Abstract
We propose a finite difference method, using a hexagonal grid, to compute displacements (stresses, velocities, accelerations) in the near-field of a 2-D in-plane stress-drop crack, in both whole space (constant stress-drop) and half-space (depth-dependent stress-drop). To exercise the method, the stress field distribution is evaluated for both fundamental 2-D shear cracks, anti-plane. In order to test the method's reliability, the results are compared with some analytical and numerical solutions available in the literature (Kostrov, 1964;Virieux andMadariaga, 1982). For the in-plane source, the results emphasize that the method can resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. Synthetic motions are computed on the fault, but also in an infinite medium and at the free surface. The rather complex waveforms generated in the near-field, even by simple sources, emphasize the contribution of all wave terms (near, intermediate and far-field) to the motion. The presence of near-field and the numerical procedure explain the significant low frequency content of the computed seismograms. The set of treated problems proves the method is stable and accurate.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aki, K. andRichards P. G. (1980),Quantitative Seismology-Theory and Methods. W. H. Freeman and Co., San Francisco, Vol. 2, 852–860.
Alterman, Z. S. andLoewenthal D. (1972),Computer generated seismograms, Methods in Computational Physics. Vol. 12 (ed. B. Bolt), 35–164.
Archuleta, R. J. (1984),A faulting model for the 1979Imperial Valley earthquake. J. Geophys. Res. (in press).
Bernard, P. andMadariaga R. (1984),A new asymptotic method for the modeling of near-field acceleragrams. Bull. Seism. Soc. Am. 74, 539–557.
Brune, J. N. (1970),Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75, 4997–5009.
Claerbout, J. F. (1976),Fundamentals of Geophysical Data Processing. McGraw-Hill, San Francisco.
Das, S. (1981),Three dimensional spontaneous rupture propagation and implications for the earthquake source mechanism. Geophys. J. R. astr. Soc. 67, 375–393.
Das, S. andAki K. (1977),Fault plane with barriers: a versatile earthquake model. J. Geophys. Res. 82, 5658–5670.
Day, S. M. (1982),Three dimensional finite difference simulation of fault dynamics: rectangular faults with fixed rupture velocity. Bull. Seism. Soc. Am. 72, 1881–1902.
Hartzell, S. H. andHelmberger D. V. (1982),Strong-motion modeling of the Imperial Valley earthquake of 1979. Bull. Seism. Soc. Am. 72, 571–596.
Haskell, N. A. (1969),Elastic displacements in the near-field of a propagting fault. Bull. Seism. Soc. Am. 59, 865–908.
Kostrov, B. V. (1964),Self similar problems of propagating of shear cracks. J. Appl. Math. Mech. 28, 1077–1087.
Kostrov, B. V. (1975),On the crack propagation with variable velocity. Int. Journ. of Fracture 11, 47–56.
Madariaga, R. (1977),High-frequency radiation from cracks (stress drop) models of earthquake faulting. Geophys. J. R. astr. Soc. 51, 625–651.
Olson, A. H. andApsel, R. J. (1982),Finite faults and inverse theory with applications to the 1979Imperial Valley earthquake. Bull. Seism. Soc. Am. 72, 1969–2001.
Radulian, M. andTrifu C-I. (1983),Wave equation solution in a homogeneous halfspace by the finite difference method for two-dimensional dynamic seismic source models. Rev. Roum. Phys. 28, 919–931.
Rirchards, P. G. (1973),The dynamic field of a grawing plane elliptical shear crack. Int. J. Solid Structures 9, 843–861.
Richards, P. G. (1976),Dynamic motions near an earthquake fault: a three-dimensional solution. Bull. Seism. Soc. Am. 66, 1–32.
Stöckl, H. (1977),Finite difference calculations of stress relaxation earthquake models. J. Geophys. 43, 311–327.
Stöckl, H. (1980),Earthquake strong motion simulated by stress drop models. PAGEOPH 118, 1248–1271.
Trifu, C-I. andRadulian M. (1985),Synthetic near-field ground motion for an antiplane stress drop model. Rev. Roum. Med. Appl. 30 (5) (in press).
Virieux, J. andMadariaga R. (1982),Dynamic faulting studied by finite difference method. Bull. Seism. Soc. Am. 72, 345–369.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Trifu, C.I., Radulian, M. Predicted near-field ground motion for dynamic stress-drop models. PAGEOPH 123, 173–198 (1985). https://doi.org/10.1007/BF00877016
Received:
Revised:
Accepted:
Issue date:
DOI: https://doi.org/10.1007/BF00877016