gravity-inversion-solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building a non-linear gravity inversion from scratch (almost)\n",
    "\n",
    "In this notebook, we'll build a non-linear gravity inversion to estimate the relief of a sedimentary basin. We'll implement smoothness regularization and see its effects on the solution. We'll also see how we can break the inversion by adding random noise, abusing regularization, and breaking the underlying assumptions.\n",
    "\n",
    "This notebook is part of the Geophysics Library lesson: [GeophysicsLibrary/non-linear-gravity-inversion](https://github.com/GeophysicsLibrary/non-linear-gravity-inversion) \n",
    "\n",
    "See the lesson material for extra code and setup instructions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports\n",
    "\n",
    "We'll use the basic scientific Python stack for this tutorial plus a custom module with the forward modelling function (based on the code from the [Harmonica](https://github.com/fatiando/harmonica) library)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# Our custom code (cheatcodes.py) with forward modelling and some utilities.\n",
    "import cheatcodes as cc "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a little trick to make the resolution of the matplotlib figures better for larger screens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rc(\"figure\", dpi=120)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assumptions\n",
    "\n",
    "Here are some assumptions we'll work with:\n",
    "\n",
    "1. The basin is much larger in the y-dimension so we'll assume it's infinite (reducing the problem to 2D)\n",
    "1. The gravity disturbance is entirely due to the sedimentary basin\n",
    "1. The top of the basin is a flat surface at $z=0$\n",
    "1. The data are measured at a constant height of $z=1\\ m$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making synthetic data\n",
    "\n",
    "First, we'll explore the forward modelling function and create some synthetic data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 100000.0)\n",
      "[  10.10105917   18.81092435   29.38998081   42.16839388   57.51774684\n",
      "   75.85246428   97.63037844  123.35222519  153.55985009  188.83290654\n",
      "  229.78383989  277.05097454  331.28955675  393.1606554   463.31788573\n",
      "  542.39199706  630.97345373  729.59323554  838.70218841  958.64936255\n",
      " 1089.65988011 1231.81297121 1385.02090173 1549.00958058 1723.30167502\n",
      " 1907.20307243 2099.79350393 2299.92208393 2506.20842163 2717.04982321\n",
      " 2930.63493217 3144.96395261 3357.87537423 3567.07887609 3770.19383914\n",
      " 3964.79265602 4148.44780248 4318.78143888 4473.51615424 4610.52535757\n",
      " 4727.88177002 4823.90248153 4897.18910944 4946.66173395 4971.58548322\n",
      " 4971.58889307 4946.67346668 4897.21419639 4823.95117457 4727.97279851\n",
      " 4610.69145219 4473.81290687 4319.30099926 4149.33939015 3966.2923388\n",
      " 3772.66640115 3571.07472151 3364.2050895  3154.79214739 2945.59306685\n",
      " 2739.36473798 2538.83917762 2346.69270631 2165.50377716 1997.6945141\n",
      " 1845.45234455 1710.63077305 1594.63228888 1498.28126903 1421.69982545\n",
      " 1364.20386762 1324.23908356 1299.37606027 1286.37970806 1281.36048532\n",
      " 1280.00436832 1277.86656035 1270.70261956 1254.80221173 1227.28696229\n",
      " 1186.33602894 1131.31108729 1062.765288    982.33628338  892.53894688\n",
      "  796.4862351   697.57464821  599.17280554  504.34781951  415.65556423\n",
      "  335.00950302  263.63067355  202.0707732   150.29253113  107.78743462\n",
      "   73.71036175   47.0131077    26.56315486   11.23920733    0.        ]\n"
     ]
    }
   ],
   "source": [
    "depths, basin_boundaries = cc.synthetic_model()\n",
    "\n",
    "print(basin_boundaries)\n",
    "print(depths)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='x [km]', ylabel='depth [km]'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5aJL/lOQdST43j4AAAABYjlkSxO9L8oTW2nPmFQwAAADLM0uTmjOTvHNegQAAALBcs1QQL0vy95O8eU6xAByaruuysbGx51i/38/m5uaCIwIAWD1TJYhVddsdPz4lycur6tNJXpPkmt33t9aunS08gNn1+/0MBoM9x7quy2AwkCDCitja2pr497XX6y04IoDjpVpr+7+56ktJdj6gdv38FVprS+1iWlUbSU6ePHlybOUAON5O/dvg4G1YDRsbGxMTQRV/gOlsb2/nxIkTSXKitXbaNzzTLjHdyoSEEABgVr1ez4c2AEsyVYLYWrv4kOIAAABgyQ7cxbSqLq2qbxwz9g1VdenBwwIAAGDRZjnm4hFJzhkzdrskD5/huQEAAFiwWRLESW6b5HOH9NwAAAAcgmmPubhXknvvuPTIqrrfrttunuSBSa6cLTQAAAAWadoupvdJctHozy3JI8fc9/4kjz1oUAAAACzetEtMn5HhvsNzMzwD8R+Nft759XWttW9srf3BtMFU1T2q6rVV9YGq+kxVXVtVb62qh037XAAAAExn2mMuPpPkM0ky6mD64dbaDXOM59ZJPpjkpUn+d5JbJPmxJC+qqru01p4yx9cCSJJ0XZeNjY2x4w7mBgCOi2mXmN6otfb+JKmqv5nkXknOTnJNkj9srX3ogM95eZLLd13+3VEy+qgkEkRgrvr9fgaDwdjxrusyGAwkiDAnW1tbp/071+v1FhgRADsdOEGsqjOSPDvJY5LcZMfQF6vq15M8rrX2pdnCu9HHMlzWCjBXm5ubE5O/SZVFYHqDwWBiEtjr9dLv9xccFQCnHDhBTHJxkp9K8ptJXpLkI0nukOGS0Mcm+XiSA33kPko+z0hymyT/OMO9jj81Q6wAwIro9XrZ3t5edhgA7GGWBPEnkjyntfYvdlz78yRvqarrR+MHXZN1SZJHj/58Q5Kfaa39xqQHVNW5GTbJ2em8A74+AADAsTNLgnjbJK8dM/baDPcMHtQvJ/mPGS4rfUCSX6uqW7