## Initial-value approach for viscoelastic responses of the Earth's mantle

** Ladislav Hanyk**
**,**
**Ctirad Matyska**
**&**
**David A. Yuen**
### Abstract

We have developed a theory based on the direct numerical integration in time
for studying the temporal viscoelastic responses of earth models to surface
loads. Modelling in the time domain is motivated by the fact that realistic
elastically compressible models generate an infinite number of modes and
the width of such "continuous spectrum" may cover several orders of magnitude
in the Laplacian spectral domain for complicated viscosity stratification,
which causes numerical difficulties for the normal-mode method. From our
numerical solutions, we have directed our attention on the influences
of elastic compressibility, thickness of the lithosphere, the nature
of the internal mantle boundaries with density jumps and the viscosity
structure near the interface between the lower and the upper mantle.
There is a great difference between the responses of compressible and
incompressible models mainly for shorter wavelengths and thus incompressible
models seem to be inadequate for short-wavelength responses.
The sensitivity of the viscoelastic responses to the lithospheric thickness
in the presence of a low viscosity asthenosphere is substantial.
This points to the need for constructing models with a 3-D viscosity variations,
which would yield more realistic lithospheric-asthenospheric structure globally
than models with a constant lithospheric thickness. The sensitivity
of the Earth's viscoelastic behaviour to the other parameters is weaker
but still is noteworthy.

In: *Dynamic of the Ice Age Earth: A Modern Perspective*, ed. P. Wu,
Trans Tech Publications 1998, pp. 135-154.