News and Announcements
ARTICLE
An efficient method to model seismic propagation in diffusive-viscous media with dipping interfaces
FENGYUAN SUN,
JINGHUAI GAO,
NAIHAO LIU
Show Less
School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China, National Engineering Laboratory for Offshore Oil Exploration, Xi’an 710049, P.R.China.,
JSE 2019, 28(1), 21–40;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Sun, F.Y., Gao, J.H. and Liu, N.H., 2019. An efficient method to model seismic propagation in diffusive-viscous media with dipping interfaces. Journal of Seismic Exploration, 28: 21-40. Partial wavefield that is not be interfered by other waves plays a significant role in seismic exploration. In many applications, geophysicists are only interested in partial wavefields. In this work, we first derive an efficient workflow to simulate partial wavefields in the diffusive-viscous media with the presence of dipping layers. It can efficiently calculate various partial wavefields for investigating the seismic exploration based on the diffusive-viscous theory. Especially, the reflection/transmission coefficients in the dip layered media are studied through the coordinate transformation and the plane wave theory. Then, a fast integral method is used to synthesize the wavefields from a point source, and the best integral path is chosen to improve the accuracy and the computational efficiency. By choosing the appropriate sign of the complex slowness, the instability phenomenon in the computation process can be avoided. The analysis and numerical examples show that the proposed method is stable and efficient.
Keywords
partial wavefield
layered diffusive-viscous media
reflectivity method
References
- Alterman, Z. and Karal, F.C., 1968. Propagation of elastic waves in layered media by
- finite difference methods. Bull. Seismol. Soc. Am., 58: 367-398.
- Arntsen, B., Nebel, A.G. and Amundsen, L., 1998. Viscoacoustic finite-difference
- modeling in the frequency domain. J. Seismic.Explor., 7: 45-64.
- Aki, K. and Richards, P.G., 2002. Quantitative Seismology. W.H. Freeman, San Francisco.
- Berkhout, A.J., Ridder, J. and van der, Wal, L.F., 1982. Acoustic Imaging by Wave Field
- Extrapolation Part I: Theoretical Considerations. Acoustical Imaging. Springer,
- New York: 513-540.
- Bourbie, T. and Gonzalez-Serrano, A., 1983. Synthetic seismograms in attenuating media.
- Geophysics, 48: 1575-1587.
- Chapman, C.H., 1978. A new method for computing seismograms. Geophys. J. Internat.,
- 54: 481-518.
- Chen, X.F., 1990. Seismogram synthesis for multi-layered media with irregular interfaces
- by global generalized reflection/transmission matrices method. I. Theory of
- two-dimensional SH case. Bull. Seismol. Soc. Am., 80: 1696-1724.
- Chen, X.F., 1996. Seismogram synthesis for multi-layered media with irregular interfaces
- by global generalized reflection/transmission matrices method. III. Theory of
- 2D P-SV case. Bull. Seismol. Soc. Am., 86: 389-405.
- Carcione, J.M. and Tinivella, U., 2001. The seismic response to overpressure: a modeling
- study based on laboratory, well and seismic data. Geophys. Prosp., 49:
- 523-539.
- Cerveny, V., 2005. Seismic Ray Theory. Cambridge University Press, Cambridge.
- Filon, L.N.G., 1930. II 一 On a quadrature formula for trigonometric integrals. P. Roy.
- Soc. Edinb. A., 49: 38-47.
- Fuchs, K. and Miller, G., 1971. Computation of synthetic seismograms with the
- reflectivity method and comparison with observations. Geophys. J. Int., 23:
- 417-433.
- Frazer, L.N. and Gettrust, J.F., 1984. On a generalization of Filon's method and the
- computation of the oscillatory integrals of seismology. Geophys. J. Internat., 76:
- 461-481.
- Goloshubin, G.M., Verkhovsky, A.M., and Kaurov, V.V., 1996. Laboratory experiments
- of seismic monitoring. Extended Abstr., 58th EAGE Conf., Amsterdam.
- Guo, H.Y., Xiao-Mei, JI and Yu-Qi, L.I., 2001. A note on symplectic, multisymplectic
- scheme in finite element method. Commun. Theor. Phys., 36: 259-262.
- Ge, Z. and Chen, X., 2007. Wave propagation in irregularly layered elastic models: a
- boundary element approach with a global reflection/transmission matrix
- propagator. Bull. Seismol. Soc. Am., 97: 1025-1031.
