Mixing_models.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Mixing Models in Geochemistry\n",
    "**Jordan Lubbers and Chuck Lewis** <br>\n",
    "*College of Earth, Ocean and Atmospheric Sciences* <br>\n",
    "*Oregon State University*\n",
    "\n",
    "# Motivation\n",
    "This notebook shows how to construct various mixing models in geochemical data for both concentrations and isotope ratios:\n",
    "\n",
    "\n",
    "We will first go through it by hand and then show how it is done in the ```magmatrace``` module.\n",
    "\n",
    "\n",
    "For a more in depth explanation of mxing theory we suggest the following references:\n",
    "\n",
    "- [Albarede (1995): *Introduction to Geochemical Modeling*](https://www.cambridge.org/core/books/introduction-to-geochemical-modeling/020E2B1DCF69C3337C0022CAE419A5DC) Chapter 1 on mass balance, mixing, and fractionation. \n",
    "\n",
    "- [Faure 1998: *Principles and Applications of Geochemistry 2$^{nd}$ edition*](https://www.pearson.com/us/higher-education/program/Faure-Principles-and-Applications-of-Geochemistry-2nd-Edition/PGM110956.html) pg. 336 eqns 18.24-18.26 as well as\n",
    "- [Faure and Mensing (2009): *Isotopes Principles and Applications 3$^{rd}$ edition*](https://www.wiley.com/en-us/Isotopes%3A+Principles+and+Applications%2C+3rd+Edition-p-9780471384373https://www.wiley.com/en-us/Isotopes%3A+Principles+and+Applications%2C+3rd+Edition-p-9780471384373) chapter 16 on Mixing Theory\n",
    "\n",
    "\n",
    "## Two component mixing\n",
    "For a two component mixture $M$, comprised of components $A$ and $B$, the concentration (e.g. Sr) of mixture $M$ is defined as (Albarede 1995 eq. 1.1.3):\n",
    "\n",
    "$$C_M = C_Af_A + C_B(1 - f_A)$$\n",
    "\n",
    "where $C$ is the concentration and $f$ is the fraction of each component in the mixture.\n",
    "\n",
    "When investigating mixtures of ratios we use the Albarede (1995):\n",
    "\n",
    "$$ \\left(\\frac{C^{i2}}{C^{i1}}\\right)_M = \\left(\\frac{C^{i2}}{C^{i1}}\\right)_A{\\varphi_A}^{i1} + \\left(\\frac{C^{i2}}{C^{i1}}\\right)_B\\left(1 - {\\varphi_A}^{i1}\\right)$$ \n",
    "\n",
    "<br>\n",
    "<center> where: </center>\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "$$ {\\varphi_A}^{i1} = \\frac{C^{i1}_Af_a}{C^{i1}_M} $$\n",
    "\n",
    "We can think of $\\varphi$ as the mass fraction of species $i$ for each component in the mixture. Note...ratios may be other isotopic systems (e.g., $\\delta^{18}O$, Os, Nd, etc.) or ratios defined by two different elements (e.g. $\\frac{FeO}{MgO}$). \n",
    "\n",
    "\n",
    "## N component mixing\n",
    "A mixture of $n$ components will have a concentration (e.g. Sr) dictated by the following relationship:\n",
    "\n",
    "$$Sr_M = Sr_Af_A + Sr_Bf_B + Sr_Cf_C + ... Sr_nf_n$$ \n",
    "\n",
    "Expanding on two component mixtures from above we can get the general form for an $n$ component mixture of ratios (Albarede, 1995 eq. 1.3.1, 1.3.2):\n",
    "\n",
    "$$  \\left(\\frac{^{87}Sr}{^{86}Sr}\\right)_M = \\sum_{j=1}^{n}\\left(\\frac{^{87}Sr}{^{86}Sr}\\right)_j\\varphi_j    $$\n",
    "\n",
    "<br>\n",
    "<center> where: </center>\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "$$ \\varphi_j = \\frac{Sr_jf_j}{Sr_M}$$ \n",
    "\n",
    "Putting it all together:\n",
    "\n",
    "$$  \\left(\\frac{^{87}Sr}{^{86}Sr}\\right)_M = \\sum_{j=1}^{n}\\left(\\frac{^{87}Sr}{^{86}Sr}\\right)_j\\frac{Sr_jf_j}{Sr_M} $$\n",
    "\n",
    "Again, while we are using Sr isotope notation as an example here, ratios may be other isotopic systems (e.g., $\\delta^{18}O$, Os, Nd, etc.) or ratios defined by two different elements (e.g. $\\frac{FeO}{MgO}$).\n",
    "\n",
    "\n",
    "# Coded Examples "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MultipleLocator, FormatStrFormatter, AutoMinorLocator\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import magmatrace_current as mt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Concentration - Ratio\n",
    "\n",
    "Consider the following example from Albarede (1995) Table 1.6 where we have concentrations and isotope values for Sr from two end-members:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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>Sr_r</th>\n",
       "      <th>Sr_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>basalt</th>\n",
       "      <td>0.704</td>\n",
       "      <td>400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gneiss</th>\n",
       "      <td>0.712</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Sr_r  Sr_c\n",
       "basalt  0.704   400\n",
       "gneiss  0.712   100"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(\n",
    "    {\"Sr_r\": np.array([0.704, 0.712]), \"Sr_c\": np.array([400, 100]),},\n",
    "    index=[\"basalt\", \"gneiss\"],\n",
    ")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\frac{^{87}Sr}{^{86}Sr}$')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraction of gneiss in mixture\n",
    "f_gneiss = np.arange(0, 1.1, 0.1)\n",
    "\n",
    "\n",
    "# mixture concentrations\n",
    "sr_c_mixes = df.loc[\"gneiss\", \"Sr_c\"] * f_gneiss + df.loc[\"basalt\", \"Sr_c\"] * (\n",
    "    1 - f_gneiss\n",
    ")\n",
    "\n",
    "# mixture ratio compositions\n",
    "sr_r_mixes = df.loc[\"gneiss\", \"Sr_r\"] * (\n",
    "    (df.loc[\"gneiss\", \"Sr_c\"] * f_gneiss) / sr_c_mixes\n",
