On strike-slip faulting in layered media

Summary We study the effects of structural inhomogeneities on the stress and displacement fields induced by strike-slip faults in layered media. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults, which are assumed to be vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity is present. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake at the crack/interface junction. Planar strike-slip faulting may take place only in mature transform zones, where a repetitive earthquake cycle has already developed, if the rheology is perfectly elastic. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth may be accommodated by multiple fault branching or by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress).

[1]  F. Smithies,et al.  Singular Integral Equations , 1955, The Mathematical Gazette.

[2]  Y. C. Fung,et al.  Foundation of Solid Mechanics , 1966 .

[3]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[4]  M. Wyss,et al.  DISPLACEMENT ON THE SAN ANDREAS FAULT SUBSEQUENT TO THE 1966 PARKFIELD EARTHQUAKE , 1968 .

[5]  J. Tchalenko.  Similarities between Shear Zones of Different Magnitudes , 1970 .

[6]  Sarva Jit Singh.  Static deformation of a multilayered half‐space by internal sources , 1970 .

[7]  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.

[8]  K. Rybicki.  Analysis of aftershocks on the basis of dislocation theory , 1973 .

[9]  R. E. Wilcox,et al.  Basic Wrench Tectonics , 1973 .

[10]  R. V. Sharp.  Surface faulting in Imperial Valley during the earthquake swarm of January–February, 1975 , 1976 .

[11]  狩野 謙一,et al.  Surface Faulting Associated with the 1978 Izu-Oshima-kinkai Earthquake. , 1978 .

[12]  J. Rundle.  Viscoelastic crustal deformation by finite quasi‐static sources , 1978 .

[13]  Paul Segall,et al.  Mechanics of discontinuous faults , 1980 .

[14]  Peizhen Zhang,et al.  Research on the geometry of shear fracture zones , 1984 .

[15]  Quasi-static crack models and the frictional stress threshold criterion for slip arrest , 1985 .

[16]  T. Wong,et al.  Effects of pressure on the micromechanics of faulting in San Marcos gabbro , 1985 .

[17]  G. Mandl,et al.  Fault geometries in basement-induced wrench faulting under different initial stress states , 1986 .

[18]  Shefa Chen,et al.  Structure and deformational character of strike-slip fault zones , 1986 .

[19]  J. C. Savage.  Effect of crustal layering upon dislocation modeling , 1987 .

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

[21]  R. Davies,et al.  Evaluation of a class of integrals occurring in mathematical physics via a higher order generalization of the principal value , 1989 .

[22]  Robert V. Sharp,et al.  Surface faulting along the Superstition Hills fault zone and nearby faults associated with the earthquakes of 24 November 1987 , 1989 .

[23]  Frank Roth,et al.  Subsurface deformations in a layered elastic half-space , 1990 .

[24]  Y. Ben‐Zion.  The response of two half spaces to point dislocations at the material interface , 1990 .

[25]  C. Scholz.  The Mechanics of Earthquakes and Faulting , 1990 .

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

[27]  Jian Lin,et al.  Change in Failure Stress on the Southern San Andreas Fault System Caused by the 1992 Magnitude = 7.4 Landers Earthquake , 1992, Science.

[28]  Static deformation of two welded elastic half-spaces caused by a point dislocation source , 1992 .

[29]  Fred F. Pollitz,et al.  Postseismic relaxation theory on the spherical earth , 1992 .

[30]  C. Scholz,et al.  The 1912 Iceland earthquake rupture: Growth and development of a nascent transform system , 1993 .

[31]  Static deformation of two welded elastic half-spaces caused by a finite rectangular fault , 1993 .

[32]  G. King,et al.  STATIC STRESS CHANGES AND THE TRIGGERING OF EARTHQUAKES , 1994 .

[33]  Nick Kusznir,et al.  Coseismic and postseismic subsurface displacements and strains for a vertical strike-slip fault in a three-layer elastic medium , 1994 .

[34]  Static deformation of two welded elastic half-spaces caused by a rectangular shear fault located on the interface , 1995 .

[35]  Antonio Piersanti,et al.  Global post-seismic deformation , 1995 .

[36]  F. Pollitz,et al.  Viscosity structure beneath northeast Iceland , 1996 .

[37]  G. King,et al.  Stress coupling between earthquakes in northwest Turkey and the north Aegean Sea , 1996 .

[38]  Antonio Piersanti,et al.  Global postseismic rebound of a viscoelastic Earth: Theory for finite faults and application to the 1964 Alaska earthquake , 1997 .

[39]  T. Yamashita,et al.  Faulting in vertically inhomogeneous media and its geophysical implications , 1998 .

[40]  Yan Y. Kagan,et al.  Spatial aftershock distribution: Effect of normal stress , 1998 .

[41]  S. Tinti,et al.  Displacements and stresses induced by a point source across a plane interface separating two elastic semi-infinite spaces : An analytical solution , 1998 .

[42]  R. Simpson,et al.  Suppression of large earthquakes by stress shadows: A comparison of Coulomb and rate-and-state failure , 1998 .

[43]  Ruth A. Harris,et al.  Introduction to Special Section: Stress Triggers, Stress Shadows, and Implications for Seismic Hazard , 1998 .

[44]  P. Bodin,et al.  Earthquake triggering by transient and static deformations , 1998 .

[45]  G. Spada,et al.  Stress diffusion following large strike-slip earthquakes: a comparison between spherical and flat-earth models , 1998 .

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

[47]  R. Simpson,et al.  Stress transfer by the 1988–1989 M = 5.3 and 5.4 Lake Elsman foreshocks to the Loma Prieta fault: Unclamping at the site of peak mainshock slip , 1999 .

[48]  Eleonora Rivalta,et al.  The edge dislocation problem in a layered elastic medium , 1999 .

[49]  M. Bonafede,et al.  On tensile cracks close to and across the interface between two welded elastic half-spaces , 1999 .

[50]  M. Belardinelli,et al.  Secondary earthquake fractures generated by a strike-slip fault in the South Iceland Seismic Zone , 2000 .