Geology Reference
In-Depth Information
2
Plate Motions
Abstract
Plate kinematics represents a fundamental sub-discipline of plate tecton-
ics. In this chapter, I describe the geometry of plate motions independently
from the geodynamic factors (forces, torques, stresses) that drive the
movement or changes in the state of motion of a tectonic plate. At this
stage, the focus is on modelling, in particular on plate reconstructions,
thereby the general description proceeds assuming that kinematic data are
already available.
In the continuum mechanics representation
of solid Earth systems, any geophysical entity
(for example, a subducting slab) is formed
by a continuous distribution of small volume
elements,
dV
, whose locations are described
by position vectors
r
in the selected reference
frame. In this representation, the
intensive
variables
(also known as
bulk properties
)are
quantities describing
local
physical properties
of the volume elements, for example their
temperature, velocity, etc. It is assumed that
these quantities vary smoothly across the region
R
, so that they can be represented mathematically
by continuous functions of position vectors
r
2
R
. Often the intensive variables are associated
having appropriate continuity properties. Typical
examples are the local temperature,
T
D
T
(
r
),
and pressure,
p
D
p
(
r
), of rocks. However, not all
of the intensive variables can be represented by
scalar fields. For instance, the displacement of
a point
r
during deformation must be described
by a vector quantity,
u
D
u
(
r
), which varies from
point to point in
R
. Therefore, intensive variables
2.1
The ContinuumMechanics
Representation
Earth's crust and mantle are deformable solids,
composed by a large number of closely spaced
microscopic mineral grains of arbitrary shape and
size. At macroscopic scale, a rigorous quanti-
tative description of the geodynamic evolution
of a rock system starts from the introduction
of infinitesimal quantities, the
volume elements
dV
, which represent the smallest chemically and
physically homogeneous parts in which a rock
assemblage can be divided. It is usually assumed
that a volume element fills a continuous region
of the three-dimensional space, namely a closed
subset
R
<
3
, and has regular shape, for ex-
ample a parallelepiped
dV
D
dxdydz
. In practice,
the computational techniques employed in plate
tectonics often require a definition of volume
elements having dimensions up to several km,
depending on the scale of the problem, yet being
small in relation to the total volume of the rock
system.
