catalog_Tools.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e05f2ba4",
   "metadata": {},
   "source": [
    "# Catalog Tools: How To\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "#### In this notebook we will show how to:\n",
    "\n",
    "<ol>\n",
    "    <li>Download catalogs</li>\n",
    "    <li>Generate synthetic earthquakes</li>\n",
    "    <li>Bin magnitudes</li>\n",
    "    <li>Calculate b-values</li>\n",
    "</ol>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "373d755b",
   "metadata": {},
   "source": [
    "## 0. Import general packages and catalog tools\n",
    "<font color=#208de2> In the main package, the analytic tools are available (b-value estimation), while other funcitons as catalog downloads, general functions and plotting are defined as subpackages. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0e98ffda",
   "metadata": {},
   "outputs": [],
   "source": [
    "#%matplotlib widget\n",
    "import datetime as dt\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "# catalog tools\n",
    "\n",
    "# analysis\n",
    "from catalog_tools import estimate_beta_elst\n",
    "from catalog_tools import estimate_beta_utsu\n",
    "from catalog_tools import estimate_beta_tinti\n",
    "from catalog_tools import estimate_beta_laplace\n",
    "\n",
    "# download\n",
    "from catalog_tools import download_catalog_sed\n",
    "from catalog_tools import prepare_sed_catalog\n",
    "\n",
    "# plots\n",
    "from catalog_tools import plot_cum_fmd\n",
    "from catalog_tools import plot_fmd\n",
    "\n",
    "# utils\n",
    "from catalog_tools import bin_to_precision\n",
    "from catalog_tools import simulate_magnitudes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab01940e",
   "metadata": {},
   "source": [
    "## 1. Download catalog"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc5d3af7",
   "metadata": {},
   "source": [
    "<font color=#208de2> Swiss Catalog. Start date and end date have to be defined as a datetime. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2c33dbd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "start_time = pd.to_datetime('2022/01/01')\n",
    "end_time = dt.datetime.now()\n",
    "min_magnitude = 0.5\n",
    "\n",
    "df = download_catalog_sed(start_time=start_time, end_time=end_time, min_magnitude=min_magnitude)\n",
    "df = prepare_sed_catalog(df, convert_to_mw=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f62bf93",
   "metadata": {},
   "source": [
    "<font color=#208de2> The output is a dataframe: </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5bf99c7a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>#EventID</th>\n",
       "      <th>time</th>\n",
       "      <th>latitude</th>\n",
       "      <th>longitude</th>\n",
       "      <th>depth</th>\n",
       "      <th>Author</th>\n",
       "      <th>Catalog</th>\n",
       "      <th>Contributor</th>\n",
       "      <th>ContributorID</th>\n",
       "      <th>mag_type</th>\n",
       "      <th>magnitude</th>\n",
       "      <th>MagAuthor</th>\n",
       "      <th>EventLocationName</th>\n",
       "      <th>event_type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023bztene</td>\n",
       "      <td>2023-01-29 04:26:46.302547</td>\n",
       "      <td>46.045869</td>\n",
       "      <td>6.906665</td>\n",
       "      <td>5.2</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>NaN</td>\n",
       "      <td>SED</td>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023bztene</td>\n",
       "      <td>MLhc</td>\n",
       "      <td>1.0</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>Chamonix F</td>\n",
       "      <td>earthquake</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023cacmgg</td>\n",
       "      <td>2023-01-29 09:07:17.278718</td>\n",
       "      <td>47.168178</td>\n",
       "      <td>9.440325</td>\n",
       "      <td>2.8</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>NaN</td>\n",
       "      <td>SED</td>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023cacmgg</td>\n",
       "      <td>MLhc</td>\n",
       "      <td>1.0</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>Buchs SG</td>\n",
       "      <td>earthquake</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023ceawhi</td>\n",
       "      <td>2023-01-31 12:36:45.308483</td>\n",
       "      <td>48.281636</td>\n",
       "      <td>7.656022</td>\n",
       "      <td>10.8</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>NaN</td>\n",
       "      <td>SED</td>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023ceawhi</td>\n",
       "      <td>MLhc</td>\n",
       "      <td>1.7</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>Colmar F</td>\n",
       "      <td>earthquake</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023cerrlm</td>\n",
       "      <td>2023-01-31 21:03:43.636245</td>\n",
       "      <td>45.892226</td>\n",
       "      <td>6.893018</td>\n",
       "      <td>3.0</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>NaN</td>\n",
       "      <td>SED</td>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023cerrlm</td>\n",
       "      <td>MLhc</td>\n",
       "      <td>0.6</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>Chamonix F</td>\n",
       "      <td>earthquake</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023cgjqje</td>\n",
       "      <td>2023-02-01 19:10:05.755205</td>\n",
       "      <td>47.374415</td>\n",
       "      <td>6.921971</td>\n",
       "      <td>5.6</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>NaN</td>\n",
       "      <td>SED</td>\n",
       "      <td>smi:ch.ethz.sed/sc20a/Event/2023cgjqje</td>\n",
       "      <td>MLhc</td>\n",
