Abstract
The accurate extraction of useful signals from the measurement data is one of the important parts and challenges of the understanding of subsurface information. The desired signal is usually hidden in the background noise, and the amplitude is weak due to the particular geological environment of the subsurface or the consistency of the measuring instrument. By extending the theory of seismic interferometry to include the effects of adjacent virtual channels and by combining super- and reverse-virtual interferometry, we obtain a hybrid virtual interferometry technique based on stacking neighboring virtual traces for wave reconstruction. We have verified the effectiveness of the processing method in suppressing noise interference and extracting useful signals using synthetic data tests. The method is applied to the processing and interpretation of acoustic measurements acquired in a cased borehole of a coal formation and an open hole of an igneous formation, where the processed waveforms are finely reconstructed, and the estimated slowness results are in good agreement with other measurements, thus providing an effective tool for data analysis.
Similar content being viewed by others
References
Al-Hagan O, Hanafy SM, Schuster GT (2014) Iterative supervirtual refraction interferometry. Geophysics 79(3):Q21–Q30
Alshuhail A, Aldawood A, Hanafy S (2012) Application of super-virtual seismic refraction interferometry to enhance first arrivals: a case study from Saudi Arabia. Lead Edge 31(1):34–39
An SP, Hu TY, Cui YF et al (2015) Auto-pick first breaks with complex raypaths for undulate surface conditions. Appl Geophys 12(1):93–100
Behr Y, Townend J, Bowen M et al (2013) Source directionality of ambient seismic noise inferred from three-component beamforming. J Geophys Res: Solid Earth 118(1):240–248
Bekara M, Van der Baan M (2009) Random and coherent noise attenuation by empirical mode decomposition. Geophysics 74(5):V89–V98
Beylkin G (1987) Discrete radon transform. IEEE Trans Acoust Speech Signal Process 35(2):162–172
Bharadwaj P, Schuster G, Mallinson I et al (2012) Theory of supervirtual refraction interferometry. Geophys J Int 188(1):263–273
Bharadwaj P, Schuster GT, Mallinson I (2011) Super-virtual refraction interferometry: theory. In: 2011 SEG Annual Meeting, OnePetro
Burns D, Cheng C (1987) Inversion of borehole guided wave amplitudes for formation shear wave attenuation values. J Geophys Res: Solid Earth 92(B12):12,713-12,725
Carcione JM, Kosloff D, Kosloff R (1988) Wave propagation simulation in a linear viscoelastic medium. Geophys J Int 95(3):597–611
Chen H (2020) Seismic frequency component inversion for elastic parameters and maximum inverse quality factor driven by attenuating rock physics models. Surv Geophys 41(4):835–857
Chen Y, Saygin E (2020) Empirical Green’s function retrieval using ambient noise source-receiver interferometry. J Geophys Res: Solid Earth 125(2):e2019JB018,261
Chen XL, Tang XM, Qian YP (2014) Simulation of multipole acoustic logging in cracked porous formations. Geophysics 79(1):D1–D10
Cheng N, Cheng C, Toksöz M (1995) Borehole wave propagation in three dimensions. J Acoust Soc Am 97(6):3483–3493
Cheng F, Xia J, Xu Z et al (2018) Frequency-wavenumber (fk)-based data selection in high-frequency passive surface wave survey. Surv Geophys 39:661–682
Claerbout JF (1968) Synthesis of a layered medium from its acoustic transmission response. Geophysics 33(2):264
Curtis A, Gerstoft P, Sato H et al (2006) Seismic interferometry-turning noise into signal. Lead Edge 25(9):1082–1092
