Skip to main content
SpringerLink
Log in

High-Resolution Sonic Slowness Estimation Based on the Reconstruction of Neighboring Virtual Traces

  • Published:
Surveys in Geophysics Aims and scope Submit manuscript

Abstract

The estimation of elastic properties of thin-bed formations from sonic logging is challenging. Standard slowness processing of sonic logging waveforms typically yields an average slowness log profile over the span of the receiver array, obscuring thin-layer features smaller than the array aperture. In order to enhance vertical resolution of the slowness logs, the subarray processing techniques have been developed. However, for the subarrays with smaller aperture, the semblance from subarray waveforms becomes susceptible to noise, which results in a low signal-to-noise (S/N) ratio for the processing slowness logs. To overcome the above drawbacks, we propose a slowness estimation method with the enhanced resolution ranging from the conventional array aperture resolution to the inter-receiver spacing based on the reconstruction of neighboring virtual traces (RNVTs). The method utilizes super-virtual interferometry to reconstruct a large number of waveforms for slowness extraction using redundant information from overlapping receiver subarrays. We validate the feasibility and effectiveness of the proposed method using synthetic numerical experiments. By adding different levels of noise to synthetic data, we conclude that the new method has better noise robustness. Finally, we apply this method to field data, and the estimated high-resolution slowness logs show good agreement in interbedded sand-shale sequences. Both numerical tests and examples of field data show that, the slowness logs estimated by the new method can be obtained with a high resolution as well as with a high S/N ratio, providing an effective method for assessing slowness properties from a borehole.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

The authors are unable or have chosen not to specify which data have been used.

Abbreviations

STC:

Slowness-time coherence

ST:

Slowness time

S/N:

Signal-to-noise

SVI:

Super-virtual interferometry

LWD:

Logging while drilling

CAL:

Caliper logging

SVI-SNV:

Stacking of neighboring virtual-traces

RNVTs:

Reconstruction of neighboring virtual traces

FTSE:

Fast arrival time and slowness estimate

PML:

Perfectly matched layer

GR:

Gamma ray

VCL:

Volume of shale

References

  • Al-Hagan O, Hanafy SM, Schuster GT (2014) Iterative supervirtual refraction interferometry. Geophysics 79(3):Q21–Q30. https://doi.org/10.1190/geo2013-0210.1

    Article  Google Scholar 

  • Alshuhail A, Aldawood A, Hanafy S (2012) Application of super-virtual seismic refraction interferometry to enhance first arrivals: a case study from Saudi Arabia. The Leading Edge 31(1):34–39. https://doi.org/10.1190/1.3679326

    Article  Google Scholar 

  • An S, Hu T, Peng G (2017) Three-dimensional cumulant-based coherent integration method to enhance first-break seismic signals. IEEE Trans Geosci Remote Sens 55(4):2089–2096. https://doi.org/10.1109/TGRS.2016.2636336

    Article  Google Scholar 

  • Assous S, Elkington P, Linnett L (2014) Phase-based dispersion analysis for acoustic array borehole logging data. J Acoust Soc Am 135(4):1919–1928. https://doi.org/10.1121/1.4868396

    Article  Google Scholar 

  • Bader S, Wu X, Fomel S (2017) Semiautomatic seismic well ties and log data interpolation, pp 2381–2385. https://doi.org/10.1190/segam2017-17744197.1

  • Bassiouni Z (1994) Theory, measurement, and interpretation of well logs. Soc Pet Eng. https://doi.org/10.2118/9781555630560

    Article  Google Scholar 

  • Bharadwaj P, Schuster G, Mallinson I et al (2012) Theory of supervirtual refraction interferometry. Geophys J Int 188(1):263–273. https://doi.org/10.1111/j.1365-246X.2011.05253.x

    Article  Google Scholar 

  • Bharadwaj P, Wang X, Schuster G et al (2013) Increasing the number and signal-to-noise ratio of OBS traces with supervirtual refraction interferometry and free-surface multiples. Geophys J Int 192(3):1070–1084. https://doi.org/10.1093/gji/ggs087

    Article  Google Scholar 

  • Bharadwaj P, Schuster GT, Mallinson I (2011) Super-virtual refraction interferometry: Theory. In: SEG international exposition and annual meeting, SEG, pp SEG–2011. https://doi.org/10.1190/1.3628000

  • Bose S, Valero HP, Dumont A (2009) Semblance criterion modification to incorporate signal energy threshold. In: SEG technical program expanded abstracts 2009. Society of Exploration Geophysicists, pp 376–380

