Geophysical Exploration of Crustal Structure

Exercise 2

Spectrum and frequency filter

This exercise uses the sample data "demo_bpf.su". Copy the sample data if you do not have one. Your reference is here.

First, display the waveform of the sample data.

$ suxwigb < demo_bpf.su perc=98 &

Display the spectrum of the data.

$ suspecfx < demo_bpf.su | suximage perc=98 &
$ suspecfx < demo_bpf.su | suxgraph &
$ suspecfx < demo_bpf.su | suop op=db | suxgraph &

"suspecfx" applies Fourier transform to data in the time domain, and then, outputs the amplitude spectrum.
To display the spectrum, you can use "suximage", "suxwigb" and "suxgraph", etc.
"suop" does an arithmetic calculation to data. The option "op=db" calculates a logarithm in dB (decibel). Type "suop" for the brief help.

Now you can see what frequency components are included in the data.

Fig: (Left) The waveform. The vertical axis is 'time (s)'. (Middle) The spectrum in a color image. The vertical axis is 'frequency (Hz)'. (Right) The spectrum in a graph style.

Then, apply some frequency filters and display the result.

From the spectrum, you can find three frequency bands, < 20 Hz, 20 - 40 Hz, 50 - 100 Hz in the data. Therefore, here we will apply filters shown in the following figure.

First, extract the signal of 20 - 40 Hz by applying the bandpass filter (a).

$ sufilter f=10,20,40,50 amps=0,1,1,0 < demo_bpf.su | suxwigb &
$ sufilter f=10,20,40,50 amps=0,1,1,0 < demo_bpf.su | suspecfx | suxgraph &

"sufilter" applies filtering in the frequency domain".
"f= " and "amps= " specifies the shape of the filter by indicating the amplitude at each frequency.
For example, "amps=1,0" (low-pass filter), "amps=0,1" (high-pass filter), "amps=0,1,1,0" (bandpass filter).

Fig: (Left) The waveform. The vertical axis is 'time (s)'. (Right) The spectrum in a graph style. The vertical axis is 'frequency (Hz)'.

Make sure that the signal of 20 - 40 Hz remains while other frequenciy bands diminish.

The filter (b) removes the frequency band of the filter (a). Note the option 'amps='.

$ sufilter f=10,20,40,50 amps=1,0,0,1 < demo_bpf.su | suxwigb &
$ sufilter f=10,20,40,50 amps=1,0,0,1 < demo_bpf.su | suspecfx | suxgraph &

Fig: (Left) The waveform. The vertical axis is 'time (s)'. (Right) The spectrum in a graph style. The vertical axis is 'frequency (Hz)'.

Note that that the signal of 20 - 40 Hz is removed.

$ sufilter f=10,20 amps=1,0 < demo_bpf.su | suxwigb &
$ sufilter f=10,20 amps=1,0 < demo_bpf.su | suspecfx | suxwigb &
$ sufilter f=40,50 amps=0,1 < demo_bpf.su | suxwigb &
$ sufilter f=40,50 amps=0,1 < demo_bpf.su | suspecfx | suxwigb &

Fig: (Left) The waveform. The vertical axis is 'time (s)'. (Right) The spectrum displayed in graph style. The vertical axis is 'frequency (Hz)'.

Fig: (Left) The waveform. The vertical axis is 'time (s)'. (Right) The spectrum in a graph style. The vertical axis is 'frequency (Hz)'.

Note the pass-band and the cut-band of each filter.

Velocity filter (f-k filter)

This exercise uses the sample data "demo_fkf.su" and "demo_fkf2.su". Copy the sample data by referring here if you do not have one.

First, display the waveform.

$ suxwigb < demo_fkf.su &

You will see three waves having different apparent velocities. Note that the wave crosses with each other.

Calculate "double Fourier transform" to convert time-space (t-x) data to frequency-wavenumber (f-k) data, and display the f-k spectrum.

$ suspecfk < demo_fkf.su | suximage &

"suspecfk" applies "double Fourier transform" in both 't' and 'x' directions and create a f-k spectrum.

Fig: (Left) The waveform. The vertical axis is 'time (s)'. The horizontal axis is 'distance (m)'. (Right) The f-k spectrum in a color image. The vertical axis is 'frequency (Hz)'. The horizontal axis is 'wavenumber (1/m)'.

Waves (1),(2),(3) in t-x plane are converted to the images indicated by the number in f-k plane. Note that the wave (3) are spatially aliased (wrap-around in the wavenumer domain).

Now apply the velocity filters. From the waveforms in t-x plane, the dip (dt/dx) of the waves (1), (2), (3) are 0.00, 0.01, 0.02, respectively.

First, try eliminating the wave (1). Since the dip (dt/dx) of the wave is zero (0) in t-x plane (the apparent velocity is infinity), apply a filter that removes the energy around the zero dips (-0.005 - 0.005). In f-k plane, the filter looks like the one in the following figure.

sudipfilt slopes=-0.01,-0.005,0.005,0.01 amps=1,0,0,1 < demo_fkf.su | suxwigb  &
sudipfilt slopes=-0.01,-0.005,0.005,0.01 amps=1,0,0,1 < demo_fkf.su | suspecfk | suximage &

"sudipfilt" applies a filter that passes and removes dipping areas in t-x plane. It "double Fourier transform" the data and apply the filter in f-k domain.
The option "slopes= " indicates the dips to be filtered as the option 'f= ' for "sufilter".
The usage of "amps= " is the same as that of "sufilter".

You will see that the wave (1) was removed as designed when displaying the t-x waveform and the f-k spectrum. Note that the wave (3) was slightly distorted because the high-frequency component of (3) was partly removed by the filter.

Next, try eliminating the wave (3). Since the dip (dt/dx) of the wave is 0.02 in t-x plane, apply a filter that removes the energy around dip=0.02 (0.0175 - 0.0225). In f-k plane, the filter is shown in the following figure.

sudipfilt slopes=0.015,0.0175,0.0225,0.025 amps=1,0,0,1 < demo_fkf.su | suxwigb &
sudipfilt slopes=0.015,0.0175,0.0225,0.025 amps=1,0,0,1 < demo_fkf.su | suspecfk | suximage &

Note that the filter failed to remove the wave (3) completely in t-x plane. The reason is clear in f-k plane. The filter did not cover the alised part of the wave (3) in the negative wavenumber. To remove the wave (3) completely, you will need to apply a filter that removes the negative wavenumber as well. As spatial aliasing cause problems in data processing, you will need care in deciding the number of receivers and their separation distance.

Homework

Homework 1

Using the sample data "demo_fkf.su", apply a filter that removes the wave (2) only while keeping the waves (1) and (3) as possible. Submit

the command line and options for your filter,
the waveform of the result of your filtering,
and the f-k spectrum of the above waveform.

Homework 2

Using the sample data "demo_fkf2.su", try eliminating the surface waves (low-frequency waves aligning from top-left to bottom-right) to emphasize the reflections. Hints are as follows.

sudipfilt slopes=(slopes to be removed from the figure of the waveforms) amps=?,?,?,? < demo_fkf2.su | .............

In this example, use the time scale in the display of the waveform image to calculate the slope.

Submit

the command line and options for your filter,
the waveform of the result of your filtering,
and the f-k spectrum of the above waveform.

Fig: (Left) Sample data "demo_fkf2.su". The vertical axis is the time (s). The horizontal axis is the distance (m).

The result after PRESERVING the surface wave only, just for your reference.

Exercise 1 < Exercise 2 > Exercise 3

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Last modified: Wed Oct 18 19:03:54 JST 2023