CALC MENU

The CALC menu has many functions for processing the
data in various ways.
Refresh
Refresh takes the data back to its initial form when it was read
into the program. It re-plots the first CWT and the original
seismogram.
Undo
This function undoes the last operation of the GUI.
Compute CWT
The CWT is computed for the seismogram shown in the seismogram
plot. The CWT TFR is then plotted in the top window.
Further processing cannot happen until the CWT is computed.
Estimate Noise
The noise is estimated for a portion of the seismogram defined in
the "Choose Noise Time Bounds" box in the lower left. The
default values for begin and end times are 0 and 1,
respectively. Here is an example with the canonical
seismogram using a time bound of [0, 60] s.

On choosing Estimate Noise, the GUI finds the mean and
standard deviation at each scale in the time interval
chosen. Note that "Donoho's Thereshold Criterion" was chosen
for this calculation. A separate plot is produced showing
the result of calculating the mean and the threshold function:

In addition, the non-Gaussianity of the distribution of wavelet
coefficients is also plotted as a function of wavelet scale:

The wavelet distribution is approximately Gaussian for scales that
fall in between the two horizontal lines bounding the value of
zero.
The noise must be estimated before using the remainder of the
commands in the CALC menu.
Note that the "Donoho's Threshold Criterion" radiobutton must be
pressed if you want to use this parameter in the noise or signal
thresholding schemes.

If the 'ECDF Method" button is pressed,

then the threshold is computed using the empirical cumulative
probability distribution (ECDF) method. The result gives a
plot of the mean and the ECDF threshold:

Using the ECDF method is recommended.
Hard Threshold Noise or
Soft Threshold Noise
These functions remove noise and reveal the signal.
Here is quick tutorial on CWT theory that explains hard and soft
thresholding:






Hard Threshold Signal or Soft Threshold Signal
These functions remove the signal and keep the noise.
This might be useful for ambient noise correlation studies to
obtain noise Green's functions.

Here's an example of removing the explosion source from the
inferred noise field using the hard thresholding method:

Correlate Template
To use this function, you need to read a CWT template into BCseis
using the Read CWT Template File from the File
menu. In addition, if you want the polygon plotted on the
CWT scalogram, use Read Polygon File from the File
menu as well.
A template file (RF3016CWT.mat) and a polygon file
(RF3016polygon.mat) are contained in the /data directory.
This function is used to experiment with different templates and
polygons on particular seismic traces from elements of an array.
The correlation is performed by
1) Calculating |W(a,tau)|^3 for both the template and data CWT.
2) Shifting the template in time lag, tau, in the interval of +
and - "Correlation Time Tolerance" (seen in the bottom right
corner of the GUI).
3) Multiplying over all scales and integrating.
"Correlation Time Tolerance" was implemented to speed the process
up for array data since the moveout of particular phases do not
change too much over the aperture of typical arrays. This
value can be changed as desired in the edit box.
Here is the result of correlating the RF3016CWT.mat template with
the original data displayed at the top of the page. The
polygon file has also been read in. The "TLIM" button was pressed
to refresh both plots to obtain the polygon outline.

Here is the correlation plot that results

Pressing the "Include Block" on the GUI will use the polygon to
zero out all other CWT coefficients to yield the estimate, in this
case, for the Rayleigh wave.

SNR Detector
A signal detector based on the Signal-to-Noise Ratio (SNR) is
implemented with this menu item. A Signal-to-Noise
seismogram is computed by dividing the noise (plus a "water level"
parameter) into the CWT of the entire seismogram. Each CWT
coefficient is replaced by the ratio of the original complex
coefficient by the absolute value of the noise estimate plus a
percentage of the maximum value of the noise. N lower
bound (see above figure) is the parameter that defines this
percentage.

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