examples/seismic/tutorials/16_source_wavefield_reconstruction.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 16 - Source Wavefield Reconstruction Strategy\n",
    "<br />\n",
    "\n",
    "<div style=\"text-align: justify\"> This notebook shows how to reconstruct backward in time the source wavefield when proper initial conditions and boundary values are chosen. This strategy is one among others adopted by the industry, to deal with the need to store the source wavefield over time to later calculate the gradient, which is propagated in the reverse direction in time. Since the acoustic wave equation, in a heterogeneous but without dissipation medium is invariant under a time reverse operation, setting the proper boundary conditions and initial values allow time reversal of the source wavefield. Therefore, the gradient can be calculated with an additional propagation without the need to store the source wavefield snapshots. For this, it would be necessary, first of all, to propagate the source field, storing it at the edges for all time steps. Then, during the reverse propagation, the previously saved wavefield is injected at the same positions as they were saved and reconstructed backwards in time in an additional discretization of the wave equation. This approach can be useful when it is not possible to save the source field in memory, which is the case for most realistic cases, and is also an alternative to using the optimal checkpointing scheme, which requires many intermediate states of wavefield to be stored in memory. To implement this source wavefield reconstruction using Devito, the following requirements are needed  </div>\n",
    "\n",
    "## Requirements\n",
    "\n",
    "- Save the source wavefield at the just within the absorbing domain at each time step. \n",
    "\n",
    "<div style=\"text-align: justify\">  This wavefield is used later as boundary conditions. At this time, Devito's SparseTimeFunction type is used to to handle the points in which the preassure wavefiled needs to be saved. Using Dussaud et al (2008)'s sugestion, in what follows this tutorial, d/2 layers of data need to be stored at each boundary, where d is the order of spatial finite-difference scheme. As shown in the figure below, the grid points represented by the blue circles are the positions where the pressure field is saved. In this particular case, considering that the discretization was 8th-order in space. Also, the inner rectangle, with black borders, is the simulation domain, and the blue dots are in the absorbing area. </div>\n",
    "\n",
    "<img src=\"boundary.png\" style=\"width:300px;\"/>\n",
    "\n",
    "- Inject the wavefield that was saved at the boundaries during backpropagation.\n",
    "\n",
    "<div style=\"text-align: justify\">  Let's start with the first step of saving the wavefields at the boundaries using the second order acoustic wave equation during forward propagation in a homogeneous model. </div>\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "from devito import configuration\n",
    "configuration['log-level'] = 'WARNING'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the physical model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from examples.seismic import Model\n",
    "from examples.seismic import plot_velocity, plot_image\n",
    "\n",
    "# Entering model dimensions\n",
    "shape = (101, 101)  \n",
    "spacing = (10., 10.) \n",
    "origin = (0., 0.)  \n",
    "\n",
    "# Define a homogeneous velocity model\n",
    "v = 2 * np.ones(shape, dtype=np.float32)\n",
    "\n",
    "# Using second-order discretization in space, \n",
    "# so the wavefield only needs to be saved in one line \n",
    "# around the model.\n",
    "space_order = 2\n",
    "nbl = 40\n",
    "model0 = Model(vp=v, origin=origin, shape=shape, spacing=spacing,\n",
    "              space_order=space_order, nbl=nbl, bcs=\"damp\")\n",
    "\n",
    "plot_velocity(model0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acquisition geometry\n",
    "\n",
    "As usual, we define the geometry. In this example, choosing a source located right in the middle of the velocity model, the receivers will not be relevant in this check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#NBVAL_IGNORE_OUTPUT\n",
    "# Define acquisition geometry: source\n",
    "from examples.seismic import AcquisitionGeometry\n",
    "\n",
    "nreceivers = shape[0]\n",
    "t0 = 0\n",
    "tn = 800.\n",
    "\n",
    "# First, position source centrally in all dimensions, then set depth\n",
    "src_coordinates = np.empty((1, 2))\n",
    "src_coordinates[0, :] = np.array(model0.domain_size) * .5\n",
    "\n",
    "# Define acquisition geometry: receivers\n",
    "\n",
    "# Initialize receivers for synthetic and imaging data\n",
    "rec_coordinates = np.empty((nreceivers, 2))\n",
    "rec_coordinates[:, 0] = np.linspace(0, model0.domain_size[0], num=nreceivers)\n",
    "rec_coordinates[:, 1] = 30.\n",
    "\n",
    "# Geometry\n",
    "geometry = AcquisitionGeometry(model0, rec_coordinates, src_coordinates, t0, tn, f0=.010, src_type='Ricker')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating the grid points in which the wavefield is stored\n",
    "\n",
    "The function below is to define the type available in Devito today to save the field in the necessary positions described above. According to the spatial discretization order, the function returns the SparseTimeFunction which contains the coordinates in which the fields need to be saved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from devito.types import SparseTimeFunction\n",
    "\n",
    "def boundary(model, geom, space_order):\n",
    "    \"\"\"\n",
    "    Calculates grid coordinates that are used to \n",
    "    store the field just inside the pml. The number \n",
    "    of layers that need to be saved depends on the \n",
    "    stencil used. For example, if space order = 2, \n",
    "    then 1 layer needs to be stored on each edge. \n",
    "    If space_order = 16, 8 layers will be stored for \n",
    "    each side of the model.\n",
    "    ----------\n",
    "    model : Model\n",
    "        Object containing the physical parameters.    \n",
    "    geometry : AcquisitionGeometry\n",
    "        Geometry object that contains the source (SparseTimeFunction) \n",
    "        and receivers (SparseTimeFunction) and their position.        \n",
    "    space_order : int, optional\n",
    "        Space discretization order.\t\n",
    "    \"\"\"\n",
    "    nx = model.shape[0]\n",
    "    nz = model.shape[1]\n",
    "    d  = space_order//2\n",
    "    npoints = 2*d*nz + 2*d*(nx-2*d)    \n",
    "        \n",
    "    bnd = np.empty((npoints, 2))\n",
    "    \n",
    "    #left \n",
    "    icount = 0\n",
    "    for i in range(d):\n",
    "        for iz in range(nz):\n",
    "            bnd[icount, 0] = i*model.spacing[0] \n",
    "            bnd[icount, 1] = (iz)*model.spacing[1] \n",
    "            icount = icount + 1\n",
