91 lines
2.5 KiB
Plaintext
91 lines
2.5 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Dispersive Signals\n",
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"Up to now,we considered the spectral content of the entire time series. In many\n",
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"cases, the spectral content varies with time in a time series and one often wants to\n",
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"find out how this happens in detail. One important example are dispersed signals in\n",
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"which energy with different frequency content arrives at different times. Most\n",
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"prominent among these are seismic surface which exhibit significant dispersion if\n",
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"epicentral distances between seismic station and source are large. Quantifying the\n",
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"dispersion allows inferences on Earth structure. \n",
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"\n",
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"<img src=\"../images/seismogram.png\" alt=\"Drawing\" style=\"width: 700px;\"/>\n",
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"<img src=\"../images/stack-surface-waves.png\" alt=\"Drawing\" style=\"width: 700px;\"/>"
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]
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},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## The Chirp or Sweep"
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]
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"plt.rcParams['figure.figsize'] = 12, 8 # Slightly bigger plots by default"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from scipy.signal import chirp\n",
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"t = np.linspace(0, 30, 30001)\n",
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"w = chirp(t, f0=0.01, f1=3, t1=np.max(t), method='linear')\n",
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"plt.plot(t, w);"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Tasks\n",
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"1. What is special about the Chirp Signal?\n",
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"2. Plot the amplitude spectrum of the chirp signal, using numpys [FFT module](https://numpy.org/doc/stable/reference/routines.fft.html), including the correct frequncies on the x-axis!\n",
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"3. Think of a solution how to visualize the increasing frequency content using the Fourier tansform"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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