Seismic response of two-dimensional absorbing structures by the ray method
Article Sidebar
Published:
Nov 5, 1987
Keywords:
Seismic response,
Ray method,
Frequencydomain approach,
Slight causal absorption,
Classical basin problem
Volumes
Vols. 1-18 (1924-1944), ISSN 0044-2801
Main Article Content
Abstract
A method of seismic response analysis of 2 — D inhomogeneous structures, based on the ray method and on the application of the Debye procedure to include slight absorption, is presented. Program package RESPO, designed for such an analysis of the seismic response on the free surface of a general 2 — D laterally varying, geological near-surface structure assuming P, SV or SH plane-wave incidence from below, is briefly described. The package is tested on the classical model of a sedimentary basin. The study differs from previous applications of the ray method to the basin model in the following aspects. The frequency-domain approach is used. A comparison of the ray method results with the results of the discrete wavenumber method for long periods is made. More attention is paid to the analysis of the formation of the wave field. This analysis reveals two main types of wave propagation inside the basin: the dominant horizontally propagating local interference waves and less expressive vertically propagating waves in the central part of the basin. Effects of slight absorption (Futterman's causal absorption) are considered. The absorption causes a decrease in amplitudes and time delays at later times. The decrease in the amplitudes is not so expressive because of large periods and relatively short travel times of the waves investigated.
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Article Details
How to Cite
Moczo, P., Bard, P.-Y., & Pšenčik, I. (1987). Seismic response of two-dimensional absorbing structures by the ray method. Journal of Geophysics, 62(1), 38-49. Retrieved from https://journal.geophysicsjournal.com/JofG/article/view/136
Section
References
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Bard, P.-Y., Gariel, J.Ch.: The seismic response od 2-D sedimentary deposits with large vertical velocity gradients. Bull. Seismol. Soc. Am. 76, 343-366, 1986
Boore, D.M., Larner, K.L., Aki, K.: Comparison of two independent methods for the solution of wave scattering problems: response of a sedimentary basin to vertically incident SH waves. J. Geophys. Res. 76, 558-569, 1971
Cerveny, V.: Approximate expressions for the Hilbert transform of a certain class of functions and their application to the ray theory of seismic waves. Stud. Geophys. Geod. 20, 125-132, 1976
Cerveny, V.: The application of ray tracing to the numerical modeling of seismic wavefields in complex structures. In: Helbig, K, Treitel, S. (Eds.) Handbook of Geophysical Exploration. Section I: Seismic exploration. Dohr, G. (Ed.) Volume on Seismic shear waves, pp. 1-124. Geophysical Press, London 1985a
Cerveny, V.: Ray synthetic seismograms for complex two-dimensional and three-dimensional structures. J. Geophys. 58, 2-26, 1985b
Cerveny, V., Frangie, A.B.: Elementary seismograms of seismic body waves in dissipative media. Stud. Geophys. Geod. 24, 365-372, 1980
Cerveny, V., Frangie, A.B.: Effects of causal absorption on seismic body waves. Stud. Geophys. Geod. 26, 238-253, 1982
Cerveny, V., Hron, F.: The ray series method and dynamic ray tracing systems for 3 - D inhomogeneous media. Bull. Seismol. Soc. Am. 70, 47-77, 1980
Cerveny, V., Pšenčik, I.: SEIS83 - Numerical modeling of seismic wave fields in 2-D laterally varying layered structures by the ray method. In: Engdahl, E.R. (Ed.) Documentation of earthquake algorithms, Report SE-35, pp. 36-40. World Data Center (A) for Solid Earth Geophysics, Boulder, CO USA 1984
Cerveny, V., Ravindra, R.: Theory of seismic head waves. Toronto: University of Toronto Press 1971
Cerveny, V., Molotkov, I.A., Pšenčik, I.: Ray method in seismology. Praha: Karlova Universita 1977
Dravinski, M.: Scattering of plane harmonic SH wave by dipping layers of arbitrary shape. Bull. Seismol. Soc. Am. 73, 1303-1319, 1983
Futterman, W.l.: Dispersive body waves. J. Geophys. Res. 67, 5279-5291, 1962
