ARTICLE

Seismic monitoring of CO2 injection using a distorted Born T-matrix approach in acoustic approximation

KENNETH MUHUMUZA1 MORTEN JAKOBSEN2 TEEMU LUOSTARI1 TIMO LÄHIVAARA1
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1 Department of Applied Physics, University of Eastern Finland, Kuopio, Finland.,
2 Department of Earth Sciences, University of Bergen, Bergen, Norway.,
JSE 2018, 27(5), 403–431;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Muhumuza, K., Jakobsen, M., Luostari, T. and Lahivaara’ T., 2018. Seismic monitoring of CO injection using a distorted Born T-matrix approach in acoustic approximation. Journal of Seismic Exploration, 27: 403-431. Monitoring the injected CO: distribution is at the core of any carbon capture and storage project. Waveform inversion methods can be used to obtain high-resolution images for monitoring the injected CO in the subsurface, but remains computationally challenging. Efficient modelling approximations are desirable for solving time-lapse inversion problems and to test the settings in which they give accurate predictions. We employed the distorted Born approximation (based on scattering integral equation) to simulate time-lapse synthetic data for a CO injection scenario with a single injector, and benchmarked it against the finite element and exact T-matrix approach. The distorted Born approximation presented, considers a general heterogeneous reference medium; and provides a framework for imaging of regions of time-lapse variation using the baseline survey as a reference and the monitor survey as perturbed to directly estimate the perturbation. Based on our simplified velocity model of CO injection, synthetic testing demonstrated that the new distorted Born approximation provides accurate predictions of the difference data seismograms. We tested the distorted Born iterative T-matrix (DBIT) inversion method on a synthetic dataset generated using T-matrix forward modelling, and 0963-065 1/18/$5.00 © 2018 Geophysical Press Ltd. 404 we investigated three inversion approaches. The inversion results showed that the DBIT method sufficiently retrieves the time-lapse velocity changes even in the cases of relatively low signal-to-noise ratio. The inversion approach that focused on the time- lapse data variation (perturbation only) gave improved results in noisy and noise free environments. We also applied DBIT inversion to a synthetic dataset generated using the finite element method, in order to avoid inverse crimes. The inversion recovered the trend of the velocity models, but with some inaccuracies in the estimates for the time- lapse velocity changes. The DBIT method which considers a dynamic background media and T-matrix approach may be a potential tool in seismic characterisation of subsurface reservoirs and efficient for monitoring of CO2 sequestration.

Keywords
waveform inversion
inverse theory
time-lapse seismic
scattering theory
wave propagation
computational seismology
CO2 sequestration
References
  1. Asnaashari, A., Brossier, R., Garambois, S., Audebert, F., Thore, P. and Virieux, J.,
  2. Time-lapse seismic imaging using regularized fullwaveform inversion with
  3. a prior model: which strategy? Geophys. Prosp., 63: 78-98.
  4. Ayeni, G. and Biondi, B., 2010. Target-oriented joint least-squares migration/inversion
  5. of time-lapse seismic data sets. Geophysics, 75: R61-R73.
  6. Ayeni, G. and Biondi, B., 2011. Wave-equation inversion of time-lapse seismic data sets.
  7. Expanded Abstr., 81st Ann. Internat. SEG Mtg., San Antonio.
  8. Barnes, C. and Charara, M., 2009. The domain of applicability of acoustic full-waveform
  9. inversion for marine seismic data. Geophysics., 74: WCC91-WCC103.
  10. Carcione, J.M., Picotti, S., Gei, D. and Rossi, G., 2006. Physics and seismic modeling for
  11. monitoring CO: storage. Pure Appl. Geophys, 163: 175-207.
  12. Cerveny, V., 2005. Seismic Ray Theory. Cambridge University Press, Cambridge.
  13. Chadwick, R., Noy, D., Arts, R. and Eiken, O., 2009. Latest time-lapse seismic data from
  14. sleipner yield new insights into CO2 plume development. Energy Proced., 1:
  15. 2103-2110.
  16. Cohen, J.K. and Bleistein, N., 1977. An inverse method for determining small variations
  17. in propagation speed. SIAM J. Appl. Mathemat., 32: 784-799.
  18. Colton, D. and Kress, R., 2012. Inverse Acoustic and Electromagnetic Scattering Theory.
  19. Springer Science & Business Media, 93.
  20. Couéslan, M.L., Smith, V., El-Kaseeh, G., Gilbert, J., Preece, N., Zhang, L. and Gulati,
  21. J., 2014. Development and implementation of a seismic characterization and CO2
  22. monitoring program for the Illinois basin—Decatur project: Greenhouse Gases.
