Kelvin-Voigt Modeling with cafwd3.m

Program cafwd3.m is a Octave program which permits one to compute the velocity dispersion and amplitude decay as a function of frequency. Given user supplied values for stiffness ($C_1 $ in $m^2/s^2$) and damping ($C_2 $ in $m^2/s$), the program computes frequency dependent phase velocity dispersion ($m/s$) and decay ($1/m$). A second plot re-expresses the amplitude decay as a quality factor, Q. This is computed by (Toksöz (22) )

$\displaystyle Q=\frac{\pi f}{\alpha V}$ (19)


where $\alpha$ is the decay in units of $1/m$, $f$ is frequency, and $V$ is velocity at that frequency. There are two ways to use the program.

To run the program, start a Octave session. Then, inside the interactive Octave text window, type:


cafwd3


With the first GUI, choose if data are to be included in the plot. If data are included, you will be prompted to use the mouse to select a frequency range to model. For the non data case, the frequency range is hardwired, and can be changed if needed by editing the program (look for fmin and fmax variables at the top). The program will do an initial case on its own. If there are data, it will look at the data and make a reasonable first guess. If there are no data, a default GUI will come up. One can then change the values for stiffness and damping and recalculate a new set of plots. Figure 25 shows examples of the two ways dispersion can be presented (ie. with or without data plots). One can keep revising the values and clicking OK as much as one wants. When done, click the “cancel” button. An example of the second Q-plot is shown in Figure 26. This corresponds to the run shown in Figure 25A. Note that the example values for $C_1 $ and $C_2 $ are different for the no data and with data cases.

Figure 25: Sample of cafwd3 calculations. (A) run without data (B) run with data for comparison
\includegraphics[scale=0.9]{FigureH}

Figure 26: Sample of cafwd3 calculations. Quality factor varies with frequency.
\includegraphics[scale=0.9]{FigureI}