6_comparisons.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d6036c64-5f6c-4cd9-840a-bf43c14ee39e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.set_option('display.max_columns', None)\n",
    "from pmagpy import ipmag, pmag\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "from vgptools.auxiliar import (get_files_in_directory, spherical2cartesian, \n",
    "                               cartesian2spherical, GCD_cartesian, shape)                              \n",
    "from vgptools.utils_compilation import dfs_vgps_recomputed_poles\n",
    "from vgptools.utils_APWPs import (running_mean_APWP, running_mean_APWP_shape, RM_stats, get_pseudo_vgps,\n",
    "                                  running_mean_VGPs_bootstrapped, running_mean_bootstrapping_direction)\n",
    "\n",
    "from vgptools.utils_visualization import  RM_stats, plot_VGPs_and_APWP, plot_APWP_RM_ensemble, quantiles, PC\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "090d6cf3-317a-439b-9d69-5ee6aa0655b9",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Compiles a DataFrame for both, the VGPs and the recomputed poles by study"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "46a2b299-9fa6-4f1c-85aa-ca59b701edc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "current_path = os.getcwd()\n",
    "data_path_VGP = current_path + '/data/vgp_database'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9f974200-5004-48d3-9429-8b7374448f14",
   "metadata": {},
   "outputs": [],
   "source": [
    "# df_filtered_vgps, df_pole_compilation = dfs_vgps_recomputed_poles(data_path_VGP, by_study = True) # takes as many as poles as are described for one are\n",
    "df_filtered_vgps = pd.read_csv(current_path +'/data/df_vgps_filtered.csv')\n",
    "df_pole_compilation  = pd.read_csv(current_path +'/data/df_pole_compilation_by_study.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55ec846e-fc9e-4b81-8791-942dbe60a9fb",
   "metadata": {},
   "source": [
    "## Set the hyperparameters for further comparissons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f8a972ef-2ab5-4ac9-881e-58a0f6c533fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "min_age = 0\n",
    "max_age = 65\n",
    "window_length = 20\n",
    "time_step = 2\n",
    "# define a list to store all the models\n",
    "models = []"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cd7ede2-b7f1-4b12-959c-00d97148e910",
   "metadata": {},
   "source": [
    "### 1. Running means classic approach on poles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b187aab-817f-4934-9115-c1bc70c1b688",
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>N</th>\n",
       "      <th>n_studies</th>\n",
       "      <th>k</th>\n",
       "      <th>A95</th>\n",
       "      <th>csd</th>\n",
       "      <th>plon</th>\n",
       "      <th>plat</th>\n",
       "      <th>method</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>157.806367</td>\n",
       "      <td>3.053286</td>\n",
       "      <td>6.447966</td>\n",
       "      <td>-67.163587</td>\n",
       "      <td>-87.015353</td>\n",
       "      <td>RM_classic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>157.806367</td>\n",
       "      <td>3.053286</td>\n",
       "      <td>6.447966</td>\n",
       "      <td>-67.163587</td>\n",
       "      <td>-87.015353</td>\n",
       "      <td>RM_classic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>694.396487</td>\n",
       "      <td>3.489190</td>\n",
       "      <td>3.073840</td>\n",
       "      <td>-15.989200</td>\n",
       "      <td>-81.836813</td>\n",
       "      <td>RM_classic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>30.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>460.397603</td>\n",
       "      <td>2.816323</td>\n",
       "      <td>3.775013</td>\n",
       "      <td>-28.128989</td>\n",
       "      <td>-82.900850</td>\n",
       "      <td>RM_classic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>40.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>254.364022</td>\n",
       "      <td>3.479776</td>\n",
       "      <td>5.078754</td>\n",
       "      <td>-28.898450</td>\n",
       "      <td>-83.239212</td>\n",
       "      <td>RM_classic</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age     N  n_studies           k       A95       csd       plon  \\\n",