TWnjnhMRfmy0dwAAAAMKVZEsQ/S3K3JG/cY+xuSU4e9Ilbax9I8oHRj5dVVZI8rape0Fr76JiHXZLkZbuunZfk1QeNAwAA4DiZJUH8+SQvrar3t9ZurCRW1QOSPCHJQ2cNboc/SfLPk9w1yZ4JYmvt6iRX77w2SiwBAADYh1kSxOclOTPJ71TVp5P8VZLbJ7llhsddPHdHgtZaa986w2vdJ8mXkrxvhucAAABgglkSxGsyPH5ip6tmeL5U1X9I8qkMK4Z/leR2GXYx7Sf51QnLSwEAAJjRgRPE1tq95xjHKW9N8uNJHp7k1kmuy3Cv4z9prf2XQ3g9AAAARmapIM5da+35SZ6/7DgAAACOo5kSxKo6J8nPJbl3hstBH9Ra266qRyf5k9ba22YPEWC5uq7LxsbGnmP9fj+bmwc98hXWz9bWVgaDwdjxruvS6/UWGBEA0zjjoA+sqm/McPnnzyRpGXYY/Ruj4W8ZXQc40vr9/tg3s13XTXwjDMfRYDBI13Vjx3u9Xvr9/gIjAmAas1QQn5HkE0m+I8PjJW7YMfZHSZ40w3MDrITNzc2xFcJxVUU47nq9Xra3t5cdBgAHMEuC+A+SPKa1dlVV3WTX2IeT3HGG5wYAAGDBDrzENMMzEK8dM3aLDM8tBAAA4IiYJUH88yT3HTN2ryQnZ3huAAAAFmyWJaa/meTfVtVVSV48unazqnpwkguT/NSswQEAALA4B04QW2uXVNU9kjwryf87uvxHSSrJb7bWXjB7eAAAACzKTOcgttYeVVWXJvm+JLdP8rEkv9ta++N5BAcAAMDizJQgJklr7YokV8whFgAAAJZoliY1AAAArJGpKohV9aUkbb/3t9Z2n48IsFa6rsvGxsbY8X6/n83NzQVGBIdva2srg8Fgz7Gu69Lr9RYcEQDzMm0FcWvX1weTfDzJC5M8I8mLRj9/aDQOsLb6/f7EN8Jd1419Ew1H2WAwSNd1e471er30+/0FRwTAvExVQWytXXzqz1X1+CQfSXLf1tp1O67fMskbk1w/pxgBVtLm5ubE6uCkyiIcdb1eL9vb28sOA4A5m2UP4oVJnrEzOUyS1tqnM6wmXjhLYAAAACzWLAninZJ8YczYF5LcYYbnBgAAYMFmSRDfleTnquqmOy9W1c2SPD7Ju2cJDAAAgMWa5RzEX0ryqiTvq6pXZLgf8Q5Jfmj0/UGzBgcAAMDiHDhBbK29tqrul+SpSR6bYTWyJfmTJD/eWnvjfEIEAABgEWapIKa19qYkb6qqr01ymyQfb63pXgoAAHAEzZQgnjJKCiWGAAAAR9gsTWoAAABYI3OpIAKwt67rsrGxMXa83+9nc3NzgRHB6W1tbWUwGIwd77ouvV5vgREBsCgqiACHpN/vT3wT3XXdxDfhsCyDwSBd140d7/V66ff7C4wIgEVRQQQ4JJubmxOrg5Mqi7BsvV4v29vbyw4DgAVTQQQAACCJBBEAAIARCSIAAABJJIgAAACMSBABAABIIkEEAABgRIIIAABAEucgAixV13Vjz0Ps9/sTz1GEWWxtbWUwGOw51nVder3egiMCYBWoIAIsSb/fH/smvOu6sW/eYR4Gg0G6rttzrNfrpd/vLzgiAFaBCiLAkmxubo6tEI6rKsI89Xq9bG9vLzsMAFaICiIAAABJJIgAAACMSBABAABIIkEEAABgZOUTxKp6ZFW1qrpu2bEAAACss5VOEKvqTkmemeSqZccCAACw7lY6QUzy60n+MMnvLzsQAACAdbey5yBW1cOSfE+S85M8ZcnhACxc13UTz0Ps9/tjz1GEra2tDAaDseNd16XX6y0wIgCOgpWsIFbVuUmeneQJrbUPLTkcgIXr9/sT37x3XTfxzT8MBoN0XTd2vNfrpd/vLzAiAI6CVa0gXpLkz5M8b78PGCWV5+y6fN48gwJYlM3NzYnVwUmVRTil1+tle3t72WEAcISsXIJYVT+c5AFJvq211qZ46IVJLjqcqAAAANbfSiWIVXVWkucm+fdJrqqqW4+GbjYav3WSz7fW/nqPh1+S5GW7rp2X5NWHEiwAAMCaWakEMcntktw+yeNHX7t9PMOE70G7B1prVye5eue1qpp/hAAAAGtq1RLEjyS5zx7Xn5BhR9MLknxsoREBAAAcEyuVILbWPpvk8t3Xq+oRSb7YWvuqMQAAAOZjJY+5AAAAYPGORILYWntEa+2sZccBAACwzlZqiSkA+9d13cTzEPv9/sSzFDnatra2MhgMxo53XZder7fAiABYB0eiggjAV+r3+xPf/HddNzF54OgbDAbpum7seK/XS7/fX2BEAKwDFUSAI2hzc3NidXBSZZH10ev1sr29vewwAFgjKogAAAAkkSACAAAwIkEEAAAgiQQRAACAEQkiAAAASSSIAAAAjDjmAmBNdV039riLfr8/8ZgMVsPW1tbY8yy7rpt4FiYAHIQKIsAa6vf7Y5OHruvGJh2slsFgkK7r9hzr9Xrp9/sLjgiAdaeCCLCGNjc3x1YIx1UVWU29Xi/b29vLDgOAY0IFEQAAgCQSRAAAAEYkiAAAACSRIAIAADAiQQQAACCJLqYAx9KkMxIT5yQuyqRzDhNnHQKweCqIAMfMpDMSE+ckLtKkcw4TZx0CsHgqiADHzKQzEhPnJC6acw4BWCUqiAAAACSRIAIAADAiQQQAACCJBBEAAIARTWoA+CqTjsFwBMb+OcYCgKNGBRGArzDpGAxHYEzHMRYAHDUqiAB8hUnHYDgCY3qOsQDgKFFBBAAAIIkEEQAAgBEJIgAAAEnsQQRgSpM6nCbHr8vppE6lupQCcNSoIAKwb5M6nCbHs8vppE6lupQCcNSoIAKwb5M6nCbHt8upTqUArAsVRAAAAJJIEAEAABixxBSAuVq3JjaTmtAkGtEAsF5UEAGYm3VsYjOpCU2iEQ0A60UFEYC5WdcmNprQAHBcqCACAACQZMUqiFV17yR/MGb4nq21KxYXDQCHYdIexWXtT3TYPQAMrWoF8ReT3HPX18mlRgTAzCbtUVzm/kSH3QPA0EpVEHd4j2ohwPqZtEdxY2Pj0Dqg7rcTqX2GABx3q1pBBOCYOcwOqDqRAsD+VGtt2THcaMcexKuTnJ3k+iRvTfLk1tofHeD5NpKcPHny5JHtnAfA0KkK40H2A6oQAnBcbW9v58SJE0lyorV22l+Eq7bE9JNJnpPk8iTXJOkl+fkkl1fV97XWfm/cA6vq3CTn7Lp83iHFCcCC9fv9A1cQVQgBYH9WqoK4l6q6dZJ3Jrm2tfatE+67OMlFe42pIAIAAMfRtBXEld+D2Fr7RJLfTfItVXXzCbdekuTErq8HHnqAAAAAa2LVlpiOU6PvY8udrbWrM9y7+OUHVY25GwAAgN1WvoJYVbdJ8v1J3t5a++yy4wEAAFhXK1VBrKqXJPlAkv+R5GNJvinJ45PcPskjlhcZAADA+lupBDHJO5L0k/zzJGcluTbJHyX5J621P11mYAAAAOtupRLE1trTkzx92XEAAAAcRyu/BxEAAIDFkCACAACQRIIIAADAiAQRAACAJCvWpOYQ3CxJuq5bdhwAAAALtyMXutl+7q/W2uFFs2RV9QNJXr3sOAAAAJbsga213zndTeueIN4qyfck+WCSG5Yczk7nZZi4PjDJe5ccC+vH/OIwmV8cNnOMw2R+cZhWdX7dLMnXJ3lLa+2Tp7t5rZeYjv4HnDZLXrSqOvXH97bWtpcZC+vH/OIwmV8cNnOMw2R+cZhWfH69bb83alIDAABAEgkiAAAAIxJEAAAAkkgQl+WjSZ40+g7zZn5xmMwvDps5xmEyvzhMazG/1rqLKQAAAPungggAAEASCSIAAAAjEkQAAACSSBAXqqrOqqpnV9VVVfXZqnp7Vf3osuPiaKmq762qS6vq3VX111X1v6vq1VX1t/e499ur6o1VdV1VfaKqXlFVd11G3BxdVfXIqmpVdd0eY+YYU6uq766qy6rq41X1map6T1X9m133mFtMraq+rapeNXqvdf3od+VmVX3trvvMLyaqqltW1TOq6g1V9dHR78GLx9y77/lUVT89mpefq6r/VVUXVdVND/U/ZkoSxMV6RZKHZ9jd6IIkf5rkpVX10KVGxVHzmCR3SfKcJPdP8rgk5ya5oqq+99RNVXX3JJcnuVmSH0nyE0nuluT/q6pzFhsyR1VV3SnJM5NctceYOcbURr/z3pLkk0n+aYb/jv1Kktpxj7nF1Krq/CR/nOHvyJ9N8v1JfivJZpKX7rjP/GI/zk7yqCR/I8mrxt00zXyqqidm+P7tFUn+UZJLkvxikufOPfoZ6GK6IFV1/ySvTfLQ1trOf6TekGQjyZ1ba19cVnwcHVV1bmvt6l3XzkrSJTnZWrvv6NpvJ7lPkvNaa58aXfuGJO9J8qzW2i8sNnKOoqp6TZKW5NokD26tnbVjzBxjKqMPHP48yQtbaxdOuM/cYmpV9ZQkT0zSa629d8f138jwjf5tW2sfN7/Yj6qqJGmttaq6XUZHWLTWLt51377mU1WdneRDGf779+gdj//FJE9JcqK1duWh/4ftgwri4vxgkuuSvGzX9ecnuWOS71x4RBxJu5PD0bXrklyZ5OuTpKq+JsNPTv/rqX+sRve9P8kfZDgfYaKqeliS70nyVW/kzTEO6JFJbpFhxXBP5hYz+Pzo+yd3Xf9Eki8lucH8Yr/ayKR7ppxP90tyZobv/Xd6foYrKB40h7DnQoK4OCeSvKu19oVd19+xYxwOpKpuleTbk2yPLp2X5Ob58vza6R1JelV15oLC4wiqqnOTPDvJE1prH9rjFnOMg7hXhtXou4/24X+hqq6uql+vqq8b3WNucVAvyDAZfF5V3XW0h+z7kzw6yXNba38d84v5mmY+nXqv/86dN7XWPpzkY1mhXECCuDhnZ/hLcbdrd4zDQT03w0/lnzr6+dR8GjfnKsltFhAXR9clGS4FfN6YcXOMg7hTkq/NcDXNIMl9k/xqhnsRLxst6TK3OJDW2l8muWeGb7Tfm+RTSV6TYeL4uNFt5hfzNM18OjvJ50YfVOx178rkAl+z7ACOmUllaptBOZCqenKSH0vy0621/7lr2JxjalX1w0kekOTbTre8JuYY0zkjwyVWT2qtPX107fKquiHDivU/SHL96Lq5xVSq6i4ZJoR/leTBGe4Z+84kv5TkrCQ/ueN284t52u98OhLzToK4ONdk708Gbjv6vtcnDzBRVV2U4S++J7bWfm3H0DWj7+PmXMtwGQ58hVHDo+cm+fdJrqqqW4+GbjYav3WG+3zMMQ7imiTflOT3dl1/XYYJ4rcnefXomrnFtJ6e5OuS3GNHleYPq+pjSS6tqhcm+cjouvnFPEzzu/CaJGdW1de21q7f497dH/IvjSWmi/POJH9rtJl1p28efT+54Hg44kbJ4cVJLm6t/fKu4fcm+Uy+PL92+uYkXWvts4cbIUfU7ZLcPsnjk3x8x9dDMlzG/PEkL445xsHstU8n+fIRF1+KucXB3SPJlXss4fvT0fdTS0/NL+Zlmvn0zh3Xb1RVd8jwd+/K5AISxMV5ZYbLG3541/WHZ3i+2H9feEQcWaMDpS9O8pTW2pN2j4+aIb0myQ9V1S13PO7OGbZifsWCQuXo+UiGc2T31+8l+ezoz79kjnFA/3X0/YJd1+8/+n6FucUMrkqyMVoJsdM9R98/ZH4xT1POp9dn+Hv0Ebue5hEZVhpfdYihTsU5iAs0OvPwO5L8QoZn1j0kyT9L8rDW2ouXGRtHR1U9PsODy1+fZK/k8IrRfXfP8FPT/z/DZTdnJtnKcBnDPVprH11UzBx9VfWf89XnIJpjTK2qfifJP8zw3K8rMvy9eFGSN7bWHjC6x9xialX1Axm+yf7vSZ6VYWfI70ryr5N8IMN91TeYX+xXVV2Q4eqZWya5NMMGW789Gr6stXb9NPOpqp6Y5MlJnpbkDUn+Tob/Fr6wtfaohfxH7YMEcYFGn2g9NcmPZDhp3p3kaa2131pqYBwpVXV5hmfT7am1Vjvu/dsZnjd2zyRfSPLmJP9y5wHCsB97JYij6+YYU6mqm2eYED40yf+VYdXnxRk2rvncjvvMLaZWVfdJ8oQk35LkVkk+mGGF52mttWt23Gd+cVpV9ZdJvmHM8DeOOudONZ+q6meSPDbJXTJctfP8JE9trX1+973LIkEEAAAgiT2IAAAAjEgQAQAASCJBBAAAYESCCAAAQBIJIgAAACMSRAAAAJJIEAEAABiRIAIAAJBEgggAAMCIBBEAplRVF1dVG31dt2vsL6vqdxcQw6t2xHDysF8PgONBgggAB3fPJPdZ0mv/q9Hrv21Jrw/AGvqaZQcAAEdVa+2KJb72XyRJVX0qye2WFQcA60UFEYBjp6rOrKq3VVVXVbfacf0OVfWRqrq8qm4yx9e7sKq+UFVPGv18l9HS0J+vql8YLUv9zOh171ZVN62qp1fVVVX1yap6ZVWdO694AGAcCSIAx05r7bNJfiTJuUkuTZKqOiPJi5NUkoe01r446+vU0DOTPDvJI1trF+265bFJ/t7o+yOT3D3Ja5L8pyTnJPmJDJeS3jfJf5w1HgA4HUtMATiWWmvvqapHJhlU1eOS3DbJvZPcr7X24Vmfv6punuRFGSZ3F7TW3rTHbZ9I8qDW2pdGj7ldhsnku1trD9zxXHdP8rNV9XWttU/NGhsAjCNBBODYaq39dlXdO8mvJrlJkl9urf3+HJ767CRvTnKnJN/dWhvXZfSyU8nhyLtG31+7675T1++cRMdSAA6NJaYAHHeXJrlpki8k+Xdzes67JfnOJK+bkBwmybW7fr7hNNfPnENsADCWBBGAY6uqbpHhMtC/SPKZzG+f31uT/HiSn6yq3xjtbwSAlWeJKQDH2a9nuGzz/86wQczLq+pftNaeNesTt9ZeUFV/neQlSW5RVQ+fR+MbADhMEkQAjqVRg5qHJfnx1tp2ku2q+rUkv1JV/6219iezvkZr7eVVdX2Slye5eVU9pLV2w+keBwDLYskLAMdOVX1zhvsNX9Ba+887hv5lkndk2Nn01vN4rdbaZUnun+QfJnn1qLspAKykaq0tOwYAOFKq6uIkF2XY3KYtY+noaF/jGUnelOTs1tqJRccAwPpRQQSAg/t8kk8u6bVfMXr9ey3p9QFYQyqIADClqrpjkjuOfvxia+1tS4jhvCS3Gf34mdE+SgCYiQQRAACAJJaYAgAAMCJBBAAAIIkEEQAAgBEJIgAAAEkkiAAAAIxIEAEAAEgiQQQAAGBEgggAAEASCSIAAAAjEkQAAACSSBABAAAY+T8kqLWHtaj+VwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cc.plot_prisms(depths, basin_boundaries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forward model some gravity data at a set of locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5e3, 105e3, 60)\n",
    "density = -300  # kg/m³\n",
    "data = cc.forward_model(depths, basin_boundaries, density, x)\n",
    "\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot(x / 1000, data, \".k\")\n",
    "plt.xlabel(\"x [km]\")\n",
    "plt.ylabel(\"gravity disturbance [mGal]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating the Jacobian matrix\n",
    "\n",
    "The first step to most inverse problems is being able to calculate the Jacobian matrix. We'll do this for our problem by a first-order finite differences approximation. If you can get analytical derivatives, that's usually a lot better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_jacobian(parameters, basin_boundaries, density, x):\n",
    "    \"\"\"\n",
    "    Calculate the Jacobian matrix by finite differences.\n",
    "    \"\"\"\n",
    "    jacobian = np.empty((x.size, parameters.size))\n",
    "    step = np.zeros_like(parameters)\n",
    "    delta = 10\n",
    "    for j in range(jacobian.shape[1]):\n",
    "        step[j] += delta\n",
    "        jacobian[:, j] = (\n",
    "            (\n",
    "                cc.forward_model(parameters + step, basin_boundaries, density, x)\n",
    "                - cc.forward_model(parameters, basin_boundaries, density, x)\n",
    "            ) \n",
    "            / delta\n",
    "        )\n",
    "        step[j] = 0\n",
    "    return jacobian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate and plot an example so we can see what this matrix looks like. We'll use a parameter vector with constant depths at first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "parameters = np.zeros(30) + 5000\n",
    "\n",
    "jacobian = make_jacobian(parameters, basin_boundaries, density, x)\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(jacobian)\n",
    "plt.colorbar(label=\"mGal/m\")\n",
    "plt.xlabel(\"columns\")\n",
    "plt.ylabel(\"rows\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve the inverse problem \n",
    "\n",
    "Now that we have a way of forward modelling and calculating the Jacobian matrix, we can implement the Gauss-Newton method for solving the non-linear inverse problem. The function below takes the input data, model configuration, and an initial estimate and outputs the estimated parameters and a list with the goal function value per iteration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def basin2d_inversion(x, data, basin_boundaries, density, initial, max_iterations=10):\n",
    "    \"\"\"\n",
    "    Solve the inverse problem using the Gauss-Newton method.\n",
