OCTAVE invR1, Rayleigh Wave Inversion

This program uses the BVAX output file, bvax.his, to invert Rayleigh wave, fundamental mode, under an elastic representation. See section 7.0.2 for details on BVAX. A companion forward problem octave code is FwdR1.m, see section 9.2.1.

To run invR1.m in octave, first execute build_disper_oct script to build an extension to octave. Edit the bvax.his file to remove any measurements that are zero or bogus velocities. Program invR1.m is hard wired to read bvax.his, so that should be the name of any edited file that will be used by invR1.m. The octave files are located at the /usr/local/share/octave/site-m/ directory.

The code is an iterative inversion which runs for a user number of inversion steps. Default is 2, but recommend 5 as a useful number. Increasing the number of singular values employed will provide additional detail in the inversion result. However, if you use too many, noise in the data may inject details in the result that are not reliable. Or the code can become unstable if too many singular values are used.

1). Enter initial soil representation file:
File model.txt is used to set an initial model of control points 
For example, with 3 control points:

3
200 300 500
.0 2.0 15.

Velocity   Depth
200 m/s    0 m
300 m/s    2.0 m
500 m/s   15.0 m

2). GUI Choose P-wave velocity option. Click on Vp/Vs ratio OR Vp=fixed (if fixed, GUI enter 
Vp m/s and Density kg/m3
3). GUI Choose density parameters, Poisson Ratio, grain density, porosity, degree water saturation.
4). GUI Informs user of Vp/Vs ratio and constant density to be used.
NOTE: Code will seek a S-wave velocity profile consistent with these results.
5). GUI Select number of singular values to use, layer thickness (constant in meters),
locksw (switch to lock some conditions), and number of iterations to do.  Typically,
5 or more are good, but for the first run, 2 is wise in case things go sidewise.

locksw   meaning
0        free bottom control, velocity and depth
1        (default) lock bottom depth, free bottom velocity
2        lock bottom velocity, free bottom depth
3        lock both bottom velocity and depth

The bottom is the deepest control point, top of the bounding half-space.

Program FwdR1.m is a manual forward program that can be used to do the inversion manually,
or to explore the fast and slow limits based on confidence limits.

The edited bvax.his file from the example in section 7.0.2 was run using a constant VpVs ratio for just 5 iterations. Density was held constant. Other settings from a GUI are Poisson Ratio=0.33, grain density 2.67 g/cc, porosity 0.33, degree water saturation 1.00. This results in VpVs=1.99 and density=2169 $kg/m^3$. Only 3 singular values included, layer thickness, deltz= 0.1 meters. The resulting velocity model

Figure 17: invR1: After 5 iterations, the resulting soil model is shown. The S-wave velocity with inverted control points is shown as the Blue curve ($m/s$). The Red curve is the P-wave velocity, and at the far right is the constant density ($kg/m^3$)

Figure 18: invR1: Progress of the inversion. The initial model dispersion is the fastest green curve. The green curve is the dispersion after 5 iterations. Data from bvax.his is in blue.

Figure 19: invR1: The code also generates a GNUPLOT file, dispcrv.gp, which shows the final solution when run with the gnuplot program.

Other output includes text files of the solution as well as a fast and slow 95% limit cases.

solution.txt (Three rows: number of control, S-velocities, Depths)
 3.00000000e+00
 9.28725027e+01 2.76581965e+02 5.00000000e+02
 0.00000000e+03.00000000e+00
 
 slow.txt
 9.08153279e+01 2.75856068e+02 5.00000000e+02
 0.00000000e+00 3.59321540e+00 1.50000000e+010 3.58000000e+00 1.50000000e+01
 
 fast.txt
 3.00000000e+00
 9.49296774e+01 2.77307861e+02 5.00000000e+02
 0.00000000e+00 3.56678460e+00 1.50000000e+01