    "    #rigth              \n",
    "    for i in range(d):\n",
    "        for iz in range(nz):            \n",
    "            bnd[icount, 0] = (nx-i-1)*model.spacing[0] \n",
    "            bnd[icount, 1] = (iz)*model.spacing[1] \n",
    "            icount = icount + 1            \n",
    "  \n",
    "    #top \n",
    "    for i in range(d):    \n",
    "        for ix in range(d,nx-d):\n",
    "            bnd[icount, 0] = ix*model.spacing[0]  \n",
    "            bnd[icount, 1] = i*model.spacing[1]  \n",
    "            icount = icount + 1\n",
    "\n",
    "    #bottom\n",
    "    for i in range(d):    \n",
    "        for ix in range(d,nx-d):\n",
    "            bnd[icount, 0] = ix*model.spacing[0] \n",
    "            bnd[icount, 1] = (nz-i-1)*model.spacing[1]\n",
    "            icount = icount + 1  \n",
    "    \n",
    "    sparse_bnd = SparseTimeFunction(name='sparse_bnd', grid=model.grid, \n",
    "                                    nt=geometry.nt, npoint=npoints, \n",
    "                                    coordinates=bnd)     \n",
    "    \n",
    "    return sparse_bnd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward Propagation (source wavefield)\n",
    "\n",
    "Once we have the points at which we will need to store the source field, we can perform direct propagation as in the following function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from devito import Eq, Operator, Function, TimeFunction, solve, Inc\n",
    "from examples.seismic.acoustic import iso_stencil\n",
    "\n",
    "def forward(model, geom, space_order=2, save=False):\n",
    "    \n",
    "    s = model.grid.stepping_dim.spacing\n",
    "    \n",
    "    # Boundary info\n",
    "    bnd = boundary(model, geom, space_order) \n",
    "\n",
    "    # Source wavefield\n",
    "    u = TimeFunction(name=\"u\", grid=model.grid, time_order=2, \n",
    "                     save=geom.nt if save else None, space_order=2)\n",
    "    \n",
    "    # often used as a preconditioner, let's also save the squared source \n",
    "    # wavefield, to compare with the field that will be reconstructed next.\n",
    "    u2 = Function(name='u2', grid=model.grid)                     \n",
    "    \n",
    "    # Derive stencil from symbolic equation\n",
    "    eqn = model.m * u.dt2 - u.laplace + model.damp * u.dt\n",
    "    stencil = [Eq(u.forward, solve(eqn, u.forward))]\n",
    "    \n",
    "    # inject source into its position\n",
    "    source = geom.src.inject(field=u.forward, expr=geom.src*s**2 / model.m)\n",
    "    \n",
    "    # Get the preassure wavefield at the boudaries using the SparseTimeFunction\n",
    "    eqb = bnd.interpolate(expr=u)\n",
    "    \n",
    "    # Accumulates forward field squared \n",
    "    u2_update = Inc(u2, u * u)\n",
    "    \n",
    "    # Create and execute operator kernel\n",
    "    op = Operator([stencil] + source + eqb + [u2_update], subs=model.spacing_map, name='Forward')\n",
    "                  \n",
    "    # Apply operator\n",
    "    op.apply(dt=model.critical_dt)\n",
    "    \n",
    "    return bnd, u, u2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we run the forward propagation by setting <em>save=True</em> to compare with later reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "bnd, u, u2 = forward(model0, geometry, space_order=space_order, save=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#NBVAL_IGNORE_OUTPUT\n",
    "from examples.seismic import plot_image\n",
    "from examples.seismic import plot_shotrecord\n",
    "\n",
    "plot_shotrecord(bnd.data, model0, t0, tn)\n",
    "plot_image(u2.data[model0.nbl:-model0.nbl,model0.nbl:-model0.nbl],cmap='jet',vmax=1e4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reconstructing source wavefield\n",
    "\n",
    "In this step, it is necessary to provide the boundary conditions that will be applied at each time step and also the initial conditions. The boundary conditions are stored in the variable <em>bnd</em> above, and the last two snapshots of the forward propagation must be passed to the backpropagation field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward(model, geom, u, boundary, space_order=2, save=False):\n",
    "    \n",
    "    m = model.m\n",
    "    s = model.grid.stepping_dim.spacing\n",
    "\n",
    "    # Symbol that keeps the reconstructed wavefield squared \n",
    "    v2 = Function(name='v2', grid=model.grid)\n",
    " \n",
    "    # Reconstructed wavefield\n",
    "    v = TimeFunction(name=\"v\", grid=model.grid, time_order=2, \n",
    "                     save=geometry.nt if save else None, space_order=2)\n",
    "    \n",
    "    # Set initial conditions\n",
    "    v.data[-1,:,:] = u.data[-1,:,:]\n",
    "    v.data[-2,:,:] = u.data[-2,:,:]\n",
    "    \n",
    "    s = model.grid.stepping_dim.spacing\n",
    "    \n",
    "    # Derive stencil from symbolic equation\n",
    "    eqn = model.m * v.dt2 - v.laplace + model.damp * v.dt.T\n",
    "    stencil = [Eq(v.backward, solve(eqn, v.backward))]\n",
    "    \n",
    "    # Insert boundary conditions\n",
    "    eqb = boundary.inject(field=v.backward, expr=boundary, p_t=model.grid.time_dim-1, increment=False)\n",
    "    \n",
    "    # remove source\n",
    "    # An important step in this reconstruction is the removal of the wavelet that was inserted \n",
    "    # during the forward propagation. Here we add the source so that it interacts \n",
    "    # destructively with the wavelet that is backpropagated.\n",
    "    src_term = geom.src.inject(field=v.backward, expr=geom.src*s**2 / m, increment=True)\n",
    "    \n",
    "    # Accumulates forward field squared (gamma v)\n",
    "    v2_update = Inc(v2, v * v)\n",
    "\n",
    "    # Substitute spacing terms to reduce flops\n",
    "    op = Operator([stencil] + eqb + src_term + [v2_update], subs=model.spacing_map,\n",
    "                  name='backward')      \n",
    "                  \n",
    "    # Apply operator\n",
    "    op.apply(dt=model.critical_dt)\n",
    "    \n",
    "    return v, v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "v, v2 = backward(model0, geometry, u, bnd, space_order=space_order, save=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_image(v2.data[model0.nbl:-model0.nbl,model0.nbl:-model0.nbl],cmap='jet',vmax=1e4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a more visual check, we can see the difference between the accumulated quadratic fields below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "image = -(v2.data[model0.nbl:-model0.nbl,model0.nbl:-model0.nbl]-\n",
    "          u2.data[model0.nbl:-model0.nbl,model0.nbl:-model0.nbl]) \n",
    "\n",
    "plot_image(image,cmap='jet',vmin=-1e-2,vmax=1e-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, to quantitatively analyze the quality of the source field reconstruction, one can use the reconstruction ratio R proposed by <em> Feng, B., and H. Wang, 2012</em>.\n",
    "\n",
    "$$\n",