- Gao, J. and Zhang, Y., 2013. Staggered-grid finite difference method with variable-order
- accuracy for porous media. Math. Probl. Engin., Article ID 157071, 1-10.
- Han, B., He, Q., Chen, Y. and Dou, Y., 2014. Seismic waveform inversion using the
- finite-difference contrast source inversion method. J. Appl. Math., Article ID
- 532159, 1-11.
- ten Kroode, F., 2002. Prediction of internal multiples. Wave Motion., 35: 315-338.
- Korneev, V.A., Goloshubin, G.M. and Daley, T.M., 2004. Seismic low-frequency effects
- in monitoring fluid-saturated reservoirs. Geophysics, 69: 522-532.
- Liu, E., Zhang, Z.J., Yue, JH. and Dobson, A., 2008. Boundary Integral Modelling of
- Elastic Wave Propagation in Multi-Layered 2D Media with Irregular Interfaces.
- Commun. Comput. Phys., 3: 52-62.
- Marfurt, K.J., 1984. Accuracy of finite-difference and finite-element modeling of the
- scalar and elastic wave equations. Geophys., 49: 533-549.
- Mars, J., Iii, R., James, W. and Lazaratos, S.K., 1999. Filter formulation and wavefield
- separation of cross-well seismic data. Geophys. Prosp., 47: 611-636.
- Min, D.J., 2002. Weighted-averaging finite-element method for 2d elastic wave equations
- in the frequency domain. J. Seis. Explor., 5: 197-222.
- Meng, W. and Fu, L.Y., 2017. Seismic wavefield simulation by a modified finite element
- method with a perfectly matched layer absorbing boundary. J. Geophys.
- Engin., 14: 852-864.
- Nowak, E.J. and Imhof, M.G., 2004. Diffractor localization via weighted Radon
- transforms. Expanded Abstr., 74th Ann. Internat. SEG Mtg., Denver:
- 2108-2111.
- Patera, A.T., 1984. A spectral element method for fluid dynamics: laminar flow in a
- channel expansion. J. Comput. Phys., 54: 468-488.
- Raikes, S.A. and White, J.E., 1984. Measurements of earth attenuation from downhole
- and surface seismic recording. Geophys. Prosp., 32: 892-919.
- Peelamedu, S.M., 1999. Active strain transfer analysis in a piezoceramic system using
- finite element method and experimental investigation. Smart Mater. Struct., 8:
- Smith, W.D., 1975. The application of finite element analysis to body wave propagation
- problems. Geophys. J. Internat., 42: 747-768.
- Shuey, R.T., 1985. A simplification of the Zoeppritz equations. Geophysics, 50: 609-614.
- Serdyukov, A.S. and Duchkov, A., 2015. Hybrid Kinematic-dynamic approach to seismic
- wave equation modeling, imaging, and tomography. Math. Probl. Eng., Article
- ID 543540, 1-8.
- Toks6z, M.N. and Johnston, D.H., 1981. Seismic Wave Attenuation. SEG, Tulsa, OK.
- Taeyoung, H., Yunseok, C., Shin, C. and Min, D.J., 2009. Numerical modeling for 3D
- acoustic wave equation in the frequency domain. J. Seismic Explor., 18: 57-79.
- Wu, C. and Harris, J. M., 2004. An optimized variable-grid finite-difference method for
- seismic forward modeling. J. Seismic Explor., 12: 343-353.
- Wang, M., Hung, B., Li, X. and Fintz, S., 2016. Challenges and strategies of interbed
- multiple attenuation in the Asia-Pacific region. Geophys. Prosp., 34: 81-85.
- Zhang, F. and Li, X., 2013. Generalized approximations of reflection coefficients in
- orthorhombic media. J. Geophys. Engin., 10: 054004.
- Zhao, H., Gao, J. and Zhao, J., 2014. Modeling the propagation of diffusive-viscous
- waves using flux-corrected transport—finite-difference method. IEEE J-Stars., 7:
- 838-844.
- Zhao, H.X., Gao, J.H. and Peng, J.G., 2017. Extended reflectivity method for modeling
- the propagation of diffusive-viscous wave in dip-layered media. Geophys.
- Prosp., 65: 4018-4022.
