3‐D subsurface displacement and strain fields for faults and fault arrays in a layered elastic half‐space

SUMMARY A quantitative model using elastic dislocation theory has been developed to model the near-field subsurface displacement field associated with faults and fault arrays within an elastic layer above an elastic half-space. A fault is modelled as a surface across which there is a discontinuity in prescribed displacements. Fault displacements may be oblique as well as dip-slip. The mathematical expressions for the surface and subsurface displacements are formed using the Thomson-Haskell matrix technique. Faults may intersect the free surface or may be blind. The model has been used to determine the 3-D surface and subsurface displacement fields for a rectangular fault with constant slip and for an elliptical fault on which the slip varies from a point of maximum displacement at the centre to zero displacement at an elliptical tip-line. The 3-D displacement field and associated strain tensor may be determined for individual slip events on a fault or for cumulative fault displacements. Displacement contour maps may be constructed for either originally horizontal, vertical or inclined horizons. The model has also been applied to multiple fault arrays.

[1]  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.

[2]  Nick Kusznir,et al.  A flexural-cantilever simple-shear/pure-shear model of continental lithosphere extension: applications to the Jeanne d’Arc Basin, Grand Banks and Viking Graben, North Sea , 1991, Geological Society, London, Special Publications.

[3]  J. Watterson.  Fault dimensions, displacements and growth , 1986 .

[4]  J. Walsh,et al.  Displacement Geometry in the Volume Containing a Single Normal Fault , 1987 .

[5]  M. A. Chinnery,et al.  Elastic Dislocations in a Layered Half-Space—I. Basic Theory and Numerical Methods , 1974 .

[6]  J. J. Walsh,et al.  Distributions of cumulative displacement and seismic slip on a single normal fault surface , 1987 .

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

[8]  Ryosuke Sato,et al.  Crustal Deformation due to Dislocation in a Multi-layered Medium , 1971 .

[9]  J. Rundle,et al.  The growth of geological structures by repeated earthquakes, 1, conceptual framework , 1988 .

[10]  T. Mikumo.  Faulting process of the San Fernando earthquake of February 9, 1971 inferred from static and dynamic near-field displacements , 1973, Bulletin of the Seismological Society of America.

[11]  Ari Ben-Menahem,et al.  Multipolar elastic fields in a layered half space , 1968 .

[12]  D. E. Smylie,et al.  The displacement fields of inclined faults , 1971, Bulletin of the Seismological Society of America.

[13]  J. C. Savage,et al.  Surface deformation associated with dip‐slip faulting , 1966 .

[14]  M. A. Chinnery.  The deformation of the ground around surface faults , 1961 .

[15]  J. Steketee,et al.  SOME GEOPHYSICAL APPLICATIONS OF THE ELASTICITY THEORY OF DISLOCATIONS , 1958 .

[16]  Takuo Maruyama,et al.  Static elastic dislocation in an infinite and semi-infinite medium , 1964 .

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

[18]  M. A. Chinnery,et al.  Elastic Dislocations in a Layered Half‐Space–II The Point Source , 1974 .

[19]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[20]  John B. Rundle,et al.  Viscoelastic‐gravitational deformation by a rectangular thrust fault in a layered Earth , 1982 .

[21]  J. Steketee.  ON VOLTERRA'S DISLOCATIONS IN A SEMI-INFINITE ELASTIC MEDIUM , 1958 .

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