Hong, T.L., Helm berger, D.V.: Glorified optics and wave propagation in nonplanar structure. Bull. Seismol. Soc. Am. 68, 1313-1330, 1978
Johnson, L.R., Silva, W.: The effects of unconsolidated sediments upon the ground motion during local earthquakes. Bull. Seismol. Soc. Am. 71, 127-142, 1981
Kjartansson, E.: Constant Q wave propagation and attentuation. J. Geophys. Res. 84, 4737-4748, 1979
Klem-Musatov, K.D., Aizenberg, A.M.: The ray method and the theory of edge waves. Geophys. J.R. Astron, Soc. 79, 35-50, 1984
Kohketsu, K.: 2-D reflectivity method and synthetic seismograms for irregularly layered structures - I. SH-wave generation. Geophys. J.R. Astron. Soc. 89, 821-838, 1987
Kravtsov, Yu.A., Orlov, Yu.I.: Geometrical optics of inhomogeneous media (in Russian). Moscow: Nauka 1980
Krebes, E.S.: The viscoelastic reflection/transmission problem: two special cases. Bull. Seismol. Soc. Am. 73, 1673-1683, 1983
Langston, Ch.A., Lee, J.J.: Effect of structure geometry on strong ground motions: the Duwamish river valley, Seattle, Washington. Bull. Seismol. Soc. Am. 73, 1851-1863, 1983
Lee, J.J., Langston, Ch.A.: Three-dimensional ray tracing and the method of principal curvature for geometric spreading. Bull. Seismol. Soc. Am. 73, 765-780, 1983a
Lee, J.J., Langston, Ch.A.: Wave propagation in a three-dimensional circular basin. Bull. Seismol. Soc. Am. 73, 1637-1653 1983b
Moczo, P., Cerveny, V., Pšenčik, I.: Documentation of earthquake algorithm - RESPO (program package). In: Zahradnik, J. (Ed.) Short description of computer programs for studying seismic response of nearsurface geological structures, pp. 14-17. Inst. Geophysics, Charles University, Prague Czech Republic 1985
Moczo, P., Cerveny, V., Pšenčik, I.: Application of ray method in seismic response analysis. In: Schenk, V., Schenkova, Z. (Eds.) Proc. of the 3rd Inter. Symp. on the Analysis of Seismicity and on Seismic Risk, Vol. II, pp. 455-463. Geophys. Inst. Czechosl. Acad. Sci. Prague 1986
Mueller, G.: Rheological properties and velocity dispersion of a medium with power-law dependence of Q on frequency. J. Geophys. 54, 20-29, 1983
Nowack, R., Aki, K.: The two-dimensional Gaussian beam synthetic method: testing and application. J. Geophys. Res. 89, 7797-7819, 1984
Sanchez-Sesma, F.J., Bravo, M.A., Herrera, I.: Surface motion of topographical irregularities for incident P, SV and Rayleigh waves. Bull. Seismol. Soc. Am. 75, 263-269, 1985
Virieux, J.: SH-wave propagation in heterogeneous media: velocitystress finite-difference method. Geophysics 49, 1933-1957, 1984
Y erokhin, L. Yu.: The seismic propagation in a valley with semielliptical boundary (in Russian). Izv. Akad. Nauk SSSR, Fizika Zemli, No. 8, 60-73, 1985
Zahradnik, J., Hron, F.: Seismic ground motion of sedimentary valley La Molina, Lima, Peru. In: Schenk, V. Schenkova, V. (Eds.) Proc. of the 3rd Inter. Symp. on the Analysis of Seismicity and on Seismic Risk, Vol. II, pp. 340-346. Geophys. Inst. Czechosl. Acad. Sci. Prague 1986
Zahradnik, J., Urban, L.: Effect of a simple mountain range on underground seismic motion. Geophys. J.R. Astron. Soc. 79, 167-183, 1984
Bard, P.-Y., Gariel, J.Ch.: The seismic response od 2-D sedimentary deposits with large vertical velocity gradients. Bull. Seismol. Soc. Am. 76, 343-366, 1986
Boore, D.M., Larner, K.L., Aki, K.: Comparison of two independent methods for the solution of wave scattering problems: response of a sedimentary basin to vertically incident SH waves. J. Geophys. Res. 76, 558-569, 1971
Cerveny, V.: Approximate expressions for the Hilbert transform of a certain class of functions and their application to the ray theory of seismic waves. Stud. Geophys. Geod. 20, 125-132, 1976
Cerveny, V.: The application of ray tracing to the numerical modeling of seismic wavefields in complex structures. In: Helbig, K, Treitel, S. (Eds.) Handbook of Geophysical Exploration. Section I: Seismic exploration. Dohr, G. (Ed.) Volume on Seismic shear waves, pp. 1-124. Geophysical Press, London 1985a
Cerveny, V.: Ray synthetic seismograms for complex two-dimensional and three-dimensional structures. J. Geophys. 58, 2-26, 1985b
