Group velocity models

We have inverted for models of surface wave group velocity at periods between 35 s and 175 s. The method and results are described in Global models of surface wave group velocity. We inverted separately for Love and Rayleigh waves at each period for a model parameterized with spherical harmonics up to degree 40.

The models are available in several forms. The original spherical harmonic coefficients are indicated by SH in the table, and they are described below. We have evaluated the spherical harmonics on a global grid and store them in the Generalized Mapping Tools (GMT) GRD format (indicated by grd in the table). We have also created images of the models which are available in either PDF for printing or as GIF images for screen viewing. For convenience, if you want to work with a number of the maps, it is easier to download them as compressed archives, and both the grd files the SH files are available.
PeriodLove wavesRayleigh Waves
35 sSH grd PDF gifSH grd PDF gif
40 sSH grd PDF gifSH grd PDF gif
50 sSH grd PDF gifSH grd PDF gif
60 sSH grd PDF gifSH grd PDF gif
70 sSH grd PDF gifSH grd PDF gif
80 sSH grd PDF gifSH grd PDF gif
90 sSH grd PDF gifSH grd PDF gif
100 sSH grd PDF gifSH grd PDF gif
125 sSH grd PDF gifSH grd PDF gif
150 sSH grd PDF gifSH grd PDF gif
175 sSH grd PDF gifSH grd PDF gif

Spherical harmonic definition

The function is calculated as:

\begin{displaymath}\frac{\delta U}{U_0}(\theta,\phi)= \sum_{l=0}^{l_{\rm max}} X... ...}(\theta)( A_{lm} \cos m \phi - B_{lm} \sin m \phi ) \nonumber \end{displaymath}  

where $\theta$ is colatitude, $\phi$ is longitude, and Xlm is defined in terms of Ylm by $Y_{lm}(\theta,\phi)=X_{lm}(\theta)e^{im\phi}$, and Ylm are fully normalized spherical harmonics as in Edmonds (1960).

As a numerical check:
l m $X_{lm}(\theta=\pi/2)$
0 0 0.2820948
1 0 -0.0000000
1 1 -0.3454942
2 0 -0.3153916
2 1 0.0000000
2 2 0.3862742

Each line of the file is "l m Alm Blm" with Blm left out if m=0.