       "0   0.0  15.0       15.0  157.806367  3.053286  6.447966 -67.163587   \n",
       "1  10.0  15.0       15.0  157.806367  3.053286  6.447966 -67.163587   \n",
       "2  20.0   4.0        4.0  694.396487  3.489190  3.073840 -15.989200   \n",
       "3  30.0   7.0        7.0  460.397603  2.816323  3.775013 -28.128989   \n",
       "4  40.0   8.0        8.0  254.364022  3.479776  5.078754 -28.898450   \n",
       "\n",
       "        plat      method  \n",
       "0 -87.015353  RM_classic  \n",
       "1 -87.015353  RM_classic  \n",
       "2 -81.836813  RM_classic  \n",
       "3 -82.900850  RM_classic  \n",
       "4 -83.239212  RM_classic  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RM_1_classic = running_mean_APWP (df_pole_compilation, \"Plon\", \"Plat\", \"mean_age\", window_length, time_step, max_age, min_age)\n",
    "RM_1_classic['method'] = \"RM_classic\"\n",
    "models.append(RM_1_classic)\n",
    "RM_1_classic.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f784289e-7ba8-4189-aa18-15a6be863226",
   "metadata": {},
   "source": [
    "### 2. Running means ensemble from pseudo-VGPs approach (Vaes et al. 2022)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "566a1884-6483-46a5-a8c8-d0a25beb3719",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 48.5 s, sys: 218 ms, total: 48.7 s\n",
      "Wall time: 48.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "RM_2_ensemble_pseudoVGP = pd.DataFrame(columns=['run','n_studies','k','A95','csd'])\n",
    "\n",
    "for i in range(100):   \n",
    "    pseudo_vgps_temp = get_pseudo_vgps(df_pole_compilation)\n",
    "    RM_APWP_parametric_temp = pd.DataFrame()\n",
    "    RM_APWP_parametric_temp = running_mean_APWP_shape(pseudo_vgps_temp, 'Plon', 'Plat', 'mean_age', window_length, time_step, max_age, min_age)\n",
    "    RM_APWP_parametric_temp['run'] = i\n",
    "\n",
    "    RM_2_ensemble_pseudoVGP = RM_2_ensemble_pseudoVGP.append(RM_APWP_parametric_temp, ignore_index=True)\n",
    "RM_2_ensemble_pseudoVGP['plon'] = RM_2_ensemble_pseudoVGP.apply(lambda row: row.plon - 360 if row.plon > 180 else row.plon, axis =1)    \n",
    "RM_2_ensemble_pseudoVGP['method'] = \"RM_pseudoVGPs_ensemble\"\n",
    "models.append(RM_2_ensemble_pseudoVGP)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8af3059d-727f-4626-a6fe-90ba3b92fdce",
   "metadata": {},
   "source": [
    "Set quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7deee0e8-3201-49ea-a68d-5a7dce7f3d92",
   "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>run</th>\n",
       "      <th>n_studies</th>\n",
       "      <th>k</th>\n",
       "      <th>A95</th>\n",
       "      <th>csd</th>\n",
       "      <th>age</th>\n",
       "      <th>N</th>\n",
       "      <th>plon</th>\n",
       "      <th>plat</th>\n",
       "      <th>foliation</th>\n",
       "      <th>lineation</th>\n",
       "      <th>collinearity</th>\n",
       "      <th>coplanarity</th>\n",
       "      <th>GCD</th>\n",
       "      <th>APW_rate</th>\n",
       "      <th>angle</th>\n",
       "      <th>method</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>23.771238</td>\n",
       "      <td>1.659824</td>\n",
       "      <td>16.613423</td>\n",
       "      <td>0.0</td>\n",
       "      <td>315.0</td>\n",
       "      <td>-50.056609</td>\n",
       "      <td>-87.161501</td>\n",
       "      <td>0.099746</td>\n",
       "      <td>0.788208</td>\n",
       "      <td>7.902175</td>\n",
       "      <td>0.887954</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>23.985074</td>\n",
       "      <td>1.618864</td>\n",
       "      <td>16.5392</td>\n",
       "      <td>2.0</td>\n",
       "      <td>328.0</td>\n",
       "      <td>-48.759449</td>\n",
       "      <td>-87.269952</td>\n",
       "      <td>0.095148</td>\n",
       "      <td>0.789994</td>\n",
       "      <td>8.302781</td>\n",
       "      <td>0.885142</td>\n",
       "      <td>0.125420</td>\n",
       "      <td>0.062710</td>\n",
       "      <td>177.871955</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>24.018298</td>\n",
       "      <td>1.593478</td>\n",
       "      <td>16.527756</td>\n",
       "      <td>4.0</td>\n",
       "      <td>338.0</td>\n",
       "      <td>-47.333592</td>\n",
       "      <td>-87.370127</td>\n",
