0

I need to calculate the seismic moment of an earthquake data, but I don't know how the FFT is applied in some data, my data is a plain text that I must import it to Mathematica

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I did this...

sis1 = Import["data.dat"];
data1 = Flatten[sis1];

ListLinePlot[data1, AxesLabel -> {Time, Amplitude}, PlotRange -> All]

enter image description here

At this point I need to apply the fast Fourier transform to the data, to calculate the seismic moment, it should look like this.

enter image description here

can someone help me? thank you

flinty
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xg3istx
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    See here for details on Fourier. Also, can you put your data in Mathematic form as a list. Further, unless you tell us the sample rate we can't work out a frequency axis. – Hugh Nov 26 '20 at 13:28
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    What have you checked in the documentation? I ask because there is a fair amount of material on Fourier transforms. – Daniel Lichtblau Nov 26 '20 at 15:51
  • Just use Periodogram or Spectrogram. It's a lot easier to use that interface than setting up the fourier transform yourself. Also you need to deal with {-5 - 3.01027 e, -6 + 2.40944 e} in your data first, as these aren't being interpreted as numbers properly. – flinty Nov 26 '20 at 17:22
  • It would be interesting to know what form of Fourier transform is normal for seismic work. In my area, structural dynamics, I do a lot with the real and imaginary parts (or modulus and phase). If relationships between two horizontal directions and the vertical direction are important then the full information in the spectrum is needed. – Hugh Nov 26 '20 at 17:40
  • Thanks Hugh for you reply, I'll tried :) – xg3istx Nov 29 '20 at 22:20

1 Answers1

1

I managed to sort your data. Here is the time history. The data is in c1.

ListLinePlot[c1]

Time history

Now we take the Fourier transform and plot

 n = Round[Length[c1]/2];
ft = Fourier[c1, FourierParameters -> {-1, -1}];
    ListLogLogPlot[Abs[ft[[1 ;; n]]]]

Fourer transform

Hope that helps.

Edit A comment below suggests you want the power spectral density. You may want this but if you have a transient a simple Fourier transform is appropriate. There are issues with the best scaling. Parsival's theorem is the usual guide for how to scale. You may have a standard for your discipline. Scaling is achieved by means of the FourierParametes. You need to read the documentation for details.

Hugh
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    @xg3istx Note that what @Hugh is plotting is the square root of the power density, while the example that you wish to match appears to be the power density. Also, n in the above is something like 1+Floor[Length[ft]/2. – John Doty Nov 26 '20 at 15:00