    "R = 1 - \\frac{\\int \\int_{\\Omega} | u_f(\\mathbf{x},t) - u_b(\\mathbf{x},t)|^2 d\\mathbf{x}dt}{\\int \\int_{\\Omega} | u_f(\\mathbf{x},t)|^2 d\\mathbf{x}dt} \n",
    "$$\n",
    "\n",
    "where $u_f$ is the forward propagated wavefield, and $u_b$ is what was reconstructed from the boundary and initial conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.999999999981469"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from devito import norm\n",
    "\n",
    "term1 = np.linalg.norm(u.data[:,nbl:-nbl,nbl:-nbl] - \n",
    "                       v.data[:,nbl:-nbl,nbl:-nbl])**2\n",
    "term2 = np.linalg.norm(u.data[:,nbl:-nbl,nbl:-nbl])**2\n",
    "R = 1 -  term1 / term2\n",
    "            \n",
    "R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FWI using the source wavefield reconstruction strategy \n",
    "\n",
    "Next, we use the strategy described above to calculate the adjoint operator performing a FWI example using the same parameters as in tutorial 03, for comparison sake.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "from devito import configuration\n",
    "configuration['log-level'] = 'WARNING'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At first, the parameters for the FWI and the true and initial models are created as in tutorial 03.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nshots = 9  # Number of shots to create gradient from\n",
    "nreceivers = 101  # Number of receiver locations per shot \n",
    "fwi_iterations = 5  # Number of outer FWI iterations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## True and smooth velocity models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#NBVAL_IGNORE_OUTPUT\n",
    "from examples.seismic import demo_model, plot_velocity, plot_perturbation\n",
    "\n",
    "# Define true and initial model\n",
    "shape = (101, 101)  # Number of grid point (nx, nz)\n",
    "spacing = (10., 10.)  # Grid spacing in m. The domain size is now 1km by 1km\n",
    "origin = (0., 0.)  # Need origin to define relative source and receiver locations\n",
    "space_order = 4\n",
    "nbl = 40\n",
    "\n",
    "true_model = demo_model('circle-isotropic', vp_circle=3.0, vp_background=2.5,\n",
    "                    origin=origin, shape=shape, spacing=spacing, nbl=nbl,\n",
    "                    space_order=space_order)\n",
    "\n",
    "smooth_model = demo_model('circle-isotropic', vp_circle=2.5, vp_background=2.5,\n",
    "                     origin=origin, shape=shape, spacing=spacing, nbl=nbl,\n",
    "                     space_order=space_order)\n",
    "\n",
    "plot_velocity(true_model)\n",
    "plot_velocity(smooth_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acquisition geometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from examples.seismic import AcquisitionGeometry\n",
    "\n",
    "def set_geometry(model, nsrc, nrec, f0, tn, t0=0):  \n",
    "\n",
    "    src_coordinates = np.empty((nsrc, 2))\n",
    "    src_coordinates[:, 0] = 30.0\n",
    "    src_coordinates[:, 1] = np.linspace(0., model.domain_size[1], num=nsrc)\n",
    "\n",
    "    # Define acquisition geometry: receivers\n",
    "    # Initialize receivers for synthetic and imaging data\n",
    "    rec_coordinates = np.empty((nreceivers, 2))\n",
    "    rec_coordinates[:, 1] = np.linspace(0, model.domain_size[0], num=nreceivers)\n",
    "    rec_coordinates[:, 0] = 980.\n",
    "\n",
    "    # Geometry\n",
    "    geometry = AcquisitionGeometry(model, rec_coordinates, src_coordinates, \n",
    "                                   t0, tn, f0=f0, src_type='Ricker')\n",
    "\n",
    "    return geometry\n",
    "\n",
    "#set geometry\n",
    "f0 = 0.010\n",
    "tn = 1000.\n",
    "geometry = set_geometry(true_model, nshots, nreceivers, f0, tn)             \n",
    "geometry0= set_geometry(smooth_model, nshots, nreceivers, f0, tn)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward propagation\n",
    "\n",
    "Before performing the forward propagation, it is necessary to define the grid points where the wavefield will be saved, this is done with the function below and depends on the size of the finite difference stencil."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from devito.types import SparseTimeFunction\n",
    "\n",
    "def boundary(model, geometry, space_order):\n",
    "    \"\"\"\n",
    "    Calculates the grid coordinates that are used to \n",
    "    store the field just inside the pml. The number \n",
    "    of layers that need to be saved depends on the \n",
    "    stencil used. For example, if space order = 2, \n",
    "    then 1 layer needs to be stored on each edge. \n",
    "    If space_order = 16, 8 layers will be stored for \n",
    "    each side of the model.\n",
    "    ----------\n",
    "    model : Model\n",
    "        Object containing the physical parameters.    \n",
    "    geometry : AcquisitionGeometry\n",
    "        Geometry object that contains the source (SparseTimeFunction) and\n",
    "        receivers (SparseTimeFunction) and their position.        \n",
    "    space_order : int, optional\n",
    "        Space discretization order.\n",
    "\t\n",
    "    \"\"\"\n",
    "    nx = model.shape[0]\n",
    "    nz = model.shape[1]\n",
    "    d  = space_order//2\n",
    "    npoints = 2*d*nz + 2*d*(nx-2*d)    \n",
    "        \n",
    "    bnd = np.empty((npoints, 2))\n",
    "    \n",
    "    #left \n",
    "    icount = 0\n",
    "    for i in range(d):\n",
    "        for iz in range(nz):\n",
    "            bnd[icount, 0] = i*model.spacing[0] \n",
    "            bnd[icount, 1] = (iz)*model.spacing[1] \n",
    "            icount = icount + 1\n",
    "    #rigth              \n",
    "    for i in range(d):\n",
    "        for iz in range(nz):            \n",
    "            bnd[icount, 0] = (nx-i-1)*model.spacing[0] \n",
    "            bnd[icount, 1] = (iz)*model.spacing[1] \n",
    "            icount = icount + 1            \n",
    "  \n",
    "    #top \n",
    "    for i in range(d):    \n",
    "        for ix in range(d,nx-d):\n",
    "            bnd[icount, 0] = ix*model.spacing[0]  \n",
    "            bnd[icount, 1] = i*model.spacing[1]  \n",
    "            icount = icount + 1\n",
    "\n",
    "    #bottom\n",
    "    for i in range(d):    \n",
    "        for ix in range(d,nx-d):\n",
    "            bnd[icount, 0] = ix*model.spacing[0] \n",
    "            bnd[icount, 1] = (nz-i-1)*model.spacing[1]\n",
    "            icount = icount + 1  \n",
    "    \n",
    "    sparse_bnd = SparseTimeFunction(name='sparse_bnd', grid=model.grid, \n",
    "                                    nt=geometry.nt, npoint=npoints, \n",
    "                                    coordinates=bnd)     \n",
    "    \n",
    "    return sparse_bnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from devito import Eq, Operator, Function, TimeFunction, solve, Inc\n",
    "from examples.seismic.acoustic import iso_stencil\n",
    "from examples.seismic import Receiver\n",