       "      <td>0.070144</td>\n",
       "      <td>0.783292</td>\n",
       "      <td>11.166945</td>\n",
       "      <td>0.853436</td>\n",
       "      <td>0.120325</td>\n",
       "      <td>0.060163</td>\n",
       "      <td>77.479034</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  run n_studies          k       A95        csd  age      N       plon  \\\n",
       "0   0      15.0  23.771238  1.659824  16.613423  0.0  315.0 -50.056609   \n",
       "1   0      15.0  23.985074  1.618864    16.5392  2.0  328.0 -48.759449   \n",
       "2   0      15.0  24.018298  1.593478  16.527756  4.0  338.0 -47.333592   \n",
       "\n",
       "        plat  foliation  lineation  collinearity  coplanarity       GCD  \\\n",
       "0 -87.161501   0.099746   0.788208      7.902175     0.887954       NaN   \n",
       "1 -87.269952   0.095148   0.789994      8.302781     0.885142  0.125420   \n",
       "2 -87.370127   0.070144   0.783292     11.166945     0.853436  0.120325   \n",
       "\n",
       "   APW_rate       angle                  method  \n",
       "0       NaN         NaN  RM_pseudoVGPs_ensemble  \n",
       "1  0.062710  177.871955  RM_pseudoVGPs_ensemble  \n",
       "2  0.060163   77.479034  RM_pseudoVGPs_ensemble  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RM_2_quantiles_plat = quantiles(RM_2_ensemble_pseudoVGP,\"age\",\"plat\") # set quantiles of latitude groupedby age for visualization purposes\n",
    "RM_2_quantiles_plon = quantiles(RM_2_ensemble_pseudoVGP,\"age\",\"plon\") # set quantiles of longitude groupedby age for visualization purposes\n",
    "RM_2_ensemble_pseudoVGP.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ec55f67-eafa-444e-a421-433213cea533",
   "metadata": {},
   "source": [
    "## 3. Running means on VGPs. \n",
    "Three different approachs as follows:\n",
    "### 3.1. Running means on the computed dataset (one run and A95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fabfa78d-bb26-4493-8ab3-0a4236927772",
   "metadata": {},
   "outputs": [],
   "source": [
    "RM_31_on_VGP = running_mean_APWP(df_filtered_vgps, 'vgp_lon_SH', 'vgp_lat_SH', 'mean_age', window_length, time_step, max_age, min_age)\n",
    "RM_31_on_VGP['method'] = \"RM_classic_VGPs\"\n",
    "models.append(RM_31_on_VGP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "832761e4-bbd1-4694-9671-5252a28e0b78",
   "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>age</th>\n",
       "      <th>N</th>\n",
       "      <th>n_studies</th>\n",
       "      <th>k</th>\n",
       "      <th>A95</th>\n",
       "      <th>csd</th>\n",
       "      <th>plon</th>\n",
       "      <th>plat</th>\n",
       "      <th>method</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>305.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>23.294563</td>\n",
       "      <td>1.704883</td>\n",
       "      <td>16.782542</td>\n",
       "      <td>-42.916770</td>\n",
       "      <td>-87.945102</td>\n",
       "      <td>RM_classic_VGPs</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>308.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>22.847346</td>\n",
       "      <td>1.713794</td>\n",
       "      <td>16.945998</td>\n",
       "      <td>-45.430085</td>\n",
       "      <td>-88.076649</td>\n",
       "      <td>RM_classic_VGPs</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>309.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>22.671004</td>\n",
       "      <td>1.717952</td>\n",
       "      <td>17.011775</td>\n",
       "      <td>-45.363582</td>\n",
       "      <td>-87.974789</td>\n",
       "      <td>RM_classic_VGPs</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age      N  n_studies          k       A95        csd       plon  \\\n",
       "0  0.0  305.0       15.0  23.294563  1.704883  16.782542 -42.916770   \n",
       "1  2.0  308.0       15.0  22.847346  1.713794  16.945998 -45.430085   \n",
       "2  4.0  309.0       15.0  22.671004  1.717952  17.011775 -45.363582   \n",
       "\n",
       "        plat           method  \n",
       "0 -87.945102  RM_classic_VGPs  \n",
       "1 -88.076649  RM_classic_VGPs  \n",
       "2 -87.974789  RM_classic_VGPs  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RM_31_on_VGP.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5dbc709-a407-4226-87c9-7ca3ff23b894",
