Abstract
It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (KENNETT, 1983; Luco and APSEL, 1983; YAO and HARKRIDER, 1983; CHEN, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (APSEL and Luco, 1983; HISADA, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (DAHLQUIST and BJÖRCK, 1974; CHANG, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.
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
Aki, K. and Richards, P. Q., Quantitative Seismology (Freeman, San Francisco, 1980).
Apsel, R. J. and Luco, J. E. (1983), On the Green’s Functions for a Layered Half-space. Part II, Bull. Seismol. Soc. Am. 73, 931–951.
Bouchon, M. (1979), Discrete Wavenumber Representation of Elastic Wave Fields in Three Space Dimensions, J. Geophys. Res. 84, 3604–3614.
Bouchon, M. (1982), The Complete Synthesis of Seismic Crustal Phases at Regional Distance, J. Geophys. Res. 87(B3), 1735–1741.
Bouchon, M. and Aki, K. (1977), Discrete Wavenumber Representation of Seismic Source Wave Fields, Bull. Seismol. Soc. Am. 67, 259–277.
CHANG, S. H. (1988), Complete Wave field Modeling and Seismic Inversion for Lossy-elastic Layered Half-space due to Surface Force, Ph. D. Thesis, University of Southern California, Los Angeles.
Chen, X. F. (1993), A Systematic and Efficient Method of Computing Normal Modes for Multi-layered Half-space, Geophys. J. Int. 115, 391–409.
Chen, X. F. (1999), Seismograms Synthesis in Multi-layered Half-space Media. Part I. Theoretical Formulations, Earthquake Res. in China 13, 149–174.
Dahlquist, G. and BjÖRck, A., Numerical Methods (Prentice-Hall Inc., Englewood Cliffs, N. J., 1974).
Dravinski, M. and Mossessian, T. K. (1988), On Evaluation of the Green Function for Harmonic Line Loads in an Elastic Half-space, J. Num. Meth. Engng. 26, 823–841.
Fucus, K. and Moller, G. (1971), Computation of Synthetic Seismograms with Reflectivity Method and Comparison with Observations, Geophys. J. R. Astr. Soc. 23, 417–433.
Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products (Academic Press, New York, 1980).
Helmberger, D. V. (1974), Generalized Ray Theory for Shear Dislocations, Bull. Seismol. Soc. Am. 64, 45–64.
Hisada, Y. (1994), An Efficient Method for Computing Green’s Functions for a Layered Half-space with Sources and Receivers at Close Depths, Bull. Seismol. Soc. Am. 84, 1457–1472.
Hisada, Y. (1995), An Efficient Method for Computing Green’s Functions for a Layered Half-space with Sources and Receivers at Close Depths (Part 2), Bull. Seismol. Soc. Am. 85, 1080–1093.
Kennett, B. L. N. Seismic Wave Propagation in Stratified Media (Cambridge University Press, New York, 1983).
Kennett, B. L. N. and Kerry, N. J. (1979), Seismic Waves in a Stratified Half space, Geophys. J. R. Astr. Soc. 57, 557–583.
Lamb, H. (1904), On the Propagation of Tremors over the Surface of an Elastic Solid, Phil. Trans. Roy. Soc. (London) A 203, 1–42.
Loco, J. E. and Apsel, R. J. (1983), On the Green’s Functions for a Layered Half-space. Part I, Bull. Seismol. Soc. Am. 73, 909–929.
Ricker, N. H., Transient Waves in Visco-elastic Media (Elsevier Scientific Publishing Co., Amsterdam, Holland, 1977).
Wang, C. Y. and Herrmann, R. B. (1980), A Numerical Study of P-, SV-, and SH-wave Generation in Plane-layered Medium, Bull. Seismol. Soc. Am. 70, 1015–1036.
Yao, Z. X. and Harkrider, D. G. (1983), A Generalized Reflection-transmission Coefficient Matrix and Discrete Wavenumber Method for Synthetic Seismograms, Bull. Seismol. Soc. Am. 73, 1685–1699.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this chapter
Cite this chapter
Zhang, HM., Chen, XF., Chang, S. (2003). An Efficient Numerical Method for Computing Synthetic Seismograms for a Layered Half-space with Sources and Receivers at Close or Same Depths. In: Ben-Zion, Y. (eds) Seismic Motion, Lithospheric Structures, Earthquake and Volcanic Sources: The Keiiti Aki Volume. Pageoph Topical Volumes. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8010-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8010-7_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-7011-4
Online ISBN: 978-3-0348-8010-7
eBook Packages: Springer Book Archive