    ") + df.loc[\"basalt\", \"Sr_r\"] * (\n",
    "    (df.loc[\"basalt\", \"Sr_c\"] * (1 - f_gneiss)) / sr_c_mixes\n",
    ")\n",
    "\n",
    "# visualize\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "\n",
    "\n",
    "ax.plot(\n",
    "    1 / sr_c_mixes, sr_r_mixes, marker=\"o\", mec=\"k\", mfc=\"w\", c=\"k\",\n",
    ")\n",
    "\n",
    "ax.plot(\n",
    "    1 / df.loc[\"basalt\", \"Sr_c\"],\n",
    "    df.loc[\"basalt\"][\"Sr_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "ax.plot(\n",
    "    1 / df.loc[\"gneiss\", \"Sr_c\"],\n",
    "    df.loc[\"gneiss\"][\"Sr_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "\n",
    "\n",
    "for x, y, e in zip(df[\"Sr_c\"], df[\"Sr_r\"], df.index):\n",
    "    ax.annotate(\n",
    "        e, xy=(1 / x, y * 1.002), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "    )\n",
    "\n",
    "ax.set_xlim(0, 0.012)\n",
    "ax.set_ylim(0.7, 0.715)\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$\\frac{1}{Sr [ppm]}$\", fontsize=20)\n",
    "ax.set_ylabel(\n",
    "    r\"$\\frac{^{87}Sr}{^{86}Sr}$\", fontsize=30, labelpad=30, rotation=\"horizontal\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ratio - Ratio\n",
    "\n",
    "Again, consider another example from Albarede (1995) Table 1.7a where we have end-member compositions for some major element data from:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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>FeO</th>\n",
       "      <th>MgO</th>\n",
       "      <th>CaO</th>\n",
       "      <th>Na2O</th>\n",
       "      <th>FeO/MgO</th>\n",
       "      <th>Na2O/CaO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>basalt</th>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gneiss</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        FeO  MgO  CaO  Na2O  FeO/MgO  Na2O/CaO\n",
       "basalt   10   10   10     2      1.0       0.2\n",
       "gneiss    5    1    4     4      5.0       1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(\n",
    "    {\n",
    "        \"FeO\": np.array([10, 5]),\n",
    "        \"MgO\": np.array([10, 1]),\n",
    "        \"CaO\": np.array([10, 4]),\n",
    "        \"Na2O\": np.array([2, 4]),\n",
    "    },\n",
    "    index=[\"basalt\", \"gneiss\"],\n",
    ")\n",
    "\n",
    "df[\"FeO/MgO\"] = df[\"FeO\"] / df[\"MgO\"]\n",
    "df[\"Na2O/CaO\"] = df[\"Na2O\"] / df[\"CaO\"]\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\frac{Na_2O}{CaO}$')"
      ]
     },
     "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": [
    "f_gneiss = np.arange(0, 1.05, 0.05)\n",
    "mg_c_mixes = df.loc[\"gneiss\", \"MgO\"] * f_gneiss + df.loc[\"basalt\", \"MgO\"] * (\n",
    "    1 - f_gneiss\n",
    ")\n",
    "ca_c_mixes = df.loc[\"gneiss\", \"CaO\"] * f_gneiss + df.loc[\"basalt\", \"CaO\"] * (\n",
    "    1 - f_gneiss\n",
    ")\n",
    "\n",
    "femg_r_mixes = df.loc[\"gneiss\", \"FeO/MgO\"] * (\n",
    "    (df.loc[\"gneiss\", \"MgO\"] * f_gneiss) / mg_c_mixes\n",
    ") + df.loc[\"basalt\", \"FeO/MgO\"] * (\n",
    "    (df.loc[\"basalt\", \"MgO\"] * (1 - f_gneiss)) / mg_c_mixes\n",
    ")\n",
    "naca_r_mixes = df.loc[\"gneiss\", \"Na2O/CaO\"] * (\n",
    "    (df.loc[\"gneiss\", \"CaO\"] * f_gneiss) / ca_c_mixes\n",
    ") + df.loc[\"basalt\", \"Na2O/CaO\"] * (\n",
    "    (df.loc[\"basalt\", \"CaO\"] * (1 - f_gneiss)) / ca_c_mixes\n",
    ")\n",
    "\n",
    "\n",
    "# visualize\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "\n",
    "ax.plot(\n",
    "    femg_r_mixes, naca_r_mixes, marker=\"o\", mec=\"k\", mfc=\"w\", c=\"k\",\n",
    ")\n",
    "\n",
    "ax.plot(\n",
    "    df.loc[\"basalt\", \"FeO/MgO\"],\n",
    "    df.loc[\"basalt\"][\"Na2O/CaO\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "ax.plot(\n",
    "    df.loc[\"gneiss\", \"FeO/MgO\"],\n",
    "    df.loc[\"gneiss\"][\"Na2O/CaO\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "\n",
    "\n",
    "for x, y, e in zip(df[\"FeO/MgO\"], df[\"Na2O/CaO\"], df.index):\n",
    "    if e == \"basalt\":\n",
    "        ax.annotate(\n",
    "            e, xy=(x, y * 0.5), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "        )\n",
    "    else:\n",
    "        ax.annotate(\n",
    "            e, xy=(x, y * 0.9), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "        )\n",
    "\n",
    "ax.set_xlim(0, 5.5)\n",
    "ax.set_ylim(0, 1.2)\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$\\frac{FeO}{MgO}$\", fontsize=20)\n",
    "ax.set_ylabel(r\"$\\frac{Na_2O}{CaO}$\", fontsize=30, labelpad=30, rotation=\"horizontal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3-component mixing with ratios\n",
    "To quote Albarede (1995):\n",
    "> Ratio-ratio relationships in mixtures inolving three or more end-members are no more difficult to handle than binary mixtures. Curved triangles are obtained in binary plots and curious surfaces may be drawn in a 3-D space using 3-D plotting programs. Different concentration ratios may produce widely different triangles and singular points may be created for a particular range of parameters.\n",
    "\n",
    "Consider the following example from Albarede (1995), Table 1.10 where we have Sr and Nd isotopic compositions for different mantle end-members."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "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>Sr_r</th>\n",
