Inversion for Stiffness and Damping (cainv3.m)

Programs bvas and bamp store their results in bvas.his and bamp.his. The Octave procedure, cainv3.m, reads these files and performs the joint inversion for soil stiffness and damping. The procedure, caplot3.m is available to produce journal quality plots of the inversion solution. The Octave procedures should be copied to the same directory where *.his files are located. Each depth interval will require a separate set of *.his files, and a separate cainv3.m run.

Start Octave, and then from the Octave text window, type the command


cainv3


Using a GUI interface, cainv3.m will prompt you as follows:
 

DIALOG WITH CAINV3.m

  1. Input Files Hardwired. The program expects the input files to have been generated by programs bvas and bamp (bvas.his and bamp.his)).
  2. Use mouse to pick min and max frequencies. Click OK, then in the graphic display, move mouse to velocity panel and click with left mouse button on the lowest frequency desired. Then move the mouse to the highest frequency desired and click again.
  3. Select initial C1, C2 and number of iterations. The default is computed from equations (4) and (5). This is usually a good choice. But you can enter different values if you wish. The maximum number of iterations is set to 10, and that is usually enough. See item (7) below.
  4. Choose Weighting. Choose one of 3 options. The weighting reduces the influence of data points which have large uncertainties. One can weight by the reciprocal of the variance or the square root of the variance estimate (stdv). If you want all data points to have an equal influence on the solution, regardless of the associated measurement uncertainties, select the no weighting option.
  5. Set Block Weighing: Velocity to Decay. This is a joint inversion which includes both velocity dispersion and decay measurements. A value near 1 will emphasize the velocity data, and largely ignore the decay information. A small value will emphasize the decay data, and discount the velocity information. Usually, one should refrain from extremes here (don't use 1 or 0), but stay in the range of 0.9 to 0.1 for useful results. This weighting is superimposed on a data type weighting (the least squares error has to be scaled to take into account the different data units). If unsure, use the default, 0.5, for generally equal weighting of velocity and decay.
  6. Continue to LSQE Plot. The procedure halts to let you view the last iteration results. When ready to move on, click on the YES button.
  7. Continue to Chi Square Plot. View the weighted least squares error (this is a scaled combination error of both data types). It should decrease with iteration number, and give you an evaluation of the number of iterations needed. When ready to move on, click on the YES button.
  8. Save Results to Disk. Chi-Square plots for velocity and decay are shown. These are based on average estimates of the data uncertainties as expressed in the average error bars. It gives you an idea of the relative balance between the residual error and the data uncertainty. In general, there is no point in obtaining a solution with Chi-square less than unity. More iterations may help if Chi-square is above unity, and can be further reduced. However, if one only focuses on one data type, the other will suffer. See Menke (7) for more. When ready to move on, click on the YES button. The program ends displaying the relaxation time for the solution, $T_r=\frac{C_2}{C_1} $