  23. Sci. Technol., 4: 626-644.
  24. Eikrem, K., Jakobsen, M. and Nevdal, G., 2017. Bayesian inversion of time-lapse
  25. seismic waveform data using an integral equation method. Abstracts, IOR 2017-
  26. 19th Europ. Symp. Improv. Oil Recov.
  27. Eikrem, K.S., Neevdal, G., Jakobsen, M. and Chen, Y., 2016. Bayesian estimation of
  28. reservoir properties: effects of uncertainty quantification of 4D seismic data.
  29. Computat. Geosci., 20: 1211-1229.
  30. Farquharson, C.G. and Oldenburg, D.W., 2004. A comparison of automatic techniques
  31. for estimating the regularization parameter in non-linear inverse problems.
  32. Geophys. J. Internat., 156: 411-425.
  33. Gritto, R., Daley, T.M. and Myer, L.R., 2004. Joint cross-well and single-well seismic
  34. studies of CO2 injection in an oil reservoir. Geophys. Prosp., 52: 323-339.
  35. Haffinger, P., Gisolf, A. and van den Berg, P., 2013. Towards high resolution
  36. quantitative subsurface models by full waveform inversion. Geophys. J. Internat.,
  37. 193: 788-797.
  38. Ikelle, L.T. and Amundsen, L., 2005. Introduction to Petroleum Seismology. SEG, Tulsa,
  39. OK.
  40. Innanen, K.A., Naghizadeh, M. and Kaplan, S.T., 2014. Perturbation methods for two
  41. special cases of the time-lapse seismic inverse problem. Geophys. Prosp., 62:
  42. 453-474.
  43. IPCC, 2014. Climate Change 2014 - impacts, adaptation and vulnerability. Regional
  44. Aspects. Cambridge University Press, Cambridge.
  45. Ivandic, M., Juhlin, C., Liith, S., Bergmann, P., Kashubin, A., Sopher, D., Ivanova, A.,
  46. Baumann, G. and Henninges, J., 2015. Geophysical monitoring at the Ketzin pilot
  47. site for CO, storage: New insights into the plume evolution. Internat. J. Greenh.
  48. Gas Contr., 32: 90-105.
  49. Jakobsen, M., 2012. T-matrix approach to seismic forward modelling in the acoustic
  50. approximation. Studia Geophys. Geodaet., 56: 1-20.
  51. Jakobsen, M. and Ursin, B., 2015. Full waveform inversion in the frequency domain
  52. using direct iterative T-matrix methods. J. Geophys. Engineer., 12: 400.
  53. Kaipio, J. and Somersalo, E., 2006. Statistical and Computational Inverse Problems.
  54. Springer Science & Business Media, 160.
  55. Kasahara, J. and Hasada, Y., 2016. Time Lapse Approach to Monitoring Oil, Gas, and
  56. CO)? Storage by Seismic Methods. Elsevier Science, Amsterdam.
  57. Kim, Y., Cho, H., Min, D.-J. and Shin, C., 2011. Comparison of frequency-selection
  58. strategies for 2D frequency-domain acoustic waveform inversion. Pure Appl.
  59. Geophys., 168: 1715-1727.
  60. Kirchner, A. and Shapiro, S.A., 2001. Fast repeat-modelling of time-lapse seismograms.
  61. Geophys. Prosp., 49: 557-569.
  62. Kouri, DJ. and Vijay, A., 2003. Inverse scattering theory: Renormalization of the
  63. Lippmann-Schwinger equation for acoustic scattering in one dimension. Phys.
  64. Rev. E, 67: 046614.
  65. Lahivaara, T., Dudley Ward, N., Huttunen, T., Rawlinson, Z. and Kaipio, J., 2015.
  66. Estimation of aquifer dimensions from passive seismic signals in the presence of
  67. material and source uncertainties. Geophys. J. Internat., 200: 1662-1675.
  68. Liao, W., 2015. An adjoint-based Jacobi-type iterative method for elastic full waveform
  69. inversion problem. Appl. Mathemat. Computat., 267: 56-70.
  70. Maharramov, M. and Biondi, B., 2014. Robust joint full-waveform inversion of time-
  71. lapse seismic data sets with total-variation regularization. arXiv: 1408.0645.
  72. Marston, P.M., 2013. Pressure profiles for CO2-EOR and CCS: Implications for
  73. regulatory frameworks: Greenhouse Gases. Sci. Technol., 3: 165-168.
  74. Moser, T.J., 2012. Review of ray-Born forward modeling for migration and diffraction
  75. analysis. Studia Geophys. Geodaet., 56: 411-432.
