Three-dimensional finite-element modelling of Earth's viscoelastic deformation: effects of lateral variations in lithospheric thickness

SUMMARY We have developed a 3-D spherical finite-element model to study the dynamic response to surface loads of a self-gravitating and incompressible Earth with 3-D viscoelastic structure. We have forced our model with the ICE-3G deglaciation history of Tushingham & Peltier to study the effects of laterally varying lithospheric thickness on observations of post-glacial rebound (PGR). The laterally varying lithospheric thicknesses are derived from estimates of the thermal structure of the oceanic lithosphere and from elastic thicknesses on continents as estimated from studies of long-term geological loads. Our calculations show that the effects of lithospheric structure on the relative sea level change (RSLC) depend on the locations of the observation sites and on the size of loads. The RSLC at the centre of the North American ice sheet is significantly less sensitive to lithospheric thickness, compared with the RSLC at the centre of the Fennoscandian ice sheet. At the peripheral bulges the RSLC tends to be more sensitive to lithospheric thickness. The RSLC is controlled by local lithospheric thickness. The RSLC at a given location, as predicted using models with laterally varying lithospheric thickness, can be reproduced using a 1-D model with a uniform lithospheric thickness equal to the local lithospheric thickness. Coupled with efficient parallel computing, we believe that the finite-element model that we present here can be used to address a variety of viscoelastic deformation problems in geodynamics.

[1]  Patrick Wu,et al.  Mode coupling in a viscoelastic self-gravitating spherical earth induced by axisymmetric loads and lateral viscosity variations , 2002 .

[2]  Z. Martinec.  Spectral, initial value approach for viscoelastic relaxation of a spherical earth with a three-dimensional viscosity—I. Theory , 2002 .

[3]  D. Wolf,et al.  Effects of lateral viscosity variations on postglacial rebound: an analytical approach , 2002 .

[4]  P. Wu.  Effects of nonlinear rheology on degree 2 harmonic deformation in a spherical self‐gravitating earth , 2002 .

[5]  G. Kaufmann,et al.  Glacial isostatic adjustment in Fennoscandia with a three-dimensional viscosity structure as an inverse problem , 2002 .

[6]  Patrick Wu,et al.  Effects of mantle flow law stress exponent on postglacial induced surface motion and gravity in Laurentia , 2002 .

[7]  Z. Martinec,et al.  Can the 1D viscosity profiles inferred from postglacial rebound data be affected by lateral viscosity variations in the tectosphere? , 2001 .

[8]  A. B. WATTS,et al.  Isostasy and Flexure of the Lithosphere , 2001 .

[9]  J. Wahr,et al.  Geodetic measurements in Greenland and their implications , 2001 .

[10]  Georg Kaufmann,et al.  Glacial isostatic adjustment in Fennoscandia for a laterally heterogeneous earth , 2000 .

[11]  Frederik J. Simons,et al.  Isostatic response of the Australian lithosphere: Estimation of effective elastic thickness and anisotropy using multitaper spectral analysis , 2000 .

[12]  Z. Martinec.  Spectral–finite element approach to three‐dimensional viscoelastic relaxation in a spherical earth , 2000 .

[13]  Louis Moresi,et al.  Role of temperature‐dependent viscosity and surface plates in spherical shell models of mantle convection , 2000 .

[14]  M. Zuber,et al.  Long‐wavelength topographic relaxation for self‐gravitating planets and implications for the time‐dependent compensation of surface topography , 2000 .

[15]  J. Tromp,et al.  Surface loading of a viscoelastic planet—III. Aspherical models , 2000 .

[16]  J. Tromp,et al.  Surface loading of a viscoelastic earth—II. Spherical models , 1999 .

[17]  W. R. Peltier,et al.  Postglacial variations in the level of the sea: Implications for climate dynamics and solid‐Earth geophysics , 1998 .

[18]  Patrick Wu,et al.  Effects of removing concentric positioning on postglacial vertical displacement in the presence of lateral variation in lithospheric thickness , 1998 .

