ka-pr/05_introduction_to_scatter_plots_and_histograms.ipynb

## 05_introduction_to_scatter_plots_and_histograms.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to scatter plots\n",
    "\n",
    "This lesson will introduce scatter plots and how to make them in several different ways.\n",
    "\n",
    "We will start buy importing the ANSS earthquake catalog which you can download [here](http://www.quake.geo.berkeley.edu/anss/catalog-search.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('data/anss.csv', delim_whitespace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Time</th>\n",
       "      <th>Lat</th>\n",
       "      <th>Lon</th>\n",
       "      <th>Depth</th>\n",
       "      <th>Mag</th>\n",
       "      <th>Magt</th>\n",
       "      <th>Nst</th>\n",
       "      <th>Gap</th>\n",
       "      <th>Clo</th>\n",
       "      <th>RMS</th>\n",
       "      <th>SRC</th>\n",
       "      <th>Event</th>\n",
       "      <th>ID</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2002/01/01</td>\n",
       "      <td>10:39:06.82</td>\n",
       "      <td>-55.214</td>\n",
       "      <td>-129.000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>Mw</td>\n",
       "      <td>78</td>\n",
       "      <td>1.07</td>\n",
       "      <td>NEI</td>\n",
       "      <td>2.002010e+11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2002/01/01</td>\n",
       "      <td>11:29:22.73</td>\n",
       "      <td>6.303</td>\n",
       "      <td>125.650</td>\n",
       "      <td>138.1</td>\n",
       "      <td>6.3</td>\n",
       "      <td>Mw</td>\n",
       "      <td>236</td>\n",
       "      <td>0.90</td>\n",
       "      <td>NEI</td>\n",
       "      <td>2.002010e+11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2002/01/01</td>\n",
       "      <td>19:53:06.95</td>\n",
       "      <td>-27.875</td>\n",
       "      <td>73.883</td>\n",
       "      <td>10.0</td>\n",
       "      <td>5.6</td>\n",
       "      <td>Mw</td>\n",
       "      <td>27</td>\n",
       "      <td>0.88</td>\n",
       "      <td>NEI</td>\n",
       "      <td>2.002010e+11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2002/01/01</td>\n",
       "      <td>21:25:20.02</td>\n",
       "      <td>-27.874</td>\n",
       "      <td>74.007</td>\n",
       "      <td>10.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>Mw</td>\n",
       "      <td>21</td>\n",
       "      <td>0.34</td>\n",
       "      <td>NEI</td>\n",
       "      <td>2.002010e+11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2002/01/01</td>\n",
       "      <td>23:13:45.20</td>\n",
       "      <td>-27.945</td>\n",
       "      <td>74.156</td>\n",
       "      <td>10.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>Mw</td>\n",
       "      <td>21</td>\n",
       "      <td>0.85</td>\n",
       "      <td>NEI</td>\n",
       "      <td>2.002010e+11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date         Time     Lat      Lon  Depth  Mag Magt  Nst   Gap  Clo  \\\n",
       "0  2002/01/01  10:39:06.82 -55.214 -129.000   10.0  6.0   Mw   78  1.07  NEI   \n",
       "1  2002/01/01  11:29:22.73   6.303  125.650  138.1  6.3   Mw  236  0.90  NEI   \n",
       "2  2002/01/01  19:53:06.95 -27.875   73.883   10.0  5.6   Mw   27  0.88  NEI   \n",
       "3  2002/01/01  21:25:20.02 -27.874   74.007   10.0  5.1   Mw   21  0.34  NEI   \n",
       "4  2002/01/01  23:13:45.20 -27.945   74.156   10.0  5.1   Mw   21  0.85  NEI   \n",
       "\n",
       "            RMS  SRC  Event  ID  \n",
       "0  2.002010e+11  NaN    NaN NaN  \n",
       "1  2.002010e+11  NaN    NaN NaN  \n",
       "2  2.002010e+11  NaN    NaN NaN  \n",
       "3  2.002010e+11  NaN    NaN NaN  \n",
       "4  2.002010e+11  NaN    NaN NaN  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are these columns?\n",
    "\n",
    "Some are self explanatory but some are not:\n",
    "\n",
    "* Magt - the way the magnitude was calculated\n",
    "* Nst - the number of stations that detected the earthquake\n",
    "* RMS - root mean square\n",
    "* \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Lat</th>\n",
       "      <th>Lon</th>\n",
       "      <th>Depth</th>\n",
       "      <th>Mag</th>\n",
       "      <th>Nst</th>\n",
       "      <th>RMS</th>\n",
       "      <th>Event</th>\n",
       "      <th>ID</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9998.000000</td>\n",
       "      <td>9998.000000</td>\n",
       "      <td>9998.000000</td>\n",
       "      <td>9998.00000</td>\n",
       "      <td>9998.000000</td>\n",
       "      <td>9.947000e+03</td>\n",
       "      <td>1.800000e+01</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.506756</td>\n",
       "      <td>45.405202</td>\n",
       "      <td>57.593392</td>\n",
       "      <td>5.37223</td>\n",
       "      <td>164.561112</td>\n",
       "      <td>1.999149e+11</td>\n",
       "      <td>1.652515e+07</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>28.593770</td>\n",
       "      <td>119.249236</td>\n",
       "      <td>105.808366</td>\n",
       "      <td>0.41369</td>\n",
