## Mantle rheology, convection and rotational dynamics

**J. Moser** ** , **
**Ctirad Matyska** ** , **
**David A. Yuen** ** , **
**A. Malevsky** ** & **
**H. Harder**
### Summary

We have examined theoretically the effects from
mantle convection on Earth rotational dynamics
for both viscoelastic and viscous mantles. Strategies
for numerical computations are proposed. A linear Maxwell viscoelastic
rheology accounting for finite deformations associated with mantle
convection is considered. For both rheologies the two sets of convection
and rotational equations can be partitioned into separate systems
with the output from convection being used as input for the rotational
equations. The differences in this convection-rotational
problem between finite-strain and small-amplitude viscoelastic
theories are delineated. An algorithm based on the usage of massively
parallel processors is proposed in which all of the different processes
in the convection-rotational problem are partitioned and the different
timescales can be dealt with together.
The coupled systems of convective-rotational
equations can greatly be simplified by using the hydrostatic
approximation for the rotational readjustment process in a viscous
Earth model. This is valid for a young Earth and for non-Newtonian
rheology. Larger amounts of contributions to the relative angular
momentum can be expected from non-Newtonian rheology.
The non-hydrostatic equatorial bulge may also
be explained as a consequence of the long-wavelength
dynamics associated with the effects of
depth-dependent physical properties on mantle convection.

Phys. Earth Planet. Inter., **79** (1993), 367-381.