   "metadata": {},
   "source": [
    "### 3.2. Running means on random samples (with replacement) from the original dataset to generate an ensemble of possible solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0d0297d5-d2df-42e0-9ad3-8df5852fc441",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 30.7 s, sys: 111 ms, total: 30.8 s\n",
      "Wall time: 30.8 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "RM_32_boots_VGPs=running_mean_VGPs_bootstrapped(df_filtered_vgps, 'vgp_lon_SH', 'vgp_lat_SH', 'mean_age', window_length, time_step, max_age, min_age, n_bst = 100)\n",
    "RM_32_boots_VGPs['method']=\"RM_bootstrapped_VGPs_ensemble\"\n",
    "models.append(RM_32_boots_VGPs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5916bd8-6046-4f15-9928-0fa33fed1549",
   "metadata": {},
   "source": [
    "Set quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "89553138-cdc6-4b42-a2bd-14a6d565a42a",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>run</th>\n",
       "      <th>N</th>\n",
       "      <th>k</th>\n",
       "      <th>A95</th>\n",
       "      <th>csd</th>\n",
       "      <th>foliation</th>\n",
       "      <th>lineation</th>\n",
       "      <th>collinearity</th>\n",
       "      <th>coplanarity</th>\n",
       "      <th>age</th>\n",
       "      <th>n_studies</th>\n",
       "      <th>plon</th>\n",
       "      <th>plat</th>\n",
       "      <th>GCD</th>\n",
       "      <th>APW_rate</th>\n",
       "      <th>angle</th>\n",
       "      <th>method</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>341.0</td>\n",
       "      <td>24.5634</td>\n",
       "      <td>1.567967</td>\n",
       "      <td>16.343339</td>\n",
       "      <td>0.188209</td>\n",
       "      <td>0.723219</td>\n",
       "      <td>3.842632</td>\n",
       "      <td>0.911428</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>-104.195237</td>\n",
       "      <td>-89.094830</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>RM_bootstrapped_VGPs_ensemble</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>346.0</td>\n",
       "      <td>23.760084</td>\n",
       "      <td>1.583776</td>\n",
       "      <td>16.617322</td>\n",
       "      <td>0.197945</td>\n",
       "      <td>0.708025</td>\n",
       "      <td>3.576881</td>\n",
       "      <td>0.90597</td>\n",
       "      <td>2.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>-122.465693</td>\n",
       "      <td>-89.047866</td>\n",
       "      <td>0.298486</td>\n",
       "      <td>0.149243</td>\n",
       "      <td>NaN</td>\n",
       "      <td>RM_bootstrapped_VGPs_ensemble</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>346.0</td>\n",
       "      <td>23.760084</td>\n",
       "      <td>1.583776</td>\n",
       "      <td>16.617322</td>\n",
       "      <td>0.197945</td>\n",
       "      <td>0.708025</td>\n",
       "      <td>3.576881</td>\n",
       "      <td>0.90597</td>\n",
       "      <td>4.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>-122.465693</td>\n",
       "      <td>-89.047866</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>RM_bootstrapped_VGPs_ensemble</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   run      N          k       A95        csd foliation lineation  \\\n",
       "0  0.0  341.0    24.5634  1.567967  16.343339  0.188209  0.723219   \n",
       "1  0.0  346.0  23.760084  1.583776  16.617322  0.197945  0.708025   \n",
       "2  0.0  346.0  23.760084  1.583776  16.617322  0.197945  0.708025   \n",
       "\n",
       "  collinearity coplanarity  age  n_studies        plon       plat       GCD  \\\n",
       "0     3.842632    0.911428  0.0       15.0 -104.195237 -89.094830       NaN   \n",
       "1     3.576881     0.90597  2.0       15.0 -122.465693 -89.047866  0.298486   \n",
       "2     3.576881     0.90597  4.0       15.0 -122.465693 -89.047866  0.000000   \n",
       "\n",
       "   APW_rate  angle                         method  \n",
       "0       NaN    NaN  RM_bootstrapped_VGPs_ensemble  \n",
       "1  0.149243    NaN  RM_bootstrapped_VGPs_ensemble  \n",
       "2  0.000000    NaN  RM_bootstrapped_VGPs_ensemble  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RM_32_quantiles_plat = quantiles(RM_32_boots_VGPs,\"age\",\"plat\") # set quantiles of latitude groupedby age for visualization purposes\n",
