7.1 Description of spherical harmonic coefficient format

We use unity-norm spherical harmonics as described in sec. B.8 of Dahlen and Tromp [1998] and the G-Cubed article to expand the tomographic and geodynamic models at discrete layers with mid-layer depth $z_i$. The sets of $\cos$ and $\sin$-coefficients $\{a_{\ell m}^i,b_{\ell m}^i\}$ we then combine into ``model'' files whose format is given in Table 1.

Table 1: Data format description of spherical harmonic models with discrete layers. (Free formatting, fields separated by white spaces.)

actual entry	example or note
$N$	number of layers, e.g. 10
$z_1$	in km, starting with the deepest level, eg. 2850
$\ell_{\mathrm{max}}$	e.g. 31
$a_{00}^1 \quad b_{00}^1$	$b_{\ell0}$ always added, even though identical to zero
$a_{10}^1 \quad b_{10}^1$
$a_{11}^1 \quad b_{11}^1$
$a_{20}^1 \quad b_{20}^1$
...
$z_2$	in km, next highest level, e.g. 2800
$\ell_{\mathrm{max}}$	same as above, redundant
$a_{00}^2 \quad b_{00}^2$
...
$z_N$	in km, shallowest level, e.g. 0
$\ell_{\mathrm{max}}$
$a_{00}^N \quad b_{00}^N$
...

All velocity and density perturbations of the spherical harmonic models are in percent from PREM, we indicate the relative deviations by $\delta v = d\ln v = \frac{d v}{v}$.