    "\n",
    "def forward(model, geom, space_order):\n",
    "\n",
    "    s = model.grid.stepping_dim.spacing\n",
    "\n",
    "    # Boundary info\n",
    "    bnd = boundary(model, geom, space_order)\n",
    "\n",
    "    # Source wavefield\n",
    "    u = TimeFunction(name=\"u\", grid=model.grid, time_order=2,\n",
    "                     save=None, space_order=space_order)\n",
    "\n",
    "    # squared source, often used as a preconditioner\n",
    "    u2 = Function(name='u2', grid=model.grid)\n",
    "\n",
    "    rec = Receiver(name='rec', grid=geom.grid, coordinates=geom.rec_positions,\n",
    "                   time_range=geom.time_axis, npoint=geom.nrec)\n",
    "\n",
    "    # Derive stencil from symbolic equation\n",
    "    eqn = model.m * u.dt2 - u.laplace + model.damp * u.dt\n",
    "    stencil = [Eq(u.forward, solve(eqn, u.forward))]\n",
    "\n",
    "    # inject source into its position\n",
    "    source = geom.src.inject(field=u.forward, expr=geom.src*s**2 / model.m)\n",
    "\n",
    "    # Create interpolation expression for receivers\n",
    "    rec_term = rec.interpolate(expr=u)\n",
    "\n",
    "    # Get the preassure wavefield at the boudaries using the SparseTimeFunction\n",
    "    eqb = bnd.interpolate(expr=u)\n",
    "\n",
    "    # Accumulates forward field squared \n",
    "    u2_update = Inc(u2, u * u)\n",
    "\n",
    "    # Create and execute operator kernel\n",
    "    op = Operator([stencil] + source + eqb + rec_term + [u2_update], \n",
    "                   subs=model.spacing_map, name='Forward')\n",
    "\n",
    "    # Apply operator\n",
    "    op.apply(dt=model.critical_dt)\n",
    "\n",
    "    return rec, bnd, u, u2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backward propagation\n",
    "\n",
    "In the following reverse propagation, the wavefield saved at the boudaries are given as well as the initial conditions, the recontruction is made using a TimeFunction called <em>v</em> in the function below. The residue is injected using a diferent TimeFunction (<em>w</em>)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from examples.seismic.acoustic import iso_stencil\n",
    "\n",
    "def gradient(data, model, geom, u, bnd, space_order):\n",
    "    m = model.m\n",
    "\n",
    "    # Wavefield symbols\n",
    "    grad = Function(name='grad', grid=model.grid)\n",
    "\n",
    "    # w is the field in which the residue is injected\n",
    "    w = TimeFunction(name='w', grid=model.grid,\n",
    "                     save=None,\n",
    "                     time_order=2, space_order=space_order)\n",
    "\n",
    "    # Set initial condition\n",
    "    v = u\n",
    "\n",
    "    # Wave equations\n",
    "    s = model.grid.stepping_dim.spacing\n",
    "    eqn = iso_stencil(v, model, 'OT2', forward=False)\n",
    "    eqs = iso_stencil(w, model, 'OT2', forward=False)\n",
    "\n",
    "    # Add expression for receiver injection\n",
    "    receivers = data.inject(field=w.backward, expr=data * s**2 / m)\n",
    "\n",
    "    # Insert u at boundaries\n",
    "    eqb = bnd.inject(field=v.backward, expr=bnd, p_t=model.grid.time_dim - 1, increment=False)\n",
    "\n",
    "    # Remove source\n",
    "    src_term = geom.src.inject(field=v.backward, expr=geom.src * s**2 / m, increment=True)\n",
    "\n",
    "    # Accumulates backwards field squared (gamma w)    \n",
    "    grad_update = Inc(grad, - v * w.dt2)\n",
    "\n",
    "    op = Operator(eqn + eqs + eqb + src_term + receivers + [grad_update], subs=model.spacing_map,\n",
    "                    name='Gradient')\n",
    "\n",
    "    op.apply(dt=model.critical_dt)\n",
    "\n",
    "    return grad                    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full-Waveform Inversion\n",
    "\n",
    "As scipy expects, the following function returns objective function value and gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from examples.seismic import Receiver\n",
    "\n",
    "def fwi_objective_shot(isrc, model, geometry, data, space_order):\n",
    "    \n",
    "    # Geometry for current shot\n",
    "    geometry_i = AcquisitionGeometry(model, geometry.rec_positions, \n",
    "                                     geometry.src_positions[isrc,:],\n",
    "                                     geometry.t0, geometry.tn, f0=geometry.f0, \n",
    "                                     src_type=geometry.src_type)    \n",
    "\n",
    "    # Devito objects for data residual\n",
    "    residual = Receiver(name='rec', grid=model.grid,\n",
    "                        time_range=geometry_i.time_axis, \n",
    "                        coordinates=geometry_i.rec_positions)\n",
    "    \n",
    "    # Forward propagation\n",
    "    d_pred, bnd, u, _ = forward(model, geometry_i, space_order)        \n",
    "\n",
    "    residual.data[:] = d_pred.data[:] - data.resample(geometry_i.dt).data[:][0:d_pred.data.shape[0], :]\n",
    "    \n",
    "    # Function value and gradient    \n",
    "    fval = .5*np.linalg.norm(residual.data.flatten())**2\n",
    "    \n",
    "    # Backward propagation\n",
    "    grad_reconst = gradient(residual, model, geometry_i, u, bnd, space_order)\n",
    "            \n",
    "    # RWII approximation\n",
    "    grad_crop = grad_reconst.data[model.nbl:-model.nbl,model.nbl:-model.nbl]   \n",
    "    \n",
    "    return fval, grad_crop.flatten().astype(np.float32)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in tutorial 04, to use the scipy optimizer the following warper needs to be defined\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wrapper for scipy optimizer: x is current model in squared slowness [s^2/km^2]\n",
    "def loss(x, model, geometry, data, space_order):\n",
    "\n",
    "    # Convert x to velocity\n",
    "    v_curr = 1.0/np.sqrt(x.reshape(model.shape))\n",
    "\n",
    "    # Overwrite current velocity in geometry (don't update boundary region)\n",
    "    model.update('vp', v_curr.reshape(model.shape))\n",
    "\n",
    "    fval = 0\n",
    "    grad = np.zeros(model.shape[0]*model.shape[1],dtype=np.float32)\n",
    "    for i in range(geometry.nsrc):        \n",
    "        args = [i, model, geometry, data[i], space_order]\n",
    "        fval += fwi_objective_shot(*args)[0]\n",
    "        grad += fwi_objective_shot(*args)[1]\n",
    "                        \n",
    "    return fval, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating the generated data with the true model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from examples.seismic.acoustic import AcousticWaveSolver\n",
    "\n",
    "def forward_modeling_shot(isrc, model, geom, space_order):\n",
    "    \n",
    "    # Geometry for current shot\n",
    "    geometry_i = AcquisitionGeometry(model, geom.rec_positions, geom.src_positions[isrc,:],\n",
    "                                     geom.t0, geom.tn, f0=geom.f0, src_type=geom.src_type)                                   \n",
    "\n",