    "RM_32_quantiles_plon = quantiles(RM_32_boots_VGPs,\"age\",\"plon\") # set quantiles of longitude groupedby age for visualization purposes\n",
    "RM_32_boots_VGPs.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4410f95-eb87-4fa8-a5f4-25f3c4007811",
   "metadata": {},
   "source": [
    "### 3.3. Propation of directional error towards the VGP level. \n",
    "We take the original directions as a PDF to generate to generate a pseudo-Dataset that incorporates the uncertinty in the directional space and time. We aaply the running means on a number of $pseudo$-VGPs to generate an ensemble of possible paths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a2094478-8b8b-4674-8b43-1ea0df4c14bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 1s, sys: 135 ms, total: 1min 1s\n",
      "Wall time: 1min 1s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "RM_33_propagation=running_mean_bootstrapping_direction(df_filtered_vgps,'plon', 'plat', 'age', window_length, time_step, max_age, min_age, n_bst = 100)\n",
    "RM_33_propagation['method']=\"RM_DirErrorPropagated_ensemble\"\n",
    "models.append(RM_33_propagation)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a70f4ee3-7aa0-43ee-bb5f-2b2f8ab05a9a",
   "metadata": {},
   "source": [
    "Set quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "02a051ee-d698-4ad6-8c92-c4042c308e09",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>run</th>\n",
       "      <th>N</th>\n",
       "      <th>k</th>\n",
       "      <th>A95</th>\n",
       "      <th>csd</th>\n",
       "      <th>foliation</th>\n",
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       "      <th>n_studies</th>\n",
       "      <th>plon</th>\n",
       "      <th>plat</th>\n",
       "      <th>GCD</th>\n",
       "      <th>APW_rate</th>\n",
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       "      <th>method</th>\n",
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       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>309.0</td>\n",
       "      <td>18.149466</td>\n",
       "      <td>1.931172</td>\n",
       "      <td>19.013107</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>-31.326308</td>\n",
       "      <td>-87.044732</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>RM_DirErrorPropagated_ensemble</td>\n",
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       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>310.0</td>\n",
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       "      <td>0.049904</td>\n",
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       "      <td>-87.186513</td>\n",
       "      <td>0.141823</td>\n",
       "      <td>0.070911</td>\n",
       "      <td>4.125393</td>\n",
       "      <td>RM_DirErrorPropagated_ensemble</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>17.717835</td>\n",
       "      <td>1.949612</td>\n",
       "      <td>19.243306</td>\n",
       "      <td>0.049764</td>\n",
       "      <td>0.671242</td>\n",
       "      <td>13.488453</td>\n",
       "      <td>0.721006</td>\n",
       "      <td>4.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>-31.487436</td>\n",
       "      <td>-87.065614</td>\n",
       "      <td>0.121443</td>\n",
       "      <td>0.060721</td>\n",
       "      <td>166.769205</td>\n",
       "      <td>RM_DirErrorPropagated_ensemble</td>\n",
       "    </tr>\n",
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       "</div>"
      ],
      "text/plain": [
       "   run      N          k       A95        csd foliation lineation  \\\n",
       "0  0.0  309.0  18.149466  1.931172  19.013107  0.051792  0.664706   \n",
       "1  0.0  310.0  17.881853   1.94326   19.15485  0.049904  0.664968   \n",
       "2  0.0  311.0  17.717835  1.949612  19.243306  0.049764  0.671242   \n",
       "\n",
       "  collinearity coplanarity  age  n_studies       plon       plat       GCD  \\\n",
       "0    12.834197    0.716498  0.0       15.0 -31.326308 -87.044732       NaN   \n",
       "1    13.324879    0.714872  2.0       15.0 -31.258511 -87.186513  0.141823   \n",
       "2    13.488453    0.721006  4.0       15.0 -31.487436 -87.065614  0.121443   \n",
       "\n",
       "   APW_rate       angle                          method  \n",
       "0       NaN         NaN  RM_DirErrorPropagated_ensemble  \n",
