(39) Evaluation of spherical harmonics coefficients — GMT 5.1.1 documentation

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# (39) Evaluation of spherical harmonics coefficients

We use a spherical harmonic model for the topography of Venus and evaluate the resulting global grid for three sets of upper order/degrees, here 30, 90, and 180; the original file (see below) goes to order and degree 720. We use the coefficients to evaluate the grids and make perspective globes of the different resolutions. The key tool used here is sph2grd.

    #!/bin/bash
    #               GMT EXAMPLE 39
    #               $Id$
    #
    # Purpose:      Illustrate evaluation of spherical harmonic coefficients
    # GMT progs:    psscale, pstext, makecpt, grdimage, grdgradient, sph2grd
    # Unix progs:   rm
    #
    ps=example_39.ps

    # Evaluate the first 180, 90, and 30 order/degrees of Venus spherical
    # harmonics topography model, skipping the L = 0 term (radial mean).
    # File truncated from http://www.ipgp.fr/~wieczor/SH/VenusTopo180.txt.zip
    # Wieczorek, M. A., Gravity and topography of the terrestrial planets,
    #   Treatise on Geophysics, 10, 165-205, doi:10.1016/B978-044452748-6/00156-5, 2007

    gmt sph2grd VenusTopo180.txt -I1 -Rg -Ng -Gv1.nc -F1/1/25/30
    gmt sph2grd VenusTopo180.txt -I1 -Rg -Ng -Gv2.nc -F1/1/85/90
    gmt sph2grd VenusTopo180.txt -I1 -Rg -Ng -Gv3.nc -F1/1/170/180
    gmt grd2cpt v3.nc -Crainbow -E16 -Z > t.cpt
    gmt grdgradient v1.nc -Nt0.75 -A45 -Gvint.nc
    gmt grdimage v1.nc -Ivint.nc -JG90/30/5i -P -K -Bg -Ct.cpt -X3i -Y1.1i > $ps
    echo 4 4.5 L = 30 | gmt pstext -R0/6/0/6 -Jx1i -O -K -Dj0.2i -F+f16p+jLM -N >> $ps
    gmt psscale -Ct.cpt -O -K -D1.25i/-0.2i/5.5i/0.1ih -Bxaf -By+lm >> $ps
    gmt grdgradient v2.nc -Nt0.75 -A45 -Gvint.nc
    gmt grdimage v2.nc -Ivint.nc -JG -O -K -Bg -Ct.cpt -X-1.25i -Y1.9i >> $ps
    echo 4 4.5 L = 90 | gmt pstext -R0/6/0/6 -Jx1i -O -K -Dj0.2i -F+f16p+jLM -N >> $ps
    gmt sph2grd VenusTopo180.txt -I1 -Rg -Ng -Gv3.nc -F1/1/170/180
    gmt grdgradient v3.nc -Nt0.75 -A45 -Gvint.nc
    gmt grdimage v3.nc -Ivint.nc -JG -O -K -Bg -Ct.cpt -X-1.25i -Y1.9i >> $ps
    echo 4 4.5 L = 180 | gmt pstext -R0/6/0/6 -Jx1i -O -K -Dj0.2i -F+f16p+jLM -N >> $ps
    echo 3.75 5.4 Venus Spherical Harmonic Model | gmt pstext -R0/6/0/6 -Jx1i -O -F+f24p+jCM -N >> $ps
    rm -f v*.nc t.cpt

Evaluation of spherical harmonics coefficients.

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