Geoscience Reference
In-Depth Information
Table 2.2 Symbols used in calculations involving rotation poles
Symbol
Meaning
Sign convention
N positive
λ p
Latitude of rotation pole P
S negative
λ x
Latitude of point X on plate boundary
W negative
φ p
Longitude of rotation pole P
E positive
φ x
Longitude of point X on plate boundary
v
Velocity of point X on plate boundary
v
Amplitude of velocity v
β
Azimuth of the velocity with respect
Clockwise positive
to north N
R
Radius of the Earth
Angular velocity about rotation pole P
Figure 2.11. A diagram showing the relative positions of the
positive rotation pole P and point X on the plate boundary.
Nisthe North Pole. The sides of the spherical triangle NPX
are all great circles, the sides NX and NP are lines of
geographic longitude. The vector v is the relative velocity at
point X on the plate boundary (note that v is perpendicular
to PX). It is usual to quote the lengths of the sides of
spherical triangles as angles (e.g., latitude and longitude
when used as geographic coordinates).
N
A
c
b
B
P
C
X
v
The distance between rotation pole and plate boundary is important (remember
the sin
θ
factor multiplying the angular velocity
ω
in Eq. (2.3)). However, it is
90 when quoting a relative
velocity for two plates, even though neither plate may extend 90
conventional to use the relative velocity at
θ =
from the
pole.
2.4.2 Calculation of the relative motion at a plate boundary
Once the instantaneous rotation pole and angular velocity for a pair of adjacent
plates have been determined, they can be used to calculate the direction and
magnitude of the relative motion at any point along the plate boundary.
The notation and sign conventions used in the following pages are given in
Table 2.2.Figure 2.11 shows the relative positions of the North Pole N, positive
rotation pole P and point X on the plate boundary (compare with Fig. 2.8(b)). In
the spherical triangle NPX, let the angles XNP
A , NPX
B and PXN
=
=
=
C ,
Search WWH ::




Custom Search