       "      <th>Sr_c</th>\n",
       "      <th>Nd_r</th>\n",
       "      <th>Nd_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>DM</th>\n",
       "      <td>0.703</td>\n",
       "      <td>40</td>\n",
       "      <td>0.5131</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EM1</th>\n",
       "      <td>0.705</td>\n",
       "      <td>400</td>\n",
       "      <td>0.5118</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EM2</th>\n",
       "      <td>0.710</td>\n",
       "      <td>20</td>\n",
       "      <td>0.5121</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Sr_r  Sr_c    Nd_r  Nd_c\n",
       "DM   0.703    40  0.5131     5\n",
       "EM1  0.705   400  0.5118    10\n",
       "EM2  0.710    20  0.5121    10"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(\n",
    "    {\n",
    "        \"Sr_r\": np.array([0.703, 0.705, 0.710]),\n",
    "        \"Sr_c\": np.array([40, 400, 20]),\n",
    "        \"Nd_r\": np.array([0.5131, 0.5118, 0.5121]),\n",
    "        \"Nd_c\": np.array([5, 10, 10]),\n",
    "    },\n",
    "    index=[\"DM\", \"EM1\", \"EM2\"],\n",
    ")\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any given combination of $f$ values (e.g., $f_{DM}$, $f_{EM1}$, $f_{EM2}$) we can use the Albarede equation 1.3.1 to calculate the ratio composition ($R_M$) of our mixture the following way:\n",
    "\n",
    "$$ R_M = R_{DM}\\frac{C_{DM}f_{DM}}{C_M} + R_{EM1}\\frac{C_{EM1}f_{EM1}}{C_M} + R_{EM2}\\frac{C_{EM2}f_{EM2}}{C_M} $$\n",
    "\n",
    "with an array of $f$ values for each of the end-members as follows:\n",
    "\n",
    "```python\n",
    "f = np.arange(0,1.1,.1)\n",
    "```\n",
    "\n",
    "Expanding on this, we can think of our mixing model as a mesh in 2-D space that is comprised of a point for each combination of the three $f$ arrays that sums to 1. To do this, we get combinations of all possible f values and then filter them where the sum of all three components is 1.\n",
    "\n",
    "```python\n",
    "# get all possible combinations\n",
    "a = np.array(np.meshgrid(f, f, f)).T.reshape(-1,3)\n",
    "\n",
    "# filter for where they sum to unity\n",
    "f_vals = a[a.sum(axis = 1) == 1]\n",
    "```\n",
    "\n",
    "For a mixing model that is spaced at 10% increments of each component this is 62 points. For a mixing model that is spaced at 5% increments this number increases to 217, and for a mixing model that is spaced at 1% increments this is 5027."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "points in mixing mesh: 5027 \n",
      "for 101 f points\n"
     ]
    },
    {
     "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>f_DM</th>\n",
       "      <th>f_EM1</th>\n",
       "      <th>f_EM2</th>\n",
       "      <th>Sr_c_mix</th>\n",
       "      <th>Nd_c_mix</th>\n",
       "      <th>Sr_r_mix</th>\n",
       "      <th>Nd_r_mix</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>10.00</td>\n",
       "      <td>0.705000</td>\n",
       "      <td>0.511800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.0</td>\n",
       "      <td>396.4</td>\n",
       "      <td>9.95</td>\n",
       "      <td>0.704998</td>\n",
       "      <td>0.511807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.0</td>\n",
       "      <td>392.8</td>\n",
       "      <td>9.90</td>\n",
       "      <td>0.704996</td>\n",
       "      <td>0.511813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.0</td>\n",
       "      <td>389.2</td>\n",
       "      <td>9.85</td>\n",
       "      <td>0.704994</td>\n",
       "      <td>0.511820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.04</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.0</td>\n",
       "      <td>385.6</td>\n",
       "      <td>9.80</td>\n",
       "      <td>0.704992</td>\n",
       "      <td>0.511827</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   f_DM  f_EM1  f_EM2  Sr_c_mix  Nd_c_mix  Sr_r_mix  Nd_r_mix\n",
       "0  0.00   1.00    0.0     400.0     10.00  0.705000  0.511800\n",
       "1  0.01   0.99    0.0     396.4      9.95  0.704998  0.511807\n",
       "2  0.02   0.98    0.0     392.8      9.90  0.704996  0.511813\n",
       "3  0.03   0.97    0.0     389.2      9.85  0.704994  0.511820\n",
       "4  0.04   0.96    0.0     385.6      9.80  0.704992  0.511827"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# f value array that will be used for each component\n",
    "f = np.arange(0, 1.01, 0.01)\n",
    "\n",
    "# all possible combinations for three f arrays\n",
    "a = np.array(np.meshgrid(f, f, f)).T.reshape(-1, 3)\n",
    "\n",
    "# where the combinations sum to 1\n",
    "f_vals = a[a.sum(axis=1) == 1]\n",
    "\n",
    "# concentrations of the mixture for Sr and Nd\n",
    "Sr_mixes = (\n",
    "    df.loc[\"DM\", \"Sr_c\"] * f_vals[:, 0]\n",
    "    + df.loc[\"EM1\", \"Sr_c\"] * f_vals[:, 1]\n",
    "    + df.loc[\"EM2\", \"Sr_c\"] * f_vals[:, 2]\n",
    ")\n",
    "Nd_mixes = (\n",
    "    df.loc[\"DM\", \"Nd_c\"] * f_vals[:, 0]\n",
    "    + df.loc[\"EM1\", \"Nd_c\"] * f_vals[:, 1]\n",
    "    + df.loc[\"EM2\", \"Nd_c\"] * f_vals[:, 2]\n",
    ")\n",
    "\n",
    "# ratio values of the mixture for 87Sr/86Sr and 144Nd/143Nd\n",
    "Sr_r_mixes = (\n",
    "    df.loc[\"DM\", \"Sr_r\"] * ((f_vals[:, 0] * df.loc[\"DM\", \"Sr_c\"]) / Sr_mixes)\n",
    "    + df.loc[\"EM1\", \"Sr_r\"] * ((f_vals[:, 1] * df.loc[\"EM1\", \"Sr_c\"]) / Sr_mixes)\n",
