Normal-fault stress and displacement through finite-element analysis

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.

[1]  J. Bielak,et al.  Domain Reduction Method for Three-Dimensional Earthquake Modeling in Localized Regions, Part II: Verification and Applications , 2001 .

[2]  Arthur Raefsky,et al.  A simple and efficient method for introducing faults into finite element computations , 1981 .

[3]  M. Dragoni,et al.  Shallow earthquakes in a viscoelastic shear zone with depth-dependent friction and rheology , 1986 .

[4]  M. Bonafede,et al.  Effects induced by an earthquake on its fault plane:a boundary element study , 2000 .

[5]  J. C. Savage.  Displacement field for an edge dislocation in a layered half‐space , 1998 .

[6]  K. Rybicki.  The elastic residual field of a very long strike-slip fault in the presence of a discontinuity , 1971, Bulletin of the Seismological Society of America.

[7]  M. Bonafede,et al.  On strike-slip faulting in layered media , 2002 .

[8]  Fred F. Pollitz,et al.  Gravitational viscoelastic postseismic relaxation on a layered spherical Earth , 1997 .

[9]  R. Cattin,et al.  Effects of superficial layers on coseismic displacements for a dip-slip fault and geophysical implications , 1999 .

[10]  Ari Ben-Menahem,et al.  Crustal deformation by earthquakes and explosions , 1970, Bulletin of the Seismological Society of America.

[11]  Herbert F. Wang,et al.  Transient stress-coupling between the 1992 Landers and 1999 Hector Mine, California, earthquakes , 2002 .

[12]  Ryosuke Sato,et al.  STATIC DEFORMATION DUE TO THE FAULT SPREADING OVER SEVERAL LAYERS IN A MULTI-LAYERED MEDIUM PART II: STRAIN AND TILT , 1975 .

[13]  Salvatore Barba,et al.  Analysis of seismological and geological observations formoderate‐size earthquakes: the Colfiorito Fault System(Central Apennines, Italy) , 2000 .

[14]  S. Tinti,et al.  Self-induced Deformation on the Fault Plane During an Earthquake Part II: Continuous Tangential Displacements , 2003 .

[15]  S. Tinti,et al.  Influence of topography on coseismic displacements induced by the Friuli 1976 and the Irpinia 1980 earthquakes (Italy) analyzed through a two‐dimensional hybrid model , 2003 .

[16]  Ryosuke Sato,et al.  STATIC DEFORMATIONS DUE TO THE FAULT SPREADING OVER SEVERAL LAYERS IN A MULTI-LAYERED MEDIUM , 1973 .

[17]  N. Miyabe.  On Crustal Deformations , 1951 .

[18]  R. Müller,et al.  3-D finite-element modelling of deformation and stress associated with faulting: effect of inhomogeneous crustal structures , 2004 .

[19]  Jiangheng He,et al.  Fault Parameters of the Nisqually Earthquake Determined from Moment Tensor Solutions and the Surface Deformation from GPS and InSAR , 2002 .

[20]  J. Bielak,et al.  Domain Reduction Method for Three-Dimensional Earthquake Modeling in Localized Regions, Part I: Theory , 2003 .

[21]  S. Barba,et al.  Dynamic modelling of stress accumulation in Central Italy: Role of structural heterogeneities and rheology , 2001 .

[22]  Y. Okada.  Internal deformation due to shear and tensile faults in a half-space , 1992, Bulletin of the Seismological Society of America.

[23]  S. Tinti,et al.  A 2-D hybrid technique to model the effect of topography on coseismic displacements. Application to the Umbria-Marche (central Italy) 1997 earthquake sequence , 2002 .

[24]  Andrea Morelli,et al.  Two-dimensional crack model of faulting in a layered elastic half-space , 1987 .

[25]  Rongjiang Wang,et al.  Erratum to: "Computation of deformation induced by earthquakes in a multi-layered elastic crust - FORTRAN programs EDGRN/EDCMP": [Computers & Geosciences, 29(2) (2003) 195-207] , 2006, Comput. Geosci..

[26]  N. Kusznir,et al.  Coseismic and postseismic subsurface displacements and strains for a dip‐slip normal fault in a three‐layer elastic‐gravitational medium , 1995 .