    "    \"\"\"\n",
    "    parameters = initial.astype(np.float64).copy() \n",
    "    predicted = cc.forward_model(parameters, basin_boundaries, density, x)\n",
    "    residuals = data - predicted\n",
    "    goal_function = [np.linalg.norm(residuals)**2]\n",
    "    for i in range(max_iterations):       \n",
    "        jacobian = make_jacobian(parameters, basin_boundaries, density, x)\n",
    "        hessian = jacobian.T @ jacobian\n",
    "        gradient = jacobian.T @ residuals\n",
    "        deltap = np.linalg.solve(hessian, gradient)\n",
    "        new_parameters = parameters + deltap\n",
    "        predicted = cc.forward_model(new_parameters, basin_boundaries, density, x)\n",
    "        residuals = data - predicted\n",
    "        current_goal = np.linalg.norm(residuals)**2\n",
    "        if current_goal > goal_function[-1]:\n",
    "            break\n",
    "        parameters = new_parameters\n",
    "        goal_function.append(current_goal)\n",
    "    return parameters, goal_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use this function to invert our synthetic data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimated, goal_function = basin2d_inversion(\n",
    "    x, data, basin_boundaries, density, initial=np.full(30, 1000),\n",
    ")\n",
    "predicted = cc.forward_model(estimated, basin_boundaries, density, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the observed vs predicted data so we can inspect the fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot(x / 1e3, data, \".k\", label=\"observed\")\n",
    "plt.plot(x / 1e3, predicted, \"-r\", label='predicted')\n",
    "plt.legend()\n",
    "plt.xlabel(\"x [km]\")\n",
    "plt.ylabel(\"gravity disturbance [mGal]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the convergence of the method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(goal_function)\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"goal function (mGal²)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally see if our estimate is close to the true model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='x [km]', ylabel='depth [km]'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = cc.plot_prisms(depths, basin_boundaries)\n",
    "cc.plot_prisms(estimated, basin_boundaries, edgecolor=\"blue\", ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perfect! It seems that our inversion works well under these conditions (this initial estimate and no noise in the data). **Now let's break it!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Your turn**\n",
    "\n",
    "**Add pseudo-random noise to the data using `np.random.normal` function and investigate the effect this has on the inversion results.** A typical gravity survey has accuracy in between 0.5-1 mGal. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "noise = np.random.normal(loc=0, scale=1, size=data.size)\n",
    "noisy_data = data + noise\n",
    "\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot(x / 1000, noisy_data, \".k\")\n",
    "plt.xlabel(\"x [km]\")\n",
    "plt.ylabel(\"gravity disturbance [mGal]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the inversion again with the noisy data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimated, goal_function = basin2d_inversion(\n",
    "    x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000),\n",
    ")\n",
    "predicted = cc.forward_model(estimated, basin_boundaries, density, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot(x / 1e3, noisy_data, \".k\", label=\"observed\")\n",
    "plt.plot(x / 1e3, predicted, \"-r\", label='predicted')\n",
    "plt.legend()\n",
    "plt.xlabel(\"x [km]\")\n",
    "plt.ylabel(\"gravity disturbance [mGal]\")\n",
    "\n",
    "ax = cc.plot_prisms(depths, basin_boundaries)\n",
    "cc.plot_prisms(estimated, basin_boundaries, edgecolor=\"blue\", ax=ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow! It seems that **small perturbations of the data led to large changes in the estimated model**. This is characteristic of an **unstable inverse problem**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can go one step further and run several of these inversion in a loop for different random noise realizations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimates = []\n",
    "for i in range(5):\n",
    "    noise = np.random.normal(loc=0, scale=1, size=data.size)\n",
    "    noisy_data = data + noise\n",
    "    estimated, goal_function = basin2d_inversion(\n",
    "        x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000),\n",
    "    )\n",
    "    estimates.append(estimated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = cc.plot_prisms(depths, basin_boundaries)\n",
    "for estimated in estimates:\n",
    "    cc.plot_prisms(estimated, basin_boundaries, edgecolor=\"#0000ff66\", ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Question time!**\n",
    "\n",
    "**Why does the inversion become more unstable for the deeper portions of the model?**\n",
