Contents
7.1.3 Windowing
Time Domain
Basic idea
Besides the manual selection directly from the screen, which is often the most reliable, but also the most time consuming, an automatic window selection module has been introduced in view of processing large amounts of data. The objective is to keep the most stationery parts of noise, and to avoid the transients often associated with specific sources (walks, industrial disturbances, close trafic ...). This objective is exactly the opposite of the usual goal of seismologists who want to detect signals, and have developed specific "trigger" algorithm to track the unusual transients.
As a consequence, we have used here an "antitrigger" algorithm, which is exactly the opposite: it detects transients but it tries to avoid them. The procedure to detect transients is very classically based on a comparison between the short term average "STA", i.e., the average level of signal amplitude over a short period of time (typically around 0.5 to 2.0 s), and the long term average "LTA", i.e., the average level of signal amplitude over a much longer period of time (typically several tens of seconds). When the ratio STA/LTA exceeds an a priori determined threshold (typical values are between 3 and 5), then an "event" is detected.
In our case, we want to select windows without any energetic transients: it means that we want the ratio STA/LTA to remain below a small threshold value "max STA/LTA" (typically around 1.5 - 2) over a long enough duration. Simultaneously, we also want to avoid noise windows with anomalously low amplitudes: we therefore also introduce a minimum threshold "min STA/LTA", which should not be reached throughout the selected noise window.
The program automatically looks for time windows satisfying the above criteria; when one window is selected, the program looks for the next time window, and allows two subsequent windows to overlap by a specified amount "overlap" (by default this option is turn off).
Window length
Figure 1: Windows length
In order for a measurement to be reliable, 'the SESAME H/V User Guidelines' recommend to fulfilled the following condition: the window length has to be larger than 10/fo, where fo is the expected H/V frequency peak. This condition is proposed so that, at the frequency of interest, there are at least 10 significant cycles in each window.
After carefully define the time duration of the window, you can select the type of windows selection you want. To do this, on the "Processing" tab of the H/V tool box (Figure 1), click on the "General Parameters" tab, and then on "length" button and select either you want to the define the time duration as equal "At least", "Exactly" to the given value in second, or "Frequency dependent" (Table 1).
| Table 1: Parameters to define the windows length | ||||||||||||
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Anti-triggering
To apply the "anti-trigger" algorithm on the current noise signal, check the box "Anti-triggering on raw signal" and activate the "Raw signal" tab to select the appropriate values.
Insert the values of the short term average "STA" and the long term average "LTA", as well as the values of the minimun and the maximun STA/LTA ratio. You can apply the anti-trigger algorithm to all components of the signal, or only to one or two single component (check the name of the selected component).
Figure 2: Anti-triggering tool box
You can also apply the "anti-trigger" algorithm on the filtered noise signal (check the box "Anti-triggering on filtered signal"). Activate the "Filter" tab, specify the type of filter you want (low pass, high pass, band pass or band reject), and give the appropriate threshold for each type of filter (Figure 5) (see description of filters here). As for the raw signal, give the values of the STA, LTA and the minimum and maximun STA/LTA ratio inside the appropriate box in the "Filtered signal" tab.
Figure 5 Anti-triggering apply to filtered signal
Bad sample tolerance / threshold
These two options allow you to optimise the number of selected windows. When the bad sample option is turn on, the algorithm of windows selection is slighty modified: although several points do not satisfy the anti-triggering criteria, the current window can be selected. The number of bad sample which are keept to define one 'good' window is defined by INT("bad sample tolerance"/deltaT). In the same way, you can defined the total amount of 'bad signal' in each window you want to keep by turning on the "Bad sample threshold" option. In this case, you give the number of 'bad point' in term of percentage of the total number of points by window.
You can turn on these two options in the same time.
Figure 6: Bad sample tolerance
Overlapping
If the total time duration of the noise signal is too short and/or if the number of selected windows is too small, you can use the overlapping option. To turn on this option, simply click on the "overlap by" box and give the specified amount of overlapped windows in percentage (Figure 8).
The number of point overlapped at the end of each window is given by INT(time*overlap/deltaT), where "time" is the window length in second, "overlap" the amount of overlapped windows in percentage and deltaT the time step.
Figure 8: Overlapping tool box
Automatic windowing
At any time you can see the windows selected according to your criteria by clicking on "Stable windows". The number of selected windows (in total, or by station) is indicated at the bottom part of the H/V tool box. By clicking on the "Inverse" button, only the windows which not fit your criteria will be selected. This option allow you to test the effects of some disturbances on the H/V ratio curve.
Manual windowing
You may prefer to select the windows manually. To do this, click on the "Add" button, switch to the signal viewer (a dashed blue line helps you to visualize the selected time range), click right to start selecting windows, move the mouse to select all the signal you want and when your selection is done, release the right button of the mouse. At this stage, the windows are selected. Note, that in case of manual windows selection, only few criteria are considered (the window length and the overlapping), the anti-triggering criteria is not considered. You can also remove specific windows by clicking on the "Remove" button and selecting these windows on the signal viewer (click right on mouse).
At any time you can reset your selection by clicking on "Clear all" button. You may also load previous windows selections from *.log file. In this case click on "Load" Button and select your input file from the browser. Note that a *.log file is automatically created each time the H/V ratio results are saved into a file.
