2021-06-28_Module_2_Anomaly_Survey.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.constants as spc\n",
    "import pandas as pd\n",
    "import altair as alt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constants\n",
    "mu_0 = spc.mu_0\n",
    "pi = spc.pi\n",
    "mag_const = mu_0/(4*pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up survey parameters\n",
    "D = 100   # Line length in m\n",
    "h = 2      # Station height in m above ground\n",
    "N=1000     # Number of points\n",
    "\n",
    "survey_line=pd.DataFrame({'x':[np.array(xi) for xi in np.vstack([np.linspace(-D,D,N),np.ones((N,))*h]).T]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up Earth's magnetic field\n",
    "latitude = 47 # Latitude\n",
    "I_Earth = np.arctan(2*np.tan(np.radians(latitude)))  # Inclination of Earth's field\n",
    "B_Earth = 50E-6  # Earth's field magnitude in T (Note: B field, need to divide by mu_0 to get H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            x  \\\n",
      "0               [-100.0, 2.0]   \n",
      "1    [-99.7997997997998, 2.0]   \n",
      "2    [-99.5995995995996, 2.0]   \n",
      "3    [-99.3993993993994, 2.0]   \n",
      "4    [-99.1991991991992, 2.0]   \n",
      "..                        ...   \n",
      "995   [99.1991991991992, 2.0]   \n",
      "996  [99.39939939939941, 2.0]   \n",
      "997   [99.5995995995996, 2.0]   \n",
      "998  [99.79979979979981, 2.0]   \n",
      "999              [100.0, 2.0]   \n",
      "\n",
      "                                                     B       delta_B  \\\n",
      "0       [3.348442958079718e-14, 2.790369131733098e-13]  1.494621e-19   \n",
      "1       [3.374764681457307e-14, 2.806673663173953e-13]  1.512479e-19   \n",
      "2     [3.4013445684554753e-14, 2.8231046426536524e-13]  1.530551e-19   \n",
      "3      [3.428185651661989e-14, 2.8396632900403374e-13]  1.548841e-19   \n",
      "4       [3.455291005139338e-14, 2.856350839250154e-13]  1.567352e-19   \n",
      "..                                                 ...           ...   \n",
      "995  [-3.6059066973361484e-14, 2.9808588063564587e-13] -7.594800e-19   \n",
      "996    [-3.577312303565529e-14, 2.963189120320797e-13] -7.539803e-19   \n",
      "997    [-3.548999768280487e-14, 2.945657965831736e-13] -7.485321e-19   \n",
      "998   [-3.5209657761048435e-14, 2.928263996310086e-13] -7.431348e-19   \n",
      "999    [-3.49320705690446e-14, 2.9110058807537165e-13] -7.377878e-19   \n",
      "\n",
      "     transect_distance            Bh            Bv  \n",
      "0          -100.000000  8.796579e-15  2.932193e-13  \n",
      "1           -99.799800  8.867202e-15  2.949816e-13  \n",
      "2           -99.599600  8.938534e-15  2.967581e-13  \n",
      "3           -99.399399  9.010585e-15  2.985489e-13  \n",
      "4           -99.199199  9.083363e-15  3.003541e-13  \n",
      "..                 ...           ...           ...  \n",
      "995          99.199199 -9.180757e-15  3.035746e-13  \n",
      "996          99.399399 -9.107003e-15  3.017435e-13  \n",
      "997          99.599600 -9.033987e-15  2.999272e-13  \n",
      "998          99.799800 -8.961702e-15  2.981254e-13  \n",
      "999         100.000000 -8.890138e-15  2.963379e-13  \n",
      "\n",
      "[1000 rows x 6 columns]\n"
     ]
    }
   ],
   "source": [
    "# Set up source parameters\n",
    "\n",
    "yd = 10.     # Depth of dipole in m\n",
    "I_dipole = np.radians(80) # Inclination of dipole in degrees (assume N pole is on +X side)\n",
