Earthquake Ground Motion Modeling. I: Deterministic Point Source
Publication: Journal of Engineering Mechanics
Volume 117, Issue 9
Abstract
A model for earthquake ground motion is developed using principles of geophysics and stochastics in a sequence of two papers. In the first paper, the earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is modeled as a concentrated seismic moment located within one of the layers. The partial differential equations for the seismic motion in each layer are solved using a Fourier finite‐Hankel transformation approach, and solutions in terms of state vectors of displacements and forces are converted to wave vectors composed of up‐going and down‐going waves. Transmission and reflection matrices are obtained for each layer, for each layer‐to‐layer interface, and for the free ground‐surface boundary to characterize their roles in transmitting and reflecting a wave motion. The use of these matrices allows the numerical calculation to be channeled in the directions of wave propagation, resulting in better numerical accuracy. An example is included for illustration.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aki, K., and Richards, P. G. (1980). Quantitative seismology—Theory and methods. W. H. Freeman and Company, San Francisco, Calif.
2.
Alekseev, A. S., and Mikhailenko, B. G. (1980). “The solution of dynamic problems of elastic wave propagation in inhomogeneous media by a combination of partial separation of variables and finite‐difference methods.” J. Geophys., 48(3), 167–172.
3.
Apsel, R. J., and Luco, J. E. (1983). “On the Green's function for a layered halfspace, Part II.” Bull. Seism. Soc. Am., 73(4), 931–951.
4.
Bouchon, M. (1979). “Discrete wave number representation of elastic wave fields in three‐space dimensions.” J. Geophys. Res., 84(B7), 3609–3614.
5.
Bouchon, M. (1981). “A simple method to calculate Green's functions for elastic layered media.” Bull. Seism. Soc. Am., 71(4), 959–971.
6.
Burridge, R., and Knopoff, L. (1964). “Body force equivalents for seismic dislocations.” Bull. Seism. Soc. Am., 54(6), 1875–1888.
7.
Chin, R. C. Y., Hedstrom, G., and Thigpen, L. (1984). “Numerical methods in seismology.” J. Computat. Phys., 54(1), 18–56.
8.
Haskell, N. A. (1964). “Radiation pattern of surface waves from point sources in a multilayered medium.” Bull. Seism. Soc. Am., 54(1), 377–393.
9.
Hudson, J. A. (1969). “A quantitative evaluation of seismic signals at teleseismic distances—I. Radiation from point sources.” Geophysical J. Royal Astronomical Soc., 18(3), 233–249.
10.
Kennett, B. L. N. (1985). Seismic wave propagation in stratified media. Cambridge University Press, Cambridge, England.
11.
Korn, M. (1987). “Computation of wavefields in vertically inhomogeneous media by a frequency domain finite‐difference method and application to wave propagation in earth models with random velocity and density perturbations.” Geophys. J. R. Astr. Soc., 88(2), 345–377.
12.
Lin, Y. K. (1965). “Transfer matrix representation of flexible airplanes in gust response study.” J. Aircraft, 2(2), 116–121.
13.
Lin, Y. K. (1976). “Random vibration of periodic and almost periodic structures.” Mechanics today, S. Nemat‐Nasser, eds., Pergamon Press, New York, N.Y.
14.
Lin, Y. K., and Donaldson, B. K. (1969). “A brief survey of transfer matrix techniques with special reference to the analysis of aircraft panels.” J. Sound Vib., 10(1), 103–143.
15.
Lin, Y. K., and McDaniel, T. J. (1969). “Dynamics of beam type periodic structures.” J. Engrg. Industry, 91(11), 1133–1141.
16.
Olson, A. H., Orcutt, J. A., and Frazier, G. A. (1984). “The discrete wave number/finite element method for synthetic seismograms.” Geophys. J. R. Astr. Soc., 77(2), 421–460.
17.
Pestel, E. C., and Leckie, F. A. (1963). Matrix methods in elastomechanics. McGraw‐Hill, New York, N.Y.
18.
Sneddon, I. N. (1951). Fourier transforms. McGraw‐Hill Book Co., Inc., New York, N.Y.
19.
Xu, P.‐C., and Mal, A. K. (1987). “Calculation of the inplane Green's functions for a layered viscoelastic solid.” Bull. Seism. Soc. Am., 77(5), 1823–1837.
20.
Yong, Y., and Lin, Y. K. (1989). “Propagation of decaying waves in periodic and piecewise periodic structures of finite length.” J. Sound Vib., 129(2), 99–118.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 117 • Issue 9 • September 1991
Pages: 2114 - 2132
Copyright
Copyright © 1991 ASCE.
History
Published online: Sep 1, 1991
Published in print: Sep 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.