    "    + df.loc[\"EM2\", \"Sr_r\"] * ((f_vals[:, 2] * df.loc[\"EM2\", \"Sr_c\"]) / Sr_mixes)\n",
    ")\n",
    "\n",
    "Nd_r_mixes = (\n",
    "    df.loc[\"DM\", \"Nd_r\"] * ((f_vals[:, 0] * df.loc[\"DM\", \"Nd_c\"]) / Nd_mixes)\n",
    "    + df.loc[\"EM1\", \"Nd_r\"] * ((f_vals[:, 1] * df.loc[\"EM1\", \"Nd_c\"]) / Nd_mixes)\n",
    "    + df.loc[\"EM2\", \"Nd_r\"] * ((f_vals[:, 2] * df.loc[\"EM2\", \"Nd_c\"]) / Nd_mixes)\n",
    ")\n",
    "\n",
    "\n",
    "# Combine it all into one dataframe\n",
    "results = pd.DataFrame(\n",
    "    {\n",
    "        \"f_DM\": f_vals[:, 0],\n",
    "        \"f_EM1\": f_vals[:, 1],\n",
    "        \"f_EM2\": f_vals[:, 2],\n",
    "        \"Sr_c_mix\": Sr_mixes,\n",
    "        \"Nd_c_mix\": Nd_mixes,\n",
    "        \"Sr_r_mix\": Sr_r_mixes,\n",
    "        \"Nd_r_mix\": Nd_r_mixes,\n",
    "    }\n",
    ")\n",
    "print(\"points in mixing mesh: {} \\nfor {} f points\".format(f_vals.shape[0], len(f)))\n",
    "results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "DM = results.loc[results[\"f_DM\"] == 0]\n",
    "EM1 = results.loc[results[\"f_EM1\"] == 0]\n",
    "EM2 = results.loc[results[\"f_EM2\"] == 0]\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(12, 5))\n",
    "\n",
    "ax[0].plot(\n",
    "    DM[\"Sr_r_mix\"], DM[\"Nd_r_mix\"], \"k--.\", markevery=20,\n",
    ")\n",
    "ax[0].plot(\n",
    "    EM1[\"Sr_r_mix\"], EM1[\"Nd_r_mix\"], \"k--.\", markevery=20,\n",
    ")\n",
    "ax[0].plot(\n",
    "    EM2[\"Sr_r_mix\"], EM2[\"Nd_r_mix\"], \"k--.\", markevery=20,\n",
    ")\n",
    "\n",
    "ax[0].plot(\n",
    "    df[\"Sr_r\"], df[\"Nd_r\"], marker=\"o\", ls=\"\", ms=30, mec=\"k\", mfc=\"w\", zorder=10\n",
    ")\n",
    "\n",
    "for val in np.array([0.2, 0.4, 0.6, 0.8]):\n",
    "\n",
    "    ax[0].plot(\n",
    "        results[results[\"f_DM\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_DM\"] == val][\"Nd_r_mix\"],\n",
    "        \"k-\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "    ax[0].plot(\n",
    "        results[results[\"f_EM1\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_EM1\"] == val][\"Nd_r_mix\"],\n",
    "        \"k-\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "    ax[0].plot(\n",
    "        results[results[\"f_EM2\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_EM2\"] == val][\"Nd_r_mix\"],\n",
    "        \"k-\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "\n",
    "\n",
    "for x, y, e in zip(df[\"Sr_r\"], df[\"Nd_r\"], df.index):\n",
    "    ax[0].annotate(e, xy=(x, y), fontsize=14, ha=\"center\", va=\"center\", zorder=10)\n",
    "\n",
    "ax[0].grid(ls=\":\", zorder=0)\n",
    "\n",
    "ax[0].set_xlim(0.7, 0.712)\n",
    "ax[0].set_ylim(0.5115, 0.5135)\n",
    "\n",
    "ax[0].set_xlabel(r\"$\\frac{^{87}Sr}{^{86}Sr}$\", fontsize=30)\n",
    "ax[0].set_ylabel(\n",
    "    r\"$\\frac{^{143}Nd}{^{144}Nd}$\", fontsize=30, labelpad=30, rotation=\"horizontal\"\n",
    ")\n",
    "\n",
    "ax[1].grid(ls=\":\", zorder=0)\n",
    "s = ax[1].scatter(\n",
    "    results[\"Sr_r_mix\"], results[\"Nd_r_mix\"], ec=\"none\", c=results[\"f_DM\"], zorder=2\n",
    ")\n",
    "\n",
    "cbar = fig.colorbar(s, ax=ax[1])\n",
    "cbar.set_label(label=\"$f_{DM}$\", fontsize=20)\n",
    "\n",
    "# plotting the 80% line for each component\n",
    "for val in np.array([0.8]):\n",
    "\n",
    "    ax[1].plot(\n",
    "        results[results[\"f_DM\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_DM\"] == val][\"Nd_r_mix\"],\n",
    "        \"r-\",\n",
    "        lw=1,\n",
    "    )\n",
    "    ax[1].plot(\n",
    "        results[results[\"f_EM1\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_EM1\"] == val][\"Nd_r_mix\"],\n",
    "        \"r-\",\n",
    "        lw=1,\n",
    "    )\n",
    "    ax[1].plot(\n",
    "        results[results[\"f_EM2\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_EM2\"] == val][\"Nd_r_mix\"],\n",
    "        \"r-\",\n",
    "        lw=1,\n",
    "    )\n",
    "\n",
    "ax[1].plot(\n",
    "    df[\"Sr_r\"], df[\"Nd_r\"], marker=\"o\", ls=\"\", ms=30, mec=\"k\", mfc=\"White\", zorder=10\n",
    ")\n",
    "\n",
    "for x, y, e in zip(df[\"Sr_r\"], df[\"Nd_r\"], df.index):\n",
    "    ax[1].annotate(e, xy=(x, y), fontsize=14, ha=\"center\", va=\"center\", zorder=10)\n",
    "\n",
    "ax[1].set_xlim(0.7, 0.712)\n",
    "ax[1].set_ylim(0.5115, 0.5135)\n",
    "\n",
    "ax[1].set_xlabel(r\"$\\frac{^{87}Sr}{^{86}Sr}$\", fontsize=30)\n",
    "ax[1].text(\n",
    "    0.5,\n",
    "    0.85,\n",
    "    \"red lines are f = 0.8 \\n for each component\",\n",
    "    transform=ax[1].transAxes,\n",
    "    fontsize=12,\n",
    ")\n",
    "\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using ```magmatrace```\n",
    "\n",
    "The ```magmatrace``` module has a function, ```ratio_mixing```, designed to calculate concentrations of mixtures and ratio compositions of mixtures using Albarede (1995)'s Equation 1.3.1. \n",
    "\n",
    "From the docs:\n",
    "\n",
    "```\n",
    "ratio_mixing(df, n_components, resolution=0.1)\n",
    "    Mixing of ratios as described by Albarede 1995\n",
    "    Introduction to Geochemical Modeling equation 1.3.1\n",
    "    \n",
    "    Inputs:\n",
    "    \n",
    "    df | pandas DataFrame\n",
    "    \n",