    "\n",
    "Hint: It's related to the physics of the forward modelling and the Jacobian matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization to the rescue\n",
    "\n",
    "To deal with the instability issues we encountered, we will apply **first-order Tikhonov regularization** (aka \"smoothness\"). \n",
    "\n",
    "First thing we need to do is create the finite difference matrix $\\bar{\\bar{R}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def finite_difference_matrix(nparams):\n",
    "    \"\"\"\n",
    "    Create the finite difference matrix for regularization.\n",
    "    \"\"\"\n",
    "    fdmatrix = np.zeros((nparams - 1, nparams))\n",
    "    for i in range(fdmatrix.shape[0]):\n",
    "        fdmatrix[i, i] = -1\n",
    "        fdmatrix[i, i + 1] = 1\n",
    "    return fdmatrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0., -1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0., -1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., -1.,  1.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0., -1.,  1.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0., -1.,  1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0., -1.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0., -1.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., -1.,  1.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "finite_difference_matrix(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use this to make a new inversion function with smoothness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def basin2d_smooth_inversion(x, data, basin_boundaries, density, initial, smoothness, max_iterations=10):\n",
    "    \"\"\"\n",
    "    Solve the regularized inverse problem using the Gauss-Newton method.\n",
    "    \"\"\"\n",
    "    parameters = initial.astype(np.float64).copy() \n",
    "    predicted = cc.forward_model(parameters, basin_boundaries, density, x)\n",
    "    residuals = data - predicted\n",
    "    goal_function = [np.linalg.norm(residuals)**2]\n",
    "    fdmatrix = finite_difference_matrix(parameters.size)\n",
    "    for i in range(max_iterations):       \n",
    "        jacobian = make_jacobian(parameters, basin_boundaries, density, x)\n",
    "        hessian = jacobian.T @ jacobian + smoothness * fdmatrix.T @ fdmatrix\n",
    "        gradient = jacobian.T @ residuals - smoothness * fdmatrix.T @ fdmatrix @ parameters\n",
    "        deltap = np.linalg.solve(hessian, gradient)\n",
    "        new_parameters = parameters + deltap\n",
    "        predicted = cc.forward_model(new_parameters, basin_boundaries, density, x)\n",
    "        residuals = data - predicted\n",
    "        current_goal = np.linalg.norm(residuals)**2\n",
    "        if current_goal > goal_function[-1]:\n",
    "            break\n",
    "        parameters = new_parameters\n",
    "        goal_function.append(current_goal)\n",
    "    return parameters, goal_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we check if it works on our noisy data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimates = []\n",
    "for i in range(5):\n",
    "    noise = np.random.normal(loc=0, scale=1, size=data.size)\n",
    "    noisy_data = data + noise\n",
    "    estimated, goal_function = basin2d_smooth_inversion(\n",
    "        x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000), smoothness=1e-5\n",
    "    )\n",
    "    estimates.append(estimated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = cc.plot_prisms(depths, basin_boundaries)\n",
    "for estimated in estimates:\n",
    "    cc.plot_prisms(estimated, basin_boundaries, edgecolor=\"#0000ff66\", ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Question time!**\n",
    "\n",
    "**What happens when the regularization paramater is extremely high?** Try to predict what the answer would be and then execute the code to check your reasoning.\n",
    "\n",
    "Hint: what is the smoothest possible model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Your turn**\n",
    "\n",
    "**Can our regularized model recover a non-smooth geometry?** For example, real sedimentary basins often have [faults](https://en.wikipedia.org/wiki/Fault_(geology)) running through them, causing sharp jumps in the sediment thickness (up or down). \n",
    "\n",
    "To answer this question:\n",
    "\n",
    "1. Use the modified model depths below (the `depths` array) that introduce a shift up or down by 1-2 km in a section of the model of about 5-10 km.\n",
    "2. Generate new noisy data with this new model\n",
    "3. Invert the noisy data and try to find a model that:\n",
    "   1. Fits the data\n",
    "   2. Is stable (doesn't vary much if we change the noise)\n",
    "   3. Recovers the sharp boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "fault_model = np.copy(depths)\n",