       "      <td>136.695802</td>\n",
       "      <td>1.062330e+10</td>\n",
       "      <td>1.697042e+07</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-65.712000</td>\n",
       "      <td>-179.994000</td>\n",
       "      <td>-0.530000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000e-02</td>\n",
       "      <td>1.129580e+05</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-18.294750</td>\n",
       "      <td>-69.652500</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>5.10000</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>2.003112e+11</td>\n",
       "      <td>5.434046e+06</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-2.424500</td>\n",
       "      <td>96.392500</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>5.20000</td>\n",
       "      <td>121.000000</td>\n",
       "      <td>2.005033e+11</td>\n",
       "      <td>5.793165e+06</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>18.309500</td>\n",
       "      <td>142.318750</td>\n",
       "      <td>45.300000</td>\n",
       "      <td>5.50000</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>2.006091e+11</td>\n",
       "      <td>2.149626e+07</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>86.276000</td>\n",
       "      <td>179.998000</td>\n",
       "      <td>691.600000</td>\n",
       "      <td>9.00000</td>\n",
       "      <td>929.000000</td>\n",
       "      <td>2.007103e+11</td>\n",
       "      <td>5.118347e+07</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Lat          Lon        Depth         Mag          Nst  \\\n",
       "count  9998.000000  9998.000000  9998.000000  9998.00000  9998.000000   \n",
       "mean      0.506756    45.405202    57.593392     5.37223   164.561112   \n",
       "std      28.593770   119.249236   105.808366     0.41369   136.695802   \n",
       "min     -65.712000  -179.994000    -0.530000     5.00000     0.000000   \n",
       "25%     -18.294750   -69.652500    10.000000     5.10000    64.000000   \n",
       "50%      -2.424500    96.392500    30.000000     5.20000   121.000000   \n",
       "75%      18.309500   142.318750    45.300000     5.50000   224.000000   \n",
       "max      86.276000   179.998000   691.600000     9.00000   929.000000   \n",
       "\n",
       "                RMS         Event   ID  \n",
       "count  9.947000e+03  1.800000e+01  0.0  \n",
       "mean   1.999149e+11  1.652515e+07  NaN  \n",
       "std    1.062330e+10  1.697042e+07  NaN  \n",
       "min    4.000000e-02  1.129580e+05  NaN  \n",
       "25%    2.003112e+11  5.434046e+06  NaN  \n",
       "50%    2.005033e+11  5.793165e+06  NaN  \n",
       "75%    2.006091e+11  2.149626e+07  NaN  \n",
       "max    2.007103e+11  5.118347e+07  NaN  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scatter plots are used to look at how two variables compare. For example, does the Magnitude of the earthquake correlate in some way to the number of stations that detected it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f348bb82a90>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='scatter', x='Mag', y='Nst')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clean this plot up a lot though. Lets start by looking at the machinery that creates it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Magnitude')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, figsize=(8,5))\n",
    "\n",
    "df.plot(ax=ax, kind='scatter', x='Mag', y='Nst', alpha=0.15, edgecolor='None'\n",
    "       ,color='violet')\n",
    "\n",
    "ax.set_ylim(0, 1000)\n",
    "ax.set_xlim(4.5, 10)\n",
    "ax.grid(True)\n",
    "ax.set_title('Does the number of stations change for the magnitude?')\n",
    "\n",
    "ax.set_ylabel('Number of Stations')\n",
    "ax.set_xlabel('Magnitude')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gutenberg-Richter plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In seismology, the Gutenberg–Richter law expresses the relationship between the magnitude and total number of earthquakes (that is the distribution) in any given region and time period of at least that magnitude.\n",
    "\n",
    "$log_{10}N = a -bM$\n",
    "\n",
    "or\n",
    "\n",
    "$N = 10^{a-bM}$\n",
    "\n",
    "Where:\n",
    "\n",
    "* $N$  is the number of events having a magnitude, $\\geq M$ \n",
    "* $a$  and $b$  are constants.\n",
    "\n",
    "It is assumed to be poissonian.\n",
    "\n",
    "To create the Gutenburg-Richter distribution of the earthquake magnitudes from the ANSS catalog, we are going to use numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6. , 6.3, 5.6, ..., 5.5, 5. , 5.5])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.Mag.values.round(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "hist, edges = np.histogram(a=df.Mag.values.round(1), bins=101, range=(0,10))\n",
    "chist = np.cumsum(hist[::-1])[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.0990099 ,  0.1980198 ,  0.2970297 ,  0.3960396 ,\n",
       "        0.4950495 ,  0.59405941,  0.69306931,  0.79207921,  0.89108911,\n",