    "    DataFrame of inputs. should be formatted as follows:\n",
    "    \n",
    "    For 2 component mixing:\n",
    "    \n",
    "    Index|Element1_c|Element1_r|Element2_c|Element2_r\n",
    "    -------------------------------------------------\n",
    "      A  |          |          |          |\n",
    "    -------------------------------------------------  \n",
    "      B  |          |          |          |\n",
    "    \n",
    "      \n",
    "    \n",
    "    For 3 component mixing:\n",
    "    \n",
    "    Index|Element1_c|Element1_r|Element2_c|Element2_r\n",
    "    -------------------------------------------------\n",
    "      A  |          |          |          |\n",
    "    -------------------------------------------------  \n",
    "      B  |          |          |          |\n",
    "    -------------------------------------------------\n",
    "      C  |          |          |          |\n",
    "      \n",
    "      \n",
    "    Where the name of each component is the index of the dataframe and the \n",
    "    concentration and ratio columns for each elemental species contain \"_c\" and \"_r\" \n",
    "    somewhere in the column header, respectively. \n",
    "    \n",
    "    n_components | int\n",
    "    \n",
    "    Number of end-member components (either 2 or 3)\n",
    "    \n",
    "    resolution | float\n",
    "    \n",
    "    The resolution you want to run your mixing model at. This is a number between 0.01 \n",
    "    and 0.5. This is how far apart to space points in the eventual mixing mesh\n",
    "    (e.g. .1 will return a mixing mesh spaced by 1O% increments for each component)\n",
    "    \n",
    "    Default is 0.1\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    Returns:\n",
    "    \n",
    "    results | pandas DataFrame\n",
    "    \n",
    "    The results of the mixing model that is n x 7 in shape:\n",
    "    \n",
    "    f_A|f_B|f_C|Element1_c_mix|Element2_c_mix|Element1_r_mix|Element2_r_mix\n",
    "    -----------------------------------------------------------------------\n",
    "    \n",
    "    Where f columns are fraction of each component in the mixture and other columns\n",
    "    Are for the concentrations and ratios of the mixture for each respective combination\n",
    "    of f values\n",
    "```\n",
    "\n",
    "Below we will create some figures from Chapter 1 in Albarede 1995, similar to above, only now we'll use the ```ratio_mixing``` function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "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>Sr_r</th>\n",
       "      <th>Sr_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>basalt</th>\n",
       "      <td>0.704</td>\n",
       "      <td>400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gneiss</th>\n",
       "      <td>0.712</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Sr_r  Sr_c\n",
       "basalt  0.704   400\n",
       "gneiss  0.712   100"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_1_6 = pd.DataFrame(\n",
    "    {\"Sr_r\": np.array([0.704, 0.712]), \"Sr_c\": np.array([400, 100]),},\n",
    "    index=[\"basalt\", \"gneiss\"],\n",
    ")\n",
    "table_1_6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "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>f_basalt</th>\n",
       "      <th>f_gneiss</th>\n",
       "      <th>Sr_c_mix</th>\n",
       "      <th>Sr_r_mix</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>100.0</td>\n",
       "      <td>0.712000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.05</td>\n",
       "      <td>0.95</td>\n",
       "      <td>115.0</td>\n",
       "      <td>0.710609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.90</td>\n",
       "      <td>130.0</td>\n",
       "      <td>0.709538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.85</td>\n",
       "      <td>145.0</td>\n",
       "      <td>0.708690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.80</td>\n",
       "      <td>160.0</td>\n",
       "      <td>0.708000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   f_basalt  f_gneiss  Sr_c_mix  Sr_r_mix\n",
       "0      0.00      1.00     100.0  0.712000\n",
       "1      0.05      0.95     115.0  0.710609\n",
       "2      0.10      0.90     130.0  0.709538\n",
       "3      0.15      0.85     145.0  0.708690\n",
       "4      0.20      0.80     160.0  0.708000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Call the function...that's it!\n",
    "results1 = mt.ratio_mixing(table_1_6, n_components=2, resolution=0.05)\n",
    "results1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Figure 1.5 Albarede (1995)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# visualize\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "\n",
    "\n",
    "ax.plot(\n",
    "    1 / results1[\"Sr_c_mix\"], results1[\"Sr_r_mix\"], marker=\"o\", mec=\"k\", mfc=\"w\", c=\"k\",\n",
    ")\n",
    "\n",
    "ax.plot(\n",
    "    1 / table_1_6.loc[\"basalt\", \"Sr_c\"],\n",
    "    table_1_6.loc[\"basalt\"][\"Sr_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "ax.plot(\n",
    "    1 / table_1_6.loc[\"gneiss\", \"Sr_c\"],\n",
    "    table_1_6.loc[\"gneiss\"][\"Sr_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "\n",
    "\n",
    "for x, y, e in zip(table_1_6[\"Sr_c\"], table_1_6[\"Sr_r\"], table_1_6.index):\n",
    "    ax.annotate(\n",
