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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>Example_PmagPy_Notebook</title>
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<h1 id="Jupyter-notebook-illustrating-the-use-of-PmagPy-for-analysis-of-paleomagnetic-data">Jupyter notebook illustrating the use of PmagPy for analysis of paleomagnetic data<a class="anchor-link" href="#Jupyter-notebook-illustrating-the-use-of-PmagPy-for-analysis-of-paleomagnetic-data">¶</a></h1><h1 id="Before-you-begin">Before you begin<a class="anchor-link" href="#Before-you-begin">¶</a></h1><p>You may be viewing this notebook as a rendered html webpage (which can be seen at this link: <a href="http://pmagpy.github.io/Example_PmagPy_Notebook.html">http://pmagpy.github.io/Example_PmagPy_Notebook.html</a>) or PDF in which case you can go ahead and simply have a look at it. However, if you wish to execute the code within a downloaded version of this notebook (which can be found here: <a href="https://github.com/PmagPy/2016_Tauxe-et-al_PmagPy_Notebooks">https://github.com/PmagPy/2016_Tauxe-et-al_PmagPy_Notebooks</a>), it is necessary to have an installed distribution of Python and to have installed the PmagPy software distribution. The instructions in the PmagPy Cookbook can help get you started in this regard:</p>
<p><a href="http://earthref.org/PmagPy/cookbook">http://earthref.org/PmagPy/cookbook</a></p>
<p>The user may also benefit from perusing the 'Survival computer skills' and 'Introduction to Python Programming' chapters of the cookbook if they are new to programming in Python.</p>
<h1 id="Introduction">Introduction<a class="anchor-link" href="#Introduction">¶</a></h1><p>This notebook was created by Nicholas Swanson-Hysell, Lisa Tauxe and Luke Fairchild. It accompanies a paper entitled:</p>
<p><strong>PmagPy: Software package for paleomagnetic data analysis and a bridge to the Magnetics Information Consortium (MagIC) Database</strong></p>
<p><em>L. Tauxe, R. Shaar, L. Jonestrask, N.L. Swanson-Hysell, R. Minnett, A.A.P., Koppers, C.G. Constable, N. Jarboe, K. Gaastra, and L. Fairchild</em></p>
<p>The analysis in this notebook uses data from two contributions within the MagIC database:</p>
<p>Halls, H. (1974), A paleomagnetic reversal in the Osler Volcanic Group,
northern Lake Superior, Can. J. Earth Sci., 11, 1200–1207,
doi:10.1139/e74-113. Link to MagIC contribution:
<a href="http://earthref.org/MAGIC/doi/10.1139/e74-113">http://earthref.org/MAGIC/doi/10.1139/e74-113</a></p>
<p>and</p>
<p>Swanson-Hysell, N. L., A. A. Vaughan, M. R. Mustain, and K. E. Asp (2014), Confirmation of progressive plate motion during the Midcontinent Rift’s early magmatic stage from the Osler Volcanic Group, Ontario, Canada, Geochem. Geophys. Geosyst., 15, 2039–2047, doi:10.1002/2013GC005180. Link to MagIC contribution:
<a href="http://earthref.org/MAGIC/doi/10.1002/2013GC005180">http://earthref.org/MAGIC/doi/10.1002/2013GC005180</a></p>
<p>To explore the use of Jupyter notebooks, follow each of these links and click on the text file icon in the Data column. Move each of the files from your download directory into a 'Project Directory' on your hard drive. In the example below, the project directory for the Halls data set is <strong>Halls1974</strong> and for the Swanson-Hysell data set, <strong>Swanson-Hysell2014</strong> within a subdirectory with the notebook code in it. If you cloned the notebook repository or downloaded a zip copy of it, you will already have these data files. Fire up a command line prompt (cmd on PCs and `terminal' in the Applications/Utilities folder on a Mac) and type <code>jupyter notebook</code> or <code>ipython notebook</code> to launch a notebook environment within your default web browser.</p>
<p>In this notebook, we will use PmagPy to:</p>
<ul>
<li>Unpack data downloaded from the MagIC database.</li>
<li>Plot directions and VGPs.</li>
<li>Calculate and plot Fisher means for directions and VGPs.</li>
<li>Conduct a bootstrap fold test on the data.</li>
<li>Conduct a common mean test between the data from the two contributions.</li>
</ul>
<h1 id="Import-necessary-function-libraries-for-data-analysis">Import necessary function libraries for data analysis<a class="anchor-link" href="#Import-necessary-function-libraries-for-data-analysis">¶</a></h1><p>The code block below imports the pmagpy module from PmagPy that provides functions that will be used in the data analysis. At present, the most straight-forward way to do so is to install the pmagpy module using the pip package manager by executing this command at the command line:</p>
<p><code>pip install pmagpy</code></p>
<p>Approachs not using pip can also work. One way would be to download the pmagpy folder from the main PmagPy repository and either put it in the same directory as the notebook or put it anywhere on your local machine and add a statement such as <code>export PYTHONPATH=$PYTHONPATH:~/PmagPy</code> in your .profile or .bash_profile file that points to where PmagPy is on your local machine (in this example in the home directory).</p>
<p>With PmagPy available in this way, the function modules from <strong>PmagPy</strong> can be imported: <strong>pmag</strong>, a module with ~160 (and growing) functions for analyzing paleomagnetic and rock magnetic data and <strong>ipmag</strong>, a module with functions that combine and extend <strong>pmag</strong> functions and exposes <strong>pmagplotlib</strong> functions in order to generate output that works well within the Jupyter notebook environment.</p>
