27.5 Program AVQ, average Q-relations

Q as a function of frequency is usually described as

$\bgroup\color{black}$q = q0*f**v$\egroup$

If several such relations are to be averaged, it is not just a question of averaging the parameters. In program AVQ, the averaging is done in the following way:

-For each relation, 1/Q is calculated at the frequencies 1, 2, 4, 8 and 16 Hz. -At each frequency, average 1/Q is calculated using the number of observations in the original determination of Q for a particular relation as weight. -A new least squares determination of $\bgroup\color{black}$v$\egroup$ in $\bgroup\color{black}$q0$\egroup$ is made with the Q-values.

The program uses an input file with q0, v and number of observations, one relation (free format) per line. An example of a run is seen below:

C:\seismo\wor>avq
 File name, enter for automag_grid.out
input.txt
 Q0,alpha,n   100.000000      0.500000000             100
 Q0,alpha,n   150.000000      0.300000012              50
 Q0,alpha,n   200.000000      0.200000003              10
 Q0,alpha,n   170.000000      0.400000006              22
 Q0,alpha,n   250.000000      0.150000006               5
 Q0,alpha,n   80.0000000      0.800000012              10
  Number of curves to average:            6
 Running average over how many, enter for average of all?

 Q0,alpha,corr   119.819160      0.437137932      0.999868274

 Output of plot in avq.eps

and the plot seen in figure 27.4 comes up.

**Figure 27.4:** Figure AVQ: The figure shows the Q-relations to be averaged and the average Q-relation (red).
$\begin{figure} \centerline{\includegraphics[width=0.9\linewidth]{fig/avq}} \end{figure}$

The program also has a special input to be used with AUTOMAG, which can output Q-relations found by grid search, see AUTOMAG for more details. These relations can be averaged over a number of relations. However, here that option is not used.