Earth deformations - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 256

19 CONTINUE
18 CONTINUE
17 CONTINUE
GO TO 20
C Modify matrix A for inner core calculation.
16 A(1,2)=A(1,2)/R
A(2,1)=A(2,1)*R
A(2,3)=A(2,3)*R
A(2,6)=A(2,6)*R
A(3,4)=A(3,4)/R
A(4,1)=A(4,1)*R
A(4,3)=A(4,3)*R
A(4,5)=A(4,5)*R*R
A(5,1)=A(5,1)/R
A(5,6)=A(5,6)/R
A(6,5)=A(6,5)*R
C Multiply A into Y to find YP for inner core.
DO 21 I=1,6
DO 22 J=1,3
DO 23 K=1,6
YP(I,J)=YP(I,J)+A(I,K)*Y(K,J)
23 CONTINUE
22 CONTINUE
21 CONTINUE
C Correct YP to give derivatives of z-variables.
C Set value of alpha plus one for first two solutions.
ANM1=AN-1.D0
DO 24 J=1,3
C Set value of alpha plus one for third solution.
IF(J.EQ.3) ANM1=AN+1.D0
YP(1,J)=YP(1,J)-ANM1*Y(1,J)/R
YP(2,J)=YP(2,J)-(ANM1-1.D0)*Y(2,J)/R
YP(3,J)=YP(3,J)-ANM1*Y(3,J)/R
YP(4,J)=YP(4,J)-(ANM1-1.D0)*Y(4,J)/R
YP(5,J)=YP(5,J)-(ANM1+1.D0)*Y(5,J)/R
YP(6,J)=YP(6,J)-ANM1*Y(6,J)/R

24 CONTINUE

20 CONTINUE

RETURN
END

3.7 Fundamental, regular solutions in the inner core
The fundamental solutions of the spheroidal system, regular at the geocentre, are
found by power series expansions for small radii followed by Runge-Kutta integ-
ration out to the inner core boundary.
For n >1, in terms of z -variables, the three fundamental solutions are given
by the expansions (3.188) through (3.193), (3.194) through (3.199), and (3.200)
through (3.205). The first two terms in the expansions of the first fundamental
solution, generated by the free constant A 1,1 , and the second fundamental solu-
tion, generated by the free constant A 6,1 , are obtained directly, as are the first
terms of the third fundamental solution, generated by the free constant A 4,0 .The
second terms of the third fundamental solution are given by the systems (3.139) for