Geopsy: H/V and Spectrum Toolboxes: Processing Tab

Use

This toolbox tab contains the smoothing and taper parameters for H/V or Spectrum curves and the way the horizontal components are processed to compute the H/V spectral ratio, described in two sections:

• the Parameters section (For H/V and Spectrum tools)

• the Horizontal components section (For H/V tool only)

Processing tab for smoothing parameters and horizontal components processing in H/V computing

Parameters section

Processing tab giving access to smoothing, parameters (for windows) and how is processed the H/V (available only for H/V computing)

This section is divided in three parts:

Smoothing

Type of smoothing applied to the windows (2 first lines). During the computing of H/V or Spectrum, the Fourier spectra can be smoothed (it is strongly recommanded) in the goal to clarify the global aspect of the curves.

For Spectrum, each Fourier spectrum (coming from a window) is smoothed and then the averaged curve is computed.

For H/V, the horizontal Fourier spectra (NS and EW, coming from a synchronous window) are first added and then the smoothing is applied on the merged horizontal Fourier spectrum and on the vertical Fourier spectrum.

The type of smoothing can be fixed using a drop box, where 4 possibilities are displayed:

1. No smoothing. This can be sometime usefull to have a rough idea about Fourier spectra;
2. Konno and Ohmachi smoothing. This smoothing use a constant bandwidth in a logarithmic scale and is strongly recommanded because this smoothing function preserves the different number of points at low and high frequency. This smoothing is controled by a smoothing constant varying in-between 0 and 100. A constant of 0 gives a very strong smoothing, when a constant of 100 a very soft smoothing, more details;
3. Constant smoothing. This smoothing function has a triangular shape centered on the current frequency and its width is equal to "Band width" given by the user. This band width varies from 0 (soft smoothing) to 100 (strong smoothing);
4. Proportional smoothing. This smoothing function has a triangular shape and its width depends upon the current frequency. The half width is defined by percentage*frequency. The value of "percentage" cannot be greater or equal to 100% (strong smoothing).

Except for No smoothing, the constants linked to the other smoothing methods can be fixed using a spin box.

Whatever the smoothing method used, even if the impact of the smoothing is minimized, the result will be different from a processing without smoothing.

Taper

Fixing the use or not of a cosine taper on the individual window.

In the goal to minimize the border effect due to the extraction of a window and so improve its properties in the frequency domain, it is strongly recommended to use a taper to avoid the creation of parasit frequencies.

The taper on windows can be applied (the corresponding check box should be checked) or not (uncheck the related box). The value of this taper can be fix using a spin box, the default value is fixed at 5% of the cut-off frequency.

It is strongly recommended to use the Taper option to avoid any problem.

Filter

Fixing the use or not of a filter on the whole signal.

This option allows to filter the signal before the extraction of the time windows.

To the contrary of the Waveform menu filter there is only a "High pass" filter allowed, rejecting frequencies below a given value

Sometimes, the taper size used in the pre-processing has a strong influence at low frequency. If the signal contains a strong and very low frequency component, then cutting into short time windows may strongly distort the observed spectra and H/V. Even when using the minimum window length criteria according SESAME guidelines (i.e. 10 times the corresponding period for the minimum frequency of interest) may be not enough to ensure a reliable H/V estimation.

In order to avoid such “taper side effects”, signals can be high-pass filtered before computing the H/V and spectra curves (Geopsy option). The higher value for the frequency of the high-pass filter is the minimum ‘reliable’ frequency, i.e. ${\frac {10}{w_{l}}}$, Effect of very low frequency on H/V.

Be careful with this option. As the signal is high pass filtered, the results below the chosen frequency will display a lake of data.
If the studied frequency is close to 1 Hz and it is applied this filter at 2 Hz, the results will lead to bad data in the frequency of interest
and then to flaky interpretation.

Horizontal components section (only available for HV toolbox)

This section is devoted to indicate how the H/V has to be computed. There are 3 different methods that can be applied.

Horizontal components section indicating the way H/V is processed (available for H/V computing) only

Squared average

The H/V is computed as followed:

• The Fourier amplitude spectrum is computed for each window of each component (N, E and Z);

• The horizontal average spectrum is computed by a combination of horizontal spectra for each window, following the formula
  $H(f)={\sqrt {\frac {N^{2}(f)+E^{2}(f)}{2}}}$

• The horizontal (averaged) and vertical spectra of each window are smoothed;

• The horizontal to vertical ratio (H/V) is computed for each window;

• The H/V is computed by averaging all H/V coming from individual windows.

Total horizontal energy

The H/V is computed as followed:

• The Fourier amplitude spectrum is computed for each window of each component (N, E and Z)
• The horizontal average spectrum is computed by a combination of horizontal spectra for each window, following the formula
  $H(f)={\sqrt {N^{2}(f)+E^{2}(f)}}$
• The horizontal (averaged) and vertical spectra of each window are smoothed
• The horizontal to vertical ratio (H/V) is computed for each window
• The H/V is computed by averaging all H/V coming from individual windows.

Directional energy

Here, the H/V is calculated along a given direction, 0° is assumed to be the North direction and 90° the East direction. From the North-South and the East-West signals, a new (and single) signal is computed geometrically. This new signal is assumed to be the horizontal signal. The direction in which the H/V will be calculated is given in a spin box allowing changes in the direction between 0° and 180°. If the user wants to compute in a direction between 180° and 360°, due to symetry the user should take the symetrical direction: wanted direction-180°. If the user wants a 220° direction, it should be entered 40° in the spin box.

• The Fourier amplitude spectrum is computed for each window of each component (recomputed horizontal and vertical)

• The horizontal (recomputed) and vertical spectra of each window are smoothed

• The horizontal to vertical ratio (H/V) is computed for each window

• The H/V is computed by averaging all H/V coming from individual windows.

Load parameters and Start section

The section at the bottom of the Time tab comprises two buttons.

Load parameters and Start section

• The Load parameters button is used to load parameters from previous H/V or spectrum processing stored in a name.log file (example).

• Press the Start button to start H/V or Spectrum processing.

If no window selection has been performed, a pup-up window appears.

Pop-up window indicating that no window selection has been performed

Simply click on the Yes button and processing will follow its way with the current Toolbox parameters.

To perform user's windowing, click on the No button.