<p>To execute the code, click on play button in the menu bar, choose run under the 'cell' menu at the top of the notebook, or type shift+enter.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">pmagpy.ipmag</span> <span class="kn">as</span> <span class="nn">ipmag</span>
<span class="kn">import</span> <span class="nn">pmagpy.pmag</span> <span class="kn">as</span> <span class="nn">pmag</span>
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<p>There are three other important Python libraries (which are bundled with the Canopy and Anaconda installations of Python) that come in quite handy and are used within this notebook: <strong>numpy</strong> for data analysis using arrays, <strong>pandas</strong> for data manipulation within dataframes and <strong>matplotlib</strong> for plotting. The call <code>%matplotlib inline</code> results in the plots being shown within this notebook rather than coming up in external windows.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="o">%</span><span class="k">config</span> InlineBackend.figure_formats = {'svg',}
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<h1 id="Background-on-the-Osler-Volcanic-Group">Background on the Osler Volcanic Group<a class="anchor-link" href="#Background-on-the-Osler-Volcanic-Group">¶</a></h1>
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<p>The data being analyzed in this notebook come from lava flows of the Osler Volcanic Group which is a sequence of Midcontinent Rift lava flows exposed on Black Bay Peninsula and the Lake Superior Archipelago in northern Lake Superior. Halls (1974; doi:10.1139/e74-113) conducted the first paleomagnetic study of these flows and determined that they were of dominantly reversed polarity with a paleomagnetic reversal very near to the top of the exposed stratigraphy. This reversal is associated with the deposition of a conglomerate unit and an angular unconformity. The data presented in Halls (1974) from the reversed polarity lavas were from flows high in the succession in close stratigraphic proximity to a sequence of felsic flows at Agate Point---one of which was dated by Davis and Green (1997; doi:10.1139/e17-039) with a resulting $^{207}$Pb/$^{206}$Pb date on zircon of 1105.3 ± 2.1 Ma. Swanson-Hysell et al. (2014; doi:10.1002/2013GC005180) conducted a paleomagnetic study that spanned more of the Osler Group flows from their base up to the upper portions of the exposed reversed polarity flows. The analysis of these data determined that there was a significant change in direction between the data from flows in the lower third of the reversed polarity stratigraphy and those in the upper third stratigraphy. This change was interpreted to be caused by a progression along the apparent polar wander path associated with equatorward motion of Laurentia.</p>
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<h1 id="Import-data-into-the-notebook">Import data into the notebook<a class="anchor-link" href="#Import-data-into-the-notebook">¶</a></h1><h2 id="Unpack-files-downloaded-from-the-MagIC-database">Unpack files downloaded from the MagIC database<a class="anchor-link" href="#Unpack-files-downloaded-from-the-MagIC-database">¶</a></h2><p>Data within the MagIC database can be downloaded as a single .txt file. This file can be split into its constituent EarthRef and pmag tables either within the Pmag GUI, using a command line PmagPy program or using the function <strong>ipmag.download_magic</strong> within the notebook as is done here. The code block below uses this function by giving the file name, specifying where it is and telling it where to unpack the data set into the magic tables. Once these tables are unpacked, we can use them for subsequent data analysis. The <code>%%capture</code> line blocks annoying messages printed by the <strong>ipmag.download_magic</strong> function.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%%</span><span class="k">capture</span>
ipmag.download_magic('magic_contribution_11087.txt',
dir_path='./Example_Data/Halls1974',
input_dir_path='./Example_Data/Halls1974',
overwrite=True,print_progress=False)
ipmag.download_magic('magic_contribution_11088.txt',
dir_path='./Example_Data/Swanson-Hysell2014',
input_dir_path='./Example_Data/Swanson-Hysell2014',
overwrite=True,print_progress=False)
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<pre>True</pre>
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<h2 id="Loading-the-unpacked-data-into-Pandas-Dataframes">Loading the unpacked data into Pandas Dataframes<a class="anchor-link" href="#Loading-the-unpacked-data-into-Pandas-Dataframes">¶</a></h2><p>With the results unpacked from MagIC, the data can now be analyzed within the notebook. The data from the Halls1974/pmag_sites.txt table can be imported in order to look at the directions from each site. A nice way to deal with data within Python is using the dataframe structure of the pandas package. The code block below uses the pd.read_csv function to create a dataframe from the pmag_sites.txt file. All MagIC formatted files are tab delimited (<code>sep='\t'</code>) with two header lines, one with the type of delimiter and MagIC table and one with the MagIC database column names. To see the formats for MagIC tables, go to <a href="http://earthref.org/MAGIC/metadata.htm">http://earthref.org/MAGIC/metadata.htm</a>.
