Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
권호 표지
DOI QR코드

DOI QR Code

Efficient 3D Acoustic Wave Propagation Modeling using a Cell-based Finite Difference Method

셀 기반 유한 차분법을 이용한 효율적인 3차원 음향파 파동 전파 모델링

  • Park, Byeonggyeong (Department of Energy Resources Engineering, Pukyong National University) ;
  • Ha, Wansoo (Department of Energy Resources Engineering, Pukyong National University)
  • 박병경 (부경대학교 에너지자원공학과) ;
  • 하완수 (부경대학교 에너지자원공학과)
  • Received : 2019.02.14
  • Accepted : 2019.05.13
  • Published : 2019.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we studied efficient modeling strategies when we simulate the 3D time-domain acoustic wave propagation using a cell-based finite difference method which can handle the variations of both P-wave velocity and density. The standard finite difference method assigns physical properties such as velocities of elastic waves and density to grid points; on the other hand, the cell-based finite difference method assigns physical properties to cells between grid points. The cell-based finite difference method uses average physical properties of adjacent cells to calculate the finite difference equation centered at a grid point. This feature increases the computational cost of the cell-based finite difference method compared to the standard finite different method. In this study, we used additional memory to mitigate the computational overburden and thus reduced the calculation time by more than 30 %. Furthermore, we were able to enhance the performance of the modeling on several media with limited density variations by using the cell-based and standard finite difference methods together.

셀 기반 유한 차분법을 사용하여 P파 속도와 밀도 변화를 고려한 3차원 시간 영역 음향 파동 전파 모델링에서 성능을 향상시킬 수 있는 방법을 살펴보았다. 일반적인 유한 차분법에서는 격자점에 탄성파 속도 또는 밀도와 같은 물성을 할당하고 계산하지만 셀 기반 유한 차분법에서는 이러한 물성을 격자점 사이의 셀에 할당한다. 격자점에서의 차분식 계산을 위해서는 주변 셀의 물성 평균값을 이용하는데 이로 인해 일반적인 유한 차분법에 비해 계산량이 증가하게 된다. 이 연구에서는 이러한 계산량 문제를 개선하기 위해 메모리를 추가로 사용하여 모델링 시간을 30 % 이상 줄일 수 있었다. 또한 밀도가 제한적으로 변화하는 매질에서 셀 기반 유한 차분법과 일반 유한 차분법을 함께 사용하여 모델링 성능을 추가로 향상시킬 수 있었다.

Keywords

MRTSBC_2019_v22n2_56_f0001.png 이미지

Fig. 1. A cell-based finite difference grid set. Numbers indicate cell order adjacent to the central grid point. The fifth cell is below the first cell.

MRTSBC_2019_v22n2_56_f0002.png 이미지

Fig. 2. Algorithmic procedures of a time-domain modeling scheme.

MRTSBC_2019_v22n2_56_f0003.png 이미지

Fig. 3. Shot gathers (y = 6.76 km) obtained using (a) the cell-based finite difference method and (b) the standard finite difference method.

MRTSBC_2019_v22n2_56_f0004.png 이미지

Fig. 4. Snapshots (y = 6.76 km) obtained using the cell-based finite difference method (a, c, e) and the standard finite difference method (b, d, f) at 1 s (a, b), 2 s (c, d), and 3 s (e, f).

MRTSBC_2019_v22n2_56_f0005.png 이미지

Fig. 5. A two-layer density model with topography.

Table 1. Profiling results from a wave propagation modeling using the cell-based finite difference method.

MRTSBC_2019_v22n2_56_t0001.png 이미지

Table 2. Profiling results using additional memory.

MRTSBC_2019_v22n2_56_t0002.png 이미지

Table 3. Profiling results from different model types.

MRTSBC_2019_v22n2_56_t0003.png 이미지

References

  1. Alford, R. M., Kelly, K. R., and Boore, D. M., 1974, Accuracy of finite difference modeling of the acoustic wave equation, Geophysics, 39(6), 834-842. https://doi.org/10.1190/1.1440470
  2. Aminzadeh, F., Burkhard, N., Nicoletis, L., Rocca, F., and Wyatt, K., 1994, SEG/EAEG 3-D modeling project: 2nd update, The Leading Edge, 13(9), 949-952. https://doi.org/10.1190/1.1437054
  3. Belytichko, T., and Mullen, R., 1978, On dispersive properties of finite element solutions, in Miklowitz, J. and Achenbach, J. D., Eds, Modern problems in elastic wave propagation, John Wiley and Sons, 67-82.
  4. Graves, R. W., 1996, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences, Bull. of the Seismol. Soc. Amer., 86(4), 1091-1106.
  5. Jeong, W., Lee, H.-Y., and Min, D.-J., 2012, Full waveform inversion strategy for density in the frequency domain, Geophys. J. Int., 188(3), 1221-1241. https://doi.org/10.1111/j.1365-246X.2011.05314.x
  6. Keys, R. G., 1985, Absorbing boundary conditions for acoustic media, Geophysics, 50(6), 892-902. https://doi.org/10.1190/1.1441969
  7. Komatitsch, D., and Tromp, J., 1999, Introduction to the spectral element method for three-dimensional seismic wave propagation, Geophys. J. Int., 139(3), 806-822. https://doi.org/10.1046/j.1365-246x.1999.00967.x
  8. Marfurt, K. J., 1984, Accuracy of finite-difference and finiteelement modeling of the scalar and elastic wave equations, Geophysics, 49(5), 533-549. https://doi.org/10.1190/1.1441689
  9. Lee, G.-H., Pyun, S., Park, Y., and Cheong, S., 2016, Improvement of reverse-time migration using homogenization of acoustic impedance, Geophys. and Geophys. Explor., 19(2), 76-83. https://doi.org/10.7582/GGE.2016.19.2.076
  10. Lee, H.-Y., Min, D.-J., Kwon, B.-D., and Yoo, H.-S., 2008, Time-domain elastic wave modeling in anisotropic media using cell-based finite-difference method, Journal of the Korean Society for Geosystem Engineering, 45(5), 536-545 (in Korean with English abstract).
  11. Lee, H.-Y., Lim, S.-C., Min, D.-J., Kwon, B.-D., and Park, M., 2009, 2D time-domain acoustic-elastic coupled modeling: a cell-based finite-difference method, Geosci. J., 13(4), 407-414. https://doi.org/10.1007/s12303-009-0037-x
  12. Min, D.-J., Shin, C., and Yoo, H. S., 2004, Free-surface boundary condition in finite-difference elastic wave modeling, Bull. Seismol. Soc. of Amer., 94(1), 237-250. https://doi.org/10.1785/0120020116
  13. Min, D.-J., and Kim, H.-S., 2006, Feasibility of the surfacewave method for the assessment of physical properties of a dam using numerical analysis, J. Appl. Geophy., 59(3), 236-243. https://doi.org/10.1016/j.jappgeo.2005.09.004
  14. Seriani, G., and Priolo, E., 1994, Spectral element method for acoustic wave simulation in heterogeneous media, Finite Elem. Anal. Des., 16(3-4), 337-348. https://doi.org/10.1016/0168-874X(94)90076-0
  15. Virieux, J., and Operto, S., 2009, An overview of full-waveform inversion in exploration geophysics, Geophysics, 74(6), WCC1-WCC26. https://doi.org/10.1190/1.3238367