In this exercise, you will: 1) measure the phase-velocity dispersion for surface waves generated by hammer strikes you did one field-school morning, and 2) invert these dispersion data for an S-wave velocity distribution with depth.
Copy and unpack this Vista project in a directory on your Linux or Windows computer. Open this project.
Look at the different shots. The shots were recorded at 1-m geophone spacings. Note the surface waves (they are the strongest). Using Vista's moveout-measurement tool, look at the velocities of these phases.
Select three good shots near the beginning, middle, and end of the profile. You will need to pick phase velocities in these shots.
Using Vista's filtering options, 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 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 better be carried out on a Linux system using Octave software (this is a free and somewhat extended version of Matlab).
Copy this archive file containing all programs into a directory on your Linux machine and unpack it there by using:
tar xvf Surface_Waves.tar
This will create a directory named 'Surface_Waves'. Change your work directory into this directory. Among the many files in it, 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)
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 n idea of the S-wave velocity distribution with depth.
Next, edit the 'model' matrix 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 will 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.