CALC MENU

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.

example with noise bounds

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:

Donohos threshold

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

kurtosis associated with Donoho's calculation

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.

Donoho's menu

If the 'ECDF Method" button is pressed,

ECDF Button

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:

ECDF Threshold


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:

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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.

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


hard threshold signal




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.

SNR Result


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