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].

Questions or comments: jbarker@binghamton.edu

Last modified: October 17, 2012 (corrected ImageMagick link; jsb)