ARTICLE

A gradient scaling method for Laplace domain full waveform inversion in acoustic-elastic coupled media

SIUNG-GOO KANG1 CHANGSOO SHIN2 WANSOO HA3 JONG KUK HONG4
Show Less
4 Division of Polar Earth-System Sciences, Korea Polar Research Institute, KIOST, Incheon 406-840, South Korea.,
2 Department of Energy Systems Engineering, Seoul National University, Seoul 151-742, South Korea. css@model.snu.ac.kr,
3 Department of Energy Resources Engineering, Pukyong National University, Busan 608-737, South Korea.,
JSE 2016, 25(3), 199–227;
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

Kang, S.-G., Shin, C., Ha, W. and Hong, J.K., 2016. A gradient scaling method for Laplace domain full waveform inversion in acoustic-elastic coupled media. Journal of Seismic Exploration, 25: 199-227. In 2D full waveform inversions of acoustic-elastic coupled media, wave propagation is described by the acoustic and isotropic elastic wave equations. To consider the irregular topography of the seafloor in full waveform inversions, the interface between the acoustic and elastic media in wave propagation modeling by the finite element method is represented using both square and isosceles triangular elements. However, numerical artifacts are generated near the seafloor, and widespread abnormal gradient directions are generated in the high velocity area in the target model, when the gradient direction is calculated during full waveform inversion in the Laplace domain. This issue generates unsuitable inversion results near the seafloor. We propose a scaling function that minimizes numerical artifacts in the gradient direction for Laplace domain full waveform inversion of acoustic-elastic coupled media. Based on a heuristic approach, we describe a gradient scaling method of Laplace-domain waveform inversion in acoustic-elastic coupled media that can be used to construct more accurate P- and S-wave velocity models of geological targets beneath the seafloor than previous methods. The technique scales the gradient direction using an accumulated gradient that is generated from the accumulated sum of the squares of the conventional gradient with respect to depth. This approach is designed to improve the imaging of large anomalies with high-velocity structures and to attenuate artifacts that are related to an irregular seafloor. We perform numerical tests using the synthetic SEG/EAGE salt model and field data. The numerical results demonstrate the validity of Laplace-domain waveform inversions that are calculated with the new scaling method for acoustic-elastic coupled media. The proposed gradient scaling method reduces artifacts more with field data than in the synthetic case. In particular, the abnormal high velocity areas near the seafloor in the inverted P- and S-wave velocity models are effectively removed by the gradient scaling method. We also conduct frequency-domain waveform inversion using the Laplace-domain inversion results as an initial model to confirm the accuracy of the inverted model of field data from our proposed inversion algorithm. The reverse time migration images and synthetic seismograms that were obtained from the field data indicate that this gradient scaling method is a useful tool for building accurate long-wavelength inverted P-and S-wave velocity models of field data from the Laplace domain full waveform inversion.

Keywords
acoustic-elastic coupled media
full waveform inversion
Laplace domain
gradient direction
scaling method
References
  1. Al-Yahya, K., 1989. Velocity analysis by iterative profile migration. Geophysics 54: 718-729.
  2. Aminzadeh, F., Burkhard, N., Nicoletis, L., Rocca, F. and Wyatt, K., 1994. SEG/EAEG 3-D
  3. modeling project: 2nd update. The Leading Edge, 13: 949-952,
  4. Bae, H.S., Shin, C., Cha, Y.H., Choi, Y. and Min, D.J., 2010. 2D acoustic-elastic coupled
  5. waveform inversion in the Laplace domain. Geophys. Prosp., 58: 997-1010.
  6. Billette, F. and Lambaré, G., 1998. Velocity macro-model estimation from seismic reflection data
  7. by stereotomography. Geophys. J. Internat., 135: 671-690. doi:
  8. 1046/j.1365-246X. 1998.00632.x
  9. Biondi, B., 1990. Seismic velocity estimation by beam stack. Ph.D. Dissertation, Stanford
  10. University, Palo Alto, CA.
  11. Biondi, B., 1992. Velocity estimation by beam stack. Geophysics, 57: 1034-1047.
  12. Bishop, T.N., Bube, K.P., Cutler R.T., Love, P.L., Resnick, J.R., Shuey, R.T., Spindler, D.A.
  13. and Wyld, H.W., 1985. Tomographic determination of velocity and depth in laterally
  14. varying media. Geophysics, 50: 903-923.
  15. 226 KANG, SHIN, HA & HONG
  16. Brenders, A.J. and Pratt, R.G., 2007. Full waveform tomography for lithospheric imaging: results
  17. from a blind test in a realistic crustal model. Geophys. J. Internat., 168: 133-151.
  18. Brossier, R., Operto, S. and Virieux, J., 2009. Seismic imaging of complex onshore structures by
  19. 2D elastic frequency-domain full-waveform inversion. Geophysics, 74: WCC105-WCC118.