    "fault_model[45:55] -= 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='x [km]', ylabel='depth [km]'>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cc.plot_prisms(fault_model, basin_boundaries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now fill out the rest of the code below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "fault_data = cc.forward_model(fault_model, basin_boundaries, density, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimates = []\n",
    "for i in range(5):\n",
    "    noise = np.random.normal(loc=0, scale=1, size=data.size)\n",
    "    noisy_data = fault_data + noise\n",
    "    estimated, goal_function = basin2d_smooth_inversion(\n",
    "        x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000), smoothness=1e-5\n",
    "    )\n",
    "    estimates.append(estimated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.5, 0.0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = cc.plot_prisms(fault_model, basin_boundaries)\n",
    "for estimated in estimates:\n",
    "    cc.plot_prisms(estimated, basin_boundaries, edgecolor=\"#0000ff66\", ax=ax)\n",
    "ax.set_ylim(5.5, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Question time!**\n",
    "\n",
    "**What would happen if we used a \"sharpness\" regularization?** Would we be able to recover the faults? What about the smoother parts of the model? \n",
    "\n",
    "One type of sharpness regularization is called \"total-variation regularization\" and it [has been used for this problem in the past](https://doi.org/10.1190/1.3524286)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extra thinking points\n",
    "\n",
    "* What happens if we get the density wrong?\n",
    "* What are the sources of uncertainty in our final solution? Is it just the noise in the data?\n",
    "* How much does the solution depend on the inital estimate?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Bonus:** Optimizing code\n",
    "\n",
    "The code we wrote is not the greatest and it does take a while to run even for these really small 2D problems. There are ways in which we can make the code fast. But before we do any of that, **we need to know where our code spends most of its time**. Otherwise, we could spend hours optimizing a part of the code that is already really fast.\n",
    "\n",
    "This can be done with tools called **profilers**, which measure the time spent in each function of your code. This is also why its very important to **break up your code into functions**. In a Jupyter notebook, you can run the standard Python profiler by using the `%%prun` cell magic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
      "text/plain": [
       "         97909 function calls (96363 primitive calls) in 2.462 seconds\n",
       "\n",
       "   Ordered by: internal time\n",
       "\n",
       "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
       "    73440    1.560    0.000    1.560    0.000 cheatcodes.py:132(kernel)\n",
       "     9180    0.698    0.000    2.258    0.000 cheatcodes.py:98(prism_gravity)\n",
       "      306    0.051    0.000    2.453    0.008 cheatcodes.py:84(forward_model)\n",
       "      306    0.021    0.000    0.101    0.000 function_base.py:23(linspace)\n",
       " 2175/629    0.018    0.000    0.134    0.000 {built-in method numpy.core._multiarray_umath.implement_array_function}\n",
       "      306    0.007    0.000    0.021    0.000 fromnumeric.py:69(_wrapreduction)\n",
       "      311    0.006    0.000    0.023    0.000 numeric.py:76(zeros_like)\n",
       "      306    0.006    0.000    0.016    0.000 numerictypes.py:358(issubdtype)\n",
       "      612    0.006    0.000    0.009    0.000 numerictypes.py:284(issubclass_)\n",
       "      955    0.004    0.000    0.004    0.000 {built-in method builtins.issubclass}\n",
       "      311    0.004    0.000    0.008    0.000 <__array_function__ internals>:2(empty_like)\n",
       "      311    0.004    0.000    0.032    0.000 <__array_function__ internals>:2(zeros_like)\n",
       "      312    0.004    0.000    0.008    0.000 <__array_function__ internals>:2(copyto)\n",
       "      306    0.004    0.000    0.110    0.000 <__array_function__ internals>:2(linspace)\n",
       "      306    0.004    0.000    0.010    0.000 <__array_function__ internals>:2(ndim)\n",
       "      306    0.004    0.000    0.032    0.000 <__array_function__ internals>:2(any)\n",
       "      306    0.004    0.000    0.008    0.000 <__array_function__ internals>:2(result_type)\n",
       "      306    0.003    0.000    0.009    0.000 {method 'any' of 'numpy.generic' objects}\n",
       "      306    0.003    0.000    0.113    0.000 cheatcodes.py:75(prism_boundaries)\n",
       "      306    0.003    0.000    0.024    0.000 fromnumeric.py:2268(any)\n",
       "        5    0.003    0.001    2.380    0.476 2590771396.py:1(make_jacobian)\n",
       "      306    0.003    0.000    0.003    0.000 {method 'reduce' of 'numpy.ufunc' objects}\n",
       "      612    0.003    0.000    0.003    0.000 {built-in method numpy.asanyarray}\n",
       "      306    0.003    0.000    0.006    0.000 _methods.py:54(_any)\n",
       "      306    0.003    0.000    0.004    0.000 numeric.py:1858(isscalar)\n",