    "    # Set equal to I_Earth for induced magnetization\n",
    "mu_magnitude = 1. # Dipole moment magnitude in Am^2\n",
    "\n",
    "# Calculate dipole moment vector\n",
    "mu = mu_magnitude*np.array([np.cos(I_dipole), -np.sin(I_dipole)])\n",
    "\n",
    "def dipole(x_survey, x_dipole, mu):\n",
    "    r = x_survey-x_dipole\n",
    "    r_magnitude = np.linalg.norm(r)\n",
    "    r_hat = r/r_magnitude\n",
    "    return mag_const*3*((np.dot(mu,r_hat)*r_hat)-mu)/(r_magnitude**3)\n",
    "    \n",
    "\n",
    "survey_line['B'] = survey_line['x'].apply(dipole,x_dipole=np.array([0, -yd]), mu=mu)\n",
    "print(survey_line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate anomaly field\n",
    "survey_line['delta_B']=survey_line['B'].apply(lambda xi: np.dot(xi,np.array([B_Earth*np.cos(np.radians(I_Earth)), \n",
    "                                                                             -B_Earth*np.sin(np.radians(I_Earth))])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Break vectors x and B into components for plotting\n",
    "survey_line['transect_distance']=survey_line['x'].apply(lambda xi: xi[0])\n",
    "survey_line['Bh']=survey_line['B'].apply(lambda xi: xi[0])\n",
    "survey_line['Bv']=survey_line['B'].apply(lambda xi: xi[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
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3.052950354690417e-13}, {\"x\": [98.59859859859861, 2.0], \"B\": [-3.6934148770364595e-14, 3.0347127576584197e-13], \"delta_B\": -2.1467752669099986e-18, \"transect_distance\": 98.59859859859861, \"Bh\": -3.6934148770364595e-14, \"Bv\": 3.0347127576584197e-13}, {\"x\": [98.7987987987988, 2.0], \"B\": [-3.663954552345598e-14, 3.016619238542799e-13], \"delta_B\": -2.1302567738205387e-18, \"transect_distance\": 98.7987987987988, \"Bh\": -3.663954552345598e-14, \"Bv\": 3.016619238542799e-13}, {\"x\": [98.99899899899901, 2.0], \"B\": [-3.634786310924539e-14, 2.9986683863066144e-13], \"delta_B\": -2.113898417442343e-18, \"transect_distance\": 98.99899899899901, \"Bh\": -3.634786310924539e-14, \"Bv\": 2.9986683863066144e-13}, {\"x\": [99.1991991991992, 2.0], \"B\": [-3.6059066973361484e-14, 2.9808588063564587e-13], \"delta_B\": -2.0976983323338742e-18, \"transect_distance\": 99.1991991991992, \"Bh\": -3.6059066973361484e-14, \"Bv\": 2.9808588063564587e-13}, {\"x\": [99.39939939939941, 2.0], \"B\": [-3.577312303565529e-14, 2.963189120320797e-13], \"delta_B\": -2.0816546783659918e-18, \"transect_distance\": 99.39939939939941, \"Bh\": -3.577312303565529e-14, \"Bv\": 2.963189120320797e-13}, {\"x\": [99.5995995995996, 2.0], \"B\": [-3.548999768280487e-14, 2.945657965831736e-13], \"delta_B\": -2.0657656403306584e-18, \"transect_distance\": 99.5995995995996, \"Bh\": -3.548999768280487e-14, \"Bv\": 2.945657965831736e-13}, {\"x\": [99.79979979979981, 2.0], \"B\": [-3.5209657761048435e-14, 2.928263996310086e-13], \"delta_B\": -2.0500294275563845e-18, \"transect_distance\": 99.79979979979981, \"Bh\": -3.5209657761048435e-14, \"Bv\": 2.928263996310086e-13}, {\"x\": [100.0, 2.0], \"B\": [-3.49320705690446e-14, 2.9110058807537165e-13], \"delta_B\": -2.0344442735303627e-18, \"transect_distance\": 100.0, \"Bh\": -3.49320705690446e-14, \"Bv\": 2.9110058807537165e-13}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot anomaly field\n",
    "anomaly_plot=alt.Chart(survey_line).mark_line().encode(\n",
    "    x=alt.X(\"transect_distance:Q\",scale=alt.Scale(domain=(-100,100))),\n",
    "    y=alt.Y(\"delta_B:Q\")\n",
    ")\n",
    "display(anomaly_plot)"
   ]
  }
 ],
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