Earth deformations - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 263

10 − 5 rad s − 1 by the World Geodetic System 1984 (WGS84) as Ω= 7.292115 ×

(Hofmann-Wellenhof and Moritz, 2006, p. 88).
The programme ICFS calculates the free solutions in the inner core, regular at
the geocentre, for a given Earth model. Of course, the solutions are only meaning-
ful for n . The filename for the Earth model is typed in on request. This can be

one of the four models listed in Appendix C, or one in a file with the appropriate
format. The Earth model is interpolated by cubic splines with calls to the sub-
routines SPMAT and INTPL, described in Section 1.6. Power series expansions of
the free solutions, regular at the geocentre, are performed with the assistance of
the double precision function subprogrammes, P1, P2, Q1 and Q2, as well as the
subroutine MATRIX, and the subroutine LINSOL, described in Section 1.5. The
subroutine REL tracks the relative error in both the power series expansions and
the Runge-Kutta integration. Derivatives of the propagator matrix, required for the
Runge-Kutta integration, are calculated by the subroutine YPRIME, described in
Section 3.6, and the Runge-Kutta integration itself is performed by the subroutine
RK4. The programme ICFS outputs the first three terms of the power series expan-
sions of the solutions regular at the geocentre, at radius RMIN, in the file fsolns.dat.
For n >0, there are three regular solutions; for n

≥| m |

0, only the third solution is non-
zero, with terms in y 1 , y 2 and y 5 . The fundamental free solutions throughout the
inner core are given in the output files, fs1.dat, fs2.dat and fs3.dat. We list the pro-
gramme ICFS below.

=

C PROGRAMME ICFS.FOR

C
C ICFS.FOR calculates the three fundamental solutions of
C the sixth-order spheroidal system, regular at the geocentre, for n>0.
C For n=0, it calculates the one solution of the fourth-order
C spheroidal system, regular at the geocentre, other than
C the trivial solution y5 constant. Interpolation of Earth model
C properties is made by calls to the subroutines SPMAT and INTPL to
C perform cubic spline interpolation. Power series expansions at
C the geocentre are continued by fourth-order Runge-Kutta integration
C by the subroutine RK4 with calls to the subroutine YPRIME to
C evaluate derivatives at each step.
C

IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION R(100),RHO(100),GZERO(100),RI(300),RHOI(300),
1 GZEROI(300),ENAME(10),NM(4),NI(4),B(98,198),C(100,100),
2 Y(6,6),YSCAL(6,3),YSCAL2(6,3),YA(6),A(6,6),AS(6,6),CAUG(6,13),
3 RM1(6,3),RM2(6,3),YP(6,6),YIC(6,3),Y1(6,6),Y2(6,6),DELTA(6,3),
4 FS(6,3)
DOUBLE PRECISION MU(100),LAMBDA(100),MUI(30),LAMBDAI(300),
1 K1(6,6)
CHARACTER*20 EMODEL
C Enter Earth model name.
WRITE(6,10)

10 FORMAT(1X,'Type in Earth model file name.')

READ(5,11)EMODEL

11 FORMAT(A20)