       "        5    0.003    0.001    0.004    0.001 linalg.py:313(solve)\n",
       "      312    0.002    0.000    0.002    0.000 {built-in method numpy.zeros}\n",
       "      306    0.002    0.000    0.002    0.000 {built-in method numpy.arange}\n",
       "      306    0.002    0.000    0.002    0.000 {method 'reshape' of 'numpy.ndarray' objects}\n",
       "      316    0.001    0.000    0.001    0.000 {built-in method builtins.getattr}\n",
       "      312    0.001    0.000    0.001    0.000 {method 'astype' of 'numpy.ndarray' objects}\n",
       "      312    0.001    0.000    0.001    0.000 multiarray.py:1071(copyto)\n",
       "      306    0.001    0.000    0.001    0.000 fromnumeric.py:70(<dictcomp>)\n",
       "      306    0.001    0.000    0.001    0.000 function_base.py:18(_linspace_dispatcher)\n",
       "      306    0.001    0.000    0.001    0.000 {built-in method _operator.index}\n",
       "      311    0.001    0.000    0.001    0.000 multiarray.py:80(empty_like)\n",
       "      311    0.001    0.000    0.001    0.000 numeric.py:72(_zeros_like_dispatcher)\n",
       "      306    0.001    0.000    0.001    0.000 fromnumeric.py:3127(ndim)\n",
       "      306    0.001    0.000    0.001    0.000 fromnumeric.py:3123(_ndim_dispatcher)\n",
       "      306    0.001    0.000    0.001    0.000 {built-in method builtins.isinstance}\n",
       "      306    0.001    0.000    0.001    0.000 {method 'items' of 'dict' objects}\n",
       "      306    0.001    0.000    0.001    0.000 fromnumeric.py:2263(_any_dispatcher)\n",
       "      306    0.001    0.000    0.001    0.000 multiarray.py:664(result_type)\n",
       "        1    0.001    0.001    2.462    2.462 3453615577.py:1(basin2d_smooth_inversion)\n",
       "        6    0.000    0.000    0.001    0.000 linalg.py:2363(norm)\n",
       "       21    0.000    0.000    0.000    0.000 linalg.py:112(isComplexType)\n",
       "        5    0.000    0.000    0.000    0.000 linalg.py:135(_commonType)\n",
       "       10    0.000    0.000    0.000    0.000 linalg.py:107(_makearray)\n",
       "       10    0.000    0.000    0.000    0.000 linalg.py:125(_realType)\n",
       "        6    0.000    0.000    0.001    0.000 <__array_function__ internals>:2(norm)\n",
       "        6    0.000    0.000    0.000    0.000 <__array_function__ internals>:2(dot)\n",
       "       17    0.000    0.000    0.000    0.000 {built-in method numpy.asarray}\n",
       "        1    0.000    0.000    2.462    2.462 {built-in method builtins.exec}\n",
       "        5    0.000    0.000    0.004    0.001 <__array_function__ internals>:2(solve)\n",
       "       10    0.000    0.000    0.000    0.000 {method 'get' of 'dict' objects}\n",
       "        6    0.000    0.000    0.000    0.000 {built-in method numpy.empty}\n",
       "        6    0.000    0.000    0.000    0.000 {method 'ravel' of 'numpy.ndarray' objects}\n",
       "        1    0.000    0.000    0.001    0.001 3264890642.py:1(finite_difference_matrix)\n",
       "        6    0.000    0.000    0.000    0.000 multiarray.py:736(dot)\n",
       "        6    0.000    0.000    0.000    0.000 linalg.py:2359(_norm_dispatcher)\n",
       "        5    0.000    0.000    0.000    0.000 linalg.py:102(get_linalg_error_extobj)\n",
       "        5    0.000    0.000    0.000    0.000 linalg.py:199(_assert_stacked_square)\n",
       "        5    0.000    0.000    0.000    0.000 linalg.py:193(_assert_stacked_2d)\n",
       "        1    0.000    0.000    0.000    0.000 numeric.py:289(full)\n",
       "        5    0.000    0.000    0.000    0.000 {method '__array_prepare__' of 'numpy.ndarray' objects}\n",
       "        5    0.000    0.000    0.000    0.000 linalg.py:309(_solve_dispatcher)\n",
       "        1    0.000    0.000    2.462    2.462 <string>:1(<module>)\n",
       "        4    0.000    0.000    0.000    0.000 {method 'append' of 'list' objects}\n",
       "        1    0.000    0.000    0.000    0.000 {method 'copy' of 'numpy.ndarray' objects}\n",
       "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%prun \n",
    "basin2d_smooth_inversion(\n",
    "        x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000), smoothness=1e-5\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `tottime` column is the amount of time spent on the function itself (not counting functions called inside it) and `cumtime` is the total time spent in the function, including function calls inside it. \n",
    "\n",
    "We can see from the profiling that the majority of the computation is spend in forward modelling, in particular for building the Jacobian. So if we can optimize `make_jacobian` that will have the biggest impact on performance of all.\n",
    "\n",
    "To start let's measure the computation time of `make_jacobian` with the `%%timeit` magic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "252 ms ± 8.78 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "make_jacobian(np.full(30, 1000), basin_boundaries, density, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, now we can try to do better.\n",