       "1  0.070911    4.125393  RM_DirErrorPropagated_ensemble  \n",
       "2  0.060721  166.769205  RM_DirErrorPropagated_ensemble  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RM_33_quantiles_plat = quantiles(RM_33_propagation,\"age\",\"plat\") # set quantiles of latitude groupedby age for visualization purposes\n",
    "RM_33_quantiles_plon = quantiles(RM_33_propagation,\"age\",\"plon\") # set quantiles of longitude groupedby age for visualization purposes\n",
    "RM_33_propagation.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9026773b-fb5b-42cd-a38d-4aa3a1c60c8b",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Get APW from Muller et al., 2016 and Torsvik and Cocks, 2017\n",
    "\n",
    "- Müller, R. D., Seton, M., Zahirovic, S., Williams, S. E., Matthews, K. J., Wright, N. M., ... & Cannon, J. (2016). Ocean basin evolution and global-scale plate reorganization events since Pangea breakup. Annual Review of Earth and Planetary Sciences, 44, 107-138. DOI:10.1146/annurev-earth-060115-012211\n",
    "- Torsvik, T. H., & Cocks, L. R. M. (2013). Gondwana from top to base in space and time. Gondwana Research, 24(3-4), 999-1030.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2347700a-bbc0-424e-bff6-007a7af9030b",
   "metadata": {},
   "outputs": [],
   "source": [
    "Torsvik2017_path = np.loadtxt('model_APWP/code_output/NAM_0_60_torsvik_2017.txt', )\n",
    "Torsvik2017_path_df = pd.DataFrame(Torsvik2017_path, columns = ['age','plon', 'plat', 'Euler_angle', 'Euler_lon', 'Euler_lat'])\n",
    "Torsvik2017_path_df = Torsvik2017_path_df[Torsvik2017_path_df['age']>0]\n",
    "Torsvik2017_path_df['method'] = \"plate model\"\n",
    "models.append(Torsvik2017_path_df)\n",
    "\n",
    "Mueller2016_path = np.loadtxt('model_APWP/code_output/NAM_0_60_muller_2016.txt', )\n",
    "Mueller2016_path_df = pd.DataFrame(Mueller2016_path, columns = ['age','plon', 'plat', 'Euler_angle', 'Euler_lon', 'Euler_lat'])\n",
    "Mueller2016_path_df = Mueller2016_path_df[Mueller2016_path_df['age']>0]\n",
    "Mueller2016_path_df['method']=\"plate model\"\n",
    "models.append(Mueller2016_path_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5092c6a4-b0f1-422a-a472-f6b845ecc97d",
   "metadata": {},
   "source": [
    "Merge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6f08583a-161f-4dfd-aab8-328fe1a2a1d0",
   "metadata": {},
   "outputs": [
    {
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       "      <th>coplanarity</th>\n",
       "      <th>GCD</th>\n",
       "      <th>APW_rate</th>\n",
       "      <th>angle</th>\n",
       "      <th>method</th>\n",
       "      <th>Euler_angle</th>\n",
       "      <th>Euler_lon</th>\n",
       "      <th>Euler_lat</th>\n",
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       "      <th>0</th>\n",
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       "      <td>0.099746</td>\n",
       "      <td>0.788208</td>\n",
       "      <td>7.902175</td>\n",
       "      <td>0.887954</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>23.985074</td>\n",
       "      <td>1.618864</td>\n",
       "      <td>16.5392</td>\n",
       "      <td>2.0</td>\n",
       "      <td>328.0</td>\n",
       "      <td>-48.759449</td>\n",
       "      <td>-87.269952</td>\n",
       "      <td>0.095148</td>\n",
       "      <td>0.789994</td>\n",
       "      <td>8.302781</td>\n",
       "      <td>0.885142</td>\n",
       "      <td>0.125420</td>\n",
       "      <td>0.062710</td>\n",
       "      <td>177.871955</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>24.018298</td>\n",
       "      <td>1.593478</td>\n",
       "      <td>16.527756</td>\n",
       "      <td>4.0</td>\n",
       "      <td>338.0</td>\n",
       "      <td>-47.333592</td>\n",
       "      <td>-87.370127</td>\n",
       "      <td>0.070144</td>\n",
       "      <td>0.783292</td>\n",
       "      <td>11.166945</td>\n",
       "      <td>0.853436</td>\n",
       "      <td>0.120325</td>\n",
       "      <td>0.060163</td>\n",
       "      <td>77.479034</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>24.0261</td>\n",
       "      <td>1.545709</td>\n",
       "      <td>16.525073</td>\n",
       "      <td>6.0</td>\n",
       "      <td>359.0</td>\n",
       "      <td>-44.442964</td>\n",