       "      <td>1.9</td>\n",
       "      <td>vsimon@sc20ag</td>\n",
       "      <td>Porrentruy JU</td>\n",
       "      <td>earthquake</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 #EventID                       time  \\\n",
       "6  smi:ch.ethz.sed/sc20a/Event/2023bztene 2023-01-29 04:26:46.302547   \n",
       "5  smi:ch.ethz.sed/sc20a/Event/2023cacmgg 2023-01-29 09:07:17.278718   \n",
       "4  smi:ch.ethz.sed/sc20a/Event/2023ceawhi 2023-01-31 12:36:45.308483   \n",
       "2  smi:ch.ethz.sed/sc20a/Event/2023cerrlm 2023-01-31 21:03:43.636245   \n",
       "1  smi:ch.ethz.sed/sc20a/Event/2023cgjqje 2023-02-01 19:10:05.755205   \n",
       "\n",
       "    latitude  longitude  depth         Author  Catalog Contributor  \\\n",
       "6  46.045869   6.906665    5.2  vsimon@sc20ag      NaN         SED   \n",
       "5  47.168178   9.440325    2.8  vsimon@sc20ag      NaN         SED   \n",
       "4  48.281636   7.656022   10.8  vsimon@sc20ag      NaN         SED   \n",
       "2  45.892226   6.893018    3.0  vsimon@sc20ag      NaN         SED   \n",
       "1  47.374415   6.921971    5.6  vsimon@sc20ag      NaN         SED   \n",
       "\n",
       "                            ContributorID mag_type  magnitude      MagAuthor  \\\n",
       "6  smi:ch.ethz.sed/sc20a/Event/2023bztene     MLhc        1.0  vsimon@sc20ag   \n",
       "5  smi:ch.ethz.sed/sc20a/Event/2023cacmgg     MLhc        1.0  vsimon@sc20ag   \n",
       "4  smi:ch.ethz.sed/sc20a/Event/2023ceawhi     MLhc        1.7  vsimon@sc20ag   \n",
       "2  smi:ch.ethz.sed/sc20a/Event/2023cerrlm     MLhc        0.6  vsimon@sc20ag   \n",
       "1  smi:ch.ethz.sed/sc20a/Event/2023cgjqje     MLhc        1.9  vsimon@sc20ag   \n",
       "\n",
       "  EventLocationName  event_type  \n",
       "6        Chamonix F  earthquake  \n",
       "5          Buchs SG  earthquake  \n",
       "4          Colmar F  earthquake  \n",
       "2        Chamonix F  earthquake  \n",
       "1     Porrentruy JU  earthquake  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa0b9f69",
   "metadata": {},
   "source": [
    "<font color=#208de2> We can plot the cumulative frequency-magnitude distribution (FMD): </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43d65445",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x131824940>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "font = {'size': 10}\n",
    "matplotlib.rc('font', **font)\n",
    "ax = plt.subplots(figsize=(8, 6))[1]\n",
    "plot_cum_fmd(ax, df['magnitude'], color='blue')\n",
    "plot_fmd(ax, df['magnitude'], color='red')\n",
    "\n",
    "ax.legend(['cumulative', 'non cumulative'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "357280e1",
   "metadata": {},
   "source": [
    "## 2. Generate synthetic earthquakes\n",
    "<font color=#208de2> First we need to define the number of earthquakes, the b-value and the completeness magnitude. For the b-value, note that beta is defined as the natural logarithm equivalent of the b-value. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "f2775fba",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 200\n",
    "b_value = 1\n",
    "beta = b_value*np.log(10)\n",
    "delta_m = 0.1\n",
    "mc = 3\n",
    "mc_generation = mc - delta_m / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0285f34",
   "metadata": {},
   "source": [
    "<font color=#208de2> Now we can generate a synthetic magnitude distribution: </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "25f3eb2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "mags = simulate_magnitudes(n,beta,mc_generation)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0920d1b",
   "metadata": {},
   "source": [
    "## 3. Bin magnitudes\n",
    "<font color=#208de2> In order to bin the magnitudes, we just need to define the step-size: </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "8784bb5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "mags_binned = bin_to_precision(mags, delta_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f2d067",
   "metadata": {},
   "source": [
    "## 4. Calculate b-values\n",
    "<font color=#208de2> We estimate the b-value from the binned sample. It is important to pass on the information of which binning (if any) is applied. Also, be cautious that beta is (as above) a factor of np.log(10) different to the b-value. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "64adffda",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_estimate = estimate_beta_tinti(mags_binned, mc=mc, delta_m=delta_m)\n",
    "# beta_estimate = estimate_beta_utsu(mags_binned,mc=mc, delta_m=delta_m)\n",
    "# beta_estimate = estimate_beta_elst(mags_binned, delta_m=delta_m)\n",
    "# beta_estimate = estimate_beta_laplace(mags_binned, delta_m=delta_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfc9800e",
   "metadata": {},
   "source": [
    "<font color=#208de2> We can plot the original and binned magnitudes and their respective b-value estimates now. Note that the data are offset by half the binning size so that the cumulative number is shown correctly. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "87bd325f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x135999990>"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "font = {'size': 10}\n",
    "matplotlib.rc('font', **font)\n",
    "ax = plt.subplots(figsize=(8, 6))[1]\n",
    "\n",
    "plot_cum_fmd(ax, mags, color='blue', b_value=b_value, mc=mc - delta_m/2)\n",
    "plot_cum_fmd(ax, mags_binned, color='red', b_value=beta_estimate/np.log(10), delta_m=delta_m)\n",
    "\n",
    "ax.legend(['Magnitudes original', 'True b-value', 'binned magnitudes', 'Fit Tinti'])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}