Geology Reference
In-Depth Information
with the quantities b n and a n representing equivalent rigid-boundary radii com-
puted from the systems (7.34), (7.36) and (7.41), augmented by the subseismic
condition. Again, the case n
0 at the inner core boundary is an exception. Since
dV 1,0 ( a + )/ dr vanishes there, a 0 becomes indeterminate.
Under the subseismic approximation, single e
=
ff
ective internal load Love numbers
for the shell and inner core, from relations (7.46)-(7.47) and (7.56)-(7.57), can be
defined as
h 1 n
b n h 2 n
b
h n =
( n +
1 )
,
(7.58)
and
h 1 I
a n h 2 n
a
h n =
+
.
(7.59)
n
The radial coe
cients of the degree- n parts of the radial displacements on the two
boundaries can be expressed as
h n
g 0 ( b ) χ n ( b ),
=
y 1, n ( b )
(7.60)
and
h n
g 0 ( a ) χ n ( a + ).
y 1, n ( a )
=
(7.61)
Since, under the subseismic approximation, there is no degree-zero deformation
field in the inner core, we have h 0 =
0.
The programme LOVE.FOR computes the internal load Love numbers for a
given Earth model. The Love numbers are only physically meaningful for
degree n ≥ | m |
, where m is the azimuthal number. Input to the programme is the
Earth model file, the name of which is typed in at the request of the programme.
The first line of this file is the name of the Earth model, in format (10A7). The
second line contains the number of Love numbers to be computed, in format (I10).
The third line gives the numbers of model points and integration steps, in format
(8I10), for each region specified by the integer variable IR
1, 2, 3, 4 for the inner
core, outer core, mantle and crust, respectively. The Earth model follows in format
(1X,F10.1,F10.2,F10.1,F10.1,F10.1), in traditional units: radius in km, density in
g
=
s 2 . The input Earth model
file is written out to the screen for verification. For each degree n , the Love numbers
h 1 n , h 2 n for the inner core, defined by expression (7.47), and the Love numbers h 1 n ,
h 2 n for the shell, defined by expression (7.46), are written out to the screen as well.
Output from the programme is contained in the file love.dat. The first line of
this file gives the Earth model name, the second line the number of Love numbers
computed, the third line the radii of the inner core boundary and the core-mantle
cm 3 ,Lam´ecoe
/
cients in kilobars and gravity in cm
/
 
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