To skip the first header line in a particular file when importing it to a DataFrame, set skiprows=1. The <code>data_frame_name.head(X)</code> function allows us to inspect the first <code>X</code> rows of the dataframe (in this case 4).</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">Halls1974_sites</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">'./Example_Data/Halls1974/pmag_sites.txt'</span><span class="p">,</span>
<span class="n">sep</span><span class="o">=</span><span class="s1">'</span><span class="se">\t</span><span class="s1">'</span><span class="p">,</span><span class="n">skiprows</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">Halls1974_sites</span><span class="o">.</span><span class="n">head</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
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<th>site_dec</th>
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<td>This study</td>
<td>Osler Volcanics, Nipigon Strait, Upper Normal</td>
<td>1</td>
<td>DE-K:FS-FD:FS-H:LP-DC2:SO-SM</td>
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<th>1</th>
<td>This study</td>
<td>Osler Volcanics, Nipigon Strait, Upper Normal</td>
<td>1</td>
<td>DE-K:FS-FD:FS-H:LP-DC2:SO-SM</td>
<td>293.1</td>
<td>34.5</td>
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<td>This study</td>
<td>Osler Volcanics, Nipigon Strait, Upper Normal</td>
<td>2</td>
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<td>42.0</td>
<td>243</td>
<td>5</td>
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<td>100</td>
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<td>This study</td>
<td>Osler Volcanics, Nipigon Strait, Upper Normal</td>
<td>2</td>
<td>DE-K:FS-FD:FS-H:LP-DC2:SO-SM</td>
<td>290.6</td>
<td>31.9</td>
<td>243</td>
<td>5</td>
<td>n</td>
<td>0</td>
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<h2 id="Filtering-by-polarity-and-tilt-correction">Filtering by polarity and tilt-correction<a class="anchor-link" href="#Filtering-by-polarity-and-tilt-correction">¶</a></h2><p>Let's start our analysis on the reversed polarity sites that are below an angular unconformity in the Halls (1974) data set. A nice thing about dataframes is that there is built-in functionality to filter them based on column values. The code block below creates a new dataframe of sites that have the site_polarity value of 'r' in the pmag_sites table. It then creates one dataframe for tilt-corrected sites (value of 100 in site_tilt_correction) and sites that have not been tilt-corrected (value of 0 in site_tilt_correction).</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">Halls1974_sites_r</span> <span class="o">=</span> <span class="n">Halls1974_sites</span><span class="o">.</span><span class="n">ix</span><span class="p">[</span><span class="n">Halls1974_sites</span><span class="o">.</span><span class="n">site_polarity</span><span class="o">==</span><span class="s1">'r'</span><span class="p">]</span>
<span class="n">Halls1974_sites_r_tc</span> <span class="o">=</span> <span class="n">Halls1974_sites_r</span><span class="o">.</span><span class="n">ix</span><span class="p">[</span><span class="n">Halls1974_sites_r</span><span class="o">.</span><span class="n">site_tilt_correction</span><span class="o">==</span><span class="mi">100</span><span class="p">]</span>
<span class="n">Halls1974_sites_r_tc</span><span class="o">.</span><span class="n">reset_index</span><span class="p">(</span><span class="n">inplace</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">Halls1974_sites_r_is</span> <span class="o">=</span> <span class="n">Halls1974_sites_r</span><span class="o">.</span><span class="n">ix</span><span class="p">[</span><span class="n">Halls1974_sites_r</span><span class="o">.</span><span class="n">site_tilt_correction</span><span class="o">==</span><span class="mi">0</span><span class="p">]</span>
<span class="n">Halls1974_sites_r_is</span><span class="o">.</span><span class="n">reset_index</span><span class="p">(</span><span class="n">inplace</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
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<h1 id="Data-analysis-and-visualization">Data analysis and visualization<a class="anchor-link" href="#Data-analysis-and-visualization">¶</a></h1><p>The data can be analyzed and visualized using PmagPy functions. We will first create a directory called 'Example_Notebook_Output' from within the notebook (using the initial ! before the command invokes a command as if typed on the command line from within a notebook) so that we have a place to put saved figures. You can do this outside of the notebook if you prefer.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="o">!</span>mkdir <span class="s1">'Example_Notebook_Output'</span>
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<pre>mkdir: Example_Notebook_Output: File exists