    "        e, xy=(1 / x, y * 1.002), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "    )\n",
    "\n",
    "ax.set_xlim(0, 0.012)\n",
    "ax.set_ylim(0.7, 0.715)\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$\\frac{1}{Sr [ppm]}$\", fontsize=20)\n",
    "ax.set_ylabel(\n",
    "    r\"$\\frac{^{87}Sr}{^{86}Sr}$\", fontsize=30, labelpad=30, rotation=\"horizontal\"\n",
    ")\n",
    "\n",
    "ax.set_title('Figure 1.5 Albarede (1995)',fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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>FeO</th>\n",
       "      <th>MgO_c</th>\n",
       "      <th>CaO_c</th>\n",
       "      <th>Na2O</th>\n",
       "      <th>FeO/MgO_r</th>\n",
       "      <th>Na2O/CaO_r</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>basalt</th>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gneiss</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        FeO  MgO_c  CaO_c  Na2O  FeO/MgO_r  Na2O/CaO_r\n",
       "basalt   10     10     10     2        1.0         0.2\n",
       "gneiss    5      1      4     4        5.0         1.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# denote columns to be used for calculating phi paramter with \"_c\"\n",
    "# remember from Albarede 1.3.2 above that the phi parameter is calculated\n",
    "# using the denominator of the ratio (in this case the MgO and CaO columns)\n",
    "\n",
    "table_1_7 = pd.DataFrame(\n",
    "    {\n",
    "        \"FeO\": np.array([10, 5]),\n",
    "        \"MgO_c\": np.array([10, 1]),\n",
    "        \"CaO_c\": np.array([10, 4]),\n",
    "        \"Na2O\": np.array([2, 4]),\n",
    "    },\n",
    "    index=[\"basalt\", \"gneiss\"],\n",
    ")\n",
    "\n",
    "table_1_7[\"FeO/MgO_r\"] = table_1_7[\"FeO\"] / table_1_7[\"MgO_c\"]\n",
    "table_1_7[\"Na2O/CaO_r\"] = table_1_7[\"Na2O\"] / table_1_7[\"CaO_c\"]\n",
    "table_1_7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "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>f_basalt</th>\n",
       "      <th>f_gneiss</th>\n",
       "      <th>MgO_c_mix</th>\n",
       "      <th>CaO_c_mix</th>\n",
       "      <th>FeO/MgO_r_mix</th>\n",
       "      <th>Na2O/CaO_r_mix</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.05</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.45</td>\n",
       "      <td>4.3</td>\n",
       "      <td>3.620690</td>\n",
       "      <td>0.906977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.90</td>\n",
       "      <td>1.90</td>\n",
       "      <td>4.6</td>\n",
       "      <td>2.894737</td>\n",
       "      <td>0.826087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.85</td>\n",
       "      <td>2.35</td>\n",
       "      <td>4.9</td>\n",
       "      <td>2.446809</td>\n",
       "      <td>0.755102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.80</td>\n",
       "      <td>2.80</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.142857</td>\n",
       "      <td>0.692308</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   f_basalt  f_gneiss  MgO_c_mix  CaO_c_mix  FeO/MgO_r_mix  Na2O/CaO_r_mix\n",
       "0      0.00      1.00       1.00        4.0       5.000000        1.000000\n",
       "1      0.05      0.95       1.45        4.3       3.620690        0.906977\n",
       "2      0.10      0.90       1.90        4.6       2.894737        0.826087\n",
       "3      0.15      0.85       2.35        4.9       2.446809        0.755102\n",
       "4      0.20      0.80       2.80        5.2       2.142857        0.692308"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results2 = mt.ratio_mixing(table_1_7, n_components=2, resolution=0.05)\n",
    "results2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Figure 1.6 Albarede (1995)')"
      ]
     },
     "execution_count": 14,
     "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": [
    "# visualize\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "\n",
    "ax.plot(\n",
    "    results2[\"FeO/MgO_r_mix\"],\n",
    "    results2[\"Na2O/CaO_r_mix\"],\n",
    "    marker=\"o\",\n",
    "    mec=\"k\",\n",
    "    mfc=\"w\",\n",
    "    c=\"k\",\n",
    ")\n",
    "\n",
    "ax.plot(\n",
    "    table_1_7.loc[\"basalt\", \"FeO/MgO_r\"],\n",
    "    table_1_7.loc[\"basalt\"][\"Na2O/CaO_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "ax.plot(\n",
    "    table_1_7.loc[\"gneiss\", \"FeO/MgO_r\"],\n",
    "    table_1_7.loc[\"gneiss\"][\"Na2O/CaO_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "\n",
    "\n",
    "for x, y, e in zip(table_1_7[\"FeO/MgO_r\"], table_1_7[\"Na2O/CaO_r\"], table_1_7.index):\n",
    "    if e == \"basalt\":\n",
    "        ax.annotate(\n",
    "            e, xy=(x, y * 0.5), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "        )\n",
    "    else:\n",
    "        ax.annotate(\n",
    "            e, xy=(x, y * 0.9), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "        )\n",
    "\n",
    "ax.set_xlim(0, 5.5)\n",
    "ax.set_ylim(0, 1.2)\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$\\frac{FeO}{MgO}$\", fontsize=20)\n",
    "ax.set_ylabel(r\"$\\frac{Na_2O}{CaO}$\", fontsize=30, labelpad=30, rotation=\"horizontal\")\n",
    "ax.set_title('Figure 1.6 Albarede (1995)',fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "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>Sr_r</th>\n",
       "      <th>Sr_c</th>\n",
