OCTAVE SASW

In theory, only two traces are needed to compute a dispersion curve. Program SASW.m permits one to select two traces and compute Rayleigh-wave velocity dispersion. Depending on the trace spacing and spectral selection, the code recommends a maximum spacing between the two traces (to avoid aliasing).

 Start an octave session and then type
       SASW

Note, capital letters are important since that
agrees with the file SASW.m

This code takes two signals from a shot gather to
compute a cross spectrum leading to a dispersion
curve.

Prompts:
1). enter file name, example: c008.seg
2). GUI Pop up to select fmin, fmax vmin vmax
3), Info GUI pops up and shows both time and
spatial sample intervals.

Recommended trace separation is indicated on
last line. If high frequencies are chosen, then
too large a separation between the two geophone
stations can lead to aliasing. 

4). GUI enter tmax, near trace number, far trace number.
For example:
tmax =1.0
trace R1 = 2
trace R2 = 3
(this would follow a recommendation that
R2-R1 be no larger than 1)

When only two offsets are used,
one should always look at the entire shot gather
first and select traces likely to be dominated by
the fundamental mode (typically close to the source).

The program produces two figures. One shows the cross power spectrum and coherence (Figure 20). The other figure shows the dispersion over a range of frequencies selected in the GUI prompt when the code is run (Figure 21).

The code determines a time shift, $\Delta t$, between geophones with a separation of $\Delta x$ to compute a phase velocity at each frequency of interest. If $\Phi$ is the unwrapped phase angle at a frequency of interest, then

$$\Delta t = \dfrac{\Phi}{2\pi} \cdot T ~~,$$ (1)

where $T$ is the period for a frequency $f$ ($T= 1/f$). The phase velocity at the frequency $f$ is

$$C(f) = \dfrac{\Delta x}{\Delta t}.$$ (2)

Figure 20: SASW: Cross spectrum amplitude and coherence reveal what range of frequencies provides useful dispersion information.

Figure 21: SASW: Dispersion computation over limited range of frequencies selected in the GUI.