  20. Bunks, C., Salek, F.M., Zaleski, S. and Chavent, G., 1995. Multiscale seismic waveform inversion.
  21. Geophysics, 60: 1457-1473. doi: 10.1190/1.1443880
  22. Chiu, S.K.L. and Stewart, R.R., 1987. Tomographic determination of three-dimensional seismic
  23. velocity structure using well-logs vertical seismic profiles and surface seismic data.
  24. Geophysics, 52: 1085-1098.
  25. Choi, Y., Min, D.-J. and Shin, C., 2008. Two-dimensional waveform inversion of multicomponent
  26. data in acoustic-elastic coupled media. Geophysics, 56: 863-881.
  27. Chung, W., Shin, C. and Pyun, S., 2010. 2D elastic full waveform inversion in the Laplace domain.
  28. Bull. Seismol. Soc. Am., 100: 3239-3249.
  29. Docherty, P., 1992. Solving for the thickness and velocity of the weathering layer using 2-D
  30. refraction tomography. Geophysics, 57: 1307-1318.
  31. Docherty, P., Silva, R., Singh, S., Song, Z. and Wood, M., 1997. Migration velocity analysis using
  32. a genetic algorithm. Geophys. Prosp., 45: 865-878.
  33. Farra, V. and Madariaga, R., 1988. Non-linear reflection tomography. Geophys. J. Internat., 95:
  34. 135-147.
  35. Gauthier, O., Virieux, J. and Tarantola, A., 1986. Two-dimensional nonlinear inversion of seismic
  36. waveforms: numerical results. Geophysics, 51: 1387-1403.
  37. Geller, R.J. and Hara, T., 1993. Two efficient algorithms for iterative linearized inversion of
  38. seismic waveform data. Geophys. J. Internat., 115: 699-710. doi:
  39. 1111/gji. 1993. 115.issue-3
  40. Ha, W., Cha, Y.H. and Shin, C., 2010a. A comparison between Laplace domain and frequency
  41. domain methods for inverting seismic waveforms. Explor. Geophys., 41: 189-197. doi:
  42. 1071/EG09031
  43. Ha, T., Chung, W. and Shin, C., 2009. Waveform inversion using a back-propagation algorithm
  44. and a Huber function. Geophysics, 74: R15-R24.
  45. Ha, W., Pyun, S., Yoo, J. and Shin, C., 2010b. Acoustic full waveform inversion of synthetic land
  46. and marine data in the Laplace domain. Geophys. Prosp., 58: 1033-1047.
  47. Ha, W. and Shin, C., 2012. Laplace-domain full-waveform inversion of seismic data lacking low
  48. frequency information. Geophysics, 77: 199-206.
  49. Hampson, D. and Russell, B., 1984. First break interpretation using generalized linear inversion.
  50. J. Canad. Soc. Explor. Geophys., 20: 40-54.
  51. Jin, S. and Madariaga, R., 1993. Background velocity inversion with a genetic algorithm.
  52. Geophysics, 20: 93-96.
  53. Kang, S.G., Bae, H. and Shin, C., 2012. Laplace-Fourier domain waveform inversion for fluid-solid
  54. media. Pure Appl. Geophys., 169: 2165-2179.
  55. Kim, M.H., Choi, Y., Cha, Y.H. and Shin, C., 2009. 2-D frequency-domain waveform inversion
  56. of coupled acoustic-elastic media with an irregular interface. Pure Appl. Geophys., 166:
  57. 1967-1985.
  58. Kolb, P., Collino, F. and Lailly, P., 1986. Pre-stack inversion of a 1-D medium. Proc. IEEE, 74:
  59. 498-508.
  60. Komatitsch, D., Barnes, C. and Tromp, J., 2000. Wave propagation near a fluid-solid interface: a
  61. spectral-element approach. Geophysics, 65: 623-631.
  62. Lailly, P., 1983. The seismic inverse problem as a sequence of before stack migrations. Expanded
  63. Abstr., Conf. Inverse Scatt.: Theory Applicat. Mathemat.: 206-220.
  64. Mora, P., 1987. Non-linear two-dimensional elastic inversion of multioffset seismic data.
  65. Geophysics, 52: 1211-1228.
  66. Operto, S., Ravaut, C., Improta, L., Virieux, J., Herrero, A. and Dell’Aversana, P., 2004.
  67. Quantitative imaging of complex structures from multi-fold wide aperture seismic data: a
  68. case study. Geophys. Prosp., 52: 625-651. doi: 10.1111/gpr.2004.52.issue-6
  69. ACOUSTIC-ELASTIC COUPLED WAVEFORM INVERSION 227
  70. Plessix, R.-E., 2009. 3D frequency-domain full-waveform inversion with an iterative solver.
  71. Geophysics, 74: WCC149-WCC157. doi: 10.1190/1.3211198
  72. Pratt, R.G., Shin, C. and Hicks, G.J., 1998. Gauss-Newton and full Newton method in frequency
  73. domain seismic waveform inversion. Geophys. J. Internat., 133: 341-362.