       "      <th>Nd_r</th>\n",
       "      <th>Nd_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>basalt</th>\n",
       "      <td>0.703</td>\n",
       "      <td>100</td>\n",
       "      <td>0.513</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gneiss</th>\n",
       "      <td>0.710</td>\n",
       "      <td>200</td>\n",
       "      <td>0.511</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Sr_r  Sr_c   Nd_r  Nd_c\n",
       "basalt  0.703   100  0.513     2\n",
       "gneiss  0.710   200  0.511    20"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_1_8 = table_1_10 = pd.DataFrame(\n",
    "    {\n",
    "        \"Sr_r\": np.array([.703,.710]),\n",
    "        \"Sr_c\": np.array([100,200]),\n",
    "        \"Nd_r\": np.array([.513,.511]),\n",
    "        \"Nd_c\": np.array([2,20]),\n",
    "    },\n",
    "    index=[\"basalt\", \"gneiss\"],\n",
    ")\n",
    "table_1_8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "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>f_basalt</th>\n",
       "      <th>f_gneiss</th>\n",
       "      <th>Sr_c_mix</th>\n",
       "      <th>Nd_c_mix</th>\n",
       "      <th>Sr_r_mix</th>\n",
       "      <th>Nd_r_mix</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>200.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.710000</td>\n",
       "      <td>0.511000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.05</td>\n",
       "      <td>0.95</td>\n",
       "      <td>195.0</td>\n",
       "      <td>19.1</td>\n",
       "      <td>0.709821</td>\n",
       "      <td>0.511010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.90</td>\n",
       "      <td>190.0</td>\n",
       "      <td>18.2</td>\n",
       "      <td>0.709632</td>\n",
       "      <td>0.511022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.85</td>\n",
       "      <td>185.0</td>\n",
       "      <td>17.3</td>\n",
       "      <td>0.709432</td>\n",
       "      <td>0.511035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.80</td>\n",
       "      <td>180.0</td>\n",
       "      <td>16.4</td>\n",
       "      <td>0.709222</td>\n",
       "      <td>0.511049</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   f_basalt  f_gneiss  Sr_c_mix  Nd_c_mix  Sr_r_mix  Nd_r_mix\n",
       "0      0.00      1.00     200.0      20.0  0.710000  0.511000\n",
       "1      0.05      0.95     195.0      19.1  0.709821  0.511010\n",
       "2      0.10      0.90     190.0      18.2  0.709632  0.511022\n",
       "3      0.15      0.85     185.0      17.3  0.709432  0.511035\n",
       "4      0.20      0.80     180.0      16.4  0.709222  0.511049"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results4 = mt.ratio_mixing(table_1_8,n_components = 2,resolution = .05)\n",
    "results4.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Figure 1.7 Albarede (1995)')"
      ]
     },
     "execution_count": 17,
     "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": [
    "# visualize\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "\n",
    "ax.plot(\n",
    "    results4[\"Sr_r_mix\"],\n",
    "    results4[\"Nd_r_mix\"],\n",
    "    marker=\"o\",\n",
    "    mec=\"k\",\n",
    "    mfc=\"w\",\n",
    "    c=\"k\",\n",
    ")\n",
    "\n",
    "ax.plot(\n",
    "    table_1_8.loc[\"basalt\", \"Sr_r\"],\n",
    "    table_1_8.loc[\"basalt\"][\"Nd_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "ax.plot(\n",
    "    table_1_8.loc[\"gneiss\", \"Sr_r\"],\n",
    "    table_1_8.loc[\"gneiss\"][\"Nd_r\"],\n",
    "    marker=\"o\",\n",
    "    ms=\"15\",\n",
    "    mfc=\"k\",\n",
    "    mec=\"r\",\n",
    ")\n",
    "\n",
    "\n",
    "for x, y, e in zip(table_1_8[\"Sr_r\"], table_1_8[\"Nd_r\"], table_1_8.index):\n",
    "    ax.annotate(\n",
    "        e, xy=(x, y*1.001), fontsize=14, ha=\"center\", va=\"center\", zorder=10\n",
    "    )\n",
    " \n",
    "\n",
    "ax.set_xlim(.7,.712)\n",
    "ax.set_ylim(.510,.514)\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$\\frac{^{87}Sr}{^{86}Sr}$\", fontsize=30)\n",
    "ax.set_ylabel(\n",
    "    r\"$\\frac{^{143}Nd}{^{144}Nd}$\", fontsize=30, labelpad=30, rotation=\"horizontal\"\n",
    ")\n",
    "ax.set_title('Figure 1.7 Albarede (1995)',fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "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>Sr_r</th>\n",
       "      <th>Sr_c</th>\n",
       "      <th>Nd_r</th>\n",
       "      <th>Nd_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>DM</th>\n",
       "      <td>0.703</td>\n",
       "      <td>40</td>\n",
       "      <td>0.5131</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EM1</th>\n",
       "      <td>0.705</td>\n",
       "      <td>400</td>\n",
       "      <td>0.5118</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EM2</th>\n",
       "      <td>0.710</td>\n",
       "      <td>20</td>\n",
       "      <td>0.5121</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Sr_r  Sr_c    Nd_r  Nd_c\n",
       "DM   0.703    40  0.5131     5\n",
       "EM1  0.705   400  0.5118    10\n",
       "EM2  0.710    20  0.5121    10"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_1_10 = pd.DataFrame(\n",
    "    {\n",
    "        \"Sr_r\": np.array([0.703, 0.705, 0.710]),\n",
    "        \"Sr_c\": np.array([40, 400, 20]),\n",
    "        \"Nd_r\": np.array([0.5131, 0.5118, 0.5121]),\n",