  • Brie A, Hsu K, Eckersley C (1988) Using the stoneley normalized differential energies for fractured reservoir evaluation. In: SPWLA Annual logging symposium, SPWLA, pp SPWLA–1988

  • Chen D, Guan W, Zhang C et al (2020) High-resolution inversion for dispersion characteristics of acoustic logging waveforms. J Geophys Eng 17(3):439–450. https://doi.org/10.1093/jge/gxaa003

    Article  Google Scholar 

  • Claerbout JF (1968) Synthesis of a layered medium from its acoustic transmission response. Geophysics 33(2):264–269. https://doi.org/10.1190/1.1439927

    Article  Google Scholar 

  • Coates R, Kane M, Chang C, et al (2000) Single-well sonic imaging: high-definition reservoir cross-sections from horizontal wells. In: SPE/CIM international conference on horizontal well technology, OnePetro. https://doi.org/10.2118/65457-MS

  • Dawood AA, Al-Shuhail A, Alshuhail A (2021) Enhancing the signal-to-noise ratio of sonic logging waveforms by super-virtual interferometric stacking. J Seism Explor 30(3):237–255

    Google Scholar 

  • Dong S, Sheng J, Schuster GT (2006) Theory and practice of refraction interferometry, pp 3021–3025. https://doi.org/10.1190/1.2370154

  • Ekstrom MP (1995) Dispersion estimation from borehole acoustic arrays using a modified matrix pencil algorithm. In: Conference record of the twenty-ninth asilomar conference on signals, systems and computers, IEEE, pp 449–453. https://doi.org/10.1109/ACSSC.1995.540589

  • Franco JA, Ortiz MM, De GS et al (2006) Sonic investigation in and around the borehole. Oilfield Rev 18(1):14–31

    Google Scholar 

  • Godio A, Dall’Ara A (2012) Sonic log for rock mass properties evaluation ahead of the tunnel face—a case study in the alpine region. J Appl Geophys 87:71–80. https://doi.org/10.1016/j.jappgeo.2012.09.007

    Article  Google Scholar 

  • Hanafy SM, AlHagan O, Al-Tawash F (2011) Super-virtual refraction interferometry: Field data example over a colluvial wedge. In: SEG international exposition and annual meeting, SEG, pp SEG–2011. https://doi.org/10.1190/1.3628001

  • Hanafy SM, Al-Hagan O (2012) Super-virtual refraction interferometry: an engineering field data example. Near Surface Geophys 10(5):443–449. https://doi.org/10.3997/1873-0604.2012032

    Article  Google Scholar 

  • Herrera RH, van der Baan M (2014) A semiautomatic method to tie well logs to seismic data. Geophysics 79(3):V47–V54. https://doi.org/10.1190/geo2013-0248.1

    Article  Google Scholar 

  • Hsu K, Baggeroer AB (1986) Application of the maximum-likelihood method (MLM) for sonic velocity logging. Geophysics 51(3):780–787. https://doi.org/10.1190/1.1442130

    Article  Google Scholar 

  • Hsu K, Chang S (1987) Multiple-shot processing of array sonic waveforms. Geophysics 52(10):1376–1390. https://doi.org/10.1190/1.1442250

    Article  Google Scholar 

  • Huang S, Torres-Verdín C (2016) Inversion-based interpretation of borehole sonic measurements using semianalytical spatial sensitivity functions. Geophysics 81(2):D111–D124. https://doi.org/10.1190/geo2015-0335.1

    Article  Google Scholar 

  • Huang S, Torres-Verdín C (2017) Fast-forward modeling of compressional arrival slowness logs in high-angle and horizontal wells. Geophysics 82(2):D107–D122. https://doi.org/10.1190/geo2016-0317.1

    Article  Google Scholar 

  • Huang S, Torres-Verdín C (2015) Sonic spatial sensitivity functions and inversion-based layer-by-layer interpretation of borehole sonic logs. In: SPWLA annual logging symposium, SPWLA, pp SPWLA–2015

  • Kazatchenko E, Markov M, Mousatov A (2003) Determination of primary and secondary porosity in carbonate formations using acoustic data. In: SPE Annual technical conference and exhibition? SPE, pp SPE–84,209. https://doi.org/10.2118/84209-MS

  • Khadhraoui B, Kisra S, Nguyen H (2018) A new algorithm for high depth resolution slowness estimate on sonic-array waveforms. In: SPWLA Annual Logging Symposium, SPWLA, p D053S012R001

