> For the complete documentation index, see [llms.txt](https://jonas.gitbook.io/seismo_rain/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jonas.gitbook.io/seismo_rain/cross-comparison-between-seismic-and-rainfall-data/visualising-rainfall-with-frequency-domain.md). # Visualising rainfall with frequency domain We can transform our waveform (count value vs. time) using the Fourier transform to generate a frequency domain plot (amplitude vs. frequency). This approach allows us to assess when a high-frequency signal is detected by the geophone.

A visualisation of how time domain can convert to frequnecy domain via Fourier Transformation (Gomede, 2023)

The provided code will generate a frequency domain plot of the seismic waveform within a 30-minute time bin. Here's a complete example specifically for the 2A.1517 station during the time interval from April 19, 2016, UTC 22:00 to 22:30. You can modify the seismic station to plot using `st[...]`, as well as adjust the time interval by changing the `start_timestep` and `end_timestep` variables. ```python import numpy as np # Recover "st" to its unprocessed state st = st.bak # Extract the trace of an individual channel # [0]: 2A.1517; [1]: 2A.199; [2]: 2A.465; [3]: 2A.763 tr = st[0] # Number of samples in 30 minutes samples_30mins = tr.stats.sampling_rate*3600*0.5 # Selecting the start and end time step for the 30-minute interval # 0 = 22:00, 1 = 22:30 , ..., 7 = 02:00(+1) start_timestep = int(samples_30mins*0) end_timestep = int(samples_30mins*1) st_30mins = tr.data[start_timestep:end_timestep] # Perform FFT on the 30-minute data fft_data = np.fft.fft(st_30mins) n = len(st_30mins) dt = 1 / tr.stats.sampling_rate # the sampling interval (s) frequencies = np.fft.fftfreq(n, dt) # Plotting the frequency domain data for the second half (only positive frequency) plt.figure(figsize=(10, 6)) plt.plot(frequencies[:n // 2], 2.0 / n * np.abs(fft_data[:n // 2]), 'b') # Only plot the first half plt.title('2A.1517..DPZ (22:00-22:30)') plt.xlabel('Frequency (Hz)') plt.ylabel('Amplitude') plt.grid() plt.show() ``` The 30-minute frequency domain at 22:00, 23:00, and 0:00 have been displayed, highlighting a blue-shaded box indicating the bandpass filter range of 80-150 Hz. Across all four stations, a notable increase in amplitude within this range suggests rainfall activity during this specific timeframe. This amplification aligns with the observed pattern in the [rainfall intensity data](/seismo_rain/rainfall-data/extracting-rainfall-data.md#plotting-the-rainfall-intensity-at-all-seismic-stations).

Frequncy domain of all four stations at 19 April 2016 22:00-22:30, 23:00-23:30 and 20 April 2016 UTC 00:00-00:30

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