       "      <td>-87.216771</td>\n",
       "      <td>0.091397</td>\n",
       "      <td>0.775079</td>\n",
       "      <td>8.480323</td>\n",
       "      <td>0.866477</td>\n",
       "      <td>0.205258</td>\n",
       "      <td>0.102629</td>\n",
       "      <td>171.346602</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>21.812417</td>\n",
       "      <td>1.590628</td>\n",
       "      <td>17.343356</td>\n",
       "      <td>8.0</td>\n",
       "      <td>375.0</td>\n",
       "      <td>-40.570209</td>\n",
       "      <td>-86.865390</td>\n",
       "      <td>0.034497</td>\n",
       "      <td>0.788156</td>\n",
       "      <td>22.846978</td>\n",
       "      <td>0.822653</td>\n",
       "      <td>0.404075</td>\n",
       "      <td>0.202038</td>\n",
       "      <td>158.978787</td>\n",
       "      <td>RM_pseudoVGPs_ensemble</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  run n_studies          k       A95        csd  age      N       plon  \\\n",
       "0   0      15.0  23.771238  1.659824  16.613423  0.0  315.0 -50.056609   \n",
       "1   0      15.0  23.985074  1.618864    16.5392  2.0  328.0 -48.759449   \n",
       "2   0      15.0  24.018298  1.593478  16.527756  4.0  338.0 -47.333592   \n",
       "3   0      16.0    24.0261  1.545709  16.525073  6.0  359.0 -44.442964   \n",
       "4   0      17.0  21.812417  1.590628  17.343356  8.0  375.0 -40.570209   \n",
       "\n",
       "        plat foliation lineation collinearity coplanarity       GCD  APW_rate  \\\n",
       "0 -87.161501  0.099746  0.788208     7.902175    0.887954       NaN       NaN   \n",
       "1 -87.269952  0.095148  0.789994     8.302781    0.885142  0.125420  0.062710   \n",
       "2 -87.370127  0.070144  0.783292    11.166945    0.853436  0.120325  0.060163   \n",
       "3 -87.216771  0.091397  0.775079     8.480323    0.866477  0.205258  0.102629   \n",
       "4 -86.865390  0.034497  0.788156    22.846978    0.822653  0.404075  0.202038   \n",
       "\n",
       "        angle                  method  Euler_angle  Euler_lon  Euler_lat  \n",
       "0         NaN  RM_pseudoVGPs_ensemble          NaN        NaN        NaN  \n",
       "1  177.871955  RM_pseudoVGPs_ensemble          NaN        NaN        NaN  \n",
       "2   77.479034  RM_pseudoVGPs_ensemble          NaN        NaN        NaN  \n",
       "3  171.346602  RM_pseudoVGPs_ensemble          NaN        NaN        NaN  \n",
       "4  158.978787  RM_pseudoVGPs_ensemble          NaN        NaN        NaN  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_all = pd.concat(models, axis=0)\n",
    "df_all.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c64dd27-525e-45c4-8392-120b307956bf",
   "metadata": {},
   "source": [
    "# Comparisons plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "aa9540df-2e29-4a81-ba58-04a51cd07d88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe0e0de7820>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title = \"comparisons\"\n",
    "\n",
    "df_method1=RM_2_ensemble_pseudoVGP\n",
    "df_method2=RM_33_propagation\n",
    "\n",
    "ensemble1_lat = quantiles(df_method1,\"age\",\"plat\") # set quantiles of latitude groupedby age for visualization purposes\n",
    "ensemble1_lon = quantiles(df_method1,\"age\",\"plon\") # set quantiles of longitude groupedby age for visualization purposes\n",
    "ensemble2_lat = quantiles(df_method2,\"age\",\"plat\") # set quantiles of latitude groupedby age for visualization purposes\n",
    "ensemble2_lon = quantiles(df_method2,\"age\",\"plon\") # set quantiles of longitude groupedby age for visualization purposes\n",
    "\n",
    "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(15,6))\n",
    "fig.suptitle(title, fontsize= 18, fontweight ='bold')\n",
    "axes[0].set_title('Latitude (°N)', fontsize=12, fontweight ='bold')\n",
    "axes[1].set_title('Longitude (°E)', fontsize=12, fontweight ='bold')\n",
    "axes[0].set_ylabel(r'Latitude (°N)', fontweight ='bold')\n",
    "axes[1].set_ylabel(r'Longitude (°E)', fontweight ='bold')\n",
    "\n",
    "axes[0].set_ylim(-90,-77)\n",
    "axes[1].set_ylim(-75,25)\n",
    "# LATITUDE\n",
    "axes[0].fill_between(ensemble1_lat.X, ensemble1_lat.q16,ensemble1_lat.q84, color= \"#f98787\", alpha=.20)\n",
