of 6
Theory of the Earth
Don L. Anderson
Appendix
Boston: Blackwell Scientific Publications, c1989
Copyright transferred to the author September 2, 1998.
You are granted permission for indi
vidual, educational, research and
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Recommended citation:
Anderson, Don L. Theory of the Earth.
Boston: Blackwell Scientific Publications,
1989.
http://resolver.calt
ech.edu/CaltechBOOK:1989.001
A scanned image of the entire book may
be found at the following persistent
URL:
http://resolver.caltech.edu/CaltechBook:1989.001
TABLE
A-1
Earth
Model
PREM and
its Functionals Evaluated at a Reference Period of
1
s.
Above
220
km
the Mantle is Transversely Isotropic (see Table A
-
2);
the Parameters Given are
"Ecluivalent"
Isotropic Moduli
and
Velocities.
Level
Radius
Depth
Density
V,
V,
Q,
QK
Qp
@
KS
P
cr
Pressure
dK/dP
B.P.
Gravity
(km)
(km)
(g/cm3)
(kmls)
(km/s)
(kmz/s2)
(kbar)
(kbar)
(kbar)
(cm/s2)
TABLE
A
-
1
(continued)
Level Radius
Depth Density
Vp
V,
Qp
QK
Qp
@
I%
P
cr
Pressure
dK/dP
B.P.
Gravity
(km)
(km)
(g/cm
3
)
(km/s)
(km/s)
(kmz/s2)
(kbar) (kbar)
(kbar)
(cm/s2)
APPENDIX
359
TABLE
A
-
1
(continued)
Level Radius
Depth
Density
V,
V,
Q,
QK
Q,
Q,
I%
P
u
Pressure
dK/dP
B.P.
Gravity
(km)
(km)
(g/cm3)
(kmls)
(kmls)
(kmz/s2)
(kbar) (kbar)
(kbar)
(cmls2)
-
-
-
-
-
Dziewonski,
A.
M.
and
D.
L.
Anderson
(1981)
Preliminary Reference Earth
Model,
Phys.
Earth
Planet.
Inter.,
25,
297
-
356
TABLE
A
-
2
Crust
and
Upper Mantle
of
PREM Including Directional Velocities, Anisotropic Elastic
Constants and
"
Equivalent
"
Isotropic Velocities. Evaluated at Reference Periods
of
1
s (top) and
200
s
(bottom).
Radius
Depth
Density
Vpv
VpH
Vsv
VSH
r)
Q@QKACLNF
v~
VS
(km)
(km)
(g/cm
3
)
(kmls)
(km/s)
(kmls)
(kmls)
(kbar) (kbar) (kbar) (kbar)
(kbar)
(kmls)
(kmls)
Dziewonski, A.
M.
and
D.
L.
Anderson
(1981)
Preliminary Reference
Earth
Model,
Phys.
Earth
Planet.
Inter.,
25,
297
-
356
TABLE
A
-
3
Conversion Factors
--
-
To
Convert
To
Multiply
by
angstrom,
bar
calorie
(g),
cal
dyne
gamma
gauss
heat
-
flow unit
(H.F.U.)
micrometer,
pm
poise
stoke
watt
Year
cm
nm
atm
dyne/cm
2
MPa
joule
g
cmls
-2
newton
cal
watt
-
second
joule
gauss
tesla
tesla
pcallcm2/s
m
W/m
2
cm
glcmls
Pa
-
s
cmZ/s
Jls
S
TABLE A
-
4
Physical Constants
TABLE
A
-
5
Earth
Parameters
Equatorial
radius,
a
Polar
radius, c
Equivolume sphere radius
Surface area
Geometric flattening,
(a
-
c)/a
Ellipticity,
(a
2
-
c
2
)!(a
z
+c
2
)
GM
Mass, M
Mean density
Moments
of
inertia
Polar,
C
Equatorial,
A
C/Ma
2
Dynamic ellipticity
C
-
A
H=-
(precession
constant),
=
1/305.51
C
C
-
A
Ellipticity coefficient,
J,
=
-
10826.3
X
Ma
Angular velocity,
Cl
7.2921
X
rad
s-I
Angular
momentum,
CCl
5.8604
X
kg
m
2
s-I
Normal gravity at equator
9.7803267 m
s-2
Normal gravity at poles
9.832186
m
s-2
Speed
of
light
Electronic charge
Permeability
of
vacuum
Permittivity of vacuum
Planck constant
Boltzmann
constant
Stefan
-
Boltzmann constant
Gravitational constant
Electron rest mass
Avogadro's
number
Gas constant
That is,
a product
of
each element
in
a row
or
column,
and
a second
-
order determinant formed
by
elements from the
other
rows and columns.
Definitions
of
determinants
of
Determinants
The
determinant
of
the second order
stands
for
the expression
(ad
-
be).
The
determinant
of
a
3
x
3
matrix,
or
array
of
num
-
bers,
may
be defined
in terms
of
determinants
of
the second
order.
The
determinant
abc
1:
r
:I
stands
for
higher order
may
be given
in
a similar
way.