    "\n",
    "For many of these problems, the biggest return on investment is **not** parallelization or going to C/Fortran. **The largest improvements come from better maths/physics**. Here, we can take advantage of potential-field theory to cut down on the computation time of the Jacobian. \n",
    "\n",
    "We'll use the fact that the difference in gravity values produced by two models is the same as the gravity value produced by the difference in the models. Meaning that $\\delta g = g(m_1) - g(m_2) = g(m_1 - m_2)$. This way, we can reduce by more than half the number of forward modelling operations we do in the finite-difference computations.\n",
    "\n",
    "So instead of calculating the entire basin model with and without a small step in a single parameter, we can only calculate the effect of that small step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_jacobian_fast(parameters, basin_boundaries, density, x):\n",
    "    \"\"\"\n",
    "    Calculate the Jacobian matrix by finite differences.\n",
    "    \"\"\"\n",
    "    jacobian = np.empty((x.size, parameters.size))\n",
    "    delta = 10\n",
    "    boundaries = cc.prism_boundaries(parameters, basin_boundaries)\n",
    "    for j in range(jacobian.shape[1]):\n",
    "        jacobian[:, j] = (\n",
    "            (\n",
    "                # Replace with a single forward modelling of a single prism\n",
    "                cc.prism_gravity(x, boundaries[j], boundaries[j + 1], parameters[j], parameters[j] + delta, density)\n",
    "            ) \n",
    "            / delta\n",
    "        )\n",
    "    return jacobian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we check if the results are still correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(\n",
    "    make_jacobian(np.full(30, 1000), basin_boundaries, density, x),\n",
    "    make_jacobian_fast(np.full(30, 1000), basin_boundaries, density, x)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can measure the time again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.63 ms ± 87.8 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "make_jacobian_fast(np.full(30, 1000), basin_boundaries, density, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This one change gave use 2 orders of magnitude improvement in the function that makes up most of the computation time. **Now that is time well spent!**\n",
    "\n",
    "We can measure how much of a difference this makes for the inversion as a whole by making a new function with our fast Jacobian matrix calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fast_basin2d_smooth_inversion(x, data, basin_boundaries, density, initial, smoothness, max_iterations=10):\n",
    "    \"\"\"\n",
    "    Solve the regularized inverse problem using the Gauss-Newton method.\n",
    "    \"\"\"\n",
    "    parameters = initial.astype(np.float64).copy() \n",
    "    predicted = cc.forward_model(parameters, basin_boundaries, density, x)\n",
    "    residuals = data - predicted\n",
    "    goal_function = [np.linalg.norm(residuals)**2]\n",
    "    fdmatrix = finite_difference_matrix(parameters.size)\n",
    "    for i in range(max_iterations):       \n",
    "        # Swap out the slow jacobian for the fast one\n",
    "        jacobian = make_jacobian_fast(parameters, basin_boundaries, density, x)\n",
    "        hessian = jacobian.T @ jacobian + smoothness * fdmatrix.T @ fdmatrix\n",
    "        gradient = jacobian.T @ residuals - smoothness * fdmatrix.T @ fdmatrix @ parameters\n",
    "        deltap = np.linalg.solve(hessian, gradient)\n",
    "        new_parameters = parameters + deltap\n",
    "        predicted = cc.forward_model(new_parameters, basin_boundaries, density, x)\n",
    "        residuals = data - predicted\n",
    "        current_goal = np.linalg.norm(residuals)**2\n",
    "        if current_goal > goal_function[-1]:\n",
    "            break\n",
    "        parameters = new_parameters\n",
    "        goal_function.append(current_goal)\n",
    "    return parameters, goal_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we can measure the computation time for both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.92 s ± 43.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "basin2d_smooth_inversion(\n",
    "        x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000), smoothness=1e-5\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "175 ms ± 12.1 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "fast_basin2d_smooth_inversion(\n",
    "        x, noisy_data, basin_boundaries, density, initial=np.full(30, 1000), smoothness=1e-5\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We changed 3 lines of code and achived a factor of 10 speedup.** Again, this could only be done because we first profiled the code and then focused on finding a fundamentally better way of calculating. "
   ]
  }
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