Seismic Wave-Field Propagation Modelling using the Euler Method
Author
Abstract
Wave-field extrapolation based on solving the wave equation is an important step in seismic modeling and needs a high level of accuracy. It has been implemented through a various numerical methods such as finite difference method as the most popular and conventional one. Moreover, the main drawbacks of the finite difference method are the low level of accuracy and the numerical dispersion for large time intervals (∆t). On the other hand, the symplectic integrators due to their structure can cope with this problem and act more accurately in comparison to the finite difference method. They reduce the computation cost and do not face numerical dispersion when time interval is increased. Therefore, the aim of the current paper is to present a symplectic integrator for wave-field extrapolation using the Euler method. Then, the extrapolation is implemented for rather large time intervals using a simple geological model. The extrapolation employed for both symplectic Euler and finite difference methods showed a better quality image for the proposed method. Finally the accuracy was compared to the finite difference method
Keywords
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16. Tal-Ezer, H., Kosloff, D., and Koren, Z., “An Accurate Scheme for Forward Seismic Modelling”, Geophysical Prospecting, Vol. 35, pp. 479-490, 1987.
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18. Moradpouri, F., Moradzadeh, A., Pestana, R. C., and Monfared, M. S., “Seismic Reverse Time Migration using a New Wave-Field Extrapolator and a New Imaging Condition”, Acta Geophysica, Vol. 64, No. 5, pp. 1673-1690, 2016.
19. Moradpouri, F., Moradzadeh, A., Pestana, R. C., and Monfared, M. S., “An Improvement in RTM Method to Image Steep Dip Petroleum Bearing Structures and its Superiority to Other Methods”, Journal of Mining and Environment, Vol. 8, No. 4, pp. 573-578, 2017
2. Li, Z., “Compensating Finite-Difference Errors in 3-D Migration and Modelling”, Geophysics, Vol. 56, pp. 1650-1660, 1991.
3. Kelly, K. R., Ward, R., Treitel, W. S., and Alford, R. M., “Synthetic Seismograms: A Finite-Difference Approach”, Geophysics, Vol. 41, pp. 2-27, 1976.
4. Virieux, J., “P-SV Wave Propagation in Heterogeneous Media: Velocity Stress Finite Difference Method”, Geophysics, Vol. 51, pp. 889-901, 1986.
5. Igel, H., Mora, P., and Riollet, B., “Anistotropic Wave Propagation through Finite-Difference Grids”, Geophysics, Vol. 60, pp. 1203-1216, 1995.
6. Etgen, J. T., and O’Brien, M. J., “Computational Methods for Large-Scale 3D Acoustic Finite-Difference Modeling, A Tutorial”, Geophysics, Vol. 72, pp. SM223-SM230, 2007.
7. Bansal, R., and Sen, M. K., “Finite-Difference Modelling of S-Wave Splitting in Anisotropic Media”, Geophysical Prospecting, Vol. 56, pp. 293-312, 2008.
8. Zhang, G., Zhang, Y., and Zhou, H., “Helical Finite-Difference Schemes for 3-D. Depth Migration”, 69th Annual International Meeting, SEG, Expanded Abstracts, pp. 862-865, 2000.
9. Fei, T., and Liner, C. L., “Hybrid Fourier Finite Difference 3D Depth Migration for Anisotropic Media”, Geophysics, Vol. 73, pp. S27-S34, 2008.
10. Moradpouri, F., Moradzadeh A., Pestana R. C., Ghaedrahmati, R., and Soleimani Monfared, M., “Improvement of Seismic Imaging Condition to Suppress RTM Artifacts”, Geophysics, Vol. 82, No. 6, pp. S403-S409, 2017.
11. Skell, R. H., Zhang G., and Schlick T., “A Family of Symplectic Integrators: Stability, Accuracy, and Molecular Dynamics Applications, SIAM Journal on Numerical Analysis”, Vol. 18, pp. 203-222, 1997.
12. Yoshida, H., “Construction of Higher Order Symplectic Integrators”, Physics Letters A, Vol. 150, pp. 262-268, 1990.
13. Deriglazov, A. A., and Filgueiras, J. G., Hamiltonian Formulation and Canonical Transformations in Classical Mechanics, Library of Physics Publication, São Paulo, 2009.
14. Chen, J., “Lax‐Wendroff and Nyström Methods for Seismic Modelling”, Geophysical Prospecting, Vol. 57, pp. 931-941, 2009.
15. Pestana, R. C., and Stoffa, P. L., “Time Evolution of the Wave Equation using Rapid Expansion Method”, Geophysics, Vol. 75, No. 4, pp. T121-T131, 2010.
16. Tal-Ezer, H., Kosloff, D., and Koren, Z., “An Accurate Scheme for Forward Seismic Modelling”, Geophysical Prospecting, Vol. 35, pp. 479-490, 1987.
17. Kosloff, D., Filho, A., Tessmer, E., and Behle, A., “Numerical Solution of the Acoustic and Elastic Wave Equation by New Rapid Expansion Method”, Geophysical Prospecting, Vol. 37, pp. 383-394. 1989.
18. Moradpouri, F., Moradzadeh, A., Pestana, R. C., and Monfared, M. S., “Seismic Reverse Time Migration using a New Wave-Field Extrapolator and a New Imaging Condition”, Acta Geophysica, Vol. 64, No. 5, pp. 1673-1690, 2016.
19. Moradpouri, F., Moradzadeh, A., Pestana, R. C., and Monfared, M. S., “An Improvement in RTM Method to Image Steep Dip Petroleum Bearing Structures and its Superiority to Other Methods”, Journal of Mining and Environment, Vol. 8, No. 4, pp. 573-578, 2017
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