Dabov K, Foi A, Katkovnik V et al (2007) Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095
Dang C, Radha H (2015) Rpca-kfe: key frame extraction for video using robust principal component analysis. IEEE Trans Image Process 24(11):3742–3753
Dawood AA, Al-Shuhail A, Alshuhail A (2021) Enhancing the signal-to-noise ratio of sonic logging waveforms by super-virtual interferometric stacking. J Ssismic Explor 30(3):237–255
De Ronde C, Humphris S, Hofig T (2019) The expedition 376 scientists. Brothers Arc Flux” in Proceedings of the International Ocean Discovery Program 376
Deighan AJ, Watts DR (1997) Ground-roll suppression using the wavelet transform. Geophysics 62(6):1896–1903
Delkhosh M, Parand K (2019) Generalized pseudospectral method: theory and applications. J Comput Sci 34:11–32
Do MN, Vetterli M (2005) The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans Image Process 14(12):2091–2106
Dong S, Sheng J, Schuster JT (2006) Theory and practice of refraction interferometry. In: 2006 SEG Annual Meeting, OnePetro
Draganov D, Campman X, Thorbecke J et al (2013) Seismic exploration-scale velocities and structure from ambient seismic noise (> 1 hz). J Geophys Res: Solid Earth 118(8):4345–4360
Duncan G, Beresford G (1995) Some analyses of 2-d median fk filters. Geophysics 60(4):1157–1168
Ellefsen K, Cheng C, Toksöz M (1991) Applications of perturbation theory to acoustic logging. J Geophys Res: Solid Earth 96(B1):537–549
Fahroo F, Ross IM (2002) Direct trajectory optimization by a chebyshev pseudospectral method. J Guid Control Dyn 25(1):160–166
Fahroo F, Ross IM (2008) Advances in pseudospectral methods for optimal control. In: AIAA guidance, navigation and control conference and exhibit, p 7309
Fornberg B (1987) The pseudospectral method; comparisons with finite differences for the elastic wave equation. Geophysics 52(4):483–501
Fornberg B, Sloan DM (1994) A review of pseudospectral methods for solving partial differential equations. Acta Numer 3:203–267
Futterman WI (1962) Dispersive body waves. J Geophys Res 67(13):5279–5291
Gottlieb D, Orszag SA (1977) Numerical analysis of spectral methods: theory and applications. SIAM
Hanafy SM, AlHagan O, Al-Tawash F (2011) Super-virtual refraction interferometry: Field data example over a colluvial wedge. In: 2011 SEG Annual Meeting, OnePetro
Hanafy SM, Al-Hagan O (2012) Super-virtual refraction interferometry: an engineering field data example. Near Surface Geophys 10(5):443–449
Hanafy S, Gupta H (2020) Seismic, super-virtual refraction interferometry. Encyclopedia of Solid Earth Geophysics, pp 1602–1607
Hertweck T, Schleicher J, Mann J (2007) Data stacking beyond cmp. Lead Edge 26(7):818–827
Hillers G, Campillo M, Ben-Zion Y et al (2014) Seismic fault zone trapped noise. J Geophys Res: Solid Earth 119(7):5786–5799
Hu TY, Wang RQ, White R (2000) Beamforming in seismic data processing. Chin J Geophys 43(1):89–100
Hu Y, Wang L, Cheng F et al (2016) Ground-roll noise extraction and suppression using high-resolution linear radon transform. J Appl Geophys 128:8–17
Jian M, Jinghuai G, Wenchao C (2006) On the denoising method of prestack seismic data in wavelet domain. In: SEG International Exposition and Annual Meeting, SEG, pp SEG–2006
Jones I, Levy S (1987) Signal-to-noise ratio enhancement in multichannel seismic data via the Karhunen-Loeve transform. Geophys Prospect 35(1):12–32
Joyce B, Patterson D, Leggett J, et al (2001) Introduction of a new omni-directional acoustic system for improved real-time lwd sonic logging-tool design and field test results. In: SPWLA 42nd Annual Logging Symposium, OnePetro