  74. Pyun, S., Son, W. and Shin, C., 2011. 3D acoustic waveform inversion in the Laplace domain using
  75. an iterative solver. Geophys. Prosp., 59: 386-399.
  76. Qin, F., Cai, W. and Schuster, G.T., 1993. Inversion and imaging of refraction data. Expanded
  77. Abstr., 81st Ann. Internat. SEG Mtg., San Antonio, 12: 613-615. doi:10.1190/1.1822567
  78. Riabinkin, L.A., 1957. Fundamentals of resolving power of controlled directional reception (CDR)
  79. of seismic waves. In: Slant Stack Processing. Geophysics Reprint Series, 1991, SEG, Vol.
  80. Translated and paraphrased from Prikladnaya 16, 3-36.
  81. Riabinkin, L.A., Napalkov, I.V., Znamenskii, V.V., Voskresenskii, I.N. and Rapoport, M., 1962.
  82. Theory and practice of the CDR seismic method. Transact. Gubkin Inst. Petrochem. Gas
  83. Product. (Moscow), 39.
  84. Shin, C. and Cha, Y.H., 2008. Waveform inversion in the Laplace domain. Geophys. J. Internat.,
  85. 173: 922-931.
  86. Shin, C. and Ha, W., 2008. A comparison between the behavior of objective functions for waveform
  87. inversion in the frequency and Laplace domains. Geophysics, 73: VE119-VE133.
  88. Shin, C., Jang, S. and Min, D., 2001. Improved amplitude preservation for prestack depth migration
  89. by inverse scattering theory. Geophys. Prosp., 49: 592-606.
  90. Shin, C. and Min, D.J., 2006. Waveform inversion using a logarithmic wavefield. Geophysics, 71:
  91. R31-R42.
  92. Shin, C., Pyun, S. and Bednar, J.B., 2007. Comparison of waveform inversion, part 1: conventional
  93. wavefield vs logarithmic wavefield. Geophys. Prosp., 55: 449-464.
  94. Shipp, R.M. and Singh, S.C., 2002. Two-dimensional full wavefield inversion of wide-aperture
  95. marine seismic streamer data. Geophysi. J. Internat., 151: 325-344.
  96. Shtivelman, V., 1996. Kinematic inversion of first arrivals of refracted waves-A combined approach.
  97. Geophysics, 61: 509-519.
  98. Sirgue, L., Barkved, O.I., Van Gestel, J.P., Askim, O.J. and Kommedal, J.H., 2009. 3D
  99. Waveform inversion on Valhall Wideazimuth OBC. Extended Abstr., 71st EAGE Conf.,
  100. Amsterdam: U038. http://www.earthdoc. org/detail. php?pubid =24070.
  101. Sirgue, L. and Pratt, R.G., 2004. Efficient waveform inversion and imaging: a strategy for selecting
  102. temporal frequencies. Geophysics, 69: 231-248.
  103. Stefani, J.P., 1995. Turing-ray tomography. Geophysics, 60: 1917-1929.
  104. Symes, W., 2008. Migration velocity analysis and waveform inversion. Geophys. Prosp., 56:
  105. 765-790. doi: 10.1111/gpr.2008.56.issue-6
  106. Symes, W. and Carazzone, J., 1991. Velocity inversion by differential semblance optimization.
  107. Geophysics, 56: 654-663.
  108. Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics,
  109. 49: 1259-1266.
  110. Vigh, D., Starr, W., Kapoor, J. and Li, H., 2010. 3D full waveform inversion on a Gulf of Mexico
  111. WAZ data set. Expanded Abstr., 80th Ann. Internat. SEG Mtg., Denver: 957-961.
  112. Virieux, J. and Operto, S., 2009. An overview of full-waveform inversion in exploration geophysics.
  113. Geophysics, 74(6): WCC1-WCC26, doi: 10.1190/1.3238367.
  114. White, D.J., 1989. Two-dimensional seismic refraction tomography. Geophys. J. Internat., 97:
  115. 223-245.
  116. Zhang, J. and Tokséz, M.N., 1998. Nonlinear refraction traveltime tomography. Geophysics, 63:
  117. 1726-1737.
  118. Zhu, X. and McMechan, G.A., 1989. Estimation of a two-dimensional seismic compressional-wave
  119. velocity distribution by iterative tomographic imaging. Internat. J. Imaging Syst. Technol.,
  120. 1: 13-17.
  121. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z., 2005. The Finite Element Method: Its Basis and
  122. Fundamentals. Butterworth-Heinemann, Oxford.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing