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Normal-fault stress and displacement through finite-element analysis
Issued date
December 2005
Issue/vol(year)
6/48 (2005)
Language
English
Abstract
We compute displacement and stress due to a normal fault by means of two-dimensional plane-strain finite-element analysis. To do so, we apply a system of forces to the fault nodes and develop an iterative algorithm serving to determine the force magnitudes for any slip distribution. As a sample case, we compute the force magnitudes assuming uniform slip on a 10-km two-dimensional normal fault. The numerical model generates displacement and stress fields that compare well with the analytical solution. In fact, we found little difference in displacements (<5%), displacement orientation (<15°), and stress components (<35%, half of which due to slip tolerance). We analyze such misfit, and discuss how the error propagates from displacement to stress. Our scheme provides a convenient way to use the finite-elements direct method in a trial-and-error procedure to reproduce any smooth slip distribution.
References
ARMIGLIATO, A. and S. TINTI (2003): Influence of topography
on coseismic displacements induced by the Friuli
1976 and the Irpinia 1980 earthquakes (Italy) analyzed
through a two-dimensional hybrid model, J. Geophys.
Res., 108, 2552, doi: 10.1029/2002JB002027.
ARMIGLIATO, A., S. TINTI and A. MANUCCI (2003a): Self-induced
deformation on the fault plane during an earthquake,
Part I. Continuous normal displacements, Pure
Appl. Geophys., 160, 1651-1678.
ARMIGLIATO, A., S. TINTI and A. MANUCCI (2003b): Self-induced
deformation on the fault plane during an earthquake,
Part II. Continuous tangential displacements,
Pure. Appl. Geophys., 160, 1679-1693.
BARBA, S. (1999): Studio dei meccanismi di deformazione della
regione italiana: vincoli geologici, geofisici e modellazione
geodinamica, Ph.D. Dissertation (Università «La
Sapienza», Roma), pp. 100 (deposited in Earth-Prints,
www.earth-prints.org, http://hdl.handle.net/2122/367).
BARBA, S., and R. BASILI (2000): Analysis of seismological
and geological observations for moderate-size earthquakes:
the Colfiorito Fault System (Central Apennines,
Italy), Geophys. J. Int., 141 (1), 241-252.
BEN-MENAHEM, A. and A. GILLON (1970): Crustal deformations
by earthquakes and explosions, Bull. Seismol.
Soc. Am., 60, 193-215.
BIELAK, J., K. LOUKAKIS, Y. HISADA and C. YOSHIMURA
(2003): Domain reduction method for three-dimensional
earthquake modeling in localized regions, Part I.
Theory, Bull. Seismol. Soc. Am., 93, 817-824.
BONAFEDE, M. and A. NERI (2000): Effects induced by an
earthquake on its fault palne: a boundary element
study, Geophys. J. Int., 141, 43-56.
BONAFEDE, M., B. PARENTI and E. RIVALTA (2002): On
strike-slip faulting in layered media, Geophys. J. Int.,
149, 698-723.
BUSTIN, A., R.D. HYNDMAN, A. LAMBERT, J. RISTAU, J. HE,
H. DRAGERT and M. VAN DER KOOIJ (2004): Fault parameters
of the Nisqually earthquake determined from
moment tensor solutions and the surface deformation
from GPS and InSAR, Bull. Seismol. Soc. Am., 94,
363-376.
CARMINATI, E., F. TONIOLO AUGIER and S. BARBA (2001):
Dynamic modelling of stress accumulation in the Central
Italy: role of structural heterogeneities and rheology,
Geophys. J. Int., 144, 373-390.
CATTIN, R., P. BRIOLE, H. LYON-CAHEN, P. BERNARD and P.
PINETTES (1999): Effects of superficial layers on coseismic
displacements for a dip-slip fault and geophysical
implications, Geophys. J. Int., 137, 149-158.
DRAGONI, M., M. BONAFEDE and E. BOSCHI (1986): Shallow
earthquakes in a viscoelastic shear zone with depth-dependent
friction and rheology, Geophys. J. R. Astron.
Soc., 86, 617-633.
MA, X.Q. and N.J. KUSZNIR (1995): Coseismic and postseismic
subsurface displacements and trains for dipslip
normal fault in a three-layer, J. Geophys. Res., 100,
12,813-12,828.
MASTERLARK, T. and H.F. WANG (2002): Transient stresscoupling
between the 1992 Landers and 1999 Hector
Mine, California, earthquakes, Bull. Seismol. Soc. Am.,
92, 1470-1486.
MELOSH, H.J. and A. RAEFSKY (1981): A simple and efficient
method for introducing faults into finite element
computations, Bull. Seismol. Soc. Am., 71, 1391-1400.
MORELLI, A., M. BONAFEDE and M. DRAGONI (1987): Twodimensional
crack model of faulting in a layered elastic
half-space, Ann. Geophysicae, 5B, 281-288.
MSC.SOFTWARE (2005): MSC.Software Corporation – 40
Years of Virtual Product Development Expertise, 12 October
2005 (on line: http://www.mscsoftware.com/).
OKADA, Y. (1992): Internal deformation due to shear and
tensile faults in a haft-space, Bull. Seismol. Soc. Am.,
82, 1018-1040.
POLLITZ, F.F. (1997): Gravitational viscoelastic postseismic relaxation on a layered spherical Earth, J. Geophys.
Res., 102, 17,921-17,941.
RYBICKI, K. (1971): The elastic residual field of a very long
strike-slip fault in the presence of a discontinuity, Bull.
Seismol. Soc. Am., 61, 79-92.
SATO, R. and M. MATSU’URA (1973): Static deformation due
to the fault spreading over several layer in a multi-layered
medium, Part I. Displacement, J. Phys. Earth, 21,
227-249.
SAVAGE, J.C. (1998): Displacement field for an edge dislocation
in a layered half-space, J. Geophys. Res., 103,
2439-2446.
TINTI, S. and A. ARMIGLIATO (2002): A2D hybrid technique
to model the effect of topography on coseismic displacements.
Application to the Umbria-Marche (Central
Italy) 1997 earthquake sequence, Geophys. J. Int.,
150, 542-557.
WANG, R., F.L. MARTIN and F. ROTH (2003): Computation
of deformation induced earthquakes in a multi-layered
elastic crust – FORTRAN programs EDGRN/EDCMP,
Comput. Geosci., 29, 195-207.
ZHAO, S., R.D. MÜLLER, Y. TAKAHASHI and Y. KANEDA
(2004): 3-D finite-element modelling of deformation
and stress associated with faulting: effect of inhomogeneous
crustal structures, Geophys. J. Int., 157, 629-
644, doi: 10.1111/j.1365-246X.2004.02200.x.
on coseismic displacements induced by the Friuli
1976 and the Irpinia 1980 earthquakes (Italy) analyzed
through a two-dimensional hybrid model, J. Geophys.
Res., 108, 2552, doi: 10.1029/2002JB002027.
ARMIGLIATO, A., S. TINTI and A. MANUCCI (2003a): Self-induced
deformation on the fault plane during an earthquake,
Part I. Continuous normal displacements, Pure
Appl. Geophys., 160, 1651-1678.
ARMIGLIATO, A., S. TINTI and A. MANUCCI (2003b): Self-induced
deformation on the fault plane during an earthquake,
Part II. Continuous tangential displacements,
Pure. Appl. Geophys., 160, 1679-1693.
BARBA, S. (1999): Studio dei meccanismi di deformazione della
regione italiana: vincoli geologici, geofisici e modellazione
geodinamica, Ph.D. Dissertation (Università «La
Sapienza», Roma), pp. 100 (deposited in Earth-Prints,
www.earth-prints.org, http://hdl.handle.net/2122/367).
BARBA, S., and R. BASILI (2000): Analysis of seismological
and geological observations for moderate-size earthquakes:
the Colfiorito Fault System (Central Apennines,
Italy), Geophys. J. Int., 141 (1), 241-252.
BEN-MENAHEM, A. and A. GILLON (1970): Crustal deformations
by earthquakes and explosions, Bull. Seismol.
Soc. Am., 60, 193-215.
BIELAK, J., K. LOUKAKIS, Y. HISADA and C. YOSHIMURA
(2003): Domain reduction method for three-dimensional
earthquake modeling in localized regions, Part I.
Theory, Bull. Seismol. Soc. Am., 93, 817-824.
BONAFEDE, M. and A. NERI (2000): Effects induced by an
earthquake on its fault palne: a boundary element
study, Geophys. J. Int., 141, 43-56.
BONAFEDE, M., B. PARENTI and E. RIVALTA (2002): On
strike-slip faulting in layered media, Geophys. J. Int.,
149, 698-723.
BUSTIN, A., R.D. HYNDMAN, A. LAMBERT, J. RISTAU, J. HE,
H. DRAGERT and M. VAN DER KOOIJ (2004): Fault parameters
of the Nisqually earthquake determined from
moment tensor solutions and the surface deformation
from GPS and InSAR, Bull. Seismol. Soc. Am., 94,
363-376.
CARMINATI, E., F. TONIOLO AUGIER and S. BARBA (2001):
Dynamic modelling of stress accumulation in the Central
Italy: role of structural heterogeneities and rheology,
Geophys. J. Int., 144, 373-390.
CATTIN, R., P. BRIOLE, H. LYON-CAHEN, P. BERNARD and P.
PINETTES (1999): Effects of superficial layers on coseismic
displacements for a dip-slip fault and geophysical
implications, Geophys. J. Int., 137, 149-158.
DRAGONI, M., M. BONAFEDE and E. BOSCHI (1986): Shallow
earthquakes in a viscoelastic shear zone with depth-dependent
friction and rheology, Geophys. J. R. Astron.
Soc., 86, 617-633.
MA, X.Q. and N.J. KUSZNIR (1995): Coseismic and postseismic
subsurface displacements and trains for dipslip
normal fault in a three-layer, J. Geophys. Res., 100,
12,813-12,828.
MASTERLARK, T. and H.F. WANG (2002): Transient stresscoupling
between the 1992 Landers and 1999 Hector
Mine, California, earthquakes, Bull. Seismol. Soc. Am.,
92, 1470-1486.
MELOSH, H.J. and A. RAEFSKY (1981): A simple and efficient
method for introducing faults into finite element
computations, Bull. Seismol. Soc. Am., 71, 1391-1400.
MORELLI, A., M. BONAFEDE and M. DRAGONI (1987): Twodimensional
crack model of faulting in a layered elastic
half-space, Ann. Geophysicae, 5B, 281-288.
MSC.SOFTWARE (2005): MSC.Software Corporation – 40
Years of Virtual Product Development Expertise, 12 October
2005 (on line: http://www.mscsoftware.com/).
OKADA, Y. (1992): Internal deformation due to shear and
tensile faults in a haft-space, Bull. Seismol. Soc. Am.,
82, 1018-1040.
POLLITZ, F.F. (1997): Gravitational viscoelastic postseismic relaxation on a layered spherical Earth, J. Geophys.
Res., 102, 17,921-17,941.
RYBICKI, K. (1971): The elastic residual field of a very long
strike-slip fault in the presence of a discontinuity, Bull.
Seismol. Soc. Am., 61, 79-92.
SATO, R. and M. MATSU’URA (1973): Static deformation due
to the fault spreading over several layer in a multi-layered
medium, Part I. Displacement, J. Phys. Earth, 21,
227-249.
SAVAGE, J.C. (1998): Displacement field for an edge dislocation
in a layered half-space, J. Geophys. Res., 103,
2439-2446.
TINTI, S. and A. ARMIGLIATO (2002): A2D hybrid technique
to model the effect of topography on coseismic displacements.
Application to the Umbria-Marche (Central
Italy) 1997 earthquake sequence, Geophys. J. Int.,
150, 542-557.
WANG, R., F.L. MARTIN and F. ROTH (2003): Computation
of deformation induced earthquakes in a multi-layered
elastic crust – FORTRAN programs EDGRN/EDCMP,
Comput. Geosci., 29, 195-207.
ZHAO, S., R.D. MÜLLER, Y. TAKAHASHI and Y. KANEDA
(2004): 3-D finite-element modelling of deformation
and stress associated with faulting: effect of inhomogeneous
crustal structures, Geophys. J. Int., 157, 629-
644, doi: 10.1111/j.1365-246X.2004.02200.x.
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