Khadhraoui B (2011) Use of differential geometry properties for multichannel first break picking. In: 73rd EAGE Conference and Exhibition incorporating SPE EUROPEC 2011, EAGE Publications BV, pp cp–238
Kimball CV, Marzetta TL (1984) Semblance processing of borehole acoustic array data. Geophysics 49(3):274–281
Kjartansson E (1979) Constant q-wave propagation and attenuation. J Geophys Res: Solid Earth 84(B9):4737–4748
Kosloff DD, Baysal E (1982) Forward modeling by a Fourier method. Geophysics 47(10):1402–1412
Kosloff D, Reshef M, Loewenthal D (1984) Elastic wave calculations by the Fourier method. Bull Seismol Soc Am 74(3):875–891
Lai J, Wang G, Fan Q, et al (2022) Toward the scientific interpretation of geophysical well logs: typical misunderstandings and countermeasures. Surv Geophys 1–32
LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444
Li S, Liu B, Xu X et al (2017) An overview of ahead geological prospecting in tunneling. Tunn Undergr Space Technol 63:69–94
Liang S, Hu T, Cui D et al (2020) Weak signal enhancement using adaptive local similarity and neighboring super-virtual trace for first arrival picking. J Geophys Eng 17(6):1005–1015
Liang C, Thornton MP, Morton P, et al (2009) Improving signal-to-noise ratio of passsive seismic data with an adaptive fk filter. In: SEG International Exposition and Annual Meeting, SEG, pp SEG–2009
Liner C (2010) An overview of wavelet transform concepts and applications. University of Houston, pp 1–17
Liu X (1999) Ground roll suppression using the Karhunen-Loeve transform. Geophysics 64(2):564–566
Liu QH, Schoen E, Daube F et al (1996) A three-dimensional finite difference simulation of sonic logging. J Acoust Soc Am 100(1):72–79
Liu GC, Chen XH, Li JY et al (2011) Seismic noise attenuation using nonstationary polynomial fitting. Appl Geophys 8(1):18–26
Liu G, Chen X, Du J et al (2012) Random noise attenuation using f-x regularized nonstationary autoregression. Geophysics 77(2):V61–V69
Lu Y, Wk L (2009) Edge-preserving polynomial fitting method to suppress random seismic noise. Geophysics 74(4):V69–V73
Lu K, Liu Z, Hanafy S et al (2020) Noise reduction with reflection supervirtual interferometry. Geophysics 85(3):V249–V256
Lv X, An S, Hu T et al (2018) Similarity-weighted super-virtual interferometry to enhance first breaks. Acta Scientiarum Naturalium Universitatis Pekinensis 54(1):87–93 (in Chinese)
Mallinson I, Bharadwaj P, Schuster G et al (2011) Enhanced refractor imaging by supervirtual interferometry. Lead Edge 30(5):546–550
Mayne WH (1962) Common reflection point horizontal data stacking techniques. Geophysics 27(6):927–938
Mikesell D, van Wijk K, Calvert A et al (2009) The virtual refraction: useful spurious energy in seismic interferometry. Geophysics 74(3):A13–A17
Moradikia M, Samadi S (2018) Sar image formation and feature separation via low rank sparse decomposition. In: Electrical Engineering (ICEE), Iranian Conference on, IEEE, pp 737–742
Nakata N, Snieder R, Tsuji T et al (2011) Shear wave imaging from traffic noise using seismic interferometry by cross-coherence. Geophysics 76(6):SA97–SA106
Nichols J, Mikesell D, Van Wijk K (2010) Application of the virtual refraction to near-surface characterization at the Boise hydrogeophysical research site. Geophys Prospect 58(6):1011–1022
Orszag SA (1972) Comparison of pseudospectral and spectral approximation. Stud Appl Math 51(3):253–259
Pitas I, Venetsanopoulos AN (1993) Knowledge-based image analysis for geophysical interpretation. J Intell Rob Syst 7:115–137