  • Kimball CV, Marzetta TL (1984) Semblance processing of borehole acoustic array data. Geophysics 49(3):274–281

    Article  Google Scholar 

  • Kosloff DD, Baysal E (1982) Forward modeling by a Fourier method. Geophysics 47(10):1402–1412. https://doi.org/10.1190/1.1441288

    Article  Google Scholar 

  • Kosloff D, Reshef M, Loewenthal D (1984) Elastic wave calculations by the Fourier method. Bull Seismol Soc Am 74(3):875–891. https://doi.org/10.1785/BSSA0740030875

    Article  Google Scholar 

  • Kozak M, Williams J (2015) Instantaneous frequency-slowness analysis applied to borehole acoustic data. ASEG Ext Abstr 2015(1):1–5. https://doi.org/10.1071/ASEG2015ab159

    Article  Google Scholar 

  • Kozak M, Kozak M, Williams J (2006) Identification of mixed acoustic modes in the dipole full waveform data using instantaneous frequency-slowness method. In: SPWLA Annual Logging Symposium, SPWLA, pp SPWLA–2006

  • Lang S, Kurkjian A, McClellan J et al (1987) Estimating slowness dispersion from arrays of sonic logging waveforms. Geophysics 52(4):530–544. https://doi.org/10.1190/1.1442322

    Article  Google Scholar 

  • Lei T, Zeroug S, Bose S et al (2019) Inversion of high-resolution high-quality sonic compressional and shear logs for unconventional reservoirs. Petrophysics 60(06):697–711. https://doi.org/10.30632/PJV60N6-2019a1

    Article  Google Scholar 

  • Li W, Tao G, Matuszyk PJ et al (2015) Forward and backward amplitude and phase estimation method for dispersion analysis of borehole sonic measurements. Geophysics 80(3):D295–D308. https://doi.org/10.1190/geo2014-0298.1

    Article  Google Scholar 

  • 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. https://doi.org/10.1093/jge/gxaa059

    Article  Google Scholar 

  • Lu K, Liu Z, Hanafy S et al (2020) Noise reduction with reflection supervirtual interferometry. Geophysics 85(3):V249–V256. https://doi.org/10.1190/tle39070518.1

    Article  Google Scholar 

  • Ma R, Zou Z, Rui Y et al (2018) A composite absorbing boundary based on the SPML and sponge absorbing boundary for pseudo-spectral elastic wave modeling. Geophys Prospect Pet 57(1):94–103

    Google Scholar 

  • Maalouf E, Torres-Verdín C (2018) Interpretation of borehole sonic measurements acquired in vertical transversely isotropic formations penetrated by vertical wells. Geophysics 83(6):D187–D202. https://doi.org/10.1190/geo2017-0757.1

    Article  Google Scholar 

  • Maalouf E, Torres-Verdín C (2018) Inversion-based method to mitigate noise in borehole sonic logs. Geophysics 83(2):D61–D71. https://doi.org/10.1190/geo2017-0334.1

    Article  Google Scholar 

  • Mahiout S, Torlov V, Gouda M, et al (2022) High resolution acoustic analysis for improved formation evaluation of carbonate and clastic reservoirs. OnePetro, p D021S064R003. https://doi.org/10.2118/211603-MS

  • Mallinson I, Bharadwaj P, Schuster G et al (2011) Enhanced refractor imaging by supervirtual interferometry. The Leading Edge 30(5):546–550. https://doi.org/10.1190/1.3589113

    Article  Google Scholar 

  • Ma J, Matuszyk PJ, Mallan RK, et al (2010) Joint processing of forward and backward extended prony and weighted spectral semblance methods for robust extraction of velocity dispersion data. In: SPWLA Annual Logging Symposium, SPWLA, pp SPWLA–2010

  • McFadden P, Drummond B, Kravis S (1986) The nth-root stack: theory, applications, and examples. Geophysics 51(10):1879–1892. https://doi.org/10.1190/1.1442045

    Article  Google Scholar 

  • Montmayeur H, Graves R (1985) Prediction of static elastic/mechanical properties of consolidated and unconsolidated sands from acoustic measurements: basic measurements. In: SPE Annual Technical Conference and Exhibition? SPE, pp SPE–14,159. https://doi.org/10.2118/14159-MS

  • Mukhopadhyay P, Cheng A, Tracadas P (2013) The differential-phase based time-and frequency-semblance algorithm for array-acoustic processing and its application to formation-slowness measurement. Petrophysics 54(05):475–481

    Google Scholar 

  • Neidell NS, Taner MT (1971) Semblance and other coherency measures for multichannel data. Geophysics 36(3):482–497

    Article  Google Scholar 

  • Nolte B, Rao R, Huang X (1997) Dispersion analysis of split flexural waves. Tech. rep., Massachusetts Institute of Technology. Earth Resources Laboratory

  • Oyler DC, Mark C, Molinda GM (2008) Correlation of sonic travel time to the uniaxial compressive strength of us coal measure rocks. In: Proceedings of the 27th international ground control in mining conference, Morgantown, WV, pp 338–346

  • Paillet FL, Cheng CH (1991) Acoustic waves in boreholes. CRC Press, Boca Raton

    Google Scholar 

  • Pardo D, Matuszyk PJ, Torres-Verdin C et al (2013) Influence of borehole-eccentred tools on wireline and logging-while-drilling sonic logging measurements. Geophys Prospect 61(s1):268–283. https://doi.org/10.1111/1365-2478.12022

    Article  Google Scholar 

  • Peyret A, Torres-Verdin C, Xu Y (2006) Assessment of shoulder-bed, invasion, and lamination effects on borehole sonic logs: a numerical sensitivity study. In: SPWLA Annual Logging Symposium, SPWLA, pp SPWLA–2006

  • Qiao BP, 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. https://doi.org/10.6038/cjg20140621

    Article  Google Scholar 

  • Qiao B, Guo P, Wang P et al (2015) Retrieval of super-virtual refraction by cross-correlation. Geophys Prospect 63(3):552–566. https://doi.org/10.1111/1365-2478.12202

    Article  Google Scholar 

  • Razak MA, Ashqar A, Das S, et al (2021) Advances in cased hole acoustic slowness measurements and its application in a depleted reservoir drilled with highly inclined well: a case study from offshore Malaysia. In: International petroleum technology conference, IPTC, p D031S008R002. https://doi.org/10.2523/IPTC-21154-MS

  • Schuster GT (2009) Seismic interferometry. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Song X, Zhao Y, Dykstra J (2017) Active damping of acoustic ringing effect for oil well sonic logging system. IEEE Trans Ind Electron 64(4):3423–3432. https://doi.org/10.1109/TIE.2016.2598315

    Article  Google Scholar 

  • Song L, Zou Z, Huang Z (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

    Google Scholar 

  • Sun X, Ayadiuno C, Li W (2019a) A statistical prony method for shear slowness estimation from dipole measurements. In: SEG International exposition and annual meeting, SEG, p D043S129R005

  • Sun X, Ayadiuno C, Li W (2019b) A statistical Prony method for shear slowness estimation from dipole measurements, pp 859–863. https://doi.org/10.1190/segam2019-3216002.1

  • Tang XM (1997) Predictive processing of array acoustic waveform data. Geophysics 62(6):1710–1714. https://doi.org/10.1190/1.1444270

    Article  Google Scholar 

  • Tang X, Reiter E, Burns D (1995) A dispersive-wave processing technique for estimating formation shear velocity from dipole and Stoneley waveforms. Geophysics 60(1):19–28. https://doi.org/10.1190/1.1443747

    Article  Google Scholar 

  • Tang XM, Cheng CHA, Cheng A (2004) Quantitative borehole acoustic methods, vol 24. Elsevier, Amsterdam

    Google Scholar 

  • Tang X, Patterson D (2001) Detecting thin gas beds in formations using Stoneley wave reflection and high-resolution slowness measurements. In: SPWLA Annual Logging Symposium, SPWLA, pp SPWLA–2001

  • Valero HP, Hsu K, Brie A (2000) Multiple-shot processing in slowness and time domain of array sonic waveforms. In: SEG international exposition and annual meeting, SEG, pp SEG–2000. https://doi.org/10.1190/1.1815743

  • Walker K, Sun Q, Wang R (2019) Wavelength-based axial resolution limitations of flexural wave dispersion sonic logging. In: SPWLA Annual Logging Symposium, SPWLA, p D043S012R002

  • Walls J (1987) Poisson’s ratio and mechanical properties from core and well log measurements. Paper SPE 16795, pp 27–30

  • Wang R, Qiao W, Ju X (2012) A multi-channel acoustic logging signal dispersion analysis method. Well Logging Technol. 36(2):135–140. https://doi.org/10.16489/j.issn.1004-1338.2012.02.006

