Weighted-averaging Finite-element Method for Scalar Wave Equation in the Frequency Domain

가중평균 유한요소법을 이용한 주파수영역에서의 인공 음향파 합성

  • 현혜자 (한국지질자원연구원 탐사개발연구부) ;
  • 서정희 (서울대학교 지구환경시스템공학부) ;
  • 민동주 (한국해양연구소 해양지질연구단)
  • Published : 2002.08.01


We develop the weighted-averaging finite-element method which uses four kinds of element sets. By constructing global stiffness and mass matrices for four kinds of element sets and then averaging them with weighting coefficients, we obtain a new global stiffness and mass matrix. With the optimal weighting coefficients minimizing grid dispersion and grid anisotropy, we can reduce the number of grid points required per wavelength to 4 for a $1\%$ upper limit of error. We confirm the accuracy of our weighted-averaging finite-element method through accuracy analyses for a homogeneous and a horizontal-layer model. By synthetic data example, we reconfirm that our method is more efficient for simulating a geological model than previous finite-element methods.


  1. Jo, C. H., Shin, C. S., and Suh, J. H., 1996, An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extra-polator: Geophysics, 61, 529-537
  2. Lysmer, J., and Drake, L. A., 1972, A finite element method for seismology: method in computational physic: Academic Press
  3. Marfurt, K. J., 1984, Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations: Geophysics, 49, 533-549
  4. Marfurt, K. J., and Shin, C. S., 1989, The future of interative modeling of geophysical exploration: in Supercomputers in Seismic Exploration: Pergamon Press
  5. Min, D. J., Shin, C. S., Kwon, B. D., and Chung, S. H., 2000, Improved frequency-domain elastic modeling using weighted averaging difference operators: Geophysics, 65, 884-895
  6. Shin, C. S., 1995, Sponge boundary condition for frequency domain modeling: Geophysics, 60, 1870-1874
  7. Shin, C. S., and Sohn, H. J., 1998, A frequency-space 2-D scalar wave extrapolator using extended 25-point finite difference operator: Geophysics, 63, 289-296
  8. Stekl, I. and Pratt, R. G., 1999, Accurate viscoelastic modeling by frequency-domain finite difference using rotated operators: Geophysics, 64, 1779-1794