       "        0.99009901,  1.08910891,  1.18811881,  1.28712871,  1.38613861,\n",
       "        1.48514851,  1.58415842,  1.68316832,  1.78217822,  1.88118812,\n",
       "        1.98019802,  2.07920792,  2.17821782,  2.27722772,  2.37623762,\n",
       "        2.47524752,  2.57425743,  2.67326733,  2.77227723,  2.87128713,\n",
       "        2.97029703,  3.06930693,  3.16831683,  3.26732673,  3.36633663,\n",
       "        3.46534653,  3.56435644,  3.66336634,  3.76237624,  3.86138614,\n",
       "        3.96039604,  4.05940594,  4.15841584,  4.25742574,  4.35643564,\n",
       "        4.45544554,  4.55445545,  4.65346535,  4.75247525,  4.85148515,\n",
       "        4.95049505,  5.04950495,  5.14851485,  5.24752475,  5.34653465,\n",
       "        5.44554455,  5.54455446,  5.64356436,  5.74257426,  5.84158416,\n",
       "        5.94059406,  6.03960396,  6.13861386,  6.23762376,  6.33663366,\n",
       "        6.43564356,  6.53465347,  6.63366337,  6.73267327,  6.83168317,\n",
       "        6.93069307,  7.02970297,  7.12871287,  7.22772277,  7.32673267,\n",
       "        7.42574257,  7.52475248,  7.62376238,  7.72277228,  7.82178218,\n",
       "        7.92079208,  8.01980198,  8.11881188,  8.21782178,  8.31683168,\n",
       "        8.41584158,  8.51485149,  8.61386139,  8.71287129,  8.81188119,\n",
       "        8.91089109,  9.00990099,  9.10891089,  9.20792079,  9.30693069,\n",
       "        9.40594059,  9.5049505 ,  9.6039604 ,  9.7029703 ,  9.8019802 ,\n",
       "        9.9009901 , 10.        ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,\n",
       "          0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,\n",
       "          0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,\n",
       "          0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,\n",
       "          0,    0,    0,    0,    0,    0, 2045, 1611, 1407, 1052,  843,\n",
       "        666,  508,  405,  295,  250,  203,  169,  121,   93,   72,   51,\n",
       "         47,   40,   25,   16,   10,   12,   11,    7,    7,    6,    9,\n",
       "          3,    2,    2,    2,    3,    0,    2,    0,    1,    1,    0,\n",
       "          0,    0,    1,    0,    0,    0,    0,    0,    0,    0,    0,\n",
       "          0,    0])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Gutenburg-Richter Distribution')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(edges[:-1], hist, marker='s', color='None', linestyle='')\n",
    "ax.plot(edges[:-1], chist, marker='^', color='red', linestyle='')\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylabel('N')\n",
    "ax.set_xlabel('Magnitude')\n",
    "# ax.set_xlim(4.5, 10)\n",
    "ax.set_title('Gutenburg-Richter Distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We quite frequently want to plot the fit of the a and b values of the gutenburg richter distribution. To do this we are going to use the equation below which calculates the maximum likelihood of the distribution and returns the parameters:\n",
    "\n",
    "* a - the \"productivity\" of the distribution, but really just the y-intercept\n",
    "* b - the \"mean magnitude\" but really it's just the slope\n",
    "* bstdev - the standard deviation of b\n",
    "* length - the number of earthquakes used to calculate the values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fmd_values(magnitudes, bin_width=0.1):\n",
    "    \"\"\"\n",
    "    params magnitudes : numpy.array\n",
    "    params bin_width : float\n",
    "    \n",
    "    returns a,b,bstd, n-values if above the earthquake count threshold\n",
    "    else returns np.nans\n",
    "    \"\"\"\n",
    "    length = magnitudes.shape[0]\n",
    "    minimum = magnitudes.min()\n",
    "    average = magnitudes.mean()\n",
    "    b_value = (1 / (average - (minimum - (bin_width/2)))) * np.log10(np.exp(1))\n",
    "    square_every_value = np.vectorize(lambda x: x**2)\n",
    "    b_stddev = square_every_value((magnitudes - average).sum()) / (length * (length - 1))\n",
    "    b_stddev = 2.3 * np.sqrt(b_stddev) * b_value**2\n",
    "    a_value = np.log10(length) + b_value * minimum\n",
    "    \n",
    "    return a_value, b_value, b_stddev, length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9.142773931842267, 1.0285721598851394, 1.535709686968831e-15, 9998)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fmd_values(df.Mag.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, b, bstd, n = fmd_values(df.Mag.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,10, 1000)\n",
    "y = 10**(a - b*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Gutenburg-Richter Distribution')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(edges[:-1], hist, marker='s', color='None', linestyle='')\n",
    "ax.plot(edges[:-1], chist, marker='^', color='red', linestyle='')\n",
    "\n",
    "ax.plot(x,y)\n",
    "\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylabel('N')\n",
    "ax.set_xlabel('Magnitude')\n",
    "ax.set_xlim(4.5, 10)\n",
    "ax.set_ylim(1e0, 1e5)\n",
    "ax.set_title('Gutenburg-Richter Distribution')"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}