach. IEEE Transactions on Signal Processing, 49(12), 3045–3054.

    Article  ADS  Google Scholar 

  • Hassani, H. (2007). Singular Spectrum Analysis: Methodology and Comparison (No. 4991). University Library of Munich, Germany.

    Google Scholar 

  • Karhunen, K. (1947). Under Lineare Methoden in der Wahr Scheinlichkeitsrechnung. Annales Academiae Scientiarun Fennicae Series A1: Mathematia Physica, 47.

    Google Scholar 

  • Karsli, H., Dondurur, D. and Çifçi, G. (2006). Application of complex-trace analysis to seismic data for random-noise suppression and temporal resolution improvement. Geophysics, 71(3), V79–V86. https://doi.org/10.1190/1.2196875.

    Article  Google Scholar 

  • Kondrashov, D. and Ghil, M. (2006). Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Processes in Geophysics, 13, 151–159.

    Article  ADS  Google Scholar 

  • Kondrashov, D., Shprits, Y. and Ghil, M. (2010). Gap filling of solar wind data by singular spectrum analysis. Geophysical Research Letters, 37(15).

    Google Scholar 

  • Kumar, V.V., Manikandan, S., Ebenezer, D., Vanathi, P.T. and Kanagasabapathy, P. (2007). High density impulse noise removal in color images using median controlled adaptive recursive weighted median filter. IAENG International Journal of Computer Science, 34(1).

    Google Scholar 

  • Liu, B. and Sacchi, M.D. (2004). Minimum weighted norm interpolation of seismic records. Geophysics, 69(6), 1560–1568.

    Article  ADS  Google Scholar 

  • Liu, C., Liu, Y., Yang, B., Wang, D. and Sun, J. (2006). A 2D multistage median filter to reduce random seismic noise. Geophysics, 71(5), V105–V110.

    Article  Google Scholar 

  • Liu, Y., Liu, C. and Wang, D. (2009). A 1-D time-varying median filter for seismic random, spike-like noise elimination. Geophysics, 74, V17–V24.

    Article  ADS  Google Scholar 

  • Loève, M. (1945). Nouvelles classes de lois limites. Bulletin de la Société Mathématique de France, 73, 107–126.

    Article  MathSciNet  MATH  Google Scholar 

  • Lu, W. (2006). Adaptive noise attenuation of seismic images based on singular value decomposition and texture direction detection. Journal of Geophysics and Engineering, 3(1), 28.

    Article  ADS  Google Scholar 

  • Naghizadeh, M. and Sacchi, M.D. (2007). Multistep autoregressive reconstruction of seismic records. Geophysics, 72(6), V111–V118.

    Article  Google Scholar 

  • Naghizadeh, M. and Sacchi, M.D. (2010). Seismic data reconstruction using multidimensional prediction filters. Geophysical Prospecting, 58(2), 157–173.

    Article  ADS  Google Scholar 

  • Oropeza, V. and Sacchi, M. (2011). Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics, 76(3), V25–V32.

    Article  ADS  Google Scholar 

  • Palus, M. and Dvorak, I. (1992). Singular-value decomposition in attractor reconstruction: Pitfalls and precautions. Physica D: Nonlinear Phenomena, 55(1), 221–234.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Porsani, M.J. (1999). Seismic trace interpolation using half-step prediction filters. Geophysics, 64(5), 1461–1467.

    Article  ADS  Google Scholar 

  • Rajesh, R. and Tiwari, R.K. (2015). Windowed SSA (Singular Spectral Analysis) for Geophysical Time Series Analysis. Journal of Geological Resource and Engineering, 3, 167–173.

    Google Scholar 

  • Rekapalli, R. and Tiwari, R.K. (2015a). A short note on the application of Singular Spectrum Analysis for Geophysical Data processing. J. Ind. Geophys. Union, 19(1), 77–85.

    Google Scholar 

  • Rekapalli, R. and Tiwari, R.K. (2015b). Singular Spectrum Based Algorithms for denoising 2D and 3D Seismic Data. Journal of Geophysics, 3, 129–137.

    Google Scholar 

  • Rekapalli, R., Tiwari, R.K., Dhanam, K. and Seshunarayana, T. (2014). T-x frequency filtering of high-resolution seismic reflection data using singular spectral analysis. Journal of Applied Geophysics, 105, 180–184. https://doi.org/10.1016/j.jappgeo.2014.03.017.

    Article  ADS  Google Scholar 

  • Rekapalli, R., Tiwari, R.K. and Seshunarayan, T. (2012). Denoising and clean reconstruction of seismic signals using Space Lagged Singular Spectral Analysis (SLSSA). AGU Fall Meeting Abstracts, San Fransisco, USA.

    Google Scholar 

  • Rekapalli, R., Priyadarshi, Shubham K. and Tiwari, R.K. (2015b). Assessment of Singular Spectrum and Wavelet based denoising schemes in generalized inversion based seismic wavelet estimation. Society of Petroleum Geophysics, Jaipur-India, https://doi.org/10.13140/RG.2.1.4344.2640.

  • Rekapalli, R., Tiwari, R.K. and Sen, M.K. (2016). Fault identification by diffraction separation from seismic reflection data using time slice SSA based algorithm. In: SEG Technical Program. Expanded Abstracts 2016, 3920–3924.

    Google Scholar 

  • Rekapalli, R., Tiwari, R.K., Sen, M.K. and Vedanti, N. (2017). 3D seismic data de-noising and reconstruction using Multichannel Time Slice Singular Spectrum Analysis. Journal of Applied Geophysics, 140, 145–153.

