seismology-RUB/DataAnalysis2021
10
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Add all notebooks for part ii of the lecture. #13

Merged
kasper merged 3 commits from develop into main 2021-06-26 16:15:50 +02:00
Conversation 2 Commits 3 Files Changed 26 +18 -53
2 changed files with 18 additions and 53 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files
Showing only changes of commit 8ce3df158c - Show all commits

52
04-FFT_DFT_and_Applications/spectrogram.ipynb
View File

@ -1,52 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Time-Frequency Analysis\n",
"## Moving window analysis\n",
"One way to analyse the time-varying frequency content of a signal is to\n",
"apply windows in the time domain to the signal and to calculate a Fourier spectrum\n",
"of the windowed part. The window marches along the signal with defined overlap creating\n",
"a series of Fourier spectra associated with the center times of the windows. The resulting amplitude\n",
"spectra are then plotted versus window center time. In more detail:\n",
"\n",
"1. Choose windowing functions: $w(t,t_m)$ with $t_m$ the center of the window.\n",
"2. Multiply windowing function with time series: $f_m(t) = f(t)w(t,t_m)$\n",
"3. Detrend the windowed signal.\n",
"4. Perform a DFT: $F_{km} = \\Delta t\\sum_{n=0}^N f_m(t)\\exp(-2\\pi i \\frac{kn}{N})$\n",
" and calculate the absolute value, $|F_{km}|$.\n",
"5. Plot the resulting matrix: $|F_{km}|$ in the time-frequency plane."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

19
README.md
View File

@ -18,4 +18,21 @@ This has been forked from [Seismo Live](http://seismo-live.org). The source code
1. Simple Cross Correlation: Use the cross-correlation to detect and determine the time shift of two test events with one template event.
2. Enhanced Picker: This has been taken from the [ObsPy Tutorial](https://docs.obspy.org/master/tutorial/code_snippets/xcorr_pick_correction.html). ObsPy is licensed under the [LGPL v3.0](https://www.gnu.de/documents/lgpl-3.0.en.html)
3. Ambient Seismic Noise Analysis from [Seismo Live](http://seismo-live.org). The source code is available at https://github.com/krischer/seismo_live (licensed under a ***CC BY-NC-SA 4.0 License***. © 2015-2019 Lion Krischer).
3. Ambient Seismic Noise Analysis from [Seismo Live](http://seismo-live.org). The source code is available at https://github.com/krischer/seismo_live (licensed under a ***CC BY-NC-SA 4.0 License***. © 2015-2019 Lion Krischer).
### 04 - FFT, DFT and Applications
Interpolation and Deciamtion of Time Series using the DFT
### 05 - Spectrogram
1. Analysing dispersive signals. How to visualize changes in frequency content over time (moving window analysis, mutiple filter technique, instantaneous frequency, continuous wavelet transform, the uncertainty problem).
2. Filtering time series with non spectral filtering method.
### 06 - Surface Waves
Analysing phase and group velocity of recorded earthquake signals at one and two seismological stations.
### 07 - Receiver Functions
How to get receiver functions from seismograms.