Prieto G, Lawrence J, Beroza G (2009) Anelastic earth structure from the coherency of the ambient seismic field. J Geophys Res: Solid Earth 114(B7)
Qiao B, Guo P, Wang P et al (2014) Effectively picking weak seismic signal near the surface based on reverse virtual refraction interferometry. Chin J Geophys 57(6):1900–1909
Qiao B, Guo P, Wang P et al (2015) Retrieval of super-virtual refraction by cross-correlation. Geophys Prospect 63(3):552–566
Rashed M (2014) Fifty years of stacking. Acta Geophys 62:505–528
Russell B, Hampson D, Chun J (1990) Noise elimination and the radon transform, part 1. Lead Edge 9(10):18–23
Sabbione JI, Sacchi MD, Velis DR (2015) Radon transform-based microseismic event detection and signal-to-noise ratio enhancement. J Appl Geophys 113:51–63
Sacchi MD, Kuehl H (2001) Arma formulation of fx prediction error filters and projection filters. J Seism Explor 9(3):185–198
Schimmel M, Gallart J (2007) Frequency-dependent phase coherence for noise suppression in seismic array data. J Geophys Res: Solid Earth 112(B4)
Schuster GT (2001) Theory of daylight/interferometric imaging-tutorial. In: 63rd EAGE conference & exhibition, EAGE Publications BV, pp cp–15
Schuster GT, Snieder R (2009) Seismic interferometry. Acoust Soc Am J 126(6):3375
Soleimani M, Jodeiri Shokri B, Rafiei M (2017) Improvement of seismic structural interpretation of Zagros fold-thrust belt by dip scanning in common diffraction surface imaging method. Acta Geod Geoph 52:283–299
Song LL, Zou ZH, Huang ZL (2019) Supervirtual refraction interferometry based on stacking of neighboring virtual-traces and its application to enhancing wide-angle obs refraction waves. Chin J Geophys 62(3):993–1006
Su Y, Wang D, Hu B et al (2023) Supervirtual refraction interferometry in the radon domain. Remote Sensing 15(2):384
Tang XM, Wang T, Patterson D (2002) Multipole acoustic logging-while-drilling. In: 2002 SEG annual meeting, OnePetro
Tang X, Cheng CHA (2004) Quantitative borehole acoustic methods, vol 24. Elsevier, Amsterdam
Tang X, Dubinsky V, Wang T, et al (2003) Shear-velocity measurement in the logging-while-drilling environment: modeling and field evaluations. Petrophys-SPWLA J Form Eval Reservoir Description 44(02)
Tang X, Patterson D (2005) Analyzing and processing acoustic logging data for poorly-bonded cased boreholes. In: SPWLA 46th Annual Logging Symposium, OnePetro
Tanimoto T, Wang J (2018) Low-frequency seismic noise characteristics from the analysis of co-located seismic and pressure data. J Geophys Res: Solid Earth 123(7):5853–5885
Toft P (1996) The radon transform. Theory and Implementation (Ph D Dissertation)(Copenhagen: Technical University of Denmark)
Trad D, Ulrych T, Sacchi M (2003) Latest views of the sparse radon transform. Geophysics 68(1):386–399
Varela CL, Rosa AL, Ulrych TJ (1993) Modeling of attenuation and dispersion. Geophysics 58(8):1167–1173
Vasconcelos I, Snieder R (2008) Interferometry by deconvolution: Part 1-theory for acoustic waves and numerical examples. Geophysics 73(3):S115–S128
Vasconcelos I, Snieder R (2006) Interferometric imaging by deconvolution: theory and numerical examples. In: 2006 SEG Annual Meeting, OnePetro
Wang Y, Lin FC, Schmandt B et al (2017) Ambient noise tomography across Mount St. Helens using a dense seismic array. J Geophys Res: Solid Earth 122(6):4492–4508
Wang H, Toksöz MN, Fehler MC (2020) Borehole acoustic logging-theory and methods. Springer, New York
Wang K, Hu T, Wang S (2022) Unsupervised learning for seismic internal multiple suppression based on adaptive virtual events. IEEE Trans Geosci Remote Sens 60:1–13