    Google Scholar 

  • Rekapalli, R., Tiwari, R.K., Sen, M.K. and N. Vedanthi (2015a). Denoising of 3D seismic data using multichannel singular spectrum based time slice and horizon processing. In: R.V. Schneider (Ed.), SEG Technical Program. Expanded Abstracts 2015, 4708–4713, Society of Exploration Geophysicists.

    Google Scholar 

  • Roberts, A. (2001). Curvature attributes and their application to 3D interpreted horizons. First Break, 19(2), 85–100. https://doi.org/10.1046/j.0263-5046.2001.00142.x.

    Article  MathSciNet  Google Scholar 

  • Sacchi, M.D. (2009). FX singular spectrum analysis. CSPG CSEG CWLS Convention, Abstracts, 392–395.

    Google Scholar 

  • Sacchi, M.D., Ulrych, T.J. and Walker, C.J. (1998). Interpolation and extrapolation using a high-resolution discrete Fourier transform. Signal Processing, IEEE Transactions on, 46(1), 31–38.

    Article  ADS  MathSciNet  Google Scholar 

  • Scales, J.A. and Snieder, R. (1998). What is noise? Geophysics, 63(4), 1122–1124.

    Article  ADS  Google Scholar 

  • Schoellhamer, D.H. (2001). Singular spectrum analysis for time series with missing data. Geophysical Research Letters, 28(16), 3187–3190.

    Article  ADS  Google Scholar 

  • Serita, A., Hattori, K., Yoshino, C., Hayakawa, M. and Isezaki, N. (2005). Principal component analysis and singular spectrum analysis of ULF geomagnetic data associated with earthquakes. Natural Hazards and Earth System Science, 5(5), 685–689.

    Article  ADS  Google Scholar 

  • Sheriff, R.E. and Geldart, L.P. (1983). Exploration seismology. Vol. 1: History, theory, and data acquisition. Cambridge University Press.

    Google Scholar 

  • Spitz, S. (1991). Seismic trace interpolation in the FX domain. Geophysics, 56(6), 785–794.

    Article  ADS  Google Scholar 

  • Spitz, S. and Deschizeaux, B. (1994). Random noise attenuation in data volumes-F-XY predictive filtering versus a signal space technique. In: 56th EAEG Meeting.

    Google Scholar 

  • Starck, J.L., Donoho, D.L. and Candès, E.J. (2003). Astronomical image representation by the curvelet transform. Astronomy & Astrophysics, 398(2), 785–800.

    Google Scholar 

  • Telford, W.M. and Sheriff, R.E. (2010). Applied geophysics (2nd Edition). Cambridge University Press.

    Google Scholar 

  • Tiwari, R.K. and Rajesh, R. (2014). Factorized Hankel optimal singular spectral approach for erratic and noisy seismic signal denoising. Journal of Applied Geophysics, 111, 95–101.

    Article  ADS  Google Scholar 

  • Trad, D., Ulrych, T. and Sacchi, M. (2002). Accurate interpolation with high-resolution time-variant Radon transforms. Geophysics, 67, 644–656. doi:https://doi.org/10.1190/1.1468626.

    Article  ADS  Google Scholar 

  • Trickett, S.R. (2002). F-x Eigen image noise suppression. Annual International Meeting, SEG Expanded Abstracts (pp. 2166–2169).

    Google Scholar 

  • Trickett, S.R. (2003). F-xy eigenimage noise suppression. Geophysics, 68, 751–759. https://doi.org/10.1190/1.1567245.

    Article  ADS  Google Scholar 

  • Trickett, S. (2008). F-xy Cadzow noise suppression. In: 78th Annual International Meeting, SEG, Expanded Abstracts (pp. 2586–2590).

    Google Scholar 

  • Ulrych, T.J., Freire, S. and Siston, P. (1988). Eigen image processing of seismic sections. 58th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts.

    Google Scholar 

  • Ulrych, T.J., Sacchi, M.D. and Graul, J.M. (1999). Signal and noise separation: Art and science. Geophysics, 64(5), 1648–1656.

    Article  ADS  Google Scholar 

  • Varadi, F., Pap, J.M., Ulrich, R.K., Bertello, L. and Henney, C.J. (1999). Searching for signal in noise by random-lag singular spectrum analysis. The Astrophysical Journal, 526(2), 1052.

    Article  ADS  Google Scholar 

  • Vautard, R. and Ghil, M. (1989). Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D: Nonlinear Phenomena, 35(3), 395–424.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Weare, B.C. and Nasstrom, J.S. (1982). Examples of extended empirical orthogonal function analyses. Monthly Weather Review, 110(6), 481–485.

    Article  ADS  Google Scholar 

  • Yilmaz, O. (2001). Seismic data analysis: Processing, inversion, and interpretation of seismic data. Society of Exploration Geophysicists. ISBN 978-1-56080-099-6.

    Google Scholar 

  • Zotov, L.V. (2012). Application of multichannel singular spectrum analysis to geophysical fields and astronomical images. Advances in Astronomy and Space Physics, 2, 82–84.

    ADS  Google Scholar 

  • Zhigljavsky, A. (2011). Singular spectrum analysis for time series. In: International Encyclopaedia of Statistical Science. Springer Berlin Heidelberg.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CSIR-NGRI, Hyderabad, India

    R. K. Tiwari & R. Rekapalli

Authors
  1. R. K. Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Rekapalli
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Capital Publishing Company

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Tiwari, R.K., Rekapalli, R. (2020). Introduction to Denoising and Data Gap Filling of Seismic Reflection Data. In: Modern Singular Spectral-Based Denoising and Filtering Techniques for 2D and 3D Reflection Seismic Data. Springer, Cham. https://doi.org/10.1007/978-3-030-19304-1_1

Download citation

Publish with us

Policies and ethics

Search

Navigation