Gravitational viscoelastic postseismic relaxation on a layered spherical Earth

Viscoelastic relaxation of a ductile asthenosphere underlying a purely elastic plate is a strong candidate process for explaining anomalous rates of crustal deformation observed following large earthquakes. The nongravitational treatment of Pollitz [1992], which is valid on a global scale and includes the effects of compressibility, is here extended to permit the calculation of gravitational viscoelastic relaxation for a specified spherically layered viscoelastic rheology following an earthquake in an elastic layer. The simple approximations we adopt make the resulting treatment particularly suitable for near-field calculations. For an asthenosphere with a Maxwell rheology, the effect of gravitational coupling is manifested only many relaxation times after the earthquake, as obtained by previous investigators. Its effect is generally to speed up the long-wavelength component of the relaxation process and attenuate the overall vertical displacement pattern. Several subtle features common to the relaxation behavior from several different fault types (thrust, rift, and strike-slip) are identified. The effect of gravitational coupling on horizontal displacements is consistent with flexure of the upper elastic plate driven by the corresponding effects on the vertical displacement. Stress diffusion away from the source region generally exhibits pulse-like behavior which is dispersive in both space and time. If the asthenosphere is confined to a relatively narrow channel, then the dispersion branches governing relaxation are radically altered, and stress diffusion effects far from the coseismic rupture zone exhibit a complicated time dependence reflecting the competing tendencies of toroidal and spheroidal mode relaxation.

[1]  Steven C. Cohen.  Postseismic surface deformations due to lithospheric and asthenospheric viscoelasticity , 1979 .

[2]  J. Woodhouse,et al.  Efficient and stable methods for performing seismic calculations in stratified media , 1980 .

[3]  C. Sanders.  Interaction of the San Jacinto and San Andreas Fault Zones, Southern California: Triggered Earthquake Migration and Coupled Recurrence Intervals , 1993, Science.

[4]  P. Molnar,et al.  Focal depths of intracontinental and intraplate earthquakes and their implications for the thermal and mechanical properties of the lithosphere , 1983 .

[5]  B. Romanowicz.  Multiplet-multiplet coupling due to lateral heterogeneity: asymptotic effects on the amplitude and frequency of the Earth's normal modes , 1987 .

[6]  K. Miyashita.  A MODEL OF PLATE CONVERGENCE IN SOUTHWEST JAPAN, INFERRED FROM LEVELING DATA ASSOCIATED WITH THE 1946 NANKAIDO EARTHQUAKE , 1987 .

[7]  F. Gilbert,et al.  An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  I. Sacks,et al.  Asthenospheric viscosity inferred from correlated land–sea earthquakes in north-east Japan , 1988, Nature.

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

[10]  W. Peltier,et al.  Viscous gravitational relaxation , 1982 .

[11]  D. Yuen,et al.  Viscous relaxation of a compressible spherical shell , 1987 .

[12]  F. Pollitz,et al.  Fossil strain from the 1811-1812 New Madrid earthquakes , 1994 .

[13]  M. Bott,et al.  Stress Diffusion from Plate Boundaries , 1973, Nature.

[14]  T. Iwasaki.  Quasi-static deformation due to a dislocation source in a Maxwellian viscoelastic earth model. , 1985 .

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

[16]  John B. Rundle,et al.  Surface deformation due to a strike-slip fault in an elastic gravitational layer overlying a viscoelastic gravitational half-space , 1996 .

[17]  W. Elsasser.  Convection and stress propagation in the upper mantle. , 1969 .

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

[19]  D. Wolf.  The normal modes of a uniform, compressible Maxwell half-space , 1985 .

[20]  Freeman Gilbert,et al.  Propagator matrices in elastic wave and vibration problems , 1966 .

[21]  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 .

[22]  M. Kramer,et al.  Crustal deformation, the earthquake cycle, and models of viscoelastic flow in the asthenosphere , 1984 .

[23]  M. Hofton,et al.  Horizontal surface deformation due to dike emplacement in an elastic‐gravitational layer overlying a viscoelastic‐gravitational half‐space , 1995 .

[24]  T. Tabei.  CRUSTAL MOVEMENTS IN THE INNER ZONE OF SOUTHWEST JAPAN ASSOCIATED WITH STRESS RELAXATION AFTER MAJOR EARTHQUAKES , 1989 .

[25]  Steven C. Cohen.  A multilayer model of time dependent deformation following an earthquake on a strike slip fault , 1982 .

[26]  H. Takeuchi,et al.  Seismic Surface Waves , 1972 .

[27]  E. Ivins,et al.  Transient creep of a composite lower crust: 1. Constitutive theory , 1996 .

[28]  F. Pollitz,et al.  Fault Model of the 1891 Nobi Earthquake from Historic Triangulation and Leveling , 1994 .

[29]  P. Molnar,et al.  A possible dependence of tectonic strength on the age of the crust in Asia , 1981 .

[30]  J. Rice,et al.  Crustal deformation in great California earthquake cycles , 1986 .

[31]  J. Rundle,et al.  Lithospheric loading by the 1896 Riku‐u Earthquake, northern Japan: Implications for plate flexure and asthenospheric rheology , 1980 .

[32]  Fred F. Pollitz,et al.  Coseismic Deformation From Earthquake Faulting On A Layered Spherical Earth , 1996 .

[33]  J. C. Savage.  Equivalent strike‐slip earthquake cycles in half‐space and lithosphere‐asthenosphere earth models , 1990 .

[34]  D. Jackson,et al.  A three-dimensional viscoelastic model of a strike slip fault , 1977 .

[35]  I. Sacks,et al.  Asthenospheric Viscosity and Stress Diffusion: A Mechanism to Explain Correlated Earthquakes and Surface Deformations In Ne Japan , 1990 .

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

[37]  W. F. Brace,et al.  Limits on lithospheric stress imposed by laboratory experiments , 1980 .

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

[39]  G. Spada,et al.  Compressible rotational deformation , 1996 .

[40]  Wolfgang Friederich,et al.  COMPLETE SYNTHETIC SEISMOGRAMS FOR A SPHERICALLY SYMMETRIC EARTH BY A NUMERICAL COMPUTATION OF THE GREEN'S FUNCTION IN THE FREQUENCY DOMAIN , 1995 .

[41]  John B. Rundle,et al.  VERTICAL DISPLACEMENTS FROM A RECTANGULAR FAULT IN LAYERED ELASTIC-GRAVITATIONAL MEDIA , 1981 .

[42]  Bernard Budiansky,et al.  Interaction of fault slip and lithospheric creep , 1976 .

[43]  F. Dahlen.  Elastic Dislocation Theory for a Self‐Gravitating Elastic Configuration with an Initial Static Stress Field , 1972 .

[44]  John B. Rundle,et al.  Static elastic‐gravitational deformation of a layered half space by point couple sources , 1980 .

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

[46]  F. Pollitz,et al.  The 1995 Kobe, Japan, earthquake: A long-delayed aftershock of the offshore 1944 Tonankai and 1946 Nankaido earthquakes , 1997, Bulletin of the Seismological Society of America.

[47]  Amos Nur,et al.  Postseismic Viscoelastic Rebound , 1974, Science.

[48]  Wayne Thatcher,et al.  Nonlinear strain buildup and the earthquake cycle on the San Andreas Fault , 1983 .