The subseismic equation and boundary conditions - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 430

boundary, and the fourth line the gravity at the inner core boundary and the core-
mantle boundary. These are followed by the e ective loadLove numbers for the inner

core, h n , the equivalent rigid-boundary radius a n ,thee

ff

ective load Love numbers
for the shell, h n , and the equivalent rigid-boundary radius b n , for each degree n .
The final line of the output file gives the coe

ff

cients a , b , c of the expression

1
h 1 =

2

a σ + b σ + c , (7.62)

for the reciprocal of the degree-one Love number of the inner core as a function
of dimensionless angular frequency σ = ω/2 ective Love numbers

represent admittances, we expect the inertial drag in the degree-one translational
modes to show up as a quadratic term and the resistance to the Coriolis acceler-
ation to register as a linear term of opposite sign, for translations in the equat-
orial plane represented by azimuthal number m =±

Ω . Since the e ff

1 (Smylie and Jiang, 1993,

pp. 1354-1355).
The programme allows the interactive input of the period in hours, the azi-
muthal number m and the switching on or o of the inertial and Coriolis terms.

The computation in the inner core begins with the power series expansions of
the fundamental solutions regular at the geocentre, followed by variable stepsize
Runge-Kutta integration, as in the programme ICFS.FOR described in Section 3.7.
The number of steps in the Runge-Kutta integrations in the mantle and crust are
those specified in the input Earth model file. As in the case of ICFS.FOR, the
programme proceeds with calls to the subroutines SPMAT and INTPL for cubic
spline interpolation of the Earth model, as 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, described in Section 3.7, and the subroutine
LINSOL, described in Section 1.5. The subroutine REL, described in Section 3.7,
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 is performed by the subroutine RK4, described in
Section 3.7.

ff

C PROGRAMME LOVE.FOR
C LOVE.FOR computes the 'effective' internal Love numbers for the shell
C (mantle plus crust) and inner core for an input Earth model.
C These Love numbers allow the radial displacement at the boundaries of
C the fluid outer core to be expressed in terms of the generalised
C displacement potential there.
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),NK(4),B(98,198),C(100,100),