Abstract
Energy transfer for a random absorptive slab with finite thickness in a half space is formulated through a multiple scattering series approach. The resulted energy series is monotonous and converges fast for realistic models. Influence of slab thickness and bottom reflection to energy distribution is discussed with numerical calculations. It is shown that the slab bottom leakage tends to reduce the level of energy density and increase the apparent energy decay slope for receivers inside the slab, and therefore push the spatial distribution of energy density close to the single scattering prediction. On the other hand, for thick slabs (thickness greater than absorption length), the deviation from single scattering prediction becomes significant for strong scattering cases, pushing results close to the solutions of infinite medium. Slab bottom reflection tends to trap the scattered energy inside the slab and therefore compensate the effects of finite thickness. Results of numerical experiments using wave propagation matrix method show good agreement with the theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Asch, M., Kohler, W., Papanicolaou, G., Postel, M., and White, B., 1991, Frequency content of randomly scattered signals, SIAM Review, 33, 519–625.
Burridge, R., Papanicolaou, G., and White, B., 1988, One-dimensional wave propagation in highly discontinuous medium, Wave Motion, 10, 19–44.
Chandrasekhar, S., 1960, Radiative Transfer, Dover (Revised version of the 1950 edition).
Davison, B., 1957, Neutron Transport Theory, Oxford University Press.
Ishimaru, A., 1978, Wave propagation and scattering in random media, Vol. 2, Academic Press.
Kohler, W.E. and Papanicolaou, G.C., 1974, Power statistics for wave propagation in one-dimension and comparison with radiative transport theory II, J. Math. Phys., 15, 2186–2197.
O’Doherty, R. F., and Anstey, N.A., 1971, Reflections on amplitudes, Geophysical Prospecting, 19, 430–458.
Resnick, J. R., 1990, Stratigraphic filtering: in Wu, R.S. and Aki, K., Eds., Scattering and Attenuation of Seismic Waves, Part III, Birkhauser, 49–66.
Richards, P.G., and Menke, W., 1983, The apparent attenuation of a scattering medium, Bull. Seis. Soc. Am., 73, 1005–1021.
Schoenberger, M., and Levin, F.K., 1974, Apparent attenuation due to intrabed multiples, Geophys., 39, 278–291.
Schultz, C.A. and Toxsöz, M.N., 1993, Enhanced backscattering of seismic waves from a highly irregular, random interface: SH-case, Preprint.
Sheng, P., White, B., Zhang, Z.-Q., and Papanicolaou, G., 1990, Wave localization and multiple scattering in randomly-layered media, in Sheng, P., Ed., Scattering and Localization of Classical Waves in Random Media, World Scientific, 563–619.
White, B., Sheng, P. and Nair, B., 1990, Localization and backscattering spectrum of seismic waves in stratified lithology, Geophysics, 55, 1158–1165.
Wu, R.S., 1985, Multiple scattering and energy transfer of seismic waves — separation of scattering effect from intrinsic attenuation—I. Theoretical modeling, Geophys. J. R. astr. soc., 82, 57–80.
Wu, R.S., 1993, Separation of scattering an absorption in 1D random media from spatio-temporal distribution of seismic energy, Expanded Abstracts of the Technical Program, SEG 63th Annual Meeting, 1014–1017.
Wu, R.S., 1995, Spatial and temporal energy distributions of multiple-scattered waves in 111) random media and the separation of scattering from absorption,-I. Theory, Submitted to Geophysics.
Wu, R.S. and Xie, X.B., 1994, Separation of scattering an absorption in 1D random media, Numerical experiments on stationary problems, Expanded Abstracts of the Technical Program, SEG 64th Annual Meeting, 1302–1305.
Wu, R.S., Xie, X.B. and Kneib, G., 1994, Spatial and temporal energy distributions of multiple-scattered waves in 1-D random media and the separation of scattering from absorption,-II. Numerical simulation, submitted to Geophysics.
Zeng, Y., Su, F. and Aki, K., 1991, Scattering wave energy propagation in a medium with randomly distributed isotropic scatterers, J. Geophys. R., 96, 607–619.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Wu, RS. (1998). Spatio-temporal distribution of seismic power for a random absorptive slab in a half space. In: Papanicolaou, G. (eds) Wave Propagation in Complex Media. The IMA Volumes in Mathematics and its Applications, vol 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1678-0_13
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1678-0_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7241-0
Online ISBN: 978-1-4612-1678-0
eBook Packages: Springer Book Archive