    "axes[0].scatter(PC(df_method1,\"age\",\"plat\",\"plon\").X, PC(df_method1,\"age\",\"plat\",\"plon\").PC()[1],color=\"#d12a2a\")\n",
    "axes[0].plot(PC(df_method1,\"age\",\"plat\",\"plon\").X, PC(df_method1,\"age\",\"plat\",\"plon\").PC()[1],color=\"#d12a2a\")\n",
    "\n",
    "axes[0].fill_between(ensemble2_lat.X, ensemble2_lat.q16,ensemble2_lat.q84, color= \"#0E7DC9\", alpha=.20)\n",
    "axes[0].scatter(PC(df_method2,\"age\",\"plat\",\"plon\").X, PC(df_method2,\"age\",\"plat\",\"plon\").PC()[1],color=\"#00497A\")\n",
    "axes[0].plot(PC(df_method2,\"age\",\"plat\",\"plon\").X, PC(df_method2,\"age\",\"plat\",\"plon\").PC()[1],color=\"#00497A\")\n",
    "\n",
    "axes[0].plot(RM_1_classic.age, RM_1_classic.plat, '-',color=\"black\") #CLASSIC\n",
    "axes[0].scatter(RM_1_classic.age, RM_1_classic.plat, color=\"black\") #CLASSIC\n",
    "\n",
    "\n",
    "# # LONGITUDE\n",
    "axes[1].fill_between(ensemble1_lon.X, ensemble1_lon.q16,ensemble1_lon.q84, color= \"#f9afaf\", alpha=.50,label=\"0.16-0.84 percentiles - $pseudo$-VGPs\")\n",
    "axes[1].plot(PC(df_method1,\"age\",\"plat\",\"plon\").X, PC(df_method1,\"age\",\"plat\",\"plon\").PC()[0], '-',color=\"#d12a2a\")\n",
    "axes[1].scatter(PC(df_method1,\"age\",\"plat\",\"plon\").X, PC(df_method1,\"age\",\"plat\",\"plon\").PC()[0],color=\"#d12a2a\")\n",
    "\n",
    "axes[1].fill_between(ensemble2_lon.X, ensemble2_lon.q16,ensemble2_lon.q84, color= \"#0E7DC9\", alpha=.20,label=\"0.16-0.84 percentiles - VGPs\")\n",
    "axes[1].plot(PC(df_method2,\"age\",\"plat\",\"plon\").X, PC(df_method2,\"age\",\"plat\",\"plon\").PC()[0], '-',color=\"#00497A\")\n",
    "axes[1].scatter(PC(df_method2,\"age\",\"plat\",\"plon\").X, PC(df_method2,\"age\",\"plat\",\"plon\").PC()[0],color=\"#00497A\")\n",
    "axes[1].plot(RM_1_classic.age, RM_1_classic.plon, '-',color=\"black\", label = \"RM classic\") #CLASSIC\n",
    "axes[1].scatter(RM_1_classic.age, RM_1_classic.plon, color=\"black\") #CLASSIC\n",
    "\n",
    "plt.legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "565b84ae-4268-4988-aada-d11b552d8757",
   "metadata": {},
   "source": [
    "# Misfit vs the Classical apporach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6385daa2-996e-426f-9f04-1097d4bb1b45",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "4e828244-5995-4398-af59-b46573afb660",
   "metadata": {},
   "source": [
    "# APWPs vs Plate Models Visualizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7a9c710-2a81-4ce0-a9f4-527fab77efbd",
   "metadata": {},
   "outputs": [],
   "source": [
    "title = \"Comparing against plate models (M2016 and T&C2017)\"\n",
    "\n",
    "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(15,6))\n",
    "fig.suptitle(title, fontsize= 18, fontweight ='bold')\n",
    "axes[0].set_title('Latitude (°N)', fontsize=12, fontweight ='bold')\n",
    "axes[1].set_title('Longitude (°E)', fontsize=12, fontweight ='bold')\n",
    "axes[0].set_ylabel(r'Latitude (°N)', fontweight ='bold')\n",
    "axes[1].set_ylabel(r'Longitude (°E)', fontweight ='bold')\n",
    "# LATITUDE\n",
    "\n",
    "axes[0].plot(Mueller2016_path_df.age, Mueller2016_path_df.plat, '-',color=\"#d12a2a\")\n",
    "# axes[0].scatter(Mueller2016_path_df.age, Mueller2016_path_df.plat,s = 1, color=\"#d12a2a\")\n",
    "axes[0].plot(Torsvik2017_path_df.age, Torsvik2017_path_df.plat, '-',color=\"#00497A\") #CLASSIC\n",
    "# axes[0].scatter(Torsvik2017_path_df.age, Torsvik2017_path_df.plat, color=\"#00497A\") #CLASSIC\n",
    "axes[0].scatter(ensemble2_lat.X, ensemble2_lat.q50,color=\"black\")\n",
    "# LONGITUDE\n",
    "\n",
    "axes[1].plot(Mueller2016_path_df.age, Mueller2016_path_df.plon, '-',color=\"#d12a2a\", label = \"Muller2016\")\n",
    "# axes[1].scatter(Mueller2016_path_df.age, Mueller2016_path_df.plon,color=\"#d12a2a\")\n",
    "axes[1].plot(Torsvik2017_path_df.age, Torsvik2017_path_df.plon, '-',color=\"#00497A\", label = \"T&C2017\") #CLASSIC\n",
    "# axes[1].scatter(Torsvik2017_path_df.age, Torsvik2017_path_df.plon, color=\"#00497A\") #CLASSIC\n",
    "axes[1].scatter(ensemble2_lon.X, ensemble2_lon.q50,color=\"black\")\n",
    "\n",
    "# axes[1].set_ylim(-100, 50)\n",
    "plt.legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "385570f0-9cb2-41b1-9994-760a72139207",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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