Harvard Seismology: Phase Velocity Maps

Note: The coefficients have been changed to a different spherical harmonic convention, which matches that listed below, not what was published in the paper (models with that convention are on the FTP site, as listed in the paper).

We have inverted for phase velocity maps from surface wave phase measurements, as part of our ongoing surface wave project. These maps are being published in Measurements and global models of surface wave propagtion, currently in press.

Here we give the spherical harmonic coefficients for all of our maps, as well as PostScript images of the maps. See below for conventions used and other notes.


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.


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.

Erik Larson, Seismology group, Department of Earth and Planetary Sciences, Harvard University.
Copyright ©1999, all rights reserved. Please email comments.
Last modified: Sat Oct 30 16:30:28 EDT 1999