**Principal Investigator**
Kurt Lambeck **Project **n55

Department of Geodynamics, **Machine** VP

Research School of Earth Sciences

**Co-Investigators **P Johnston,
C Smither and A P Purcell

Department of Geodynamics, Research School of Earth Sciences

**Mantle Viscosity, Glacial Rebound and Sea-Level
Change**

Large-scale variations in the loading of the Earth's surface produce corresponding deformations which can be used to constrain both the load history and the Earth's rheological response. In the case of post-glacial rebound these deformations are preserved in the sea-level record and the detail they provide of the de-glaciation process in turn places important constraints on the climatology of the Holocene.

**What are the basic questions addressed?**

Accurately modelling post-glacial sea-level change requires that a wide range of different effects be considered: the addition of meltwater to the ocean basins and their resultant loading, unloading under the ice sheets, the gravitational attraction between the ice sheets and the melt-water and the melt- water and itself, and the effect of internal mass redistribution on the shape of the geoid. The complexity of the relationship between rheology and sea-level change and uncertainty in both the load-history and the sea-level record limit the accuracy of the inversion procedure though strong constraints can be placed on both the deglaciation process and the Earth's rheology

**What are the results to date and future of the
work?**

The numerical and theoretical development of the propagator matrix technique, and the adoption of a seismological formulation have greatly increased numerical stability, but raised several peripheral issues. The reliability of the collocation technique for inverting the Laplace transform has been called into question and an investigation started to more completely determine its short- comings and the factors that govern its stability. Incorporating the pre- stress and dilatational terms analytically into the newly developed propagator matrix procedure has established the relative importance and effect of each, allowing a fully compressible body to be considered.

**What computational techniques are used and why
is a supercomputer required?**

Modelling the earth as a Maxwell viscoelastic body we invoke the correspondence principle to transform the problem into a series of elastic calculations. Each elastic problem is either an iterative spherical harmonic formulation or an analysis using the propagator matrix procedure. In the former case we need to model to sufficiently high degree to obtain the desired resolution while in the latter, aliasing of the origin after inverting from the Fourier domain makes a large grid size necessary. In either instance the sheer size of the problem means that inversion via bilinear transform or collocation in a reasonable amount of time is most readily achieved in a supercomputer environment, the geometry of the VP being very well-suited to both elastic formulations.

**Publications**

*Constraints on the Late Weichselian ice sheet
over the Barents Sea from observations of raised shorelines*.
K. Lambeck, Quat. Sci. Rev., vol. **14** pp 1-16 (1995).

*Late Devensian and Holocene shorelines of the
British Isles and North Sea from models of glacio-hydro-isostatic
rebound*. K. Lambeck, J. Geol. Soc. Lond.,
vol. **152** pp 437-448 (1995).

*Glacial isostacy and water depths in the Late
Devensian and Holocene on the Scottish shelf of the Outer Hebrides*.
K. Lambeck J. Quaternary Science, vol. 10 pp 83-86 (1995).