In this exercise, you will: 1) measure the phase-velocity dispersion for surface waves generated by hammer strikes you did at the end of the field-school day, and 2) invert these dispersion data for an S-wave velocity distribution with depth.
To begin, copy to your computer and and unpack this archive (prepared by Yichuan) in a directory on your Windows computer. This should create a directory 'surface_waves' containing a SEG-Y file with data, Vista geometry file, and subdirectory 'matlab' for Matlab processing.
Create a new Vista project and load in it the SEGY file and geometry.
Look at the shots. The shots were recorded at 0.5-m geophone spacings. Note the surface waves (they are the strongest). Ignore or kill the noisy records resulting from (maybe) malfunctioning channels in the recorder. Reasons of this noise are currently unknown' however, it should not prevent you from using the records in this lab.
Using Vista's moveout-measurement tool, look at the velocities of these phases.
Look for surface-wave reflections from the vertical wall of the vault. The wall was somewhere near the middle of the line. Try determining its location more precisely.
Select two-three good shots within the part f the line outside of the vault. You will need to pick phase velocities in these shots.
Using filtering options included in Vista displays, apply narrow band-pass filtering to the records. Use the following Ormsby filter bands (with approximately half-octave increments): 0.7f- 1.0f- 1.4f- 2.0f , with f = 10, 14, 20, 28, 40, 56 Hz, etc., and then going down: f = 7, 5, 3.5, 2.5, 1.75, 1.25 Hz. For each frequency band, measure the phase velocities and save them in a table as functions of the central frequency 1.2f .
Plot (using Matlab, Octave or Excel) the obtained phase-velocity curves for the three shots along the profile. Are there any significant differences between them? Do they show normal or inverse dispersion?
What is the percentage of velocity variation across the available frequency band?
What are the limitations for extending the frequency band to toward lower and higher frequencies? Which end of the band (low- or high-frequency) should be most important for subsequent inversion?
Inversion of the surface-wave dataset should be carried out by using Matlab.
Change your work directory into this directory 'matlab'. Among the many files in this directory, you will need:
load_data.m (loads phase velocities picked at different frequencies)
process.m (executes the following two programs)
rayleigh.m (performs Rayleigh-wave phase-velocity modeling)
rayleigh_result.m (plots results)
These codes have been written for Octave software, and so to run them on Matlab, all commentary indicators '#' may need to be replaced with '%'.
In program load_data.m , you will need to edit matrices 'phvel_data_1' and similar to include the picked values of phase velocities. Then enter Octave by typing 'octave', and in the resulting shell, type 'load_data'. This program will display a plot of the input phase-velocity data, and also a plot of the same phase velocities versus half-wavenumbers. This plot should give you an idea of the S-wave velocity distribution with depth.
Next, edit the matrix called 'model' in 'rayleigh.m' to input the starting velocity model. Use P-wave velocities twice larger than the S-wave velocities. Pay attention to the units used in Octave files (depths in km, velocities in km/s, but densities in g/cm3).
Execute 'process' in Octave. This may take 1-2 min, and a plot of the phase-velocity data combined with modeled curves of up to 10 Rayleigh-wave modes should appear (this plot is created by 'rayleigh_result.m'). Your task now is to adjust your 'model' so that the lowest modeled phase-velocity curve (called "fundamental mode") matches the observed data.
After an acceptable fit is achieved, discuss the resulting velocity model. Discuss the reasons for S-wave velocity increasing with depth and explain how this increase is related to the observed velocity dispersion.