Plate Motions - Quantitative Plate Tectonics - page 74

Table 2.4 Q tensors and areas of the 25 MORVEL plates
Plate

A Q 11 Q 22 Q 33 Q 12 Q 13 Q 23 Diag. Err.

AMU 0.130659 0.108248 0.089481 0.063589 0.028732 0.036320 0.051295 0.0000 %

ANT 1.434290 1.328262 1.176115 0.364247 0.050791 0.052812 0.080667 0.0015 %

ARB 0.120824 0.074248 0.066810 0.100589 0.048782 0.029553 0.031041 0.0004 %

AUS 0.935403 0.602384 0.568115 0.700304 0.230373 0.218401 0.241845 0.0002 %

CAR 0.103729 0.094940 0.014300 0.098213 0.024762 0.006107 0.020566 0.0024 %

COC 0.072230 0.071072 0.003020 0.070372 0.005543 0.001064 0.010141 0.0028 %

CAP 0.203647 0.196537 0.022175 0.188580 0.021636 0.007182 0.045603 0.0005 %

EUR 1.218422 1.017712 0.913393 0.505738 0.041466 0.222433 0.315605 0.0000 %

IND 0.30636 0.286350 0.042306 0.284051 0.057048 0.013096 0.060493 0.0021 %

JDF 0.006315 0.005162 0.004356 0.003111 0.001501 0.001916 0.002491 0.0079 %

LWA 0.117115 0.063149 0.081116 0.089959 0.043343 0.036053 0.029664 0.0026 %

MAC 0.007890 0.006131 0.007510 0.002139 0.000812 0.003172 0.001465 0.0000 %

NAM 1.440479 1.282025 1.008008 0.590974 0.079145 0.026680 0.378356 0.0017 %

NUB 1.440653 0.372568 1.301217 1.207515 0.051346 0.005428 0.044223 0.0002 %

NAZ 0.403564 0.391445 0.070630 0.345043 0.014536 0.003992 0.115869 0.0012 %

PAC 2.681816 1.204054 2.045135 2.114430 0.400314 0.062295 0.057354 0.0002 %

PHB 0.144484 0.081761 0.078620 0.128588 0.062670 0.029123 0.029347 0.0003 %

RIV 0.002486 0.002289 0.000489 0.002193 0.000625 0.000239 0.000763 0.0201 %

SAM 1.023883 0.624948 0.586878 0.835938 0.344415 0.181243 0.174029 0.0001 %

SCO 0.042001 0.036816 0.034549 0.012637 0.005706 0.012013 0.014486 0.0000 %

SOM 0.354795 0.221032 0.153739 0.334814 0.154901 0.024755 0.035861 0.0007 %

SUR 0.027055 0.018681 0.026496 0.008933 0.001954 0.012245 0.002957 0.0000 %

SUN 0.281465 0.232911 0.054798 0.275220 0.093052 0.004760 0.016178 0.0002 %

SAN 0.004543 0.003525 0.004269 0.001292 0.000527 0.001817 0.000940 0.0000 %

YTP 0.062249 0.051303 0.024035 0.049159 0.019688 0.011653 0.022080 0.0008 %

Earth 12.566357 8.377553 8.377560 8.377628 0.000004 0.000012 0.000029 0.0001 %

Av.%.error 0.0001 % 0.0003 % 0.0002 % 0.0006 % 0.0000 % 0.0000 % 0.0000 %

Units are in steradians

where C i is a constant that is assumed to be
independent from the subduction velocity, and
the line integral is calculated following a coun-
terclockwise path.
If we expand the triple vector product in
( 2.72 ), we obtain the following simple expression
for the torque:
N i D C i Z
T i

introduce the torques ( 2.73 ) in the total torque
balance equation, we obtain a more realistic equa-
tion, which potentially can be solved to determine
the absolute Euler vector of the reference plate:
X

i !

C j

i

¨ r D X
j

j
f r

j

D i Q r

i

X
i

dl D C i r f r i

i

(2.73) ¨ ir

D i Q (2.74)

This is a system of three equations in the
unknown components of ¨ r , which can be solved
if the drag coefficients D i and the constants C j are
known. In this instance, the lithosphere always
has a non-zero angular momentum, even when
D i D D for all plates.

In this expression, r i and r f are, respectively,
the position vectors of the start and end points
of the trench line T i . Therefore, we see that
the torque exerted on a subducting plate by the
attached slab only depends from the width of
the subduction zone, not by its curvature. If we