Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Acoustic Full-waveform Inversion using Adam Optimizer

Adam Optimizer를 이용한 음향매질 탄성파 완전파형역산

  • Kim, Sooyoon (Department of Ocean Energy and Resources Engineering, Korea Maritime and Ocean University) ;
  • Chung, Wookeen (Department of Energy and Resources Engineering, Korea Maritime and Ocean University) ;
  • Shin, Sungryul (Department of Energy and Resources Engineering, Korea Maritime and Ocean University)
  • 김수윤 (한국해양대학교 해양에너지자원공학과) ;
  • 정우근 (한국해양대학교 에너지자원공학과) ;
  • 신성렬 (한국해양대학교 에너지자원공학과)
  • Received : 2019.10.25
  • Accepted : 2019.11.28
  • Published : 2019.11.30
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Abstract

In this study, an acoustic full-waveform inversion using Adam optimizer was proposed. The steepest descent method, which is commonly used for the optimization of seismic waveform inversion, is fast and easy to apply, but the inverse problem does not converge correctly. Various optimization methods suggested as alternative solutions require large calculation time though they were much more accurate than the steepest descent method. The Adam optimizer is widely used in deep learning for the optimization of learning model. It is considered as one of the most effective optimization method for diverse models. Thus, we proposed seismic full-waveform inversion algorithm using the Adam optimizer for fast and accurate convergence. To prove the performance of the suggested inversion algorithm, we compared the updated P-wave velocity model obtained using the Adam optimizer with the inversion results from the steepest descent method. As a result, we confirmed that the proposed algorithm can provide fast error convergence and precise inversion results.

본 연구에서는 Adam 최적화 기법을 이용한 음향매질에서의 탄성파 파형역산 방법을 제안하였다. 탄성파 파형역산에서 최적화에 사용되는 기본적인 최대 경사법은 계산이 빠르고 적용이 간편하다는 장점이 있다. 하지만 속도 모델의 갱신에 일정한 갱신 크기를 사용함에 따라 오차가 정확하게 수렴하지 않는다. 이에 대한 대안으로 제시된 다양한 최적화 기법들의 경우 정확성은 높지만 많은 계산 시간을 필요로 한다는 한계가 있다. Adam 최적화 기법은 최근 딥 러닝 분야에서 학습 모델의 최적화를 위해 사용되는 기법으로 다양한 형태의 모델에 대한 최적화 문제에서 가장 효율적인 성능을 보이고 있다. 따라서 Adam 최적화 기법을 이용한 파형역산 방법을 개발하여 탄성파 파형역산에서의 오차가 빠르고 정확하게 수렴하도록 하였다. 제안된 역산 기법의 성능을 검증하기 위해, 일정한 갱신 크기를 가지는 최대 경사법을 이용하여 수행된 역산 결과와 제안된 Adam 최적화 기반 파형역산을 수행하여 갱신된 P파 속도 모델을 비교하였다. 그 결과 제안된 기법을 통해 빠른 오차 수렴 속도와 높은 정확도의 결과를 확인할 수 있었다.

Keywords

References

  1. Brossier, R., Operto, S., and Virieux, J., 2009, Seismic imaging of complex onshore structures by 2D elastic frequencydomain full-waveform inversion, Geophysics, 74(6), WCC105. https://doi.org/10.1190/1.3215771
  2. Dozat, T., 2016, Incorporating Nesterov Momentum into Adam, ICLR 2016 Workshop.
  3. Duchi, J., Hazan, E., and Singer, Y., 2011, Adaptive subgradient methods for online learning and stochastic optimization, J. Mach. Learn. Res., 12, 2121-2159.
  4. Gauthier, O., Virieux, J., and Tarantola, A., 1986, Twodimensional nonlinear inversion of seismic waveforms: Numerical results, Geophysics, 51, 1387-1403. https://doi.org/10.1190/1.1442188
  5. Ha, T., Chung, W., and Shin, C., 2009, Waveform inversion using a back-propagation algorithm and a Huber function norm, Geophysics, 74(3), R15-R24. https://doi.org/10.1190/1.3112572
  6. Ha, J., Shin, S., Shin, C., and Chung, W., 2015, Time domain full waveform inversion of seismic data for the East sea, Korea, using a pseudo-hessian method with source estimation, J. Seism. Explor., 24, 419-437.
  7. Hu, W., Abubakar, A., Habashy, T. M., and Liu, J., 2011, Preconditioned non-linear conjugate gradient method for frequency domain full-waveform seismic inversion, Geophys. Prospect., 59(3), 477-491. https://doi.org/10.1111/j.1365-2478.2010.00938.x
  8. Kingma, D., and Ba, J., 2014, Adam: A method for stochastic optimization, arXiv preprint, arXiv:1412.6980.
  9. Kolb, P., Collino, F., and Lailly, P., 1986, Pre-stack inversion of a 1-d medium, Proceedings of the IEEE, 74, 498-508. https://doi.org/10.1109/PROC.1986.13490
  10. Martin, G., Wiley, R., and Marfurt, K, J., 2006, Marmousi2: An elastic upgrade for Marmousi, The Leading Edge, 25(2), 156-166. https://doi.org/10.1190/1.2172306
  11. Mora, P. R., 1987, Nonlinear two-dimensional elastic inversion of multioffset seismic data, Geophysics, 42, 1211-1288. https://doi.org/10.1190/1.1442384
  12. Nesterov, Y., 1983, A method for unconstrained convex minimization problem with the rate of convergence O (1/$k^2$), Doklady AN USSR, 269, 543-547.
  13. Operto, S., Virieux, J., Dessa, J., and Pascal, G., 2006, Crustal seismic imaging from multifold ocean bottom seismometer data by frequency domain full waveform tomography: Application to the eastern Nankai trough, J. Geophys. Res. Solid Earth, 111, B09306.
  14. Pratt, R. G., 1990, Inverse theory applied to multi-source crosshole tomography. part 2: elastic wave-equation method, Geophys. Prospect., 38, 311-329. https://doi.org/10.1111/j.1365-2478.1990.tb01847.x
  15. Pratt, R. G., Shin, C., and Hicks, G. J., 1998, Gauss-newton and full Newton methods in frequency-space seismic waveform inversion, Geophys. J. Int., 133, 341-362. https://doi.org/10.1046/j.1365-246X.1998.00498.x
  16. Qian, N., 1999, On the momentum term in gradient descent learning algorithms, Neural networks, 12(1), 145-151. https://doi.org/10.1016/S0893-6080(98)00116-6
  17. Roden, J., and Gedney, S., 2000, Convolutional PML (CPML): An efficient FDTD implementation of the C-PML for arbitrary media, Microw. Opt. Techn. Let., 27(5), 334-339. https://doi.org/10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A
  18. Ruder, S., 2016, An overview of gradient descent optimization algorithms, arXiv preprint, arXiv:1609.04747.
  19. Shin, C., 1988, Nonlinear elastic wave inversion by blocky parameterization, Ph.D. thesis, University of Tulsa, 30p.
  20. Shin, C., Yoon, K., Marfurt, K. J., Park, K., Yang, D., Lim, H. Y., Chung, S., and Shin, S., 2001, Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion, Geophysics, 66, 1856-1863. https://doi.org/10.1190/1.1487129
  21. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49, 1259-1266. https://doi.org/10.1190/1.1441754
  22. Tieleman, T., and Hinton, G., 2012, Lecture 6.5 - RMSProp, COURSERA: Neural Networks for Machine Learning, Technical report.
  23. Zeiler, M. D., 2012, Adadelta: an adaptive learning rate method, arXiv preprint, arXiv:1212.5701.