  76. Newton, R.G., 2013. Scattering Theory of Waves and Particles. Springer Science &
  77. Business Media.
  78. Nowroozi, D., Lawton, D.C. and Khaniani, H., 2016. A framework for full waveform
  79. modeling and imaging for CO: injection at the FRS project. Abstracts,
  80. GeoConvention 2016.
  81. Pevzner, R., Urosevic, M., Popik, D., Shulakova, V., Tertyshnikov, K., Caspari, E.,
  82. Correa, J., Dance, T., Kepic, A. and Glubokovskikh, S., 2017. 4D surface seismic
  83. tracks small supercritical CO, injection into the subsurface: CO2CRC Otway
  84. project. Internat. J. Greenh. Gas Contr., 63: 150-157.
  85. Pratt, R.G., 1999. Seismic waveform inversion in the frequency domain, Part 1: Theory
  86. and verification in a physical scale model. Geophysics, 64: 888-901.
  87. Prieux, V., Operto, S., Brossier, R. and Virieux, J., 2009. Application of acoustic full
  88. waveform inversion to the synthetic Valhall velocity model. Expanded Abstr.,
  89. 79th Ann. Internat. SEG Mtg., Houston.
  90. Queier, M. and Singh, S.C., 2013. Full waveform inversion in the time lapse mode
  91. applied to CO storage at Sleipner: Geophys. Prosp., 61: 537-555.
  92. Raknes, E.B., Weibull, W. and Arntsen, B., 2013. Time-lapse full waveform inversion:
  93. Synthetic and real data examples. Expanded Abstr., 83rd Ann. Internat. SEG
  94. Mtg., Houston.
  95. Raknes, E.B., Weibull, W. and Arntsen, B., 2015. Seismic imaging of the carbon dioxide
  96. gas cloud at Sleipner using 3D elastic time-lapse full waveform inversion.
  97. Internat. J. Greenh. Gas Contr., 42: 26-45.
  98. Romdhane, A. and Querendez, E., 2014. CO> characterization at the sleipner field with
  99. full waveform inversion: Application to synthetic and real data. Energy Proced.,
  100. 63: 4358-4365.
  101. Shahin, A., Stoffa, P.L., Tatham, R.H. and Seif, R., 2011. Accuracy required in seismic
  102. modeling to detect production-induced time-lapse signatures. Expanded Abstr.,
  103. 81st Ann. Internat. SEG Mtg., San Antonio.
  104. Sheen, D.H., Tuncay, K., Baag, C.E. and Ortoleva, P.J., 2006. Time domain Gauss-
  105. Newton seismic waveform inversion in elastic media. Geophys. J. Internat., 167:
  106. 1373-1384.
  107. Shi, J.-Q., Xue, Z. and Durucan, S., 2007. Seismic monitoring and modelling of
  108. supercritical CO; injection into a water-saturated sandstone: Interpretation of P-
  109. wave velocity data. Internat. J. Greenh. Gas Contr., 1: 473-480.
  110. Sirgue, L. and Pratt, R.G., 2004. Efficient waveform inversion and imaging: A strategy
  111. for selecting temporal frequencies. Geophysics, 69: 231-248.
  112. Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation.
  113. Geophysics, 49: 1259-1266.
  114. Thierry, P., Operto, S. and Lambaré, G., 1998. Fast 2-D ray+Born migration/inversion in
  115. complex media. Geophysics, 64: 162-181.
  116. Virieux, J. and Operto, S., 2009. An overview of full-waveform inversion in exploration
  117. geophysics. Geophysics, 74: WCC1-WCC26.
  118. White, D., 2011. Geophysical monitoring of the Weyburn CO); flood: Results during 10
  119. years of injection. Energy Proced., 4: 3628-3635.
  120. Willemsen, B., Cao, J. and Roy, B., 2016. The impact of the acoustic approximation on
  121. time-lapse FWI. Expanded Abstr., 86th Ann. Internat. SEG Mtg., Dallas: 5435-
  122. Zhang, F., Juhlin, C., Ivandic, M. and Liith, S., 2013. Application of seismic full
  123. waveform inversion to monitor CO injection: Modelling and a real data example
  124. from the Ketzin site, Germany. Geophys. Prosp., 61: 284-299.
  125. Zhang, F., Juhlin, C., Niemi, A., Huang, F. and Bensabat, J., 2016. A feasibility and
  126. efficiency study of seismic waveform inversion for time-lapse monitoring of
  127. onshore CO, geological storage sites using reflection seismic acquisition
  128. geometries. Internat. J. Greenh. Gas Contr., 48: 134-141.
  129. Zhang, H., 2006. Direct Non-linear Acoustic and Elastic Inversion: Towards
  130. fundamentally new comprehensive and realistic target identification. Ph.D. thesis,
  131. University of Houston.
  132. Zhang, Z. and Huang, L., 2013. Double-difference elastic-waveform inversion with prior
  133. information for time-lapse monitoring. Geophysics, 78: R259-R273.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing