tutorials/1D Travel-time tomography using the Eikonal equation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "emerging-diagram",
   "metadata": {},
   "source": [
    "# Traveltime tomography using the Eikonal equation\n",
    "\n",
    "@Author: Ettore Biondi - ebiondi@caltech.edu"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "level-cargo",
   "metadata": {},
   "source": [
    "In this notebook, we provide an example of how to solve a traveltime tomography problem using the solution to the Eikonal equation. This equation can be written as follows:\n",
    "\\begin{eqnarray}\n",
    "\\nabla \\tau(\\mathbf{x}) \\cdot \\nabla \\tau(\\mathbf{x})= \\|\\nabla \\tau(\\mathbf{x})\\|^2 = \\frac{1}{v^2(\\mathbf{x})},\n",
    "\\end{eqnarray}\n",
    "where $v$ is the wave speed, $\\tau$ is the traveltime, and $\\mathbf{x}$ denotes the spatial variables (i.e., $x$, $y$, and $z$). To solve the previous partial-differential equation (PDE), we employ the fast-marching method described by [Sethian (1996)](https://www.pnas.org/content/pnas/93/4/1591.full.pdf). The solution of the Eikonal equation depends non-linearly on the velocity parameter $v$. Hence, we express its discrete solution as follows:\n",
    "\\begin{eqnarray}\n",
    "\\pmb{\\tau} = \\mathbf{f}(\\mathbf{v}).\n",
    "\\end{eqnarray}\n",
    "The Jacobian $\\mathbf{F}$ of the non-linear operator $\\mathbf{f}$ obeys the following equation:\n",
    "\\begin{eqnarray}\n",
    "2[\\nabla \\tau(\\mathbf{x})] \\cdot [\\nabla \\delta\\tau(\\mathbf{x})] = \\delta v(\\mathbf{x}),\n",
    "\\end{eqnarray}\n",
    "where $\\delta\\tau$ represents the traveltime perturbation due to the velocity perturbation $\\delta v(\\mathbf{x})$. The previous relation when discretized represents a linear system of equations that can be solved by forward substitution [Li et al. (2013)](https://pi.math.cornell.edu/~vlad/papers/DSR_Geophysics_2013.pdf). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "formed-greene",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING! DATAPATH not found. The folder /tmp will be used to write binary files\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/nas/home/fpicetti/miniconda3/envs/occd/lib/python3.10/site-packages/dask_jobqueue/core.py:20: FutureWarning: tmpfile is deprecated and will be removed in a future release. Please use dask.utils.tmpfile instead.\n",
      "  from distributed.utils import tmpfile\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import occamypy as o\n",
    "\n",
    "# Plotting\n",
    "from matplotlib import rcParams\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import matplotlib.pyplot as plt\n",
    "rcParams.update({\n",
    "    'image.cmap'     : 'jet',\n",
    "    'image.aspect'   : 'auto',\n",
    "    'image.interpolation': None,\n",
    "    'axes.grid'      : True,\n",
    "    'figure.figsize' : (10, 6),\n",
    "    'savefig.dpi'    : 300,\n",
    "    'axes.labelsize' : 14,\n",
    "    'axes.titlesize' : 16,\n",
    "    'font.size'      : 14,\n",
    "    'legend.fontsize': 14,\n",
    "    'xtick.labelsize': 14,\n",
    "    'ytick.labelsize': 14,\n",
    "    'text.usetex'    : True,\n",
    "    'font.family'    : 'serif',\n",
    "    'font.serif'     : 'Latin Modern Roman',\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "legitimate-association",
   "metadata": {},
   "source": [
    "Let's start by implementing the fast-marching method to solve the non-linear PDE defined by the Eikonal equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "finnish-resolution",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Functions for solving Eikonal equation in 1D\n",
    "def sorting(tt, idx, ordering=\"a\"):\n",
    "    if ordering == \"a\":\n",
    "        sorted_indices = np.argsort(tt[idx])\n",
    "    elif ordering == \"d\":\n",
    "        sorted_indices = np.argsort(-tt[idx])\n",
    "    else:\n",
    "        raise ValueError(\"Unknonw ordering: %s! Provide a or d for ascending or descending\" % ordering)\n",
    "    \n",
    "    # Sorting indices\n",
    "    idx_sort = [idx[id] for id in sorted_indices]\n",
    "    return idx_sort\n",
    "\n",
    "\n",
    "# Fast-Marching-Method (FMM) \n",
    "def FMM_tt(tt, vv, dx, status, trial_idx):\n",
    "    \"\"\"Function to perform fast-marching method\"\"\"\n",
    "    nx = vv.shape[0]\n",
    "    dx_inv = 1.0 / dx\n",
    "    # Various necessary variables\n",
    "    drxns = [-1, 1]\n",
    "    nbrs = np.zeros(2, dtype=int)\n",
    "    # FFM main loop\n",
    "    while len(trial_idx) > 0:\n",
    "        # Getting trial point with smallest traveltime\n",
    "        active_idx = trial_idx.pop(0)\n",
    "        status[active_idx] = 'k'\n",
    "\n",
    "        # Creating indices of neighbouring points\n",
    "        for idx in range(2):\n",
    "            nbrs[idx] = active_idx + drxns[idx]\n",
    "\n",
    "        # Loop over neighbourning points\n",
    "        for idx, nb in enumerate(nbrs):\n",
    "            # If point is outside the domain or has a known traveltime skip it\n",
    "            if nb < 0 or nb >= nx or status[nb] == 'k':\n",
    "                continue\n",
    "            # Checking if the velocity model is positive\n",
    "            if vv[nb] > 0:\n",
    "                fdt = np.zeros(2)\n",
    "                order = np.zeros(2)\n",
    "                # Computing forward and backward derivatives from nb\n",
    "                for ii in range(2):\n",
    "                    nb_i = nb + drxns[ii]\n",
    "                    if (nb_i < nx and 0 <= nb_i) and status[nb_i] == 'k':\n",
    "                        order[ii] = 1\n",
    "                        fdt[ii] = drxns[ii] * (tt[nb_i]-tt[nb]) * dx_inv\n",
    "                    else:\n",
    "                        order[ii] = 0\n",
    "                # Selecting upwind derivative \n",
    "                if fdt[0] > -fdt[1]:\n",
    "                    ii, idrx = 0, -1\n",
    "                else:\n",
    "                    ii, idrx = 1, 1\n",
    "                # Selecting correct neighbourning point\n",
    "                nb_i = nb + idrx\n",
    "                # Updating traveltime by solving quadratic equation\n",
    "                if order[ii] == 0:\n",
    "                    a = b = c = 0\n",
    "                else:\n",
    "                    a = dx_inv * dx_inv\n",
    "                    b = -2 * a * tt[nb_i]\n",
    "                    c = tt[nb_i] * tt[nb_i] * a - 1.0 / (vv[nb]*vv[nb])\n",
    "                # Point out of bounds\n",
    "                if a == 0:\n",
    "                    continue\n",
    "                det = b*b - 4.0*a*c\n",
    "                if det < 0.0:\n",
    "                    # Negative determinant; set it to zero\n",
    "                    new_t = - b / (2 * a)\n",
    "                else:\n",
    "                    new_t = (- b + np.sqrt(det)) / (2*a)\n",
    "                # Checking if new traveltime is smaller than current estimate for this point\n",
    "                if new_t < tt[nb]:\n",
    "                    tt[nb] = new_t\n",
    "                    if status[nb] == 'u':\n",
    "                        trial_idx.append(nb)\n",
    "                        status[nb] = 't'\n",
    "                    else:\n",
    "                        trial_idx = sorting(tt, trial_idx)\n",
    "    return"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "controlling-peninsula",
   "metadata": {},
   "source": [
    "Let's wrap this function into an operator class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "based-figure",
   "metadata": {},
   "outputs": [],
   "source": [
    "class EikonalTT_1D(o.Operator):\n",
    "\n",
    "    def __init__(self, vel, tt_data, dx, SouPos, RecPos):\n",
    "        \"\"\"1D Eikonal-equation traveltime prediction operator\"\"\"\n",
    "        # Setting Domain and Range of the operator\n",
    "        self.setDomainRange(vel, tt_data)\n",
    "        # Setting acquisition geometry\n",
    "        self.nSou = SouPos.shape[0]\n",
    "        self.nRec = RecPos.shape[0]\n",
    "        self.SouPos = SouPos.copy()\n",
    "        self.RecPos = RecPos.copy()\n",
    "        dataShape = tt_data.shape\n",
    "        if dataShape[0] != self.nSou:\n",
    "            raise ValueError(\"Number of sources inconsistent with traveltime vector (shape[0])\")\n",
    "        if dataShape[1] != self.nRec:\n",
    "            raise ValueError(\"Number of receivers inconsistent with traveltime vector (shape[1])\")\n",
    "        self.dx = dx\n",
    "        self.nx = vel.shape[0]\n",
    "\n",
    "    def forward(self, add, model, data):\n",
    "        \"\"\"Forward non-linear traveltime prediction\"\"\"\n",
    "        self.checkDomainRange(model, data)\n",
    "        if not add: \n",
    "            data.zero()\n",
    "        dataNd = data.getNdArray()\n",
    "        velNd = model.getNdArray()\n",
    "        # Initialization\n",
    "        tt = np.zeros(self.nx)\n",
    "        for iShot in range(self.nSou):\n",
    "            # Initial conditions\n",
    "            status = np.array([\"u\"] * self.nx) # All points are unknown\n",
    "            tt.fill(np.inf)\n",
    "            trial_idx = []\n",
    "            # Initial conditions\n",
    "            idx = self.SouPos[iShot]\n",
    "            tt[idx] = 0.0\n",
    "            status[idx] = 't' # Trial status\n",
    "            trial_idx.append(idx)\n",
    "            # Sorting trial time ascending order\n",
    "            trial_idx = sorting(tt, trial_idx)\n",
    "            FMM_tt(tt, velNd, self.dx, status, trial_idx)     \n",
    "            for iRec in range(self.nRec):\n",
    "                dataNd[iShot, iRec] += tt[self.RecPos[iRec]]\n",
    "        return"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "surgical-voice",
   "metadata": {},
   "source": [
    "We can now use this operator to compute some traveltimes using a simple velocity model in which a Gaussian anomaly is placed at its center."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "outdoor-minute",
   "metadata": {},
   "outputs": [
    {
     "data": {
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nrnZHU1CKvHfysl7a93HWvi9/fqUWzKqNqCIAaUIABpBqX1p7txpm3JoV4lpPv/7o1Q/GOQNT5e76V989qMw1SO6eX69fenRJdEUBSJUxA7CZzTKzpZP4mDXWawJA3MyeUa3/Zd3dWft27PlYJzquR1RR+XujvUM/br+Yte/3fu4eVVUyJgOgNKrG+dpXJe2WlG8z1prgXABIhF/55J368x8f05EL1yQNTs21/a/b9S//0f0RV1ae/rjto6ztT981T60rmiKqBkAajReA97j7y/m+oJk1TqEeACi56soK/ebau/TlnT8Z3vfinhP6rXV3af5MelIL6d2PL+tHH17I2vfb6+/mwTcAJTXm75vc/S/C+8zsy2b2RPD5DjN70cweD533jcKXCQDF9fMPL9LihunD2z19A/oPf3M0uoLK1PM/zB79/cTSRj26lHETAKWVb8PVEXd/2cx+V9Jhd39S+bdIAEDsVFdWaMtnm7P2/ec3julqd29EFZWfIxeu6fvvZS828k/WLo+oGgBplm8AHlquZ72kF4PPZxeuHACIzuY1SzS37tbyu103+/Stt09FWFF5+S9vHsua+eHe22bR+wsgEvkG4OVm9oik5e7+dhHqAYDITK+p1K988s6sfd9845g8M7VhUrp7+7Vzb/a8v7/x6WX0/gKIRL4BeIcGR383mNlsM/u6pOYJzgGAxPjFR5coY3E4vX/mqt460RlZPeXi+++dVuf1W+0ks6dX6wsP3hZhRQDSLK8A7O6X3f0P3P1I8PlX3P0Pi1UcAJTaoobpenzVgqx933zjeETVlI/w3+HG1bertroyomoApN14C2HMNrOvBzM/LC1hTQAQqV957I6s7e+8c0qd13siqib5Dp25qj3HLmXt++XQ3zEAlNJ406BljvBuMLOvmdkXWekNQLn77IqmrCnRbvYN6HvvnhnnDIzn5X3Zvb+fap6r5U31EVUDADm2QLj7N9z9q5Jek/R0EIafKG5pABCNygrT5jVLsvZ9++2TEVWTbAMDrr/8SfZMGr/4iSVjHA0ApZFvD/CRoAf4q5KOBC0SXzOzh4tTHgBE4+cfXpS1/fdHO3Sq80ZE1STX7qMdOn25e3h7enWlNty7YJwzAKD48p0FYpi7vxW0SHxVg9Ojfd3MvlzA2gAgMkvn1emhJQ3D2+6DvcDIz7dDo7+fu2+BZtRURVQNAAyadADO5O5/4e5fkcQyyADKxj98KHsU+NssipGXnr4Bfe/d01n7wn+nABCFKQfgzFFfd7881dcDgLj4Bw/epsx1GvafuqKPzl2NrqCE+dGH57Pm/m2YUa3P3M3KbwCil1cANrOnzKzDzC4GHx2SthapNgCI1PxZtfqp5XOz9jEbRO6+Gxr9/dkHblNNVUF+8QgAU5LvT6IGd29097nBR6OkZ4pRGADEwRcezP6V/asHzkZUSbL09Q/o9ffPZe37wgOs/AYgHvINwLtG2fdiIQoBgDhad8/8rDaId09e1unLzAYxkT3HLo1Y+vgTyxojrAgAbsk3AF8ysyfM7OGhD9ECAaCMzZ9Zq4czZoOQpF2MAk8oPFL++Kr5qqqk/QFAPOQ7F80zktZL6sjYt1rSPylYRQAQMxvuXaC3jncOb79y4Kx+9VNLI6sn7tx9RABm7l8AcZLvP8cPu/sad//c0IekLcUoDADi4nOh8PZG+0Vd6e4d42h8cLZLxzuuD2/XVFbosyuY/QFAfOQbgNtH2Xe4EIUAQFwtb6rXsnl1w9u9/a4fHjofYUXx9uqB7JkyfuquuaqfxuIXAOIj3wC8zMyeN7MvBh9PiR5gAGXOzEb8Cv+/Hzo3xtH476F/HND+ACBu8g3Az0i6LGlO8NEgae54JwBAOXh81fys7R99eEHuHlE18XX5Rq/ePtGZtW/tyvmjHwwAEcn3d1JPuftbmTvMbLSp0UYwsxZJ33D31RMc16xbD9o1S9ru7p151gkABdVyxxzV1VTqWk+/JOn81Zs6dPaqVi2cFXFl8fLjwxfVP3DrHwZ3z6/XoobpEVYEACPlOwI8Z5R96yY6yczWB5+25PAeG919u7u/5O7bJH01nwIBoBhqqir0qdCqcH/9AX3AYT/6MPvvhKWPAcRRvgE4q9831x5gd9/l7vtyfI8Noe2GHM8DgKIKh7kffXghokriK/x38pkV8yKqBADGlm8APhIshDHLzF7R4BzAXyl0UWb2qpk1BCPHOwv9+gAwGZ+5OzvMvXmkQ929/RFVEz/HLl4bMf3ZY6z+BiCG8grA7r5Z0mvBx9fd/RkVPqBuktQo6YikFnfPqccYAIpt2bw6Lc7oZ+3pG9DfH+kY54x0+evQ6O+apXM0o4bpzwDEj433FLOZPTHGl5ZLuqTBeYGfdvcnc3ozM3d3m+CYoX7hZkkvSHou6AUe7dgtChbiaGpqWr1jx45cykCEurq6VF9fH3UZyAHXanR/+t5N/fDjvuHtzy+t0i+tmhZhRfG5Vv9mX7f2nbs1Ir55RbV+trkmworiJy7XCuPjOiXH2rVr97r7mnzPmygAfyTpVQ1OfTaaBkmr3f3RnN5sggAczACxcSjwBtt7JS2baCaIlStX+qFDh3IpAxFqa2tTa2tr1GUgB1yr0X3v3dP6p9+89UjDfYtm6bv/7DMRVhSPa9U/4Hrk/3pFV7pv/ePgO7/1ad2/eHaEVcVPHK4VJsZ1Sg4zm1QAnuh3U0+7+2sTvPEj+b7pONZLGm55cPd2M9uuwZaIzgK+DwBMyiebs2eCOHD6ii5f79XsGdURVRQPB09fyQq/DTOqde9tTBEHIJ7G7AE2s4cnCr+SNMq8wI/nU4CZNZtZQ7C5S4MhOPweoy3BDAAl11hXoxULbv1q1F3afZQ+4DdDvdCPLm1URcW4HW8AEJnxHoL7xWC2h3w+Zkv6XPiFzGy9mT0bfL41o89XGpxGbbM0HHTbzexZM9sY9Pi+ULhvFwCmLjwK/OaRixFVEh9vtmf/HYT/jgAgTsZrgXhRUk4Pt2Xw4LzsnYMzOeySNOJhNnffFNp+Kc/3BICSemzZXP3HHx8b3g6PfqbNwIDr70Oj4Ex/BiDOxgzAQWvDW2N9HQDS6hOhcPfeycu62t2rmbXp7AP+4NxVdV7vHd6eWVule+j/BRBj+S6EAQCp1zRzmpY31Q1vD7i05+ilCCuK1huHs9sfPrG0UZX0/wKIMQIwAExCuMf1jRT3AYdbQOj/BRB3BGAAmITHwg/CtaezD9jdR6yG91gz/b8A4o0ADACTEH7Ia/+py+ru7R/j6PJ19OJ1XbzWM7xdV1PJ/L8AYi+vAGxmXy5WIQCQJAtm1er2OdOHt3v7Xe+dHGvRzPK171h27/Mjd8xRVSVjKwDiLd+fUr9oZk+Y2dJiFAMASbL6zjlZ23uPpe9BuL3Hs7/nljsaoikEAPKQbwBe5+4vS7IgCOe16hsAlJOWOwjA4RHgltA/CgAgjvIKwO5+OfjziKS5krab2fNm9kQxigOAOAuPAO87fknuHlE1pXelu1eHzl7N2vfIHQRgAPE33kpwI5jZ85I6JW2StFPShiAMy8zWSbro7m8XuEYAiKVVC2dqenWlbgQPv13o6tHxjuu6c27dBGeWh7ePdyoz769YUK/Z09O5GAiAZMm3BWKDpMPufpe7f3Uo/AbaJTUXrjQAiLeqygo9vKQha9++4+lpgwh/r+GWEACIq3wD8HPu/idjfU2Do8MAkBppfhAu/L3S/wsgKfJqgZD06tAnZrZMgyO+h939qLs/U9DKACABRgbgzmgKKbH+Adfbxzuz9oX/LgAgrvIdAd489Im7H3H31yS1FLYkAEiOR0LTfh06c0XXbvZFU0wJHT7fpasZ32fDjGo1z0tH7zOA5JtwBNjMZktaF2yuNrPwep8bJL1c6MIAIAkaZtRo2bw6HblwTZI04NL+U1f0iWXlvRzwT050Zm0/dHuDzCyaYgAgTxMGYHe/bGZvabDHt1lS5k+4S5K2Fak2AEiEh26fPRyApcFwWPYB+OPOrO2HQg8DAkCc5dQDHMz28IyZrQvaHgAAgQdvb9C33j41vB0Oh+XonY+zl31+eMnsiCoBgPzluxDGiPDLssgA0i48+lnuAfhmX78Onr6Ste/B2xuiKQYAJmHcEWAze9zdX8/Y/mL4EEkbJX2+CLUBQCLct2iWqipMfQODq0Kc6Lihjms9aqyribiy4jh4+qp6+2+tgLG4Ybrm1U+LsCIAyM9EI8DbzOzhjO1nJM3J+GjQ4JLIAJBatdWVWrlwZta+ch4FDj8AF14MBADibtwRYHdfE9r1lLu/lbnDzHYVvCoASJiHljRo/6lbbQHvnListSvnR1hR8YQD8IO30/8LIFnynQe4PbMNwswel3S4sCUBQPI8FAqBZT0CzAwQABIu3wC8RtJdQxtBf/D6glYEAAkUDoHvfNwpdx/94AS70t2rw+dvTflWYdIDixkBBpAs+QZgd/evhPZ1FqgWAEisu5rqNb26cnj7QlePTl3ujrCi4njvZPb0Z3fNr1fdtJxm1ASA2Mg3AI+27DFLIQNIvarKCt23aFbWvv2hsFgOwgH4gcUN0RQCAFOQbwB+zcz2mNnzwcduSfuKURgAJM2IAHzqyhhHJtd7J7O/pwcWzxrjSACIr7x+b+Xub5nZOkmbg13bglXiACD17luU3Qu7/1T5jwDfT/8vgATKu3HL3S+b2eHgc8IvAATuW1zeI8BXu3vVfuHWA3Bm0j23MQIMIHnyaoEws2VmtkfSc5K+Yma7WQoZAAbdPX+mqittePv05W51XOuJsKLCOnj6atb28iYegAOQTPn2AK9z9zXu/nl3/5y7P6rBpZABIPVqqiq0YkH2inDl1Abxbrj9YRGjvwCSKd8APFrLw1uj7AOAVAo/CBd+aCzJwrNa0P8LIKnyDcDLctwHAKkUDoVlPQJMAAaQUPk2b+01s1ckvSJprgbnAN5a8KoAIKHCI8AHyuRBuOs9fTp8vitr3720QABIqLxGgN39LUlPS7Lg45lgOWQAgKRVC2fJbj0HpyMXr6nrZl90BRXIwdNXNZCxsvPSuTM0q7Y6uoIAYArybYGQux9x9z9w96+4+xFmgQCAW+qmVWnZvLrhbXfp4OnkjwKHWznuo/0BQIKN2wJhZl/M4TU2Sfp8YcoBgOS7f9FstZ+/NV/u/pOX9ejSxggrmrpwiA+3egBAkkw0AvyMpOWS5ozzMbeYBQJA0pTjksgHQnMAswAGgCSb6CG4p4K+3zGZ2a4C1gMAiTdySeRkB+D+AdehM9nfw70EYAAJNu4I8Gjh18yeMrPng8/XSTqcyxuZWYuZ7c3x2I1mtsXM1pvZ+lzOAYC4CI8Af3D2qm729UdUzdQdvXhN3b0Dw9uNdTWaP3NahBUBwNTkuxTy14NP90mSu78macKAmhFiW3I4dqOkZnffLqldTLMGIGHm1NVoccP04e2+AdeHZ7vGOSPewv2/99w2U5Y51QUAJEy+8wDvdve/MLNHMvZ1TnSSu++SlOsPzK3uvjw4r13S6jxrBIDI3btolk523hje3n/qcmIXjgjPZXzPQtofACRbvtOgzQn+zJgNcuJR3VyZWYuCQB18DgCJVE4PwoVHgFkAA0DS5TsCfCRYCe6SmbWr8CvBNUvqCNogdpnZs5L2DY0gA0BS3B96EO69k8ldEvkgM0AAKDPm7hMflXmC2TJJGzU4/dmLE80SETrX3X3MPggz2yLphaFjzKxB0hF3nzPO8VskqampafWOHTty/j4Qja6uLtXX10ddBnLAtZqaju4B/W9tt1ogaiqlf7d+hiqK0DtbzGvV1eP60uvXh7crTXphwwxVVdADPBncV8nAdUqOtWvX7nX3Nfmel9cIsJl9zd2/KukP8n2jHHUoeMBOkty908wazKw56AfOEjwot12SVq5c6a2trUUqC4XS1tYmrlMycK2mxt31+7t3qeNajySpp1+6475Hddf8wv9PtZjX6u8+uiC9/ubw9oqFs7T+8c8U5b3SgPsqGbhO5S/fHuBNZvZFM3u4GMUoI/xm6NRgMAaAxDCzUfqAk9cGcWCUGSAAIOnyDcCr3f1PJF02syfM7ImpFmBmzUGrw9CsDx1D22bWLKnd3Tun+j4AUGrhh8XCYTIJwv2/LIABoBzkFYDd/XLw5xFJJun3zOzFic4LFrR4Nvh8a2hxi62SNmdsb5L01aC/92lJ6/KpEQDiIhwWw2EyCUbOAUwABpB8+fYAP6/BloRNkl5VDkslS8PzAO+StG2Ur20KbXdKei6fugAgjsJhMRwm466nb0AfnmMGCADlJ99p0DZI+rq731WMYgCgnDTPq1NNVYV6+gaXET5/9aYudN3UvPpkLCN8+HyXevtvzRS0cFatGutqIqwIAAoj3x7g54IeYADABKoqK7RiQfasD0kaBR5tCWQAKAf59gD/RbEKAYByNLIPOMkBmPYHAOUh3xFgAEAeRvYBJ+dBOFaAA1CuCMAAUETh0HjgVDJGgN2dEWAAZYsADABFdM/C7NB4+HyXbvb1R1RN7s5fvamLwSp2klRbXaFl8+oirAgACocADABFNHtGtRY3TB/e7htwfXi2K8KKcrM/NPq7csFMVVZYRNUAQGERgAGgyMKzJyThQTjaHwCUMwIwABRZEh+EG7EE8iICMIDyQQAGgCJL4lRojAADKGcEYAAoshEjwGeuyN3HODp63b39aj+f3ae8aiGLYAAoHwRgACiyOxpnqK6mcni783qvTl/ujrCi8X1w9qoGMvL5ksbpmllbHV1BAFBgBGAAKLKKCtPKhcl5EG5E+8NC2h8AlBcCMACUwMgH4eIcgFkBDkB5IwADQAkkaSaI8Gp1BGAA5YYADAAlkJQRYHfXwTPZtYVnsQCApCMAA0AJrFo4U5axkNqRi9d0vacvuoLG8PGlG7rafauumdOqdPuc6eOcAQDJQwAGgBKom1alpXPrhrfdpUNn4tcGER6ZXnXbTFWwBDKAMkMABoASCS+JfCCGbRA8AAcgDQjAAFAi4enE4tgHzApwANKAAAwAJZKEmSDCD8ARgAGUIwIwAJTIPYuyw+T7p69oYCA+SyJf7e7VsYvXh7crTFq5gCWQAZQfAjAAlMii2bWaVVs1vH2tp18nLl0f54zSej/0UF5zU72mZyzhDADlggAMACViZrp3UXz7gOn/BZAWBGAAKKFwqDwQoz7g8ApwLIABoFwRgAGghEYE4FPxGQEOT8sWHq0GgHJBAAaAEgqPqsalBaKvf2BED3B43mIAKBcEYAAoobvm16syY2W1k503dPlGb4QVDTpy4Zp6+gaGt+fVT9P8mbURVgQAxUMABoASqq2u1PKmuqx978dgFJj2BwBpQgAGgBIbuSBGDALwqfAMELQ/AChfBGAAKLGRfcDRzwQxYgSYGSAAlDECMACU2IgR4DPRjgC7+4gR4PtogQBQxgjAAFBi4QB86MxV9fUPjHF08Z2/elMXr/UMb0+rqtDSuXXjnAEAyUYABoASa5o5TfPqpw1v3+wb0JEL1yKrJ9z+sGrhTFVV8r8HAOWLn3AAEIHwQ2bhEFpKzAABIG0IwAAQgTg9CDdyBggCMIDyRgAGgAjEaSq08HszAwSAcleyAGxmLWa2N89zXihWPQAQpXCbQVQB+HpPn9pD/cerCMAAylxJArCZrQ8+bcnjnBZJW4pTEQBEq3lenWqqbv0IPnf1pi523Sx5HYfOXJX7re07585Q/bSqktcBAKVUkgDs7rvcfV+epzVL6ixCOQAQuarKCq1YUJ+1L4o+4PB70v4AIA1i2QNsZhvd/aWo6wCAYrpnYXbYPHD6cslrCL8nARhAGsQuAJtZs6T2qOsAgGIb+SBc6UeAmQECQBrFsdGrJdfRXzPboqBPuKmpSW1tbcWsCwXQ1dXFdUoIrlXx3bzYn7W9+8NTamvrzPt1JnutBty1/+T1rH2Xj+1X27mDeb8WcsN9lQxcp/IXqwAcPCy3K9fj3X27pO2StHLlSm9tbS1SZSiUtrY2cZ2SgWtVfI9c79XW3a8Mb5++Ln3ypz+j2urKvF5nstfqo3NduvmDHw5vN8yo1hM/s1ZmlvdrITfcV8nAdSp/sWuBkLTZzLYEo7sNwefNURcFAIU2e0a17micMbzdP+AlnQ7tvZPZ/b8PLJ5N+AWQCpGPAAfhtsPdO919V+hrLwSjvABQlh5YPFvHO261Ibx78rIeuWNOSd77nY+zA/D9i2eX5H0BIGolmwfYzJ4NPt+aMS+wJG2VtDl0fEPoeEaAAZSlcOh89+PSzQQx2ggwAKRBSUaAg5HdXZK2jfK1TaPs6wyOHXE8AJSTB28PBeCTpQnA/QOu/acIwADSKY49wACQGvcvyg6dH57rUndv/xhHF86RC1261nPrfRpmVOv2OdOL/r4AEAcEYACI0GgPwh0owYNw4ZFmHoADkCYEYACI2AOhNohwb24xvPtxdsim/QFAmhCAASBi4fAZnp2hGN492TluDQBQzgjAABCxcPgs9gjw4ANw2SPATIEGIE0IwAAQsfCDcB+cvarrPX1Fe7/28126nvEA3BwegAOQMgRgAIjY7BnVWjavbnh7wIs7H/Bbxzuzth+4vYEH4ACkCgEYAGLgkSUNWdtvnegs2nu9deJS1nbLHQ2jHwgAZYoADAAx8EgohL51/NLoBxZAeAS4VEsvA0BcEIABIAbCIXTf8U65e8Hfp+tmnw6dvZq17+HbGwr+PgAQZwRgAIiBlQtnqrb61o/k81dv6mTnjYK/z09OdCozV981v16zZ1QX/H0AIM4IwAAQA9WVFXpwcUPWvnCrQiGEWyvCvccAkAYEYACIiZF9wJ0Ffw/6fwGAAAwAsREOo+HZGqbK3UfMLhEO3QCQBgRgAIiJcBjdf/KKbvb1j37wJBzvuK6Oaz3D23U1lVqxYGbBXh8AkoIADAAxsWBWrRY33FqRrad/oKALYuw5mj2i/NCSBlVWsAAGgPQhAANAjKxZmt0G8eaRjoK99hvtF7Pf6076fwGkEwEYAGLksWVzs7bDoXUq3jiS/VqfbJ47xpEAUN4IwAAQI59sbsza3nP0knr7B6b8uic7b+hEx615hWsqK5gBAkBqEYABIEaWzavT/JnThrdv9PbrnQL0Ab8ZGkl+eEmDptdUTvl1ASCJCMAAECNmNqI1oRBtEOHXCI80A0CaEIABIGaKE4CzH6aj/xdAmhGAASBmHitwH/DJzhs63nF9eLu60uj/BZBqBGAAiJnmeXVqGtEH3Dnp13vjMP2/AJCJAAwAMTNaH3DbofOTfr22D7LPpf0BQNoRgAEghtaubMra3nXw3KRep7d/QD88lH1u68r5k64LAMoBARgAYqh15XxlrlJ88PQVneq8MfYJY9hz9JKudPcNbzfW1ejhJQ0FqBAAkosADAAx1FhXo5bQg2qvv5//KPDr75/N2m5d2aTKzGQNAClEAAaAmHr8nuxWhdcOnh3jyLG9FgrN61YtmFJNAFAOCMAAEFPhsPq3hy/qek/fGEePdOTCNbWfvza8XVVh+uyKeQWrDwCSigAMADG1YkG9bp8zfXi7p29Af/PhhZzPD48YP9bcqJm11QWrDwCSigAMADFlZlq3KrsN4ltvn8z5/Jf3ZR+7ltkfAEASARgAYu0fPLQoa/vVA2d1sevmhOe9d/KyDpy+MrxdYdLPPXhbwesDgCQiAANAjK2+c46a59UNb/f2u7719qkJz9u550TW9mdXNOm22dPHOBoA0oUADAAxZmbatGZJ1r6de07I3cc8p7u3f0RIfjL0GgCQZgRgAIi5X2hZnDV37/tnrurdk5fHPP6VA2d1+Ubv8HZjXY3W3cP0ZwAwhAAMADE3f1atWldkL438fNvhUY8dGHC98MPsr/2jhxerpoof9wAwhJ+IAJAATz6a3cLw/ffOaPfRjhHHvfzWSe0/dSVrX/hcAEi7kgVgM2sxs705Hvds8LHTzBpKUB4AxNr6exbowdtnZ+37/e8e1MDArV7g6z19+sMfHMo65gsP3qaVC2eWpEYASIqSBGAzWx982jLBcQ2S1rj7NnffJulFSa8VuTwAiL2KCtM//7l7s/b95ESn/sPfHpEkubu+/v33deZK9/DXayor9NzPrCppnQCQBFWleBN33yUNPs08gTWSnpO0PdjeJWmnmTW4e2fRCgSABPjEskb9zH0L9d/2nxne9/vfPagVcyr09bd/pPfPXM06/tc/vVRLGmeUukwAiL1Y9QAHQXlTxq7mYH9nJAUBQMx85X9YpWmhB9o+uDQwIvzOq5+m31x7VylLA4DEiFUAliR335ex+aSkbVHVAgBxs3RenZ7/n1pUWz32j++5dTX603/8qGbVVpewMgBIDhtvMvWCv5mZu/uEfRDBsQ2Sdrr7hnGO2SJpiyQ1NTWt3rFjR0HqRPF0dXWpvr4+6jKQA65VvH10qV9/tK9b13qz9zdNN/3OmlotrIvd+AbEfZUUXKfkWLt27V53X5PveXEOwC9Iei7X9oeVK1f6oUOHJj4QkWpra1Nra2vUZSAHXKv4O9FxXX/+d0f1/pETWrhwoW6bXatf/+llaqyribo0jIH7Khm4TslhZpMKwCV5CC5fZvasgvDLA3AAMLoljTP0z79wr9razqm19aGoywGAxIj8d2Rm1pw516+ZbZT0UkboXT/aeQAAAMBklGwe4GBUV2a2NWNeYEnaKmlz8LVmSTslHTYzNzMPvg4AAAAURCnnAd6lUWZ0cPdNGZ+3S8qpRxgAAACYjMhbIAAAAIBSIgADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUIQADAAAgVQjAAAAASBUCMAAAAFKFAAwAAIBUKVkANrMWM9ubw3HNZvasma0P/mwoQXkAAABIiapSvImZrZfUIaklh8NfcPcNwXntkrZKerqI5QEAACBFSjIC7O673H3fRMeZWXPovHZJm4tWGAAAAFInbj3ALZI6wzvDwRgAAACYrLgF4MZR9nVIaihxHQAAAChTJekBLhYz2yJpS7B508zei7Ie5GSepAtRF4GccK2Sg2uVHFyrZOA6JcfKyZwUtwA82mhvo0Zpi5Akd98uabskmdked19TzOIwdVyn5OBaJQfXKjm4VsnAdUoOM9szmfPi1gKxT6O0QQQPwwEAAABTFnkADub9bZBGBt3g4bcdUdQFAACA8lSSADy0qEXw+dZgXuAhW5U91dmmoYUwJG1091znAN5eoHJRXFyn5OBaJQfXKjm4VsnAdUqOSV0rc/dCFwIAAADEVuQtEAAAAEApxW0WiLwEPcIbNfjwXIuk7e7eGWlRGJWZbZV0WIM93Zsldbj7S9FWBUkysxZJ33D31aH93F8xM8614v6KmeBaDbX7PSrpqaH7h3srXia4VtxbMZHRPtugwev04tAqw5O5p5I+AvyCu29z912SXtJgPzHi6wVJRyQ18AMkHjJ+oLSM8mXurxiZ4FpJ3F+xETzYvSa4f7ZJelHSaxmHcG/FRA7XSuLeioudkvYE12C3pG9kfC3veyqxATi8PHIwg8TmMQ5H9Ha7u7n7nOCHDGLA3XcN/Qs6E/dX/Ix1rQLcX/GyRtJzGdu7JLWYWQP3VuyMea2Cbe6t+FidMarbqMG1Iyb9/6vEBmANjoJ0hneG/yIQL8GvmhB/3F8JxP0VD8Eo1KaMXc3B/k5xb8XKBNdqGPdW9EJT5W7SrVHeSd1TSQ7AIxbM0OgrySEemoNf4bYHU+HxwyTeuL+ShfsrZkKj9U9KGho95N6KmXGulcS9FSvB2hHPStoZ/ONFmuQ9leiH4JAcmb86MrMXJL0qaXl0FQHlg/srvoJfpbe4+4aoa8H4RrtW3Fvx4u7tZrZd0lYz2ziVnuwkjwCPlu4bNcowOKKX0U819GsMft0Xb9xfCcL9FWtblf0rdu6t+ApfK+6tGAraU3ZK2hlcn0ndU0kOwPs0yrB3eDllRC/49VH4qVrEG/dXQnB/xVfwq9rn3L0zI0hxb8XQaNeKeys+ghWF92bs2hP82ahJ3lOJDcDhbyxodt4RUTkY3x5JXxvaMLONGpymBDHF/ZUo3F8xNHQdMh6mWi9xb8XRWNdK3Ftx0qHBKeqGrJHU7u7tk72nEr0UcnjiY6Yoia+MicY7JS139+fGPwOlEIxwtGjwV3/bJL069GAB91e8THCtuL9iJLh3Dod2t7v78oyvc2/FQA7XinsrJoJ/gAyN9K6WtHUo/E7mnkp0AAYAAADyldgWCAAAAGAyCMAAAABIFQIwAAAAUoUADAAAgFQhAAMAACBVCMAAkBBm1mJmW4OpmQr1mhuD12wo1GsCQNwRgAEgOdZI+pq77wtWRjoczI05ae7+kqTdGmUlJQAoVwRgAEigYBGMXVHXAQBJRAAGgOTqjLoAAEgiAjAAAABShQAMABEIHj7ba2avBtvPBj29Wyb5ejuD11sfPCy318y2BNtbggfdmoOvPTvZ9wGAclAVdQEAkEbu/pKZ7ZL0WjADQ7u7L5/MawXnvxg80Da0b5ek1e6+PdjeK2l3cMw+M7skafsUvw0ASCRGgAEgIu7eKek5Sa9J2jfJl2kOzg8/EHdR0t6M7Q5J7ZN8DwAoKwRgAIhWe/Ax2enMOjUYoncWqiAAKHcEYACISNC60OLumyRtMLP1eb5EgwZbJ3ZJaqevFwByQwAGgAgEYTWzReFVSTvN7Nkcz2/R4MIYT5tZs6TDkl4IHnBrkfSkpE3BQ28bM45tCN67Idf3AoByY+4edQ0AgBwEwXVH0DtcyNfdKGmfu9MjDCAVGAEGAABAqhCAAQAAkCoEYABIjj2SvjqJh+XGFLRVPKrBadIAIBXoAQYAAECqMAIMAACAVCEAAwAAIFUIwAAAAEgVAjAAAABShQAMAACAVCEAAwAAIFX+fyG93qg8dQ2BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sampling along the z direction\n",
    "dx = 0.1\n",
    "nx = 301\n",
    "x = np.linspace(0,(nx-1)*dx,nx)\n",
    "# Velocity model\n",
    "vv = o.VectorNumpy(np.zeros(nx), ax_info=[o.AxInfo(nx,0.,1.,\"velocity [km/s]\")])\n",
    "vv.set(2.0)\n",
    "vv[:] -= 0.8 * np.exp(-0.5*(x-(nx/2.0)*dx)**2)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, vv.plot(), lw=4)\n",
    "ax.set_xlabel(\"x [km]\"), ax.set_ylabel(vv.ax_info[0].l)\n",
    "ax.set_xlim(0,30), ax.set_ylim(1,2.5)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "better-wages",
   "metadata": {},
   "source": [
    "Let's compute the traveltime for a single source and receivers at every grid point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "material-surface",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Source/Receiver positions\n",
    "SouPos = np.array([0])\n",
    "RecPos = np.arange(0, nx)\n",
    "\n",
    "# Data vector\n",
    "tt_data = o.VectorNumpy((1, nx)).zero()\n",
    "\n",
    "# Setting Forward non-linear operator\n",
    "Eik1D_Op = EikonalTT_1D(vv, tt_data, dx, SouPos, RecPos)\n",
    "Eik1D_Op.forward(False, vv, tt_data)\n",
    "\n",
    "# Plotting traveltime vector\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(RecPos * dx, tt_data[0, :], lw=4)\n",
    "ax.set_xlabel(\"x [km]\"), ax.set_ylabel(\"Traveltime [s]\")\n",
    "ax.set_xlim(0,30), ax.set_ylim(0,16)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "interested-powder",
   "metadata": {},
   "source": [
    "Let's implement and test the linearized Eikonal equation operators. Again we first define the functions to solve the forward and adjoint PDEs, and then we wrap it within an operator class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "stock-terminology",
   "metadata": {},
   "outputs": [],
   "source": [
    "def FMM_tt_lin_fwd(delta_v, delta_tt, vv, tt, dx):\n",
    "    \"\"\"Fast-marching method linearized forward in 1D\"\"\"\n",
    "    nx = delta_v.shape[0]\n",
    "    drxns = [-1, 1]\n",
    "    nbrs = np.zeros(2, dtype=int)\n",
    "    dx_inv = 1.0 / dx\n",
    "    \n",
    "    tt_idx = np.arange(nx)\n",
    "    # Sorting traveltime in ascending order\n",
    "    tt_idx = sorting(tt, tt_idx)\n",
    "    \n",
    "    # Scaling the velocity perturbation\n",
    "    delta_v_scaled = - 2.0 * delta_v / (vv * vv * vv)\n",
    "\n",
    "    # Looping over all indices to solve linear equations from increasing traveltime values\n",
    "    for idx_t0 in tt_idx:\n",
    "        # If T = 0 or v = 0, then assuming zero to avoid singularity\n",
    "        if tt[idx_t0] == 0.0 or vv[idx_t0] == 0.0:\n",
    "            continue\n",
    "        # Creating indices of neighbouring points\n",
    "        for idx in range(2):\n",
    "            nbrs[idx] = idx_t0 + drxns[idx]\n",
    "\n",
    "        # Loop over neighbourning points to find up-wind direction\n",
    "        fdt = np.zeros(2)\n",
    "        order = np.zeros(2, dtype=int)\n",
    "        for idx, nb in enumerate(nbrs):\n",
    "            # If point is outside the domain skip it\n",
    "            if nb < 0 or nb >= nx:\n",
    "                continue\n",
    "            if vv[nb] > 0.0:\n",
    "                order[idx] = 1\n",
    "                fdt[idx] = drxns[idx] * (tt[nb]-tt[idx_t0]) * dx_inv\n",
    "            else:\n",
    "                order[idx] = 0\n",
    "        # Selecting upwind derivative \n",
    "        if fdt[0] > -fdt[1] and order[0] > 0:\n",
    "            ii, idrx = 0, -1\n",
    "        else:\n",
    "            ii, idrx = 1, 1\n",
    "        # Computing t0 space derivative\n",
    "        fdt0 = idrx * (tt[idx_t0 + idrx] - tt[idx_t0]) * dx_inv * dx_inv\n",
    "        delta_tt[idx_t0] += (2.0 * fdt0 * delta_tt[idx_t0 + idrx] - idrx * delta_v_scaled[idx_t0]) / (2.0 * fdt0)\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "egyptian-marina",
   "metadata": {},
   "outputs": [],
   "source": [
    "def select_upwind_der(tt, idx_t0, vv, dx_inv):\n",
    "    nbrs = np.zeros(2, dtype=int)\n",
    "    drxns = [-1, 1]\n",
    "    # Creating indices of neighbouring points\n",
    "    for idx in range(2):\n",
    "        nbrs[idx] = idx_t0 + drxns[idx]\n",
    "\n",
    "    # Loop over neighbourning points to find up-wind direction\n",
    "    fdt = np.zeros(2)\n",
    "    order = np.zeros(2, dtype=int)\n",
    "    for idx, nb in enumerate(nbrs):\n",
    "        # If point is outside the domain skip it\n",
    "        if nb < 0 or nb >= nx:\n",
    "            continue\n",
    "        if vv[nb] > 0.0:\n",
    "            order[idx] = 1\n",
    "            fdt[idx] = drxns[idx] * (tt[nb]-tt[idx_t0]) * dx_inv\n",
    "        else:\n",
    "            order[idx] = 0\n",
    "    # Selecting upwind derivative \n",
    "    if fdt[0] > -fdt[1] and order[0] > 0:\n",
    "        idrx = -1\n",
    "    else:\n",
    "        idrx = 1\n",
    "    return idrx, order\n",
    "            \n",
    "def FMM_tt_lin_adj(delta_v, delta_tt, vv, tt, dx):\n",
    "    \"\"\"Fast-marching method linearized adjoint in 1D\"\"\"\n",
    "    nx = delta_v.shape[0]\n",
    "    dx_inv = 1.0 / dx\n",
    "    tt_idx = np.arange(nx)\n",
    "    # Sorting traveltime in descending order\n",
    "    tt_idx = sorting(tt, tt_idx, ordering=\"d\")\n",
    "    \n",
    "    # Looping over all indices to solve linear equations from increasing traveltime values\n",
    "    for idx_t0 in tt_idx:\n",
    "        # Identify the type of row (i.e., central, edge, or initial conditions)\n",
    "        if tt[idx_t0] == 0.0 or vv[idx_t0] == 0.0:\n",
    "            continue\n",
    "        else:\n",
    "            idrx0, order0 = select_upwind_der(tt, idx_t0, vv, dx_inv)\n",
    "            # Computing k0 (derivative coefficient at the current index)\n",
    "            k0 = 2.0 * np.sign(idrx0) * idrx0 * (tt[idx_t0 + idrx0] - tt[idx_t0]) * dx_inv * dx_inv\n",
    "            nb = idx_t0 - idrx0\n",
    "            # Checking if at a boundary\n",
    "            if nb < 0 or nb >= nx:\n",
    "                delta_v[idx_t0] =  delta_tt[idx_t0] / k0\n",
    "            else:\n",
    "                # Computing k1 (derivative coefficient at the forward or backgward index)\n",
    "                idrx1, order1 = select_upwind_der(tt, nb, vv, dx_inv)\n",
    "                k_fb = 2.0 * np.sign(idrx1) * idrx1 * (tt[nb + idrx1] - tt[nb]) * dx_inv * dx_inv\n",
    "                delta_v[idx_t0] += (delta_tt[idx_t0] + k_fb * delta_v[nb]) / k0\n",
    "            \n",
    "    # Scaling the velocity perturbation\n",
    "    delta_v[:] = 2.0 * delta_v / (vv * vv * vv)\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "preceding-burns",
   "metadata": {},
   "outputs": [],
   "source": [
    "class EikonalTT_lin_1D(o.Operator):\n",
    "\n",
    "    def __init__(self, vel, tt_data, dx, SouPos, RecPos):\n",
    "        \"\"\"1D Eikonal-equation traveltime prediction operator\"\"\"\n",
    "        # Setting Domain and Range of the operator\n",
    "        super(EikonalTT_lin_1D, self).__init__(domain=vel, range=tt_data)\n",
    "        # Setting acquisition geometry\n",
    "        self.nSou = SouPos.shape[0]\n",
    "        self.nRec = RecPos.shape[0]\n",
    "        self.SouPos = SouPos.copy()\n",
    "        self.RecPos = RecPos.copy()\n",
    "        dataShape = tt_data.shape\n",
    "        if dataShape[0] != self.nSou:\n",
    "            raise ValueError(\"Number of sources inconsistent with traveltime vector (shape[0])\")\n",
    "        if dataShape[1] != self.nRec:\n",
    "            raise ValueError(\"Number of receivers inconsistent with traveltime vector (shape[1])\")\n",
    "        self.dx = dx\n",
    "        self.nx = vel.shape[0]\n",
    "        # Background model\n",
    "        self.vel = vel.clone()\n",
    "        self.vel.copy(vel)\n",
    "\n",
    "    def forward(self, add, model, data):\n",
    "        \"\"\"Forward linearized traveltime prediction\"\"\"\n",
    "        self.checkDomainRange(model, data)\n",
    "        if not add: \n",
    "            data.zero()\n",
    "        dataNd = data.getNdArray()\n",
    "        modelNd = model.getNdArray()\n",
    "        vel0Nd = self.vel.getNdArray()\n",
    "        # Initialization\n",
    "        tt0 = np.zeros(self.nx)\n",
    "        for iShot in range(self.nSou):\n",
    "            ###################################\n",
    "            # Computing background traveltime #\n",
    "            ###################################\n",
    "            # Initial conditions\n",
    "            status = np.array([\"u\"] * self.nx) # All points are unknown\n",
    "            tt0.fill(np.inf)\n",
    "            trial_idx = []\n",
    "            # Initial conditions\n",
    "            idx = self.SouPos[iShot]\n",
    "            tt0[idx] = 0.0\n",
    "            status[idx] = 't' # Trial status\n",
    "            trial_idx.append(idx)\n",
    "            # Sorting trial time ascending order\n",
    "            trial_idx = sorting(tt0, trial_idx)\n",
    "            FMM_tt(tt0, vel0Nd, self.dx, status, trial_idx) \n",
    "            ###################################\n",
    "            # Computing linearized traveltime #\n",
    "            ###################################\n",
    "            delta_tt = np.zeros(self.nx)\n",
    "            FMM_tt_lin_fwd(modelNd, delta_tt, vel0Nd, tt0, self.dx)\n",
    "            for iRec in range(self.nRec):\n",
    "                dataNd[iShot, iRec] += delta_tt[self.RecPos[iRec]]\n",
    "        return\n",
    "    \n",
    "    def adjoint(self, add, model, data):\n",
    "        \"\"\"Adjoint linearized traveltime prediction\"\"\"\n",
    "        self.checkDomainRange(model, data)\n",
    "        if not add: \n",
    "            model.zero()\n",
    "        dataNd = data.getNdArray()\n",
    "        modelNd = model.getNdArray()\n",
    "        vel0Nd = self.vel.getNdArray()\n",
    "        # Initialization\n",
    "        tt0 = np.zeros(self.nx)\n",
    "        for iShot in range(self.nSou):\n",
    "            ###################################\n",
    "            # Computing background traveltime #\n",
    "            ###################################\n",
    "            # Initial conditions\n",
    "            status = np.array([\"u\"] * self.nx) # All points are unknown\n",
    "            tt0.fill(np.inf)\n",
    "            trial_idx = []\n",
    "            # Initial conditions\n",
    "            idx = self.SouPos[iShot]\n",
    "            tt0[idx] = 0.0\n",
    "            status[idx] = 't' # Trial status\n",
    "            trial_idx.append(idx)\n",
    "            # Sorting trial time ascending order\n",
    "            trial_idx = sorting(tt0, trial_idx)\n",
    "            FMM_tt(tt0, vel0Nd, self.dx, status, trial_idx) \n",
    "            ###################################\n",
    "            # Computing velocity perturbation #\n",
    "            ###################################\n",
    "            delta_tt = np.zeros(self.nx)\n",
    "            delta_v = np.zeros(self.nx)\n",
    "            # Injecting traveltime to correct grid positions\n",
    "            for iRec in range(self.nRec):\n",
    "                delta_tt[self.RecPos[iRec]] = dataNd[iShot, iRec]\n",
    "            FMM_tt_lin_adj(delta_v, delta_tt, vel0Nd, tt0, self.dx)\n",
    "            modelNd[:] += delta_v\n",
    "        return\n",
    "    \n",
    "    def set_vel(self, vel):\n",
    "        \"\"\"Function to set background velocity model\"\"\"\n",
    "        self.vel.copy(vel)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "retained-release",
   "metadata": {},
   "source": [
    "Let's start by testing the adjointness of the forward and adjoint methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "appreciated-nightlife",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dot-product tests of forward and adjoint operators\n",
      "--------------------------------------------------\n",
      "Applying forward operator add=False\n",
      " Runs in: 0.008758783340454102 seconds\n",
      "Applying adjoint operator add=False\n",
      " Runs in: 0.011502265930175781 seconds\n",
      "Dot products add=False: domain=6.980588e-01 range=6.980588e-01 \n",
      "Absolute error: 7.771561e-16\n",
      "Relative error: 1.113310e-15 \n",
      "\n",
      "Applying forward operator add=True\n",
      " Runs in: 0.008133649826049805 seconds\n",
      "Applying adjoint operator add=True\n",
      " Runs in: 0.013436317443847656 seconds\n",
      "Dot products add=True: domain=1.396118e+00 range=1.396118e+00 \n",
      "Absolute error: 1.554312e-15\n",
      "Relative error: 1.113310e-15 \n",
      "\n",
      "-------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# Dot-product test for the linearized Eikonal equation in 1D\n",
    "Eik1D_Lin_Op = EikonalTT_lin_1D(vv, tt_data, dx, SouPos, RecPos)\n",
    "Eik1D_Lin_Op.dotTest(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "colonial-luxury",
   "metadata": {},
   "source": [
    "The linearization error of the linearized Eikonal operator $\\mathbf{F}$ should follow:\n",
    "\\begin{eqnarray}\n",
    "e = \\|\\mathbf{f}(\\mathbf{v}+\\alpha\\Delta\\mathbf{v})-\\mathbf{f}(\\mathbf{v})-\\alpha\\mathbf{F}(\\mathbf{v})\\Delta\\mathbf{v}\\|_2=\\mathcal{O}(\\alpha^2) \\;\\rm{as}\\; \\alpha \\to 0,\n",
    "\\end{eqnarray}\n",
    "where $\\alpha$ is the scale associated with the velocity perturbation $\\Delta\\mathbf{v}$. Let's test if this is the case for our operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "elementary-nursing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Eik1D_NlOp = o.NonlinearOperator(Eik1D_Op, Eik1D_Lin_Op, Eik1D_Lin_Op.set_vel)\n",
    "alpha, err = Eik1D_NlOp.linTest(vv)\n",
    "M = err[0]/(alpha[0]*alpha[0])\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(alpha,err, lw=4, label=\"Computed error\")\n",
    "ax.loglog(alpha,M*alpha*alpha, lw=3, ls=\"--\", label=\"Theoretical bound\")\n",
    "\n",
    "ax.set_xlabel(r\"$\\alpha$\"), ax.set_ylabel(\"e [s]\")\n",
    "ax.set_xlim(1e-6,1)\n",
    "ax.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "white-marijuana",
   "metadata": {},
   "source": [
    "## Eikonal traveltime tomography "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "southeast-medication",
   "metadata": {},
   "source": [
    "Now that we are confident that our operators are working properly, we can set up an inversion problem. We are going to solve a bounded non-linear L2-norm problem defined as follows:\n",
    "\\begin{equation}\n",
    "\\phi(\\mathbf{v}) = \\frac{1}{2}\\|\\mathbf{f}(\\mathbf{v}) - \\pmb{\\tau}_{obs}\\|_2^2,\\\\\n",
    "\\text{s.t.} \\; \\mathbf{v}_{l} \\leq \\mathbf{v} \\leq \\mathbf{v}_{u}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "angry-columbia",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Source/Receiver positions\n",
    "SouPos = np.arange(0, nx, 150)\n",
    "RecPos = np.arange(0, nx, 10)\n",
    "\n",
    "# Data vector\n",
    "tt_data = o.VectorNumpy((SouPos.shape[0], RecPos.shape[0])).zero()\n",
    "\n",
    "# Instantiating non-linear operator\n",
    "Eik1D_Op = EikonalTT_1D(vv, tt_data, dx, SouPos, RecPos)\n",
    "Eik1D_Op.forward(False, vv, tt_data)\n",
    "Eik1D_Lin_Op = EikonalTT_lin_1D(vv, tt_data, dx, SouPos, RecPos)\n",
    "Eik1D_NlOp = o.NonlinearOperator(Eik1D_Op, Eik1D_Lin_Op, Eik1D_Lin_Op.set_vel)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "coupled-check",
   "metadata": {},
   "source": [
    "Let's generated the observed data using 3 sources and receivers every 1 km."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "imposed-argentina",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating observed data\n",
    "Eik1D_Op.forward(False, vv, tt_data)\n",
    "tt_data_obs = tt_data.clone()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "lasting-alberta",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,3, sharey=True)\n",
    "\n",
    "axs[0].scatter(RecPos*dx, tt_data_obs.plot()[0], linewidth=4)\n",
    "axs[0].set_ylabel(\"traveltime [s]\")\n",
    "axs[0].set_xlabel(\"x [km]\")\n",
    "axs[0].set_ylim([0.0, 16.0])\n",
    "axs[0].autoscale(enable=True, axis='x', tight=True)\n",
    "\n",
    "axs[1].scatter(RecPos*dx, tt_data_obs.plot()[1], linewidth=4)\n",
    "axs[1].set_xlabel(\"x [km]\")\n",
    "axs[1].autoscale(enable=True, axis='x', tight=True)\n",
    "\n",
    "axs[2].scatter(RecPos*dx, tt_data_obs.plot()[2], linewidth=4)\n",
    "axs[2].set_xlabel(\"x [km]\")\n",
    "axs[2].autoscale(enable=True, axis='x', tight=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "developed-trustee",
   "metadata": {},
   "source": [
    "We start the inversion by assuming a velocity model in which the Gaussian anomaly is not present."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "basic-uganda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vv_init = vv.clone().set(2.0)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, vv.plot(), lw=4, label=\"True\")\n",
    "ax.plot(x, vv_init.plot(), c=\"red\", ls=\"--\", lw=4, label=\"Initial\")\n",
    "ax.set_xlabel(\"x [km]\"), ax.set_ylabel(vv.ax_info[0].l)\n",
    "ax.set_xlim(0,30), ax.set_ylim(1,2.5)\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vocal-composer",
   "metadata": {},
   "source": [
    "Let's compare the traveltime difference between the initially predicted and observed traveltimes for each source."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d5459d38",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating initial data\n",
    "Eik1D_Op.forward(False, vv_init, tt_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "korean-sight",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,3, sharey=True)\n",
    "\n",
    "axs[0].scatter(RecPos*dx, tt_data_obs.plot()[0], label=\"observed\")\n",
    "axs[0].scatter(RecPos*dx, tt_data.plot()[0], c=\"r\", ls=\"--\", label=\"initial\")\n",
    "axs[0].legend()\n",
    "axs[0].set_ylabel(\"traveltime [s]\")\n",
    "axs[0].set_xlabel(\"x [km]\")\n",
    "axs[0].set_ylim([0.0, 16.0])\n",
    "axs[0].autoscale(enable=True, axis='x', tight=True)\n",
    "\n",
    "axs[1].scatter(RecPos*dx, tt_data_obs.plot()[1], label=\"observed\")\n",
    "axs[1].scatter(RecPos*dx, tt_data.plot()[1], c=\"r\", ls=\"--\", label=\"initial\")\n",
    "axs[1].set_xlabel(\"x [km]\")\n",
    "axs[1].autoscale(enable=True, axis='x', tight=True)\n",
    "\n",
    "axs[2].scatter(RecPos*dx, tt_data_obs.plot()[2], label=\"observed\")\n",
    "axs[2].scatter(RecPos*dx, tt_data.plot()[2], c=\"r\", ls=\"--\", label=\"initial\")\n",
    "axs[2].set_xlabel(\"x [km]\")\n",
    "axs[2].autoscale(enable=True, axis='x', tight=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "worse-singles",
   "metadata": {},
   "source": [
    "We now solve the non-linear constrained optimization problem using the solver L-BFGS-B."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fundamental-chocolate",
   "metadata": {},
   "outputs": [],
   "source": [
    "minBound = o.VectorNumpy((nx,)).set(1.)\n",
    "maxBound = o.VectorNumpy((nx,)).set(3.)\n",
    "\n",
    "Stop  = o.BasicStopper(niter=250)\n",
    "BFGSBsolver = o.LBFGSB(Stop, m_steps=30)\n",
    "\n",
    "filt = o.VectorNumpy((15,)).set(1.)\n",
    "SmoothOp = o.ConvND(vv_init, filt)\n",
    "\n",
    "mask = o.VectorNumpy((nx,)).zero()\n",
    "mask[int(nx*0.25):int(nx*0.75)] = 1.0\n",
    "\n",
    "Eik1D_Inv_NlOp = o.NonlinearOperator(Eik1D_Op, Eik1D_Lin_Op*SmoothOp, Eik1D_Lin_Op.set_vel)\n",
    "\n",
    "L2_tt_prob = o.NonlinearLeastSquares(vv_init.clone(), tt_data_obs, Eik1D_Inv_NlOp,\n",
    "                                     minBound=minBound, maxBound=maxBound, grad_mask=mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "stuck-supervision",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##########################################################################################\n",
      "            L-BFGS-B Solver \n",
      "    Max steps to invert the Hessian: 30 \n",
      "    Restart folder: /tmp/restart_2022-04-22T01-46-03.542275/\n",
      "##########################################################################################\n",
      "\n",
      "iter = 000, obj = 9.37e+00, rnorm = 4.33e+00, gnorm = 1.08e+02, feval = 0001, geval = 001\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "iter = 167, obj = 5.98e-06, rnorm = 3.46e-03, gnorm = 4.37e-03, feval = 0168, geval = 168\n",
      "iter = 168, obj = 5.36e-06, rnorm = 3.27e-03, gnorm = 2.68e-02, feval = 0169, geval = 169\n",
      "iter = 169, obj = 5.11e-06, rnorm = 3.20e-03, gnorm = 1.13e-02, feval = 0170, geval = 170\n",
      "iter = 170, obj = 5.05e-06, rnorm = 3.18e-03, gnorm = 5.24e-03, feval = 0171, geval = 171\n",
      "iter = 171, obj = 5.03e-06, rnorm = 3.17e-03, gnorm = 4.04e-03, feval = 0172, geval = 172\n",
      "iter = 172, obj = 4.93e-06, rnorm = 3.14e-03, gnorm = 9.31e-03, feval = 0173, geval = 173\n",
      "iter = 173, obj = 4.89e-06, rnorm = 3.13e-03, gnorm = 4.68e-03, feval = 0174, geval = 174\n",
      "iter = 174, obj = 4.86e-06, rnorm = 3.12e-03, gnorm = 4.30e-03, feval = 0175, geval = 175\n",
      "iter = 175, obj = 4.82e-06, rnorm = 3.11e-03, gnorm = 5.37e-03, feval = 0176, geval = 176\n",
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      "iter = 177, obj = 4.48e-06, rnorm = 2.99e-03, gnorm = 1.85e-02, feval = 0178, geval = 178\n",
      "iter = 178, obj = 4.36e-06, rnorm = 2.95e-03, gnorm = 8.65e-03, feval = 0179, geval = 179\n",
      "iter = 179, obj = 4.33e-06, rnorm = 2.94e-03, gnorm = 4.25e-03, feval = 0180, geval = 180\n",
      "iter = 180, obj = 4.30e-06, rnorm = 2.93e-03, gnorm = 4.06e-03, feval = 0181, geval = 181\n",
      "iter = 181, obj = 4.27e-06, rnorm = 2.92e-03, gnorm = 4.66e-03, feval = 0182, geval = 182\n",
      "iter = 182, obj = 4.25e-06, rnorm = 2.92e-03, gnorm = 3.61e-03, feval = 0183, geval = 183\n",
      "iter = 183, obj = 4.16e-06, rnorm = 2.89e-03, gnorm = 8.87e-03, feval = 0184, geval = 184\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 184, obj = 4.13e-06, rnorm = 2.87e-03, gnorm = 4.44e-03, feval = 0185, geval = 185\n",
