Phase Velocity Models (Ekström, Tromp & Larson, 1997)

We have inverted for phase velocity maps from surface wave phase measurements. These maps are being published in Ekström, Tromp & Larson (1997).

Downloads
Spherical Harmonic Coefficients Love waves at 35s, 37s, 40s, 45s, 50s, 60s, 75s, 100s, and 150s Rayleigh waves at 35s, 37s, 40s, 45s, 50s, 60s, 75s, 100s, and 150s All models, as a gzip-compressed tar file Postscript Files Love waves at 35s, 37s, 40s, 45s, 50s, 60s, 75s, 100s, and 150s Rayleigh waves at 35s, 37s, 40s, 45s, 50s, 60s, 75s, 100s, and 150s

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 X_lm is defined in terms of Y_lm by $Y_{lm}(\theta,\phi)=X_{lm}(\theta)e^{im\phi}$ , and Y_lm 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 A_lm B_lm" with B_lm left out if m=0.

Postscript File Notes

The PostScript files are a map of each model. They are drawn from the spherical harmonic coefficients in the corresponding files, with the degree zero term (global average) not included. The maps are centered on longitude 135W. The scale on the right of each map gives the maximum and minimum of the map, rounded to the larger half percent. These maps are designed to allow you to compare the maps with your spherical harmonic plotting package. They were made with the Generalized Mapping Tools (GMT) software package.

Reference

Ekström, G., Tromp, J. & Larson, E.W.F., 1997.
Measurements and global models of surface wave propagation.
J. Geophys. Res. 102(B4), 8137-8157.