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<h2 id="Calculating-Fisher-means">Calculating Fisher means<a class="anchor-link" href="#Calculating-Fisher-means">¶</a></h2><p>Fisher means for the data can be calculated with the function <strong>ipmag.fisher_mean</strong>. This function takes in a list of declination values, a list of inclination values and returns a dictionary that gives the Fisher mean and associated statistical parameters. This dictionary is printed out for the mean of the tilt-corrected data within the first code block. These dictionary objects are given names such that we can subsequently access the values. The second code block uses the <strong>ipmag.print_direction_mean</strong> to print out a formatted version of these same results.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">Halls1974_r_is_mean</span> <span class="o">=</span> <span class="n">ipmag</span><span class="o">.</span><span class="n">fisher_mean</span><span class="p">(</span><span class="n">Halls1974_sites_r_is</span><span class="o">.</span><span class="n">site_dec</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span>
<span class="n">Halls1974_sites_r_is</span><span class="o">.</span><span class="n">site_inc</span><span class="o">.</span><span class="n">tolist</span><span class="p">())</span>
<span class="n">Halls1974_r_tc_mean</span> <span class="o">=</span> <span class="n">ipmag</span><span class="o">.</span><span class="n">fisher_mean</span><span class="p">(</span><span class="n">Halls1974_sites_r_tc</span><span class="o">.</span><span class="n">site_dec</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span>
<span class="n">Halls1974_sites_r_tc</span><span class="o">.</span><span class="n">site_inc</span><span class="o">.</span><span class="n">tolist</span><span class="p">())</span>
<span class="k">print</span> <span class="n">Halls1974_r_tc_mean</span>
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<pre>{'csd': 12.780983354077163, 'k': 40.164419949836713, 'n': 25, 'r': 24.402456203028084, 'alpha95': 4.6244793676899487, 'dec': 114.96744501761694, 'inc': -57.572956213862817}
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="s1">'The mean for the tilt-corrected Halls (1974) Osler directions is:'</span>
<span class="n">ipmag</span><span class="o">.</span><span class="n">print_direction_mean</span><span class="p">(</span><span class="n">Halls1974_r_tc_mean</span><span class="p">)</span>
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<pre>The mean for the tilt-corrected Halls (1974) Osler directions is:
Dec: 115.0 Inc: -57.6
Number of directions in mean (n): 25
Angular radius of 95% confidence (a_95): 4.6
Precision parameter (k) estimate: 40.2
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<h2 id="Plotting-the-Halls-(1974)-results">Plotting the Halls (1974) results<a class="anchor-link" href="#Plotting-the-Halls-(1974)-results">¶</a></h2><p>The code block below creates a figure with an equal area stereonet and uses the <strong>ipmag.plot_di</strong> function to plot the data both in tilt-corrected and <em>in situ</em> coordinates. The figure can be saved out of the notebook using the <code>plt.savefig()</code> function. The saved figure file type can be .png, .eps, .svg among others. Saved figures can be used as is for publication or, if necessary, exported vector graphics (e.g. .eps and .svg files) can be edited with software such as Adobe Illustrator or Inkscape.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">num</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
<span class="n">ipmag</span><span class="o">.</span><span class="n">plot_net</span><span class="p">(</span><span class="n">fignum</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">ipmag</span><span class="o">.</span><span class="n">plot_di</span><span class="p">(</span><span class="n">Halls1974_sites_r_is</span><span class="o">.</span><span class="n">site_dec</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span>
<span class="n">Halls1974_sites_r_is</span><span class="o">.</span><span class="n">site_inc</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span><span class="n">color</span><span class="o">=</span><span class="s1">'r'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'Halls (1974) site means (in situ)'</span><span class="p">)</span>
<span class="n">ipmag</span><span class="o">.</span><span class="n">plot_di</span><span class="p">(</span><span class="n">Halls1974_sites_r_tc</span><span class="o">.</span><span class="n">site_dec</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span>
<span class="n">Halls1974_sites_r_tc</span><span class="o">.</span><span class="n">site_inc</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span><span class="n">color</span><span class="o">=</span><span class="s1">'b'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'Halls (1974) site means (tilt-corrected)'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">9</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="s1">'Example_Notebook_Output/Halls_1974_sites.svg'</span><span class="p">)</span>
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