      "iter = 185, obj = 4.11e-06, rnorm = 2.87e-03, gnorm = 3.63e-03, feval = 0186, geval = 186\n",
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      "iter = 192, obj = 2.09e-06, rnorm = 2.04e-03, gnorm = 6.65e-03, feval = 0193, geval = 193\n",
      "iter = 193, obj = 2.07e-06, rnorm = 2.03e-03, gnorm = 3.00e-03, feval = 0194, geval = 194\n",
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      "iter = 197, obj = 1.97e-06, rnorm = 1.99e-03, gnorm = 6.51e-03, feval = 0198, geval = 198\n",
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      "iter = 199, obj = 1.95e-06, rnorm = 1.97e-03, gnorm = 2.19e-03, feval = 0200, geval = 200\n",
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      "iter = 202, obj = 1.49e-06, rnorm = 1.73e-03, gnorm = 6.50e-03, feval = 0203, geval = 203\n",
      "iter = 203, obj = 1.48e-06, rnorm = 1.72e-03, gnorm = 2.57e-03, feval = 0204, geval = 204\n",
      "iter = 204, obj = 1.47e-06, rnorm = 1.71e-03, gnorm = 1.66e-03, feval = 0205, geval = 205\n",
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      "iter = 209, obj = 7.57e-07, rnorm = 1.23e-03, gnorm = 1.20e-03, feval = 0210, geval = 210\n",
      "iter = 210, obj = 7.55e-07, rnorm = 1.23e-03, gnorm = 1.14e-03, feval = 0211, geval = 211\n",
      "iter = 211, obj = 7.53e-07, rnorm = 1.23e-03, gnorm = 1.12e-03, feval = 0212, geval = 212\n",
      "iter = 212, obj = 7.50e-07, rnorm = 1.22e-03, gnorm = 1.37e-03, feval = 0213, geval = 213\n",
      "iter = 213, obj = 7.48e-07, rnorm = 1.22e-03, gnorm = 9.86e-04, feval = 0214, geval = 214\n",
      "iter = 214, obj = 6.26e-07, rnorm = 1.12e-03, gnorm = 7.73e-03, feval = 0215, geval = 215\n",
      "iter = 215, obj = 6.10e-07, rnorm = 1.10e-03, gnorm = 4.75e-03, feval = 0216, geval = 216\n",
      "iter = 216, obj = 6.02e-07, rnorm = 1.10e-03, gnorm = 2.09e-03, feval = 0217, geval = 217\n",
      "iter = 217, obj = 6.00e-07, rnorm = 1.10e-03, gnorm = 1.06e-03, feval = 0218, geval = 218\n",
      "iter = 218, obj = 5.99e-07, rnorm = 1.09e-03, gnorm = 9.37e-04, feval = 0219, geval = 219\n",
      "iter = 219, obj = 5.97e-07, rnorm = 1.09e-03, gnorm = 1.12e-03, feval = 0220, geval = 220\n",
      "iter = 220, obj = 5.95e-07, rnorm = 1.09e-03, gnorm = 8.40e-04, feval = 0221, geval = 221\n",
      "iter = 221, obj = 5.80e-07, rnorm = 1.08e-03, gnorm = 3.24e-03, feval = 0222, geval = 222\n",
      "iter = 222, obj = 5.76e-07, rnorm = 1.07e-03, gnorm = 1.40e-03, feval = 0223, geval = 223\n",
      "iter = 223, obj = 5.75e-07, rnorm = 1.07e-03, gnorm = 8.17e-04, feval = 0224, geval = 224\n",
      "iter = 224, obj = 5.40e-07, rnorm = 1.04e-03, gnorm = 1.59e-03, feval = 0225, geval = 225\n",
      "iter = 225, obj = 5.32e-07, rnorm = 1.03e-03, gnorm = 1.20e-03, feval = 0226, geval = 226\n",
      "iter = 226, obj = 5.31e-07, rnorm = 1.03e-03, gnorm = 7.84e-04, feval = 0227, geval = 227\n",
      "iter = 227, obj = 5.18e-07, rnorm = 1.02e-03, gnorm = 2.23e-03, feval = 0228, geval = 228\n",
      "iter = 228, obj = 5.15e-07, rnorm = 1.02e-03, gnorm = 1.06e-03, feval = 0229, geval = 229\n",
      "iter = 229, obj = 5.14e-07, rnorm = 1.01e-03, gnorm = 8.63e-04, feval = 0230, geval = 230\n",
      "iter = 230, obj = 5.12e-07, rnorm = 1.01e-03, gnorm = 1.20e-03, feval = 0231, geval = 231\n",
      "iter = 231, obj = 5.11e-07, rnorm = 1.01e-03, gnorm = 7.35e-04, feval = 0232, geval = 232\n",
      "iter = 232, obj = 4.50e-07, rnorm = 9.49e-04, gnorm = 5.27e-03, feval = 0233, geval = 233\n",
      "iter = 233, obj = 4.39e-07, rnorm = 9.37e-04, gnorm = 2.09e-03, feval = 0234, geval = 234\n",
      "iter = 234, obj = 4.35e-07, rnorm = 9.33e-04, gnorm = 1.36e-03, feval = 0235, geval = 235\n",
      "iter = 235, obj = 4.31e-07, rnorm = 9.28e-04, gnorm = 1.62e-03, feval = 0236, geval = 236\n",
      "iter = 236, obj = 4.30e-07, rnorm = 9.27e-04, gnorm = 6.73e-04, feval = 0237, geval = 237\n",
      "iter = 237, obj = 4.15e-07, rnorm = 9.11e-04, gnorm = 1.64e-03, feval = 0238, geval = 238\n",
      "iter = 238, obj = 4.12e-07, rnorm = 9.08e-04, gnorm = 1.13e-03, feval = 0239, geval = 239\n",
      "iter = 239, obj = 4.10e-07, rnorm = 9.06e-04, gnorm = 1.22e-03, feval = 0240, geval = 240\n",
      "iter = 240, obj = 4.09e-07, rnorm = 9.04e-04, gnorm = 6.99e-04, feval = 0241, geval = 241\n",
      "iter = 241, obj = 4.05e-07, rnorm = 9.01e-04, gnorm = 1.56e-03, feval = 0242, geval = 242\n",
      "iter = 242, obj = 4.04e-07, rnorm = 8.99e-04, gnorm = 6.29e-04, feval = 0243, geval = 243\n",
      "iter = 243, obj = 3.89e-07, rnorm = 8.82e-04, gnorm = 2.74e-03, feval = 0244, geval = 244\n",
      "iter = 244, obj = 3.85e-07, rnorm = 8.77e-04, gnorm = 1.11e-03, feval = 0245, geval = 245\n",
      "iter = 245, obj = 3.80e-07, rnorm = 8.72e-04, gnorm = 1.03e-03, feval = 0246, geval = 246\n",
      "iter = 246, obj = 3.80e-07, rnorm = 8.71e-04, gnorm = 6.20e-04, feval = 0247, geval = 247\n",
      "iter = 247, obj = 3.78e-07, rnorm = 8.69e-04, gnorm = 1.28e-03, feval = 0248, geval = 248\n",
      "iter = 248, obj = 3.77e-07, rnorm = 8.68e-04, gnorm = 5.76e-04, feval = 0249, geval = 249\n",
      "iter = 249, obj = 3.69e-07, rnorm = 8.59e-04, gnorm = 2.69e-03, feval = 0250, geval = 250\n",
      "iter = 250, obj = 3.66e-07, rnorm = 8.56e-04, gnorm = 6.85e-04, feval = 0251, geval = 251\n",
      "Terminate: maximum number of iterations reached\n",
      "\n",
      "##########################################################################################\n",
      "            L-BFGS-B Solver end\n",
      "##########################################################################################\n",
      "\n"
     ]
    }
   ],
   "source": [
    "BFGSBsolver.run(L2_tt_prob, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "turned-place",
   "metadata": {},
   "source": [
    "Let's see if the inversion was able to retrieve the Gaussian anomaly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "adult-veteran",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, vv.plot(), lw=4, label=\"True\")\n",
    "ax.plot(x, vv_init.plot(), c=\"red\", ls=\"--\", lw=4, label=\"Initial\")\n",
    "ax.plot(x, L2_tt_prob.model.plot(), c=\"black\", ls=\":\", lw=4, label=\"Inverted\")\n",
    "ax.set_xlabel(\"x [km]\"), ax.set_ylabel(vv.ax_info[0].l)\n",
    "ax.set_xlim(0,30), ax.set_ylim(1,2.5)\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11350c9f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}