Effect of Grid Step Sizes on Computational Time Using Finite-Difference Method for Seismic Wave Modeling
Applied and Computational Mathematics
Volume 5, Issue 2, April 2016, Pages: 56-63
Received: Sep. 5, 2015;
Accepted: Sep. 21, 2015;
Published: Apr. 15, 2016
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Olowofela Joseph. A., Department of Physics, Federal University of Agriculture (FUNAAB), Abeokuta, Nigeria
Akinyemi Olukayode. D., Department of Physics, Federal University of Agriculture (FUNAAB), Abeokuta, Nigeria
Ajani Olumide. O., Department of Physics and Solar Energy, Bowen University, Iwo, Nigeria
Finite-difference method, a popular seismic forward modeling method is a technique which allows us to numerically solve partial differential equations like the wave equation solved in this paper. Beyond its use in standard data acquisition, it is a very instructive tool to understand how waves propagate in the earth's subsurface. Since the accuracy obtainable by using the finite difference scheme lies solely on its stability and ability to handle grid dispersion, this is achievable by applying appropriate grid step sizes. The developed finite-difference method was employed to generate snapshots of synthetic seismograms to highlight the effect of grid step sizes on computational time while ensuring numerical stability of the scheme used through accurate discretization of the medium and adopting Perfectly Matched Layer (PML) absorbing boundary conditions. Results shows that for a grid size of 5m x 5m x 5m having 260 x 260 x 100 grid points and time step of 100 - 500, the wavefield propagating is horizontally symmetric. From the results, the importance of grid step sizes on computational time is re-emphasized.
Olowofela Joseph. A.,
Akinyemi Olukayode. D.,
Ajani Olumide. O.,
Effect of Grid Step Sizes on Computational Time Using Finite-Difference Method for Seismic Wave Modeling, Applied and Computational Mathematics.
Vol. 5, No. 2,
2016, pp. 56-63.
Bohlen, T. & E. H. Saenger., 2006: Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves, Geophysics, 71, No. 4, Pages T109-T115.
Collinos, F. and Tsogka, C., 2001, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 66, No 1, 294 – 307.
Higham N. J., 1996. Accuracy and stability of numerical algorithms, Society for Industrial and applied Mathematics, Philadelphia, ISBN 0-8987 - 1355-2.
Kriiger, O. S., Saenger E. H., Oates, S. J and Shapiro, S. A., 2007, A numerical study on reflection coefficients of fractured media. Geophysics, 72, No. 3. D61 – D67.
Kurzmann, A. Przebindowska, A, Köhn, D. and Bohlen, T., 2013: Acoustic full waveform tomography in the presence of attenuation: a sensitivity analysis, Geophysical Journal International, 195 (2), 985 – 1000.
Moczo, P., Jozef, K and Halada, L., (2004), The finite-difference method for seismologist.
Moczo, P., J. Kristek, M. Galis., P. Pazak., M. Balazovjech., 2007, The Finite-Difference and Finite-Element Modeling of Seismic Wave Propagation and Earthquake motion. Acta Physica Slovaca, 57, No. 2, 177-406.
Olowofela, J. A., Akinyemi, O. D., and Ajani, O. O., (2015): Stability analysis for finite-difference schemeused for seismic imaging using amplitude and phase portrait. Applied and Computational Mathematics 4(1): 1-6.
Saenger, E. & T. Bohlen., 2004: Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid, Geophysics, 69, No. 2, 583-591.
Virieux, J., 1986, P – SV wave propagation in heterogeneous media: Velocity – Stress finite-difference method: Geophysics, 51, 889-901.