Geoscience Reference
In-Depth Information
Example: calculation of relative motion at a plate boundary
Calculate the present-day relative motion at 28
◦
S, 71
◦
Wonthe Peru-Chile Trench
using the Nazca-South America rotation pole given in Table 2.1. Assume the radius
of the Earth to be 6371 km:
λ
x
=−
28
◦
,
x
=−
71
◦
λ
p
=
56
◦
,
p
=−
94
◦
ω
=
7
.
2
×
10
−
7
180
×
7
.
2
×
10
−
7
deg yr
−
1
rad yr
−
1
=
These values are substituted into Eqs. (2.12), (2.14), (2.7) and (2.8)inthat order,
giving
cos
−
1
[sin(
a
=
−
28) sin(56)
+
cos(
−
28) cos(56) cos(
−
94
+
71)]
26
◦
=
86
.
(2.15)
=
sin
−
1
cos(56) sin(
−
94
+
71)
sin(86
.
26)
C
=−
12
.
65
◦
(2.16)
180
×
7
.
2
×
10
−
7
×
6371
×
10
5
v
=
×
sin(86
.
26)
=
7
.
97 cm yr
−
1
(2.17)
β
=
90
−
12
.
65
=
77
.
35
◦
(2.18)
Thus, the Nazca plate is moving relative to the South American plate at 8 cm yr
−
1
with azimuth 77
◦
; the South American plate is moving relative to the Nazca plate at
8cmyr
−
1
, azimuth 257
◦
(Fig. 2.2).
2.4.3 Combination of rotation vectors
Suppose that there are three rigid plates A, B and C and that the angular velocity
of A relative to B,
B
A
, and that of B relative to C,
C
B
, are known. The motion
of plate A relative to plate C,
C
A
, can be determined by vector addition just as
for the flat Earth:
A
=
C
B
+
B
A
(2.19)
C
(Remember that in this notation the first subscript refers to the 'fixed' plate.)
Alternatively, since
B
A
=−
A
B
, Eq. (2.19) can be written as
B
+
B
C
+
C
A
=
0
(2.20)
A
The resultant vector
C
A
of Eq. (2.19) must lie in the same plane as the two
original vectors
B
A
and
C
B
. Imagine the great circle on which these two poles