    Article  Google Scholar 

  • Wang R, Coates R, Zhao J (2021) Borehole sonic data dispersion analysis with a modified differential-phase semblance method. Petrophysics 62(04):379–392. https://doi.org/10.30632/PJV62N4-2021a3

    Article  Google Scholar 

  • Wang R, Hornby B, Walker K et al (2021) Advanced monopole and dipole sonic log data processing—part 1: real time. Geophysics 86(2):D77–D91. https://doi.org/10.1190/geo2020-0326.1

    Article  Google Scholar 

  • Wang R, Hornby B, Chang C, et al (2018) Enhanced-resolution dipole sonic logging data processing. In: SEG technical program expanded abstracts 2018. Society of exploration geophysicists, pp 679–683. https://doi.org/10.1190/segam2018-2995738.1

  • Wapenaar K, Fokkema J (2006) Green’s function representations for seismic interferometry. Geophysics 71(4):SI33–SI46. https://doi.org/10.1190/1.2213955

    Article  Google Scholar 

  • Wapenaar K, Draganov D, Snieder R et al (2010) Tutorial on seismic interferometry: part 1—basic principles and applications. Geophysics 75(5):75A195-75A209. https://doi.org/10.1190/1.3457445

    Article  Google Scholar 

  • 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. https://doi.org/10.1190/1.3463440

    Article  Google Scholar 

  • Wapenaar K, Draganov D, van der Neut J, et al (2005) Seismic interferometry: a comparison of approaches, pp 1981–1984. https://doi.org/10.1190/1.1851182

  • 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. https://doi.org/10.1109/TGRS.2023.3249250

    Article  Google Scholar 

  • Xu S (2023) Integrated multipole acoustic modeling and processing in general stressed formations, part 1: an effective approach study. Geoenergy Sci Eng 228(211):981. https://doi.org/10.1016/j.geoen.2023.211981

    Article  Google Scholar 

  • 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 61:1–16. https://doi.org/10.1109/TGRS.2023.3274517

    Article  Google Scholar 

  • 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. https://doi.org/10.6038/cjg20170734

    Article  Google Scholar 

  • 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. https://doi.org/10.1109/TGRS.2022.3219083

    Article  Google Scholar 

  • Xu X, Zou Z, Han M et al (2023) Deep-learning velocity model building by jointly using seismic first arrivals and early-arrival waveforms. Chin J Geophys. https://doi.org/10.6038/cjg2023Q0847. (in Chinese)

    Article  Google Scholar 

  • Zeng F, Yue W, Li C (2018) Dispersion analysis of borehole sonic measurements by Hilbert transform and band-pass filters. Geophysics 83(4):D127–D150. https://doi.org/10.1190/geo2017-0580.1

    Article  Google Scholar 

  • Zeroug S, Sinha BK, Lei T et al (2018) Rock heterogeneity at the centimeter scale, proxies for interfacial weakness, and rock strength-stress interplay from downhole ultrasonic measurements. Geophysics 83(3):D83–D95. https://doi.org/10.1190/geo2017-0049.1

    Article  Google Scholar 

  • 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, pp 1683–1686. https://doi.org/10.1190/1.1815742

Download references

Acknowledgements

This work was supported in part by was supported in part by the National Natural Science Foundation of China (42004097), 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). The authors would like to thank the Editor in Chief, Michael J. Rycroft, and three anonymous reviewers for their constructive comments and suggestions.

Author information

Authors and Affiliations

  1. Key Laboratory of Submarine Geosciences and Prospecting Techniques, Ministry of Education (MOE), College of Marine Geosciences, Ocean University of China, Qingdao, 266100, Shandong, China

    Song Xu, Shun Li & Zhihui Zou

  2. Evaluation and Detection Technology Laboratory of Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, 266061, Shandong, China

    Song Xu & Zhihui Zou

  3. Frontiers Science Center for Deep Ocean Multispheres and Earth System, Ocean University of China, Qingdao, 266100, Shandong, China

    Song Xu & Zhihui Zou

Authors
  1. Song Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhihui Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Song Xu.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, S., Li, S. & Zou, Z. High-Resolution Sonic Slowness Estimation Based on the Reconstruction of Neighboring Virtual Traces. Surv Geophys (2024). https://doi.org/10.1007/s10712-023-09820-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10712-023-09820-w

Keywords

Search

Navigation