    "        \"Nd_c\": np.array([5, 10, 10]),\n",
    "    },\n",
    "    index=[\"DM\", \"EM1\", \"EM2\"],\n",
    ")\n",
    "table_1_10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "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>f_DM</th>\n",
       "      <th>f_EM1</th>\n",
       "      <th>f_EM2</th>\n",
       "      <th>Sr_c_mix</th>\n",
       "      <th>Nd_c_mix</th>\n",
       "      <th>Sr_r_mix</th>\n",
       "      <th>Nd_r_mix</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>10.00</td>\n",
       "      <td>0.705000</td>\n",
       "      <td>0.511800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.0</td>\n",
       "      <td>396.4</td>\n",
       "      <td>9.95</td>\n",
       "      <td>0.704998</td>\n",
       "      <td>0.511807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.0</td>\n",
       "      <td>392.8</td>\n",
       "      <td>9.90</td>\n",
       "      <td>0.704996</td>\n",
       "      <td>0.511813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.0</td>\n",
       "      <td>389.2</td>\n",
       "      <td>9.85</td>\n",
       "      <td>0.704994</td>\n",
       "      <td>0.511820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.04</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.0</td>\n",
       "      <td>385.6</td>\n",
       "      <td>9.80</td>\n",
       "      <td>0.704992</td>\n",
       "      <td>0.511827</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   f_DM  f_EM1  f_EM2  Sr_c_mix  Nd_c_mix  Sr_r_mix  Nd_r_mix\n",
       "0  0.00   1.00    0.0     400.0     10.00  0.705000  0.511800\n",
       "1  0.01   0.99    0.0     396.4      9.95  0.704998  0.511807\n",
       "2  0.02   0.98    0.0     392.8      9.90  0.704996  0.511813\n",
       "3  0.03   0.97    0.0     389.2      9.85  0.704994  0.511820\n",
       "4  0.04   0.96    0.0     385.6      9.80  0.704992  0.511827"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results3 = mt.ratio_mixing(table_1_10, n_components=3, resolution=0.01)\n",
    "results3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Figure 1.9 Albarede (1995)')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "DM = results3.loc[results[\"f_DM\"] == 0]\n",
    "EM1 = results3.loc[results[\"f_EM1\"] == 0]\n",
    "EM2 = results3.loc[results[\"f_EM2\"] == 0]\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "ax.plot(\n",
    "    DM[\"Sr_r_mix\"], DM[\"Nd_r_mix\"], \"k--.\", markevery=20,\n",
    ")\n",
    "ax.plot(\n",
    "    EM1[\"Sr_r_mix\"], EM1[\"Nd_r_mix\"], \"k--.\", markevery=20,\n",
    ")\n",
    "ax.plot(\n",
    "    EM2[\"Sr_r_mix\"], EM2[\"Nd_r_mix\"], \"k--.\", markevery=20,\n",
    ")\n",
    "\n",
    "ax.plot(\n",
    "    table_1_10[\"Sr_r\"],\n",
    "    table_1_10[\"Nd_r\"],\n",
    "    marker=\"o\",\n",
    "    ls=\"\",\n",
    "    ms=30,\n",
    "    mec=\"k\",\n",
    "    mfc=\"w\",\n",
    "    zorder=10,\n",
    ")\n",
    "\n",
    "highlight = 0.5\n",
    "for val in np.array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]):\n",
    "\n",
    "    ax.plot(\n",
    "        results3[results3[\"f_DM\"] == val][\"Sr_r_mix\"],\n",
    "        results3[results3[\"f_DM\"] == val][\"Nd_r_mix\"],\n",
    "        \"k-\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "    ax.plot(\n",
    "        results[results[\"f_EM1\"] == val][\"Sr_r_mix\"],\n",
    "        results[results[\"f_EM1\"] == val][\"Nd_r_mix\"],\n",
    "        \"k-\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "    ax.plot(\n",
    "        results3[results3[\"f_EM2\"] == val][\"Sr_r_mix\"],\n",
    "        results3[results3[\"f_EM2\"] == val][\"Nd_r_mix\"],\n",
    "        \"k-\",\n",
    "        lw=0.5,\n",
    "    )\n",
    "\n",
    "    if val == highlight:\n",
    "\n",
    "        ax.plot(\n",
    "            results3[results3[\"f_DM\"] == val][\"Sr_r_mix\"],\n",
    "            results3[results3[\"f_DM\"] == val][\"Nd_r_mix\"],\n",
    "            \"r-\",\n",
    "            lw=2,\n",
    "        )\n",
    "        ax.plot(\n",
    "            results[results[\"f_EM1\"] == val][\"Sr_r_mix\"],\n",
    "            results[results[\"f_EM1\"] == val][\"Nd_r_mix\"],\n",
    "            \"r-\",\n",
    "            lw=2,\n",
    "        )\n",
    "        ax.plot(\n",
    "            results3[results3[\"f_EM2\"] == val][\"Sr_r_mix\"],\n",
    "            results3[results3[\"f_EM2\"] == val][\"Nd_r_mix\"],\n",
    "            \"r-\",\n",
    "            lw=2,\n",
    "        )\n",
    "\n",
    "\n",
    "for x, y, e in zip(table_1_10[\"Sr_r\"], table_1_10[\"Nd_r\"], table_1_10.index):\n",
    "    ax.annotate(e, xy=(x, y), fontsize=14, ha=\"center\", va=\"center\", zorder=10)\n",
    "\n",
    "ax.grid(ls=\":\", zorder=0)\n",
    "\n",
    "ax.set_xlim(0.7, 0.712)\n",
    "ax.set_ylim(0.5115, 0.5135)\n",
    "\n",
    "ax.set_xlabel(r\"$\\frac{^{87}Sr}{^{86}Sr}$\", fontsize=30)\n",
    "ax.set_ylabel(\n",
    "    r\"$\\frac{^{143}Nd}{^{144}Nd}$\", fontsize=30, labelpad=30, rotation=\"horizontal\"\n",
    ")\n",
    "\n",
    "ax.text(\n",
    "    0.5,\n",
    "    0.85,\n",
    "    \"red lines denote f = {} \\n for each component\".format(highlight),\n",
    "    transform=ax.transAxes,\n",
    "    fontsize=12,\n",
    ")\n",
    "ax.set_title('Figure 1.9 Albarede (1995)',fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}