Geology Reference
In-Depth Information
Table 2.2
The NUVEL-1A velocity model
Plate
¨
x
¨
y
¨
z
¨
œ
e
¥
e
Africa
0.002401
0.007939
0.013891
0.9270
59.160
73.174
Antarctica
0.000689
0.006541
0.013676
0.8695
64.315
83.984
Arabia
0.008195
0.005361
0.016730
1.1107
59.658
33.193
Australia
0.009349
0.000284
0.016253
1.0744
60.080
C
1.742
Caribbean
0.001332
0.008225
0.011550
0.8160
54.195
80.802
Cocos
0.008915
0.026445
0.020895
1.9975
36.823
108.629
Eurasia
0.000529
0.007235
0.013123
0.8591
61.066
85.819
India
0.008181
0.004800
0.016760
1.1034
60.494
30.403
North America
0.001768
0.008439
0.009817
0.7486
48.709
78.167
Nazca
0.000022
0.013417
0.019579
1.3599
55.578
90.096
South America
0.000472
0.006355
0.009100
0.6365
54.999
85.752
¨
z
2
)
1/2
is the angular velocity in deg/Myr;
¨
x
,
¨
y
,and
¨
z
are expressed in rad/Myr;
œ
e
and
¥
e
are, respectively, the latitude and longitude of the Euler pole with respect to the Pacific
(
¨
x
2
¨
y
2
¨
D
C
C
so on. Thus, in general, the finite reconstruction
poles associated with the kinematics of a set of
continental plates can be calculated only
after
the
stage transformations have been determined by
concatenation of stage matrices.
This formula allows to calculate the squared
sum of misfits between predicted and observed
spreading rates and azimuths of relative veloci-
ties. Each plate is assumed to have
n
i
boundaries
that are spreading ridges, and for each of these
boundaries, there are
N
ij
spreading rate data at
locations represented by position vectors
r
k
.Let
¨
i
¨
j
be the predicted relative angular velocity
of the
i
th plate with respect to an adjacent plate
separated by a spreading ridge. By (
2.17
), the
predicted linear velocity between the two plates
at a location
r
k
is given by: (¨
i
¨
j
)
r
k
.If
n
k
and
v
(
r
k
) are respectively a versor normal to the
ridge axis and the observed average spreading
velocity at
r
k
, then the weighted misfit between
observed and predicted spreading rates is given
by the scalar difference between the projections
of
v
(
r
k
)and(¨
i
¨
j
)
r
k
onto the axis of
n
k
,
divided by the standard error ¢
k
attributed to
v
(
r
k
). Similarly, it is assumed that the
i
th plate
has
m
i
generic boundaries, each having
M
ij
di-
rectional observations. Let
s
(
r
k
) be a unit ver-
sor representing one of these observations. The
predicted direction is clearly given by the versor
of the theoretical linear velocity (¨
i
¨
j
)
r
k
.
Therefore, the weighted misfits of azimuth data
can be defined as the magnitudes of the vector
differences between predicted and observed di-
rection versors, divided by the standard error ¢
k
.
Tab le
2.2
lists the Euler vectors of NUVEL-
1A (DeMets et al.
1994
), one of the most widely
2.9
Current Plate Motions
We are going to conclude this chapter, dedicated
to plate kinematics, with a description of the
techniques used for the determination of the mod-
ern plate motions. The first models of current
plate kinematics were based on a combination of
heterogeneous data, represented by seismic slip
vectors, averaged spreading rates, and transform
fault azimuths (Chase
1978
; Minster and Jordan
1978
; DeMets et al.
1990
). Each of these mod-
els specified a set of
n
1 Euler vectors, ¨
i
,
n
being the number of modern plates, relative to
a reference plate, for example the Pacific plate.
The models were obtained through least squares
procedures that minimized the quantity:
(
v
.
r
k
/
¨
i
¨
j
r
k
n
k
¢
k
)
2
N
ij
n
i
X
n1
X
X
¦
2
D
iD1
jD1
k
D
1
"
s.r
k
/
#
2
¨
i
¨
j
r
k
LJ
LJ
¨
i
¨
j
r
k
LJ
LJ
M
ij
n1
X
X
m
i
X
1
¢
k
C
i
D
1
j
D
1
kD1
(2.57)
