Auxiliary material for the Paper 2007JB005448
Body tides of a convecting, laterally heterogeneous, and aspherical Earth
L. Metivier
Johns Hopkins University, Department of Earth and Planetary Sciences, Baltimore,
Maryland, USA
C.P. Conrad
Department of Geology and Geophysics, University of Hawaii, Honolulu, Hawaii, USA
Metivier, L., and C. P. Conrad (2008), Body tides of a convecting, laterally heterogeneous,
and aspherical Earth, J. Geophys. Res., 113, XXXXXX, doi:10.1029/2007JB005448.
Introduction
Seismic tomography surveys and fluid dynamic studies show that thermal convection
within Earth's mantle produces significant lateral heterogeneity exemplified by
superplumes, superswells, and subducting slabs. To determine the influence of this
heterogeneity on body tides, we used a tomographic model to constrain lateral variations
in mantle density and rigidity. This heterogeneity drives convective flow that deflects
Earth's surface and core mantle boundaries by a few kilometers; we used a viscous flow
model to constrain this dynamically-supported asphericity. After verifying this complete
Earth model using geoid observations, we used the spectral element method to determine
how Earth's body tides are perturbed compared to a spherical Earth. Indeed, the laterally
heterogeneous structure of the Earth induces small perturbations to the tidal Love
numbers (see article, eqs. (7)-(9)). These three auxiliary files present tables of the
perturbations to the tidal Love numbers (see more details below).
Note that, for all the files:
1) The spherical harmonics are normalized using the norm (for degree n and order m):
sqrt( (2n+1) (2-delta(0,m)) (n-m)!/(n+m)! )
2) The perturbed Love number coefficients dh, dl, dw, dk, dd, depend on degrees and
orders n, m, n', m' (see article, eqs. (7)-(9)). The coefficients have to be multiplied by 1e-
6.
Degree 1 toroidal components (dw) are not presented here because they correspond to
rigid rotations of the Earth.
1. 2007jb005448-ts01.txt Table of perturbed semi-diurnal Love numbers (n = 2, |m| = 2), up to degree 20. The
values in the table have to be multiplied by 1e-6.
2. 2007jb005448-ts02.txt Table of perturbed diurnal Love numbers (n = 2, |m| = 1), up to degree 20. The values in
the table have to be multiplied by 1e-6.
3. 2007jb005448-ts03.txt Table of perturbed long period Love numbers (n = 2, |m| = 0), up to degree 20. The
values in the table have to be multiplied by 1e-6.