Export Microtremor Results in Frequency domain

[lukemilner]

Hi Marc,

I was wondering if there was a method to export results in the frequency domain using Geopsy. I have imported data in the time domain, and applied the FFT (by selecting view --> frequency (amplitude)). Now I want to export the results, ideally as a .hv file.

I know that there is a way of doing this for H/V spectra. However, I was hoping to export individual NS, EW and vertical components in the frequency domain if possible.

Many thanks,

Luke

[admin]

Hi Luke,

If you go to "File/Export" menu, you can export as a multi-column text file. If the current state is frequency domain, you will get the raw FFT spectrum (real and imaginary part for each frequency), not the smoothed and processed like in HV tool.

Best regards,

Marc

[lukemilner]

Hi Marc,

Thanks for getting back to me.

I just wanted to clarify- for the 'frequency (amplitude)' plot (under view) I assume this displays the 'real' component (i.e. the second column in the .txt file), whilst the 'frequency (phase)' plot displays the 'imaginary' component (i.e. the third column in the .txt file)?

Thanks,

Luke

[lukemilner]

Also, I am not sure what the units for the Fourier Amplitude Spectrum are according to the Geopsy FFT.

The data I uploaded in the time domain was in terms of 'counts' (i.e. counts vs time) and after applying the FFT the y axis (i.e. the Fourier Amplitude spectrum') is labelled with 'counts/sqrt(Hz)' against 'frequency' on the x axis.

upload1.png

(141.42 KiB) Not downloaded yet

upload2.png

(117.03 KiB) Not downloaded yet

Can you please clarify what the scientific units are for the Fourier transformed amplitude? I don't think they can simply be ('sqrt(Hz))')?


Many thanks,

Luke

[admin]

I just wanted to clarify- for the 'frequency (amplitude)' plot (under view) I assume this displays the 'real' component (i.e. the second column in the .txt file), whilst the 'frequency (phase)' plot displays the 'imaginary' component (i.e. the third column in the .txt file)?

Frequency (amplitude) is not the real part but the absolute value: sqrt(Re^2+Im^2). Phase is the phase of the complex number.

Also, I am not sure what the units for the Fourier Amplitude Spectrum are according to the Geopsy FFT.

According to McNamara and Buland (2004), the power spectral density (PSD) is obtained (after some pre-processing steps) by multiplying the Fourier components by a factor 2*Dt/N (equation 3) where Dt is the sampling period and N is the number of samples. Geopsy uses FFTW library to compute Fourier amplitude spectra. The result is always multiplied by the square root of this factor. Doing this, the amplitude spectrum values are independent of the sampling frequency and the signal duration. You can check yourself by decimating or oversampling a signal. The amplitude spectrum should remain the same.

PSD has (waveform unit)^2/Hz units. This is a power density, a power per unitary frequency range. PSD is the square of the amplitude spectrum, hence the units of amplitude spectrum are (waveform unit)/sqrt(Hz).

Waveform units can be m/s, m/s^2 or simply counts if no correction (counts to volts and eventually volts to m/s) is applied after digitization.

[luigiV]

Hi Marc
Taking up the final part of your answer I ask you why if in the header of my Saf file I impose that the data units are m / s the ordinate of the PSD is always (counts) ^ 2 / Hz?

SESAME ASCII data format (saf) v. 1 (this line must not be modified)
SAMP_FREQ = 125
NDAT = 675000
START_TIME = 2020 12 02 00 00 00.000
SENSOR_TYPE =
SENSOR_ID =
GAIN =
SENS_DAMPING =
STA_X =
STA_Y =
STA_Z = 0
STA_CODE =
UNITS = m / s
CH0_ID =
CH1_ID =
CH2_ID =
#### --------------------------------

Should I replace in the title of the Y axis counts with m/s using Property Editor?

Is it possible to plot the individual spectral components of motion as in the image I am attaching?
Thanks
luigi

[admin]

If you want to change the units, you have to make sure that the input signal is effectively in m/s. Usually digitizers output only counts and the manufacturer provides the conversion factors to volts and m/s (for the sensor). If you enter these factors in CountPerVolt and VoltPerUnit fields of a table (Set headers, Set data fields), you will get graphics in m/s instead of counts.

If your signal values are already in m/s, you are free to modify the axis title in properties. The SAF keyword "UNITS" is ignored. One trick to get m/s everywhere in geopsy plots is to set CountPerVolt to 0.5 and VoltPerUnit to 2, so the the resulting factor is 1. Any value different from 1 for these factors switches to Volt (if only CountPerVolt is not 1) or m/s (both different from 1) instead of counts.

The individual smoothed spectra are obtained with Spectrum Tool shipped within the same plugin as the HV tool.