Cerveny, V., Frangie, A.B.: Elementary seismograms of seismic body waves in dissipative media. Stud. Geophys. Geod. 24, 365-372, 1980
Cerveny, V., Frangie, A.B.: Effects of causal absorption on seismic body waves. Stud. Geophys. Geod. 26, 238-253, 1982
Cerveny, V., Hron, F.: The ray series method and dynamic ray tracing systems for 3 - D inhomogeneous media. Bull. Seismol. Soc. Am. 70, 47-77, 1980
Cerveny, V., Pšenčik, I.: SEIS83 - Numerical modeling of seismic wave fields in 2-D laterally varying layered structures by the ray method. In: Engdahl, E.R. (Ed.) Documentation of earthquake algorithms, Report SE-35, pp. 36-40. World Data Center (A) for Solid Earth Geophysics, Boulder, CO USA 1984
Cerveny, V., Ravindra, R.: Theory of seismic head waves. Toronto: University of Toronto Press 1971
Cerveny, V., Molotkov, I.A., Pšenčik, I.: Ray method in seismology. Praha: Karlova Universita 1977
Dravinski, M.: Scattering of plane harmonic SH wave by dipping layers of arbitrary shape. Bull. Seismol. Soc. Am. 73, 1303-1319, 1983
Futterman, W.l.: Dispersive body waves. J. Geophys. Res. 67, 5279-5291, 1962
Hong, T.L., Helm berger, D.V.: Glorified optics and wave propagation in nonplanar structure. Bull. Seismol. Soc. Am. 68, 1313-1330, 1978
Johnson, L.R., Silva, W.: The effects of unconsolidated sediments upon the ground motion during local earthquakes. Bull. Seismol. Soc. Am. 71, 127-142, 1981
Kjartansson, E.: Constant Q wave propagation and attentuation. J. Geophys. Res. 84, 4737-4748, 1979
Klem-Musatov, K.D., Aizenberg, A.M.: The ray method and the theory of edge waves. Geophys. J.R. Astron, Soc. 79, 35-50, 1984
Kohketsu, K.: 2-D reflectivity method and synthetic seismograms for irregularly layered structures - I. SH-wave generation. Geophys. J.R. Astron. Soc. 89, 821-838, 1987
Kravtsov, Yu.A., Orlov, Yu.I.: Geometrical optics of inhomogeneous media (in Russian). Moscow: Nauka 1980
Krebes, E.S.: The viscoelastic reflection/transmission problem: two special cases. Bull. Seismol. Soc. Am. 73, 1673-1683, 1983
Langston, Ch.A., Lee, J.J.: Effect of structure geometry on strong ground motions: the Duwamish river valley, Seattle, Washington. Bull. Seismol. Soc. Am. 73, 1851-1863, 1983
Lee, J.J., Langston, Ch.A.: Three-dimensional ray tracing and the method of principal curvature for geometric spreading. Bull. Seismol. Soc. Am. 73, 765-780, 1983a
Lee, J.J., Langston, Ch.A.: Wave propagation in a three-dimensional circular basin. Bull. Seismol. Soc. Am. 73, 1637-1653 1983b
Moczo, P., Cerveny, V., Pšenčik, I.: Documentation of earthquake algorithm - RESPO (program package). In: Zahradnik, J. (Ed.) Short description of computer programs for studying seismic response of nearsurface geological structures, pp. 14-17. Inst. Geophysics, Charles University, Prague Czech Republic 1985
Moczo, P., Cerveny, V., Pšenčik, I.: Application of ray method in seismic response analysis. In: Schenk, V., Schenkova, Z. (Eds.) Proc. of the 3rd Inter. Symp. on the Analysis of Seismicity and on Seismic Risk, Vol. II, pp. 455-463. Geophys. Inst. Czechosl. Acad. Sci. Prague 1986
Mueller, G.: Rheological properties and velocity dispersion of a medium with power-law dependence of Q on frequency. J. Geophys. 54, 20-29, 1983
Nowack, R., Aki, K.: The two-dimensional Gaussian beam synthetic method: testing and application. J. Geophys. Res. 89, 7797-7819, 1984
Sanchez-Sesma, F.J., Bravo, M.A., Herrera, I.: Surface motion of topographical irregularities for incident P, SV and Rayleigh waves. Bull. Seismol. Soc. Am. 75, 263-269, 1985
Virieux, J.: SH-wave propagation in heterogeneous media: velocitystress finite-difference method. Geophysics 49, 1933-1957, 1984
Y erokhin, L. Yu.: The seismic propagation in a valley with semielliptical boundary (in Russian). Izv. Akad. Nauk SSSR, Fizika Zemli, No. 8, 60-73, 1985
Zahradnik, J., Hron, F.: Seismic ground motion of sedimentary valley La Molina, Lima, Peru. In: Schenk, V. Schenkova, V. (Eds.) Proc. of the 3rd Inter. Symp. on the Analysis of Seismicity and on Seismic Risk, Vol. II, pp. 340-346. Geophys. Inst. Czechosl. Acad. Sci. Prague 1986
Zahradnik, J., Urban, L.: Effect of a simple mountain range on underground seismic motion. Geophys. J.R. Astron. Soc. 79, 167-183, 1984