[institut] Predavanja prof. A.Forte-a na Matematickom institutu i Institutu za geofiziku

[Katedra za astronomiju]

Sreda 10. maj, 12 casova
MATEMATICKI INSTITUT SANU, sala 2


Alessandro M. Forte
GEOTOP - Departement des Sciences de la Terre et de
l'Atmosphre Universite du Qubec  Montral, Qubec, Canada


"A NUMERICAL INVESTIGATION OF TIME-DEPENDENT THERMAL CONVECTION IN
EARTH'S INTERIOR"

Abstract: The physical and mathematical formulation of a model of
thermal convection in a viscous fluid will be presented. This model will
be used to explore the dynamics in Earth's 3000 kilometre-thick rocky
shell called the mantle. The discussion will first focus on the
mathematical and numerical development of a model of time-dependent,
compressible thermal convection in 3-D spherical geometry which is based
on a pseudo-spectral solution of the coupled equations of energy and
momentum conservation assuming a linear viscous rheology. The equations
of mass and momentum conservation are solved only once using generalized
spherical harmonic basis functions to obtain spectral Green functions.
These Green functions describe the viscous impulse response of the
mantle and they are used to mathematically predict the flow induced by
an arbitrary distribution of density perturbations. With this approach,
the thermal convection problem is effectively reduced to the solution of
the conservation of energy equation. The present-day distribution of
temperature anomalies in Earth's mantle may be derived from global
seismic tomographic images of three-dimensional (3-D) structure inside
our planet. These estimates of mantle thermal structure provide a
starting point for numerical reconstructions of the spatial and temporal
evolution of the 3-D structure and flow in the mantle. The Rayleigh
number which characterizes the convective vigour in the mantle is
estimated to be very high and therefore the effect of thermal diffusion
will be much weaker than thermal advection in most of the mantle. This
assumption will be used as a basis for reconstructing past thermal
states in the mantle.





Cetvrtak 11. maj, 14 casova
Institut za geofiziku, RGF, Djusina 7, sala 167


Alessandro M. Forte
GEOTOP - Departement des Sciences de la Terre et de l'Atmosphre
Universite du Qubec  Montral, Qubec, Canada


SEISMIC AND GEODYNAMIC CONSTRAINTS ON PRESENT-DAY DYNAMICS IN EARTH'S
MANTLE

Abstract: Seismic tomography provides models of global,
three-dimensional (3-D) mantle structure with increasingly improved
vertical and horizontal resolution. These seismic models of
heterogeneity in the mantle may be interpreted in terms of the density
perturbations which drive the convective flow in the mantle. Direct
calculations of this flow are shown to provide very good matches to a
variety of important geophysical surface 'observables', such as the
geoid or free-air gravity anomalies, core-mantle boundary topography,
and dynamic surface topography. These tomography-based convective flow
calculations require, as necessary inputs, the depth dependence of the
effective mantle viscosity and the scaling coefficient between
perturbations of seismic velocity and density. The convection-related
geophysical data may therefore be employed, in inverse calculations, to
constrain both the rheological and thermo-chemical structure of the
mantle. The tomography-based mantle flow models have been reformulated
to handle very large radial gradients in viscosity and they incorporate
surface tectonic plates whose movements are predicted, rather than
imposed. This viscous flow theory, in combination with mantle density
anomalies derived from 3-D seismic tomography models, is used to invert
a wide range of surface convection data to obtain new inferences of the
radial profile of mantle viscosity. These viscosity inversions have
revealed the presence of a strong maximum in viscosity in the lower
mantle, near 2000 km depth. This rheological stratification provides an
obstacle to convective mixing and it yields a transition to a flow
patters in the deep mantle which is strongly dominated by the longest
horizontal wavelengths.