[19]  L. Guillou-Frottier,et al.  Heat flow and thickness of the lithosphere in the Canadian Shield , 1998 .

[20]  Patrick Wu,et al.  Lateral asthenospheric viscosity variations and postglacial rebound: A case study for the Barents Sea , 1998 .

[21]  Patrick Wu,et al.  Dynamics of the Ice Age Earth: A Modern Perspective , 1998 .

[22]  Bradford H. Hager,et al.  Localization of the gravity field and the signature of glacial rebound , 1997, Nature.

[23]  G. Nolet,et al.  Upper mantle S velocity structure of North America , 1997 .

[24]  J. Mitrovica,et al.  Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial , 1997 .

[25]  J. Mitrovica,et al.  New inferences of mantle viscosity from joint inversion of long‐wavelength mantle convection and post‐glacial rebound data , 1996 .

[26]  M. Gurnis,et al.  Constraints on the lateral strength of slabs from three-dimensional dynamic flow models , 1996 .

[27]  Louis Moresi,et al.  Numerical investigation of 2D convection with extremely large viscosity variations , 1995 .

[28]  Patrick Wu,et al.  Can observations of postglacial rebound tell whether the rheology of the mantle is linear or nonlinear , 1995 .

[29]  J. Wahr,et al.  The viscoelastic relaxation of a realistically stratified earth, and a further analysis of postglacial rebound , 1995 .

[30]  Eugene M. Lavely,et al.  Three‐dimensional seismic models of the Earth's mantle , 1995 .

[31]  S. Grand.  Mantle shear structure beneath the Americas and surrounding oceans , 1994 .

[32]  P. Wu.  Postglacial rebound in a power-law medium with axial symmetry and the existence of the transition zone in relative sea-level data , 1993 .

[33]  W. Peltier,et al.  ICE-3G: A new global model of late Pleistocene deglaciation based upon geophysical predictions of po , 1991 .

[34]  W. Peltier,et al.  A complete formalism for the inversion of post-glacial rebound data: resolving power analysis , 1991 .

[35]  K. Lambeck,et al.  Holocene glacial rebound and sea-level change in NW Europe , 1990 .

[36]  D. Forsyth,et al.  Variations in effective elastic thickness of the North American lithosphere , 1990, Nature.

[37]  P. Gasperini,et al.  Lateral heterogeneities in mantle viscosity and post‐glacial rebound , 1989 .

[38]  M. Zuber,et al.  Effective Elastic Thicknesses of the Lithosphere and Mechanisms of Isostatic Compensation in Australia , 1989 .

[39]  B. Hager,et al.  Long-wavelength variations in Earth’s geoid: physical models and dynamical implications , 1989, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[40]  K. Lambeck,et al.  Late Pleistocene and Holocene sea‐level change in the Australian region and mantle rheology , 1989 .

[41]  D. Yuen,et al.  The effects of upper‐mantle lateral heterogeneities on postglacial rebound , 1986 .

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

[43]  M. Steckler,et al.  Observations of flexure and the rheology of the oceanic lithosphere , 1981 .

[44]  N. Ribe,et al.  Observations of flexure and the geological evolution of the Pacific Ocean basin , 1980, Nature.

[45]  L. Cathles,et al.  The Viscosity of the Earth's Mantle , 1975 .

[46]  G. Kaufmann,et al.  Postglacial Rebound with Lateral Heterogeneities: from 2D to 3D modeling , 1998 .

[47]  Patrick Wu,et al.  Some effects of lateral heterogeneities in the upper mantle on postglacial land uplift close to continental margins , 1997 .

[48]  G. Spada,et al.  Lateral viscosity variations and post‐glacial rebound: Effects on present‐day VLBI baseline deformations , 1997 .

[49]  Patrick Wu,et al.  Deformation of an incompressible viscoelastic flat earth with powerlaw creep: a finite element approach , 1992 .

[50]  Patrick Wu,et al.  Viscoelastic versus viscous deformation and the advection of pre-stress , 1992 .