Animations illustrating simple wave propagation concepts
Jeffrey S. Barker
Department of Geological Sciences
SUNY Binghamton
Below are the first attempts I've made to generate animated GIF files
illustrating simple seismic wave propagation concepts. The models
are generated using the sufdmod2 acoustic finite difference program from
the SU package.
The results are plotted with SU's supsmovie, which
generates a multi-page Postscript file. This is converted into GIF
files for individual frames using the convert program from
ImageMagick.
These are then edited using xv,
cropped to include only the portion
of the image that has changed since the previous frame, and saved (xv does
a nice job of reducing the size of the GIFs). Finally, and animated GIF89a
file is generated from all the individual GIFs using GIFMerge.
The animations are designed to loop five times, but I have found that this
does not work correctly under Netscape 2.0; rather it continues to
reload. The looping animation does appear to work under Netscape 3.0.
Finally, the annotated still images were edited from the individual GIFs
using xpaint.
For more information on animated GIFs, see Royal
Frazier's GIF Animation
on the WWW page.
The first animation illustrates P waves traveling outward from the source,
reflecting from a higher-velocity material below and from the free surface
above. The change in polarity upon reflection from the free surface is
apparent, as is the change in curvature of the refracted wave, which
results in the bending of the raypath (according to Snell's law). The
still image below is annotated to show the model, which
consists of a constant-velocity layer (Vp=6.0 km/s, thickness 30 km) over
a constant-velocity halfspace (Vp=8.0 km/s). The source is located at
a depth of 20 km. Click on the still image to view the animation
[371 Kbytes].
The next animation shows the same model, but looking at greater distances
and later times. In this case, the refracted wave in the lower medium
is clear, the head wave can be seen to develop with a cross-over distance
of about 120 km. The linearity of the head wave as it propagates upward
is particularly well illustrated by the animation. There is a weak
numerical artifact (which appears as a wave propagating up from the bottom
of the image) due to not-quite absorbing boundary conditions. The amplitudes
in this figure are greatly enhanced so that the head wave is visible;
unfortunately, so are the numerical errors.
Once again, click on the still image to view the animation
[311 Kbytes].
Finally, with a slightly more extreme model (Vp=3.0 km/s in the layer),
we can see how the multiple reflections in the layer (crust) generate
an interference phenomenon which propagates outward. Amplitude decreases
rapidly into the halfspace. So, although generated using only P waves
(an acoustic problem) these are analogous to the surface waves which would
be generated by multiple reflections of P and S waves. Note that the
interference pattern is a cross-hatched pattern of high and low amplitudes
(white and black). If observed with borehole instruments, these "surface
waves" would appear to arrive at different times with depth. There would
appear to be an upward and downward propagation of this vertically standing
wave. Once again, click on the image to see the animation [725 Kbytes].
Here is an animation of S wave amplification at San Francisco due to the
Loma Prieta earthquake. This is an acoustic wave propagation
model, but by using S wave velocities, it provides an adequate (though
incomplete) simulation of SH wave propagation. The velocity model is
from Wald, et al (BSSA 81,1540-1572, 1991) with the top layer removed.
This is an average of two models from Dietz and Ellsworth (GRL, 17, 1417-
1420, 1990). In this model, the Moho is at 25 km depth. I have put the
source at 11 km depth (the upper asperity in the Loma Prieta source
models). I have also applied absorbing boundary conditions at the free
surface, simply to reduce surface waves and multiple reverberations.
These simply distract the viewer, while not changing the result. San
Francisco (including the Marina District, Bay Bridge, and I880 in Oakland)
are all at about 95 km distance. In the animation, you can see the S wave
propagate outward, and become weaker (the shading goes to gray). The Moho
reflection is seen as a brighter patch (first white, then black) propagating
upward and to the right, arriving at the surface at about 90-95 km. This
accounts in part for the higher level of ground motion experienced in San
Francisco.
Click on the still image to view the animation
[273 Kbytes].
Barker's HomePage
Department HomePage
Binghamton University HomePage
Questions or comments:
jbarker@binghamton.edu
Last modified: July 30, 2007 (reformatting only; jsb)