Wang K, Hu T, Wang S et al (2022) Seismic multiple suppression based on a deep neural network method for marine data. Geophysics 87(4):V341–V365
Wang K, Hu T, Zhao B (2023) Seismic internal multiple attenuation based on self-supervised deep learning with a local orthogonalization constraint. IEEE Trans Geosci Remote Sens
Wang Y, Luo Y, Schuster GT (2009) Interferometric interpolation of missing seismic data. Geophysics 74(3):SI37–SI45
Wapenaar K, Fokkema J (2006) Green’s function representations for seismic interferometry. Geophysics 71(4):SI33–SI46
Wapenaar K, Draganov D, Neut J et al (2004) Seismic interferometry: a comparison of approaches. Seg Technical Program Expanded Abstracts 23(1):1981
Wapenaar K, Draganov D, Snieder R et al (2010) Tutorial on seismic interferometry: Part 1 - basic principles and applications. Geophysics 75(5):75A195-75A209
Wapenaar K, Slob E, Snieder R et al (2010) Tutorial on seismic interferometry: Part 2-underlying theory and new advances. Geophysics 75(5):75A211-75A227
Wei ZT, Tang XM (2012) Numerical simulation of radiation, reflection, and reception of elastic waves from a borehole dipole source. Geophysics 77(6):D253–D261
Xu S (2023) Acoustic-wave radiations of mono-and dual-sources in poorly bonded cased boreholes: modeling and field applications. IEEE Trans Geosci Remote Sens 61:1–10
Xu S, Su YD, Tang XM (2017) A super-mixing-virtual interferometric array signal processing technique and its applications to cased-hole acoustic logging. Chin J Geophys 60(7):2904–2912
Xu S, Tang X, Torres-Verdín C et al (2018) Seismic shear wave anisotropy in cracked rocks and an application to hydraulic fracturing. Geophys Res Lett 45(11):5390–5397
Xu S, Tang XM, Su YD et al (2020) Crack-induced shear-wave orthorhombic anisotropy: Modeling and inversion of shear-wave borehole measurements. J Geophys Res: Solid Earth 125(3):e2019JB018,741
Xu S, Zou Z, Tang X (2022) Estimation of elastic wave velocity from logging-while-drilling measurement in unconsolidated formation of accretionary wedge in nankai trough. IEEE Trans Geosci Remote Sens 60:1–13
Xu S, Zou Z (2023) Supervirtual interferometry as a tool for slowness estimation of logging-while-drilling multipole acoustic data. IEEE Trans Geosci Remote Sens
Yilmaz Ö (2001) Seismic data analysis: Processing, inversion, and interpretation of seismic data. Society of Exploration Geophysicists
Zhang T, Tang X (2000) Waveform inversion of array acoustic log data for high-resolution formation slowness estimation. In: SEG Technical Program Expanded Abstracts 2000. Society of Exploration Geophysicists, p 1683–1686
Acknowledgements
The second field data used in this study are provided by the IODP and available from http://publications.iodp.org/index.html. This work was supported in part by the National Key R&D Program of China (grant no. 2021YFE0108800), in part by the Young-Talents-Project Start-up Foundation of Ocean University of China (202212017), and in part by the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology (2019QNRC001). Dr. Song Xu thanks Drs. Douglas Schmitt, Yanxin Yin, and Ying Liu for their valuable comments and suggestions that have helped improve the manuscript. The authors would like to thank the Editor in Chief, Michael J. Rycroft, and the anonymous reviewers for their constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Xu, S., Li, S. & Zou, Z. Hybrid Virtual Interferometry Technique Based on Stacking of Neighboring Virtual Traces to Enhance Acoustic Logging Data. Surv Geophys 45, 745–771 (2024). https://doi.org/10.1007/s10712-024-09825-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10712-024-09825-z