Note that this raytrace applet is in polar coordinates, while the one in the Miscellaneous section is in rectangular coordinates. Someday it'd be nice to combine them and choose between solar, solid earth, and ocean acoustic scenarios in addition to geometry (...someday). Meanwhile...
One approximation to the propagation of waves in a spherical medium is with a technique called raytracing. We specify a set of rays, normal to the wavefronts, and we can set properties of the environment like dimensions and wavespeeds, and then we can watch where the wave energy goes by watching where the rays go. If the wave velocity is a non-constant function of the radius these rays will curve, sometimes overlapping each other, sometimes leaving wide gaps in where they return to the surface. These behaviors affect how well we can try to resolve a velocity profile by only analyzing signals we receive at the surface.
This raytracing approach is used for seismic waves in the Earth, for acoustic waves in the ocean, and also for acoustic waves traveling through the Sun (it is the Sun example that is implemented here, but that is only a matter of dimensions and velocity presets). It turns out this raytracing approach does have limitations however; it assumes that the wavelength is much smaller than features in the velocity profile. As frequencies get lower the wavelengths get longer, and at some point this assumption breaks down. But raytracing works fine for higher frequencies, and for the lower frequencies there are exact or normal mode solutions that can be used. Meanwhile the raytracing makes for a much more intuitive demonstration applet!
Click a screen size to begin
the applet:
Sm (700x500),
Med (900x640),
Lrg (1200x860)
To run the applet: click the link for the size appropriate
for your screen. The green question-mark on the top right
offers a brief help listing, but the most immediate way to
start is to :
• right-click the WaveVel-vs-Depth plot on the left
• pick some premade velocity profile off the menu
• click the swirling-arrows ("run") button at the top to
create the rays in the plot on the right.
• once you get the hang of it be sure to try clicking in
some of your own velocity profiles!
This applet is also available in the Java "jarfile" called
spheraydemo.jar in the Downloads section if you would like to be
able to run the thing while offline. Please note however
that this will also require your copying the small or
medium or large applet webpage (not this one!) to your
local machine and modifying the path in its HTML to
reflect the folder on your machine where you saved the
jarfile.
Do please feel free to
contact me if you have problems getting this applet to run
in your browser, after you have been sure to download that
latest (1.4.0 or later) Java plug-in above, and have
checked to see that you can run one of Sun's
Java example applets A, or Java example applets B. (These two pages look the same but
have slightly different code for different browser
types.)