    "    solver = AcousticWaveSolver(model, geometry_i, space_order=space_order)\n",
    "    d_obs, _, _ = solver.forward(vp=model.vp)\n",
    "\n",
    "    return d_obs\n",
    "\n",
    "dobs = []\n",
    "for i in range(geometry.nsrc):\n",
    "    args = [i, true_model, geometry, space_order]\n",
    "    dobs.append(forward_modeling_shot(*args))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running the 2D FWI example by calling the ```optimize.minimize``` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of iterations has been exceeded.\n",
      "         Current function value: 240.545472\n",
      "         Iterations: 5\n",
      "         Function evaluations: 11\n",
      "         Gradient evaluations: 11\n",
      "     fun: 240.54547232020673\n",
      "     jac: array([-32.624546, -33.016766, -31.025126, ...,  47.275032,  40.43739 ,\n",
      "        29.714577], dtype=float32)\n",
      " message: 'Maximum number of iterations has been exceeded.'\n",
      "    nfev: 11\n",
      "     nit: 5\n",
      "    njev: 11\n",
      "  status: 1\n",
      " success: False\n",
      "       x: array([0.16538788, 0.16400471, 0.16280915, ..., 0.15776934, 0.15828195,\n",
      "       0.15899657], dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "from examples.seismic import plot_image\n",
    "\n",
    "# Initial guess\n",
    "v0 = smooth_model.vp.data[nbl:-nbl, nbl:-nbl]\n",
    "m0 = 1.0 / (v0.reshape(-1).astype(np.float32))**2\n",
    "\n",
    "# FWI with the conjugate gradient method\n",
    "result = optimize.minimize(loss, m0, args=(smooth_model, geometry0, dobs, space_order), method='CG', jac=True,\n",
    "                           options={'maxiter':fwi_iterations, 'disp':True})\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting inverted velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1IvLE2n0vZA8uCIIgKDMHVeSeInKdWb5CVa/wMovI2cDlwAdV9TovXwc/StPZ6pInr6LpFd4I3Bv4aeCdIvIMVb1y2o4XsoETGUsGNojyYDBDh3QiekG3x5knUeT7SLf54o6dq27bddsrxPtIoo+M01Yi0SzgrZVttBDxJC00TiYSqa1l/iKZjTNFxzDpGqluHlTvbo7HrXXj3qvc2BWMdxrFZ6KCktzoRSzx5M6JbRVelJPBlru9JYuyphOxpFfwvPTy7TUAd+6FPTT6+HGJsu4Qu+EWVT2/JqOInAa8CxgCz97lcZ4J/JWq/k2+QVVfkB3nncC1wKuBqQ1cSJRBEARLh6B7/FQfSeQwTU/rPOAxrRNJbdl/DnwH3b23CVR1G3gbcD8Rue+0/AvZgwuCIAjKnIhIJiKyArydZizco1X1k7vcxbOALeD3Zzj81E7rwjZwO11+K7+sb6R+bUe+3N1B1cQDKRvYnASw7R5omcsFpQGZHm6g3DnqDBOyiOM1KDWaYL5vk1HyAzmDf0+UR+UsERzmKXnOsqtZZMS91rlWNivKjY7npE338zKuxKid6yfzVaSzHfgDvW35tIy3zfPIhLq57krY+RzT3xw/IMXO3JiTc8bt+0DvHvBW4CLgkt268ovIKvA04M8cj8yuMgPgqcDNqvqlafkXtoELgiAIDpQ3Ak8BXgUcFZFHmG1HVPWIiJwDfBa4XFUvz8pfApyFI0+KyNOBJwDvAT5P42TyfODhNBFUphINXBAEwZKhJ2a6nMe235e1H8sraKKPCNCn29/jWcCtwJ86+7+RJgTYa2kawqPAdcDFqlo1Xi4auCAIgiVkFtl7N6jquRV5bsIZ266qT5hS9loa+XNmFraB27GDWXfZo8dy49jW8VS/0u85eSYc21r+3HjBkq0NL7fbpZFMTL6CrW9UqEMX85jA0npr20tog6xMmOAqAvDW2/rqinh2t+JEou6+ptWqvO9SEOVaav59y8T4jOnYv9ETAa9n+MNfE4lk4ply8tVOCpra2px0fkzXbue7/HvDf5LzKRxHvA0Znj3e/n4Ms6hG6TAB79nffyeTuzsL28AFQRAEHnuKRrI0xDi4IAiCYClZyB6c6lji29gad93vWk/FISv9rfS7pQjZxYDG48fPxC1vCEEiN2Z6kHr5Rt1y5WS+7uPPW3avCoabnVsybMAJzJLPpVY7b1wNtZE/Ro40VJ6nbVzRaimzLtuukcI/9DQgsQ2SbfKU9m3TpQgjdn/W/b4UkDiREruHBkxGFfHK27QfOcSTOGsDJ9ceZ2LITAWeLJnO+ZiWsduGHcMEdmJRnuwsZAMXBEEQFND9m6FjkYgGLgiCYAnZTbitZWUhGzgFttou+rHN8fp+pnvZbvzKQE0+Kz1kkksiX9bXp2shnc8pK+PIl7VlataXcKXHQuBkz6Myl/S8eeO8CCdQGeVkBinW5itdz21Heix7bvr79o5Ti6d0ec7A+Xpbn56du6/geenv248wkkh83vqJudnsu9idr96LcnoQ5XxZHOmxJGt6npP5JfO9hs07XnA7tvfNRivJvSjtXJFb7QuT39mQKMPJJAiCIFhSFrIHFwRBEJSJHtyCNnCqwsawuXn9pA+aD4YcL6/aeeP643TfpPP9ed5SJUepWhnRC+S8ZzmrJAOatOtNl/XprfdWz9lBfhwrDXtyZS4dJPWxMg17w/OUBF+W3C5Ij6m3ZfeDUJIrE+mw9Pvj5LPPTek5rIlrUCrvPe95mcRbsiKIMvgDum26PyFr2uNMlxiLHpFWrnSky3x/tdejiuxBTJ498/BZj+ph9lANEy/KVqI0z7NOHuakZCEbuCAIgqBEDPSGsMEFQRAES8pcGzgRebKIvENEPicix0TkBhF5tYicnuU7U0R+W0RuEZGjIvJBEXnoPOsSBEFw0qI7MwrM/lkG5i1Rvgi4GXgZcAR4GM2UCReKyPeo6kgaofsq4FzgBcBtwEuBa0Tku2qmOx8pbLS6M2aYQH5TvEgiqzZdGAwgPWvvqOvuJ0E8CvYwEnuUdSHuLg+phdHLlxwzkygSGd8sFJ9l8xcoqY9Zn0dZsPaTGnsc+EMyvIAppclck+vkDAUA3+6WRJDAL5OkTZ7t2h+HQr7EtpXY4zw7ZrqzZBiH2ZRPPmpJopI4QwNqJy+1Q3ZK9rQae1zpOL7dLy3v2efSc/bL2IhHezW75bfdi160vW3zpGVssOUde1wME5hk3g3cpdnMrB8WkVtpJrR7FHA18Hjge4GLVPUaABH5CM3cPy8B/u2c6xQEQXDSEQ3cnCVKZ9rxj7bfZ7ffjwe+sNO4teVup+nVPWGe9QmCIDgZURpVYS+fZeBEeFFe0H5/uv1+CPCpjnzXA88UkdNU9c7SDpWxRDks3AkbtWGl7+VJl6vckWf5W1CMdCGd2SaHFozTNdFPJub7shKfEVrsvvJAF3Y5l0mOUxha4MmVExEgdhmlpHxtTJru9eDLksNCQOUtW8bkK8mS3lAH55FstiWyoHmOnfwTwy4cWdLmq5bxilFJbNqJUJIPLXBlTf84NvqQO7dbUj49qH8+3fudWK7sDCXPpWtGyKKSmGfPDhMYliKZmDLHI5ksid1snuxrAyciZwOXAx9U1eva1WcBN3Vkv7X9PhMoNnBBEARBmZAo97GBE5HTgHcBQ+DZc9jfc4HnAvRXT5+SOwiC4OQmGrh9auBE5DCNTe084ILMM/I2ml5azllm+wSqegVwBcDg1HvrsVb3WetZmSjzJDNpK3/YueFWsitgt/XtHHJ7jF5Qkg88WTKXMtJt3TJa7XxyFinNcZZG7TXru/eV50sioTgROSD1Uk082xy5Mce/hr6M6MmSQ5NvM4v8vGm2DZ30LAyyZ8o+ltbTt+9puTM8k3kRKzHaZ9xKnKUyNkJQbVQSP9iyH1XEnxuuIDc6EUsSFTIvg7+/Grx3eTI6zniFNwfcMNO5t7b957rZaUiWsA8NnIisAG8HzgceraqfzLJcD/xAR9EHAzdPs78FQRAEZTQimQDzH+jdA94KXAQ8UVWv7cj2buBsEbnAlDsDuLTdFgRBEAR7Zt49uDcCTwFeBRwVkUeYbUdaqfLdwEeAK0XkxYwHegvwqzUHUcYebFYiWc2a68Or422nrI3/zRxaHedZXUn/5QysRGk9rAp/Bbz/SSWFIJEPEtXJSBmZPOZ5CorZYGWa7UzTs/nsntMB4FlFvRHDM8iVWgjQnCxWSCujwqBtb9B1fj2sLLlhtllZciOry9C5b3tlWJvR1O2Q0W/zAel97DMxXl8KFOwN6C55UVZ5RJa8KB2JsTSfW+q52V1mwkPUpiuvxyyyby697+CZESAf0N3tOZl7MI86nuvJgd5Tq7v0zDsW5WPb78toGjH7+TEAVR0BlwAfAH4TeCeNJ/WFqvr5OdcnCILgpERV9vRZBubag1PVcyvz3Qo8p/0EQRAEcyY6cAs6XU6PsTxzymB8G884nN7SM08b/ws59fA4vTqwsoY/INQbBDpTLLp82fGwsv+cJme2NxKjlfusp6A5Uj6QOI1N6Wh6xYnaKuRKMikyGVzevat8d97hawfBbxsZb+h4SkIqSx4zZda9g04c2GTUkk7rkOje6d3yJEuba6/RJvJ52jy5rjS3mxf/sehF2bPbnAHcRc/L6bLkhPxaMYecZG/2LO+8F3NSHe9IgG3z8CeDvkfdeQCG9hlvn+to0CZZyAYuCIIgKLMsMuNeiAYuCIJgyVimKW/2Qkx4GgRBsITst5NJ7fyfHeVeLiLqfNazvD0ReamI3CQi6yLyCRH5wdprsJA9uJ7AqSvN35MzDo2F6ntml/U+3zhIyuxQCkhs8TT4SXfiiochX+HY3bw52yB1Be8ZF3E1bsbWbXrUy2wso+58NlxIbkpKstnq22uTB2h2yieXaYZ/l6U5tbzAx1vW5T87N9fuljwgmTVsZJdtvkqLWGJ3sxc3exVlvDw0D6+NeGLPszZqTW77TA5ZYXcbFIYJeOnqwMlO+aYOu7O75fM3Vj2Te4xWAr6deFSIZDJybG0jxx6XbztepGCX3iemzv/plPtt4L3ZulPbdflY6F9qj3MZ8DHgacDbROQSVX3PtAouZAMXBEEQHDg1839O0I6HTia2FpFn0LRHbzHr7kXTuL1GVV/Xrr5GRB4IvAaY2sCFRBkEQbCE7LdEWTn/Zy3PAv4X8D6z7jHAKnBllvdK4KEi8oBpO13IHlxP4HA7POC0NTNM4NTU1frcbz50PP2lWzaPp48ZrSp3v7V4skY+tCCJEOIVmkEvKEf7sDJPd4SSXDpMgh07EuOEhOUGTh5n1Nx1vDJ6iUci7SQyzXgHW5n4YZc9WfKO7bQCyVyCVufd3uxeD6lkqTMME0ii/trXL9d57f7GoXfWbeBlk17Jb3ZNVXJXemdbSW50Ax87QwEm8jkSZR5sebeyZP4c2/KloQG7pXb4jydDQndUkjydDy2oudsH5GOyE4Lx08VcBhG5P3Ah8AbVxCbwEGAD+ExW5Pr2+8HAjaV9L2QDFwRBEPjMKdjyPUXkOrN8RTurSyfO/J81/CjN/6u3ZOvPAr6mk/HPbjXbi0QDFwRBsGzMZ5jALap6fk3GPc7/+Uzgr1T1b3ZZbioL2cCJKCv95u5ZKWJjM+3Hf/bzx46nt5MgpuM8+UPgepJZiSOTC/zoJ3VPmB/VpJCPblk0iRySyTzqBOB1XUzzejrXQzOZR7e7JdMS6TWw+x6TBk5O92xlyWPm/lpZcpiriNsb4/Roy6Q3u9dDJktm8mUNYidNsw9i5q3ZW6UTWTuetIGgV7PbZpcLtzTddVUkk6yajpTpRRvJ83nvzkSwZPv+2ePb9y1Zn5X3ZMlC9BOLdwkn39FuWTJxzC1EMknKOBFOmmXjLe3U7UQxZf7PaWX/OfAdwL/r2HwbcA8RkawXt9Nzu7WjTEI4mQRBECwhO4O9Z/3UkM3/+biO+T+n8SxgC/j9jm3XA2vAt2brH9x+/+20nUcDFwRBsIScgIHeNfN/lsqv0oxr+zPHI/O9NI3fj2TrfxT4lKoWHUxgQSVKi+2635VN3rU9GktAnvwwOSeWM6C0MAg1kVysXlCQP7zHpxRQuMYtqhQgtmfW2EHgSZ0LUZDtM++c5kQdakmCJZv0MJEYx+nNTB20suRtQ0dy3R5L1s2yCZqQSJQ2nUmHs8iSFqu1jaxcmYXGtsdxPDSHjOXKY9lFt9Mc7sj5sAu50pPACxKl9+5Mvi+7G7Td5JsuRRa9Iyvf/xq8uRzzbd4ccJNyo83XXb5027xeygkY6D11/k8ROQf4LHC5ql6elb+ERm7MnUsAUNUvi8jrgZeKyB3Ax4Gn0jSoj6+p4MI3cEEQBMGBYOf/vCzb9gqaqCZCMwlGVzv8LBo72p8WjnEZcCfwQuA+wA3AD6lqqcxxooELgiBYMpRJ56+5H6Ni/k9VvQmn/6yqT6govw28sv3smmjggiAIlpCYTWCBG7idm7dlbDTHNtM7OjTGHNflPxPh+9Y2ZfINHNMJwLZjR+g79oF8eZZoCqmrc/eTnGsCNpc975G1t0zsytatOyhz7pJdY+cpBQe2aevab6OVrGfDBFK7m7FfDY3dbTsJVA4jM0wgiV6yj47XXvSTfDhCv+IiGnveuqwkm1bN/V0174F9jkvDUNxDZstuJJPkPcjfMa98YZiAY+urdfOfpS/jXg4niDL4bv5ptBK/jD9kIKvCtHs1n3FwC8/CNnBBEASBT0x4GsMEgiAIgiVlIXtwqnLcZXzTRs3YSv+x2O6+Gz0h0+RsvkHfutWb9ZqXMQFwe92yxETA2URacVyya12dzYbSnGs2kok9BVt+Ul5MhM3jqZ6N2NBdrQlSF+rsXjlDA5LAyWb9nVng5FTXtLKkTRtJsmv57kRN3aw2LumrfJd5EA6Za7hiblYe2WVgZFF1pOkcK3V7c7uVAjS7QwbygOaFaCpddallMsyh3eaknfcI8qEB4/T2dvfvQp7Pk+rzWnZeD7NOO45zMrKQDVwQBEFQZr+9KBeBaOCCIAiWkHAyWdAGToHNVqLKwwlbRkaasfLLoBBlwZIGSx7vK1fHPBnPOluOcpHBypqOLClZ3exhvXmwklplT7g1OtstVvKZnB/PlDH7K0WdSI5p0p580xx3nLbSmY1Ycpe58Ot5QJEkKslmd/ruLEmWsB6WNliz2PNMvSiHJiiz9Ti1HpWr2fM1S0SN9Blzoo0UopL0+93rS2U8ibL8IHbLimq9iUuaniNXTsqN3RFLSnO7uZ6TlQ3UoP2dys8+GrhwMgmCIAiWlIXswQVBEAQFKgMmLzsL2cCNFDaOS1SOByHAwA7atvJcySts+vGL87RZKYRuSRAKcqPj7QkFmcatdLbeej7agaeOxNoUMWVsf78y5nASRLkgv9j5razn5NC8pHdZaWfiJmw76WXQaew9cXxWC4PTbfwDez23J+6BOYon6dUGay5E/U7lbeuBbNP+/krBnz0Sed57X/OdJe9yt4yYS/rbzjZProSC52ThuvcSz+vJi6AdZU5GFrKBC4IgCMpEAxc2uCAIgmBJiR5cEATBEhLj4Ba0gVOFY63LuNXQ+9n9XLEe1UZDT6OVpGX6FVEWioGTra3A5kmLuGVKQWp7Xn0qH+TEXODIF7l90gRmQYztwNZ5cjjC9HRu/0kjRXTXeWBOM5uGNHWf7xmX+VLgZDuZ6V4nMt0rkj2IvUH3NntuvdXu/Bl9Z31uB3Xv1ah7famMN3wA/Kgknm0O/HfRNcIVnklrX7S2X3GClk+WN+tze5pjd/OimuTbPFmx9JuzM+wphglMspANXBAEQVAgZhMAooELgiBYOsKLsmEhG7gRY4nSqhWHM3nNSpZWrlwd2PW5DDhOe+7IE+77Tj4pBI+tmTsrL7NXmUbsuBirs/ge3TNR82Ll3k32FOwtWTUa6WHr7p7dt6EcNhUw0l3frs9kSCtRzuB+n5CHnXGxD5iTblaYIoPufElUk7T0qSbbqSaKz4q5njYwOFQOkcmX5/gj6gVrzpdrhgzkY8Ds496z0mFhyJDFkzgnh7uYfN48b6UAzZVDMuzZ7bwKM8SaXnoWsoELgiAIysRA72jggiAIlpJQKBe0gVO6A2msZLLG2oqRt4xqtbpigzCnZbxufho4xPcKS+ed8wPEJp6TZqN4MiR1Mo1l0k3YRj/oLlMiccIs6CeebJR6qKZlVvrd+0vkSnOvTst0HludoY53PrJy5Qy4gX2nbHPLzPFnR4xba16XfnLduz2NV7Nr7t2ffuKxW4e6CzPKmu68c16NcnneLnTudnIPnlyYeJj6kUw86bEkUXqUvbC7dxA2uAVt4IIgCIIy0cBFJJMgCIJgSVnIHpwAq20X/bAJqHzaWvqX5QzjQHfKIStLdg/GhlyGq6tPGvjYJAteYZ6Ml+6qThDy6lnyeHPTlftOJdJscHgSNNd48FmnP/HlsTXzVKZeZd0BgCfrVrfe9X51ggIU9+1XJ8Grdn4+qaTlBQquPKjDhAQu3edt50/MJf18HzvMcj2K52ZXOEEGvHkRJ45Zew0rgg+UBr6PvHneMsfc2YJZj9Ndt0A1nExgQRu4IAiCoEwolNHABUEQLCVhgwsbXBAEQbCkLGQPri9wWmt7+4a1saB91qnpX5Z7nTk2GFiX/aEJdjqc8NkdJ70/QPsZMSDV+vO62SEE0/+e5Vp/EoHBiaxQGz3Bc//Psdd90O+2SUB+rbsrYY8/aT/qHl7hRYwBPzJMMmwjq4O3rdrd3Fmf32t1JshMAwWb9RNBf7vL1Np7/Cg+fkSevjOMpTDvrhvEOH+8k/Nz7E+loSuurS85Rv4UOu9LYeJeNyizU5cSpWeqK5BRBFueJHpwQRAES4bSOJns5TMNEXmyiLxDRD4nIsdE5AYRebWInF5TRxF5kIi8TURuMeVfmOW5SUS04/PEmmMsZA8uCIIgKHMCenAvAm4GXgYcAR4GvBy4UES+R9UP5Coi5wNXAx8Cfgy4Hfg24LSO7O9r92u5oaaCC9nA9QROaSXKU9fG6886I+2Qfuv9Tzme/vJXN4+n77jLBNnNQqKkc185UllBphFPfslutd1FLo2Md5wex9YniZWcBJntTpfKjzwtJcOed9/Ijfn1GLh18P8VunOEOfPzDbJgy33jvm639ZN0+nwk0TrMQiJd5lFrvGDchXOzUldyf5xgvJDek6F5KO1cYlZqz8sn25J8pWOaus3guu7JwRPX0C46w0Dy98XDdjRKkp4X+FhLQZDd61Entc9zSEdpPjgvmMsJUCgvVdWvmOUPi8itwFuAR9E0YBOISA/4T8Cfq+qTzKZrnOPcoqrXzlLBhWzggiAIgoMla9x2+Gj7fXah6KOABwE/Me865YQNLgiCYNnQncHes39m5IL2+9OFPI9svw+JyLUisiUiXxaRXxex814d51IRuUtENtr8T6ytzEL24ARYayWyNaOHDTIJysoHVubZGmpnGjKJMjvm8XQWhSN5GPrdeqFkRltJZMHuyAz5Q1ZwTOukFAzC86LMcYMl2xpk0S0sXoDo3POyRlZcNSE1BoNMFrX5Vuz6cXole9pXkmfHlhmvz71VbWQW736Urrs13idy4XZ6PkOzvLU9rtyWUdeHJm3XA2wmz/j4QMMkncma5kHwpNBctq+VEi1e9JNEds8vopUVzepZIqaMnPPMTQU1gZMnjrNHLbImwlG+za/LnqoCcE8Ruc4sX6GqV3iZReRs4HLgg6p6nZcP+Ob2+4+A3wB+Hji/LXt/wMqWV9H0Cm8E7g38NPBOEXmGql457QQWsoELgiAIfJQ6T8gp3KKq59dkFJHTgHcBQ+DZU7Lv/MW5UlV/sU1/SET6wGtE5EGq+mkAVX1Bdpx3AtcCrwamNnAhUQZBECwhusdPLa2seBVwHvAYVT0ypchX2+8PZOvf334/zCuoqtvA24D7ich9p9VtX3twIvJe4DHAq1T1F8z6M4HXAk8EDgMfAX5GVT9Zt189LhVZGeGOu1K95MZ/vOt42ko2G5tWfkn37UkuPcd7DlJPLhKPOce9Mdtmg9xaRayX16XSY6wGV76YCEjszMNVmJPLLg963dLjSjZ534qRGFfMfH1rRm600qOd66/ZNurcZtevZmVWBuNtVpYcmPX9XKLsj7clA8/NPRxl/5xTecxIlNvjc94epWW2hj2Tls71m1vj9Rtb6fXc2LTb+qaMTSdFUllzy0r63V6c4HtyWrlvwpuX6UwMuraXx2yrD7DcLcmn3qp+HbzB3aVgy7XUzUG5+/2eCERkBXg7jcT46Mrf8OunbK8Vvqde7X3rwYnI04Hv7FgvNK39xcALgB8EVoBrROR++1WfIAiCk4n9djJp3f3fClwEPHEXrvx/BmzQdH4sF7ffrv1ORAbAU4GbVfVL0w60Lz24tof2a8DPAL+fbX488L3ARap6TZv/IzRGxJcA/3Y/6hQEQXAycQIGer8ReArwKuCoiDzCbDuiqkdE5Bzgs8Dlqnp5Uy/9qoi8Gvj3IvJ1mvFy5wO/CLxFVT8DxztJTwDeA3yexsnk+cDDgafXVHC/JMpfAT6lqn8gIl0N3Bd2GjcAVb1dRK6iOZmpDZyqHJd0No332B3Hcvmku6frDnImfSiSAdRYSTGrT5JvTN+TK4GeOVAif5oqT8whZ9MVcuXE4FDH5ywZvJxts7JiOs/bOE/uvbpivB1tetVIj6ur6XGsFHloVZ20kSFX03t7aHXbbNvuXL+6kroarqyYbYNxetAfp60kCdAzurGVJa1nbX6vrWQ5GhlZMpEo02u4uTV+NbeG3RKjlR43NlNX1nWzvL7RM+u7080+xGzzjpm+LzUemnm815EjZRY9FdVJOyqV4r/XntxY8qLcduTKWeZvm/AQrSmzW4myshe2Rx7bfl/WfiyvoIk+IjR+1rlaeDlwB/BTNBFRvkhjtvolk+dG4F7t+rOAozS9u4tV9X01FZx7AycijwSeSYc82fIQ4FMd668Hnikip6nqnfOuVxAEQTA/VPXcijw30TGaQxuj6Ovbj1f2Whr5c2bm2sCJyCrwZuB1qurFCjsLuKlj/a3t95nARAMnIs8FnguwslYVyzMIguCkRDkhPbi7PfPuwb2ExivyVXPeL+0AwysADp9+77h1QRAEBbR6GPzyMrcGTkS+hUaH/TFgTURMGGTWROQeNJrrbTS9tJyz2u/bph1LgR25f92YVXob6Q21uvnA8RctadvJJuv2XHClT+ppXf4z4T0dDmDtXOaQmU3As5VJhSt/s+9u92qbr58Vsja4gbWnOXY2gLVVY2tLbGvj9OG11LZ1eM3Y2sy2w2vbJj3sTDdlxsuHVsf+72tJejMpszLYMulx+YFZP+ilx+n1xvURsfa4cXqk6fVQszwa9TvzbQ1To+RwOH41N7fGF3Fja5xvY3O8ft2kAdY3xsvHNgZmfd+sT+12x4yt7lhit5POdFMHa5+zQxjMMIOt9F6nwaPtejPkYML9froNLB2OkdngbLrSBmcXt51jTszjV/HXO7ete3b/UvNUFckougFzHSZwHnCIZnT5beYDjRHxNuChNLa2h3SUfzCN62fY34IgCPZK1+jt3XyWgHlKlH8NXNix/hqaRu93gM8A7waeLSIXqOqHAUTkDOBSJocUBEEQBMFMzK2BU9Wv0Uxel9BKYZ9T1Q+1y++miVxypYi8mKZn91KaXvev1h0LtnZkPRONQSZcg01EDBNYNwkanLvie3MrOTIC5NLIOG2liAnJxZYxS4l0mc+jlWwz602hnhEvSn/CPFkyD2Kcuvn3TXq8/lDu8p9IkeNanHLISo+5RLlt8g0704cPbZr8aRiOw2sb5vhOemU9KbNqlvt2CEGvED16vxilYTS2k2ECY7V/Y+vQ8fTm5nj9+qa1CMCx9fHysY1Vkx5Ll3etp7LmISNZHlrvm3zmvmdy9DHzvAyMiaBvruHEc5zcuvFzUJL+PNf+dG637jylfXv7zcuk5bvXg//OFeXGymE+uyUkygOIRdnO8noJTRyy3wTeSTPt6IWq+vkTXZ8gCIJlJBTKEzCbgHaEtFbVW4HntJ8gCIJgjuxxTrelYSGny1FgvZ0vK3PQSrBeg6kkN07nMkAi/VVGElBHv7TyR17eC+rsSZeQeV+ZitqgzGo9JTOPyGQ+Nmf+tdwj0sqSa6vdsuShVB3jFCM/erLkKYdSSe6Uw2Pd6hQjP55yaJw+fGgsNx5eS+XGQ0aiPLQ6DrK9ZtK91ZLmcwCypCWTRftG2u2bcz20dfR4en3l1OPp1dWxdAmwMhjPG7m2Or5BqytrJk96D1YHY8ly0B+n+yYQdb+f1dO8TD33hfGFojTCiPFKzT0anbjlVpb0Io9A7i3p7CtrEKyU6eWrbUNq5cbaOQYtpfnpTnYWsoELgiAIykQPLhq4IAiCpSQauAVt4EYKx1p1pe8MWAZYM66Lary9bGDcvIyV6zxVofTcWLnS5ssDHUu3qlmUNSWRWcw59LtrWpJfkznbCoO2PW9JK0ueknlE1siSVpIEOPWQlSWNt6QjSx7KJcrVYyY9lvFYOWDpcd6Y8zkk4yGjdtB5s6wV6XTXvjdf3S+lHdCuXgRy/ODTaRDmLGhDoqZ2v2NWlszjrI8c+TKRK9MibgNRajhm8YismvetcMyd+kzU3y9y0rCQDVwQBEFQJnpwBzBMIAiCIAhOBNGDC4IgWDKU6MHBgjZwI+DYaFKsPtTz72jPsbv1M/tVHtmki0l34nHauuIn9ri8kPg2iqrjOlq9ta3lESSSwMkm34oTUBnSYMkr5mlZWxlXZm01PQG7fMhEKEkCIq9kLuomksjqytget2oCH9v1NlByszy21bmRtZeNwfiGrIw2kk1JUOdVa+fqjkzTbJPO9LaxmdlJWifybZu0eSmG2+lzuLrdXcbmk+3cQNj9krjRRjIbXBLI2YleUmoQ3IDI+XtYiHh0fH2+PMPEpulwou4M0cAtaAMXBEEQlIn2LRq4IAiCpSR6cAvawKnCetsvHxS691ZuXDVnaqW2eQRbtupJ7TPlRT+pkThyvOgHkp2blS/TSCZ2mEAebHmcXjWyZJIepGe9OhiLJismnazPJEobVaPfH5m0nX/Nysxp+ZOdXjZMwM5b1zOhbgbmeto58ACGw7FkOTD3Y3UwXr81SI9jn5fVlXF6a9uuT+tqtw2G42dvYCOm9LLzqZDxEtmuYEaolShr5mnLlVMbbch7fUvDM2SGcQId0RCDloVs4IIgCIIy0fBFAxcEQbB0hBdlw2I2cDKWJk8xksCpK+kdPc0ErD1sonBYWSWPZGLxno+SQ2QavqTbo3IeiKOZWImkn51cMg+eE2x5kAX+sMtWrrRy0iCTKG1wXpsvCX6dS1BJYOzp18pGzZhYViO9yZJFMtkjXlQTSO9J30kPMoly0O+WGFeSZ0CyMt3pRELPnl27LZ/3cYfUozILtuzOJ9ddfnLnpi7O+zZRB7O+JLHad3mW6Ek751M7N93JxEniTx0EQRCcbCxmDy4IgiAoEhLlgjZwPWCt7ct/w8pYYzjzlPSOnnX6uMN/aNXKheM8o8K8UfN8QHzvqDxf3TbPq8sO7p4IJG0HgTtyUDbdVyprGhnRS+fLnvQ4i/nbGs0128O2GdjcM555PStb17qlLgqjsafj9ih9lXMJd7ekMpwvH9ttfUeOnnw+7HPYvT5/XzxZsMbrGTIPS0eWzAM0u9jjl2TBWi9om67UKKf+NsVAb2BBG7ggCIKgzLzt/otINHBBEARLhhJOJhBOJkEQBMEMiMiTReQdIvI5ETkmIjeIyKtF5PTK8g8SkbeJyC2m/AuzPD0ReamI3CQi6yLyCRH5wdo6LmQPrgccbvX+M0xg3286I813zn3GYwM2NscC+9H1cXozjdnLaLv7f8/drbfvRj+odEdObHXmb05ut0td++lM5+7mNZNt1pLY3WzQ31FqLOz3bEDh8WPd27ZBmBfycfcxBuPc5maDLXvXcBZKNjhx7GS5K31iT0sMUH6ZvZpPPff9ZJhAZjTzIpmMzIaJ+O4V9ay1x9dSO5xpH3gRcDPwMuAI8DDg5cCFIvI9qupaNUXkfOBq4EPAjwG3A98GnJZl/aX2OJcBHwOeBrxNRC5R1fdMq+CSvfFBEAQBnJAG7lJV/YpZ/rCI3Aq8BXgUTQM2gYj0gP8E/LmqPslsuibLdy+axu01qvq6nTwi8kDgNcDUBi4kyiAIgmVE9/iZtvu0cdvho+332YWijwIeBLx+yiEeA6wCV2brrwQeKiIPmFbHxezBmUgmdl6ybzwjla0e9U/H2z7yyXHE142tsWyVS5Te/FIHwUzBlgs+x16+cpQFk8ZJF8rMwsiR1EpSWyLJ9Yad63ujLEBzbwGjnJiH0pMhJ4ucmOER9c+HlTXFzZcV6sw3zzOb5X2fx0/Efo1eOaCfrwva708X8jyy/T4kItcC/xS4DfhD4OdU9Vi7/SHABvCZrPz17feDgRtLlYkeXBAEQbBnRORs4HLgg6p6XSHrN7fffwS8H3g08Ks0trjfN/nOAr6mk+MdbjXbiyxmDy4IgiDwmc9A73uKiG2orlDVK7oyishpwLuAIfDsKfvd6Vhdqaq/2KY/JCJ94DUi8iBVLfUAq1nMBk7HDmSbw3H//tY7UgnqQx8fn97GxliLHJpsM8kSM5XxC3leVQctkcJ8JaBgDiSOab4Ak3sE7jCKKVRmwvPCnMi3x33PS66c02wCt6jq+dMyichh4CrgPOACVT0ypchX2+8PZOvfT+M88jAaifM24B4iIlkvbqfnditTCIkyCIJgCdlnHxMARGQFeDtwPvA4Vf1kRbHrp2zf+Rd3PbAGfGu2/cHt999OO1A0cEEQBMGuad393wpcBDxRVa+tLPpnNM4jj8nWX9x+78ii7wW2gB/J8v0o8ClVLTqYwIJKlCNgfdT05e/YHPfpv3J7Pq5w7C25tuIEW8768XuVGDRZr515OvZgUpVeZd7xC8fxtpXKa026MhDsXr35SoPGRUad23pmPbIE/+fMOdhz286zOU9yzVx7JXKJMw2ATWd6lL2WqTcsnekJnHdplrPxnsL8ffOkw70POs+f3f2RjU9ALMo3Ak8BXgUcFZFHmG1HVPWIiJwDfBa4XFUvb+v1VRF5NfDvReTrNOPlzgd+EXiLqn6mzfdlEXk98FIRuQP4OPBUmgb18TUVXMgGLgiCIChzAmz4j22/L2s/llfQRDURoM+kWng5cAfwUzSDub8IvJYmconlMuBO4IXAfYAbgB9S1T+tqWA0cEEQBEvIfjdwqnpuRZ6b6Og0t04jr2fKYG9V3QZe2X52TTRwQRAES0fMJwAL2sApsNneu6NmmMDXjqW94EF/LP6fuja+2SuDcZk8qGuNTaA8mWKt3c3Zd0GO9+qWaO3WvpFN5mrz2XrabFmRxH7iTRSZ29b2Gty3VxGsObGtAb3etkmPI5lgg5Usw4SniTHIXI/edpat2yZZizfxb76ndPJgMenu9fm+R85zPGm3m1bjMp4NzU7ou50//DZ6CvbZM1ny45i0Z5PMUXehjiV4qveNhWzggiAIAh+dz0DvhScauCAIgiUkZvRe0AZOgWF7745tjzvoR7fSzvqhDTv/WbdgMOj7AYmTYxZlmumyZL56FlnBc81PJFIr80wEJLbpcT4rzYy20zJDs2znztpO1qdl7LLNZ+tTcjf3KA0TsJJlItf1FvIRr6M/1l8l0/RqZMlaaXk0snPtFe61m06Pmz5H43Qqgaf19yRTj4kAz862ZD66zFyRzPvmSJyzqN6T9e8ej1C76526lYY5nKws8dsfBEFw8hLtW0QyCYIgCJaUhezB9YC1jv57LoXYoMqbxrFuxXjW5VJOv9ctDLhei9TLkvPE9ZxMvNrSGmw7suT29jg9nJAou9NbJt/KMJOtBo5UZeXK3LMukbS6/3dZ2SyP1JHcR+ceLh2JJuU/bepIw6PsOm+b+eXsPbD3cLidlhkOeyZt89l0Wp/kmbLyuPN85ts8uTKVHtNnoNcbZ/RmAcxV3Z5zSWeRKOujr3SfUP4bU3PcsMEtaAMXBEEQTCHat2jggiAIlo0Y5t2wkA2cAKsd+kF/wguqOxCslT96eXxmk1MSicD3lKyRH0qKQiJ5FPJ5pMGju9OQSUDb3emt7bTQwMhOm8ZL1V7r3BN1YGSr/lbf5DPeq8P0wttB+SsDK4+NyyfefJre7MQj0J74MluZk4HR6au8bZZH5hoOh+P1W8NUrNsy923L3LcNk97cSi/opimz6Twrm5mEvTWemjGTx03w6Oy9rPGi9DwlYfK3oatM/r7MovBVeWHnedyAEnVBI2YZyH+ysJANXBAEQVBAwwYH0cAFQRAsJdG+RQMXBEGwlEQDt6ANXE/gcGsW6BkBe7Wf2Y8cP980OHK6TdycddROpui5NNvgz3mZNJrC7oczWLvG0Ng+ekMbmDc/5tj+YuvWM5XpZROJ9pJzs9Eg7L7ySCQ2cPCoM18arSQLtuxEMukb295SBFs2jIwta2u4mmzb3Fo7nt7YHG/b2Fo1eVaSMhub4+Vjm+OfhvUNm07tdusbve60mYjY2twANofG7mbS1h6XD3HxXsXkPbLP50T+7omER+a5K9ng9jrJqmXiN8exwdcNAvHNzBpuJkttgg+CIAhOYhayBxcEQRD4KCFRwoI2cAKstBrEiumDHh6kd3TVnN2KkS9LXX8rU9S673uRDaQQONUrk8gsRYmyO23JpRAbpKRnTtS6Z09KqVba8Tr8eQXG+Wrm15vM1x30t3oOOlOf1dH68fTK2kZWTS+mxd2M0VhyHSZy4+FxevNQUuTY+nh5fXMsV961vmrypLLmXRtjifKuY+OX55iRJe9aT6/ZXevje33MyJIbm+M865skbG2Nn7dNI48PCxKlJ7clsZLNszrIzBX22bdTCdoykxKlrY+ti82Tl3Hy4ZNEY3F+f0rs5JvIHg3cYjZwQRAEQZlo36KBC4IgWD5UYxwc+9TAicjjgJ8HHg6MgL8HXqKqV7fbzwReCzwROAx8BPgZVf1k3f7HHpNrRjE5lDqFcXjFRM4w+fYai3fC07DXLUX2Ci48nhRZDhhr8iUV8o+TYJ5367GWXo+J0C7j4slcc4U5wpK54rygvVl0CxtFw03biBqZB6DxDrReg2urYxlvbWs9KbMy2OhM9wZWw9pHGdNez8zTcGu41pm23pHrGyZtZEjIPCI3rCxpZMiN9PU/tt4tRVqJ8thGet/sciJLbo3PbXMzfaY2jUQ5HNroJXUejZ6kn3hHZhK2fcZHvW7pcfKYRr405ZN6pkX8wOu1bU2t62RQxdy9KEXkJ4B3AR8DngQ8BXgbcEq7XYCrgIuBFwA/CKwA14jI/eZdnyAIgpMR1b19loG59uBE5FzgDcCLVfUNZtP7TPrxwPcCF6nqNW25jwA3Ai8B/u086xQEQXAysiyN1F6Yt0T5HJpe+28V8jwe+MJO4wagqreLyFXAE6ho4BovyiZ9yHhOnraW3tHDa93S4cjxjoJUFfCCt/Z6vvwxi0dkOmi6e1/5curdOL3OkHqiWU9D67026RU2vkBJIOckcHMqBGyZZTtv3MZWdxpg3chY65vGM8+4wh42ktqh1dQD8PCalSUPmfR4IsDVlVQHXFsZa2org3G+gUn3+8OkTN8MIpckMPe4/poHgjbXOplzbXtg0qkUaiXYreE4baXH9U27PpMbN2y+8b7XN7qlx2bZDtQ298CRIQE2zCW10qP1lNzKAmtvDe371z3QuzT/WfKOmAVbJB/obWVJkvnxxqu3s0DjecBnc1Sz48zb02yaZaC450VZ8qjsMrnolOOcLMxbonwk8HfA00TksyIyFJHPiMjzTZ6HAJ/qKHs98C0ictqc6xQEQRCchMy7B/fN7ee1wMuAz9LY4H5DRAaq+h+As4CbOsre2n6fCdyZbxSR5wLPBVhZO33O1Q6CIFguwoty/g1cDzgd+Neq+sftuqtb29xLReTXZ92xql4BXAFw+PR7H1cCVo1EefopaV/9G061HnjjfHbg6XCbhNyTaoeSd6SVD/qOLJnLmn3H+8vzyMzz1cgXUnCvTOaQsxsmBtiaTWbA8baZAy6fQ87KUxtG6rLzvB1bT+u2ujqWyw6t9kx6vO+1FSNRrqX60dqKlShHJr1t8qQ3e2WwPTWdxLIkj3lZ9wNivUyt96mVdoe5zGs8Rm3azs22sdmdhlSW3DADsK30aONF5sub5h3ZSGJe5nJjt0fk0JlvEHypuyjdmYe8b0/V81rMNiQekY7nZC71SfK4dB8o/71I3kVv0Hcp4IHdl00XvErdfUX7NneJ8qvt9wey9e8H7g3cF7iNppeWc1b7fduc6xQEQRCchMy7gbt+yvZRm+chHdseDNysqhPyZBAEQbAL9jhEoKb3JyJPFpF3iMjnROSYiNwgIq8Wkak2JBFR5/NdWb6bnHxPrLkM827g3tl+PyZbfzFwRFW/BLwbOFtELtjZKCJnAJe224IgCIK7Py8Ctmn8LS4G3gQ8D/iA+IFrLb8HfHf2+fuOfO/ryPfhmgrO2wb3HuAa4M0ick/gH2icTH4AeHab5900kUuuFJEX00iSL6WRnH+19kA7fzCsLev0U9Jret79Tjme/tItJorF0bG4vrHpuwZ7/2JyG1wvscFJZ768TN8ZGpBGZkiNArXBnz28P2X2PDNzSRK1ITm+sWnmtqjN5LxtAFyTHqQXZGBu5MrKON/airXhYdanNqdVs3HNRLBZXRmZdFrPFROxxAbntelJG5xJV9rgEnunsQXZiC+5Dc5GerHRXDbN8IrNrfH6fNiFtbttmpEOm8aetrGV1j917TcBnu38bROu9I6bv8mjrrt9RmmIDN3bvHkRJ2Z2TKLwjNePkqDj+b66hy2kdrssik+Fc/7EUByTdt/rGV74E2CDu1RVv2KWPywitwJvAR4FXD2l/D+q6rUVx7mlMt8Ec23gVHWn6/hq4BU0tra/A35EVX+/zTMSkUuA1wG/CRyiafAuVNXPz7M+QRAEJyPK/ntRZo3bDh9tv8/e14NXMvdQXar6dVV9vqreW1VXVfWf7DRuJs+tqvocVT1LVU9R1e9X1U/Muy5BEAQnK7rHz4zsmJ4+XZH3eSKyISJ3icjVIvJ9Tr5L2zwbInJtrf0NFnQ2AQU2WzlhKwnsm94WK1/2jTy2YtKj7ApIMidV9/Enhgk422y6Xxgm4EUyqY2YYin9abOXJ5FsbPnsnG3UF39uN/+gfmDc9ASsfGnv1cBKnANf4lxJJM5e5/pBdq9tAO4VM9wkeW5yOdrIkrWRJhJ5y1xfG3w6j5qRSpRmvUnb9ZvD9B4MjcSYuvJbSS49aOrab+psTiCvZ50zQrrsSvJ0vwdNPi/aT512Z6PJJNFTslzJkpGTk/faBlsuSKmzUPlanahhAvcUkevM8hXtcK1ORORs4HLgg6p6nZev5UrgT4EvAOcAL6YZUvZoVf2QyXcVTa/wRhpP/J8G3ikiz1DVK6edwEI2cEEQBMG+c4uqnl+TsY1A9S5gyNjfwkVVn2EW/6uIvIsmwtUraSJi7eR7QXacdwLX0pjBpjZwc5cogyAIgoPnRM0mICKHaXpa5wGPUdUju6+r3gH8Z+CfTcm3TTM7zf1E5L7T9ruQPbiRwl3DRgy4w0TE+OrtqX7yP2++63jaSgxWZsklhcQryvGSm4ww0h19xEvnx0m8MPu+TGOP480158uIIIknmQlS63i/5fuw1y2ReQqy1ajyTUm95IxcWSv59ru3edJnvs1KYKknbO7JOv0e5Hj3ZGQDWWfy+rYTCWToeC1OeDc621KJNK1nnRyd4gVBTp7j/DrZ69u9elKe7znPhBN0fDJo+DidBS8a55moZrdsbR1eJbuGs3g6u9fXiYqS40Vf2n8nShCRFeDtwPnAo2vn9Cywm2pPzbuQDVwQBEFQoHGj3NdDtGPd3gpcBFwyqyt/u68zgEuAv5ySbwA8lSYoyJem7TcauCAIgmAW3kgzzvlVwFEReYTZdkRVj4jIOTRB9y9X1csBRORFwLfTjJnecTJ5EXAf4Ed2diAiT6eZQu09wOdpnEyeDzwceHpNBReygRspHGt1hhUzwPW2o7nX4ViMsHPDDfq+eFAzdiTP4SkJtf+f/Pnccs/LbjnGk2byU0mkDBvk1uw3lxQ9udHKW1uZB9+2I4PVypp5oNwdvMG+4Hvm9QqSYs/xliyVcetQ0qNcidKkM51p5ObrTucexKOKY5ZwPYOz87TPpJWJ7T1cyS+OI+16cmdznO5jel6UE3MhWvk1We8fM7n3I5vPHj+9oEmwdBskobOWk3V1399sB9PGzp+ADhzAY9vvy9qP5RXAy2lq3ie96zcAT2o/3wB8HfgL4N+oqu3B3Qjci2Z2mrOAo8B1wMWqaifRdlnIBi4IgiAos9/tm6qeW5HnJrLmWVWvonFKmVb2Whr5c2aigQuCIFhCYrqcaOCCIAiWkmjgFrSBU2CzDSFwzERzuGMjdwMfp639aG1lvL40eWmyvlQhG91CraDemWyXrUt2nR3B3ea4SsuEEc4MDUhseN3ROSaWHZvRZBSO8bYkCsfI5knLpBFpxuu3HZvELC9v6dz63vWYso9p63O8cygNz3Anp03y11XAO2fIg4YbG5p5jwZpjGtW+vbZMbZc+xpkZZL6YJ9d37bWc4zONbZoSCOZeHbUol3XeT4m7HZOGfs7k9/r/P3pojTsYScd7dkkC9nABUEQBGWiBxcNXBAEwdKh+N7IJxML28B1efoPs8inG8Z9fcXMg2VdhnPJpcYVf0KOSiKjdEs2krtxO67ojid/u79uWdMes1ors/vddYmyHOJFy0jmJRumR900kqWVKzdNesPk2c4kOSt/2mnObL58rrtZKIwwqSy/t0rY43tRQAAGThQOE4eaQRapZ9XIjavmQIm3elZ/u++Zegy171h3kYS591g8udGRHiGNbJIMryjIzHZ/SeDzwvAOdZ7xcYbowUHEogyCIAiWlIXtwQVBEAQ+0YNb0AauBxxq+/yryfxcmQyYyGPdkl7+DFhvSy/4ay4H2X6wrUIiV0xEVjBpK+lZiTOvW6KZdHtupjJmdkznvOf9Hngyqw3wPMx0GitLHht2p+8w6aO5zjOy+uWmWW+1aaORQjb5nXND8gnyZkG80B12fe7iaR8q85r2TFqMvt5bTcsbfexUs6vTzbx3hwtvfxJo2F6OglRmKQUdrlF5y16D9jnu9o6c8Eq1kXsK779Hcj7J3HB5tKFuM0JS5/zcrImj4Flr6Yp0M/m+BwvZwAVBEARTiBYuGrggCIJlJCTKBW3gRGCt9fhaMyrNamHQtr3ZVh6TbMCxzddP9mckwUxvnGUAciox2B3YAc/+zlJppu6giSxp9m0HbeeK3F5fklqnTi+48IapTyJLbhvpEWB4zOxgw+Qz6VFWZh7y44nASpF9G6Vgzaw/lJbpj7cdZVxm1ZzySnb6+ftz/PCVAQdmcOB1A1HnQc+T4NHOfI7lgd72ecfP6JAGgjYBpnt+Pe2mvnmv84Dmve7XP5VcJ+bum6938LKykA1cEARB4KOEQgnRwAVBECwlIVFGAxcEQbB8xEBvYEEbuJ6MbW9rNvrCIL2jNkhsadLGGkq2hkSf7/n5PJIHsRC9wK5IhiPMcBxrd3PtgRPbuveV41XHi/IC/j1xI4dM2M/sTKBmOEAyTGBBbG45aodA2A32oc5eZV1hGvk1r4ncUxucvETyHJlnIg06nNu5u23gs9if7cObPtPpvtxrYCOPZNejXzE0oJ9V2Q3AXTi1JJJJe93S7Fo1efOyE5FMgiAIgqVkIXtwQRAEgU84mTQsZAMnjAPDWllyNQucPDBawMCRDvu5xNDz0t3BkZvjdOfrF+TKniN/JBHAsyCqiYJjJRu7Gh/PDdu6TeeyaDKEYAYpxXPjLs1FlgQENusPmfXreeQOK0WWIoQsE8l5Zg+lkSztNVwp3AP7jiRBnUvz49m0c6nzZ6pnHpjt7bqn1z771q1+FonUjYpSfI67owX1Jl7smkgmvvzqmQTywyTRgpxnPBTKBW3ggiAIgjLRwIUNLgiCIFhSFrYHtyNpWU/JQyuZF+VgMj/4HlGQBlX25MpBpu3YbYm3ZiFAc+JtWSmjef/IEskFX3LxZMVEFsnnrUu8tfYWpLZf8GS1c5NZqcxGqjlsdKr1iQtqvAZNFI80kvV6WmYRvSqTSCZOGpLoJ6eY62mDk+dROOyy53VckgS9Zyp/Dkep1m4rbcpk0T7Mga2nbymo827Jn2nvfUvmb8zz2N8PR/6clGzN78So+9xK7ERmimDLkyxsAxcEQRD4hEQZDVwQBMHSoTHQG1jQBk5Ej8spVto6lDnWra1YzydvX+lyL5HUuuXK3IsyyWcktUR6LAyqrcUbEO4Fkp2Qhiq8x7bzoK6j7n2XPC9r3quJ624lYJO2HpWHzbXNA8x+XdfYNTYQs277+Q4aK7la71GbzoIt22t4yLwjVtJfyQdtO2lLSQbzJPDJoOGO15/ZWy/zNEw8OSsGpE/I/pXvv4vdt5UUe/lLNk6qNXHQLbFCJl+aMvZdzL29nUOm+/WLnDSEk0kQBEGwlCxkDy4IgiAoExJlNHBBEARLSTRwC9zA7dw8G0XklLVUUL/HaeONQ2O0GabRXhPSwLLdbv79zEVdXJfq3RvaSpEVvOe1xv2/WTb7dmxopWECnut3bVDXUtSLfnJ9pw8ZyM9t29hFjlJpj7M3zkZCOYgAzZIbdj1b22GTtra59IKe4tg0+75ZuMoeVXKlT9z3R6WddQ8NSK6AZM+hM+GoN+RHsvKpfdEOR3AylbDHzAvZSCbOsIf898Net3SYkvnNmsFEvN/tm4g8GXg6cD5wL+Bm4I+BX1bVO6aU9ar3MFX9a5OvB/wc8BPAfYAbgMtV9R01dVzYBi4IgiDoRjkhPbgX0TRqLwOOAA8DXg5cKCLfozr13+HvAW/O1v19tvxL7XEuAz4GPA14m4hcoqrvmVbBaOCCIAiCWbhUVb9ilj8sIrcCbwEeBVw9pfw/quq13kYRuRdN4/YaVX1du/oaEXkg8BpgORs4VWGzDdJqXZAPraZd/2+9/1jO+eItY5fwYxvjPxa5JOe59peiOfSS+an8fJY0+khag3Ee/y+YF7EkddvO3JErZMkJ6c8ZdlCKVFETiDmfx8vKuYkcbNJ2SEju4n6qHUJgruG6lStzGVDM42+jnJgoIBPDB+xcc8lYjcKfVS/4s53DTbJI4UmUklVn/Th9KDu1JGJJ4mK/+7/1xagk7hCTOu0vke7scXIzQPJidQ8ZUOcZyvMVgyU7JMcpnJpdtHVQJ8IJZO+iHSaQmEv843RyAsbBZY3bDh9tv8+ewyEeA6wCV2brrwR+V0QeoKo3lnYQwwSCIAiWkJ3B3rN+ZuSC9vvTFXmfJyIbInKXiFwtIt+XbX8IsAF8Jlt/ffv94GkHiAYuCIJgCdE9foB7ish15vPc0vFE5GzgcuCDqnrdlOpdCfwU8C+B5wLfCFwtIo8yec4CvqaTUtatZnuRhZQoRwrHhk0n/ejGuLN++9FUJvqHfzx2PN13ZMReLoXYtOMRmasatbLkPKmZm63khenJkhNRSRIp0673ZU3PSbX0p9C7htaTrG88JXOJ0tbnNGfP6+QBiW3Ea+uiaT0qN9MyVkdL5EpLLlfa43jpXKL0ZEmz3lynTJ1P5oDL5ToPNwC3ue55FA4rS/qRUPI7b2R4p26alUmkRHvZTDZJoopkkVC6D4NauTOvzEzRT7qjnHjRSiB9rrft8270+X72kuWBsveJW1T1/JqMInIa8C5gCDx7Wn5VfYZZ/K8i8i7gU8ArgUfOUNdOogcXBEGwhJwoiVJEDgNXAecBj1HVI7uvq94B/Gfgn5nVtwH3kMnxVjs9t1uZQjRwQRAES8bOMIH9buBEZAV4O81YuMep6ifnUPUdrgfWgG/N8uzY3v522s4WXqLsb4zb6LU7UmmoJ2MPuFMPG3nL6DeDTBlKvPmSLXWuU7UPhjdQuuydaPJ5HpEl6dBKjHa9I0PmdRh5xy+UmcVYnfgcOh6VuUSzYoPZmvWnFe7b+sjefBOsOBm5n70iVpa00mHtgPDEo7JwHCtZJrLk+Bys52Q/846slSUtiZzs3MM8GLc9TP1YZCPDmYpuO88npFKirU8SjME+kxMSXvd7nXpEpmVq52lMyiRFuuXKfr7fZBD4eLWVMvNgy71uxTbdbbmqe6YdhP1W4CLgkpLLf8W+zgAuAf7SrH4vsAX8CPAKs/5HgU9N86CEBW3ggiAIgjInYKD3G4GnAK8CjorII8y2I6p6RETOAT5LE33kcgAReRHw7cA1wBeAc2jGu92HpjFr669fFpHXAy8VkTuAjwNPpWlQH19TwWjggiAIgll4bPt9WfuxvIImqokAfdKO5g3Ak9rPNwBfB/4C+Deq+pfpbrgMuBN4IeNQXT+kqn9aU8Fo4IIgCJaNvY1lqzuE6rkVeW4isw2o6lU0Tik1x9im8ax85e5ruKAN3AhYb6Ov9oxJ5I6NVNsemGEDNuLJYROU2U6KCqlNzp+8NNPqa4LUlh42x85Vihph3fxd9+588lKTcduxoZWP2b1+wl5SM4Sh0r7hDh/IzRjJtvGBBqbQ4YJdZj25vyb6SR7JxNrdvKgmRexxnCEDkEZZSWfyPI61IObXw0PNhcpd8RNbm7VzWVf8zJU+CbCcGHbr6mOvWzGqiGNossdU/xVNI/+Y49hznji8Y76ttswlQzXs0Ii0cjaQ9MDcSPuOT9jgugK85+9EbT2XmIVs4IIgCAKfHS/Kk525DhMQke8VkfeLyJdF5A4R+biIPCfLc0hEXisiXxSRYyLyERH53+dZjyAIgpOdAwrVdbdibj04EfknwAeBa4EfB+4Cngz8joisqeqb2qy/A/wr4MXAPwDPB94nIt9t5wEqHouxDGWlss3ttI9+bMsMDTARKMRxOQZYtUEjjMxiJYJcovCUldJD4m3y3PLzQp50WBthxHPzz4/pD0fozpNv84YjlKKs1DAZTNfIksnGwvAO665utm2YIkPNxpHYZSsjWk2uOvCyXd/vXg9JtdOhAeP0LP9UJ58P49buDAnJr+AQ51rbChUuR1IFq4WW5pNLIpk4ZQpu9X5w8rSMF2A5jXDkVzPZub1veZyXpD7dsmQ+h5yd42/QPvsnKIjSQjFPifJpNGaBS1X1znbdB9qG75nAm0TkO4EfBp6jqv8PgIh8mGZA3+VUun4GQRAEZZakE7Yn5ilRrtIMyjuWrb/dHOfxbZ4/2tmoqkPgD4HHiEjlVMxBEARBiZAo59uD+z3gecCvi8iraCTKpwDfD+wE1nwIcKOq3pWVvZ6mgXwg46kQXERgrW0yV5x5ryC9SVvGGW7LBqOY6Ncbqct6NJnjTJTxtIGSROlsK0kmieekk682KklNhJKJ/VV4VObLibem9eDLJUq7b7rpmfs7yrz57D81K90lHmq5a52do8ts65tCm1mRdVu5RMOy0mVBbvQo6EuJLGnW58+7pec8fLXz+CX3MPGizHdo8vmVcctYkkuQebxa701XMjVlcm/PZC5Em8/xqITU27E2qokXlD0xHeTBlu0xbSBqs2E4EWx5Mp2Lxfl7eTIytwZOVT/VTnXwTpppEKDprf2kqv5hu3wWTQDNnOrpD4IgCIKghnk6mXwb8A6aHthP0kiVTwB+S0TWVfWte9z/c2nmDaK3evoeaxsEQbDELJHMuBfmKVH+Mk2P7RJV3ZlQ689F5BuB/yAif0DTezuno+zU6Q9U9QrgCoC10+6thwfN3Vs1csOhlfSOrpouvvU6Knk+eYGLrdblzWFVouhRaQd3F8p43l+5rOitT8t0e1sWPSI9uTKrZxI01ymfX47dvowlT1axnmjOPGJAVnGbz5TP6mU94KwkNyzU39s2KDxHdpuVsFYTSX68fpbgyvljk3q8GqnNBggonGciC5prW3rf6geHW+9CI1c65SV/wqwcnTzvpp7ZRUw8J+36ykHf3nySEy9MUrduKXOQPbsD5zmwRPs2XyeThwKfMI3bDn9JM1vrvWh6dw8QkVOyPA8GNpmcmjwIgiDYNYLq3j7LwDwbuC8B3yUiq9n6fwGs0/TOrgJWaJxPABCRAU2E6Per6sYc6xMEQXDSEl6U85UofwN4G3CViPwmjQ3u8cDTgV9T1U3gr0Tkj4A3tBPl3UjjefkAzDQJ0xAZSzWnrI7vxOFMojxkBm2vmDNdsVPBZw5v3oDumniTOd6cb+BLkbUynu8R6R/TnQ+u0iPS9bIrziHX7aU24SHqlPdks1qSAb7ZtsTD0hkQnv8D7Bt9y8p124W6lWS94/uVfLm7kM032KNEmWPvaSLJFSRsd0C3qdAwuwDJHIxJGWd9RvIuOuXzyyfOs1t6PpLncBaPSmd9L7tZnjNs6boPzHO440k+y2/UsjNPL8q3i8jjgJ8DfptmBsnP0kQqebPJ+mya+YNeCdwD+ARwsap+fF51CYIgOJlRwgYHcw62rKp/BvzZlDzHgJ9tP0EQBME+EOPgYjaBIAiCpWRZ7Gh7YSEbuJ4oa+0wAWtnOzUL9HVodSxKJ/O82SgAmfHDtbvV6tuuPcx3QR45YkJpmIC3PhlykJc36ZogyhP1dOxuk3PIddvdaqNolGx1NSSmHGs7ye6Bdb1O7E+FazgyD4I7pCSjZmq0Wm+vnmN3yyOX1M1RmD2TyZxp4/XbSRDjgvHUtYGlx7E2uSp7XLY/cYxonp2t2db9HCQRTvJr2Ot+jkt2cu+6O1P6Te7DHtP+ZuU2OHN9VvoV+z1Jmet0OUEQBEFwd2Ehe3BBEASBj2rY4GCBG7gdmdFGLzm8lnbSTzHLA+NT3a+MauJRG6S2V5CwrDSSBpItPJVWUqvQvWojoZQkwbqhCQX51SmTu86XZJ8arFxn951IFJm8ZiU6ewZ2XyWpy6rbtVLqqFLr9oIlJ3UpTZk2wxCCJI6040qf32tvbsVRQW60V3t71H2zSm7+qeZb576fWhtMmX63DAm5bN15yHrTReFmJcF2zEHt79QgG840SKI07QwTyJ/vyrotMQvbwAVBEAQ+Wt36Li9hgwuCIAiWkoXswQljL6I1cwanHsokSjOR1ooN+1CrS9rAp6UoHE7gYuvRuL2dHtM6pkkSmNbR2rLjinM6VqbJJYtZtL80kohdX5hHy6YTb9G649REQikhjnQ4EWvZzgGXlJHO9U19uo9Ze2lL3pa7pVZ6nOV/vHff8n0VPSy7dgCZFOkEaC5VzpEyPU/JbNeZR6ZJZw9I6pFsnkPrbZrVVL2X1FAKFK7OTR1NSJTjfF1elErY4GBBG7ggCIKgTNjgooELgiBYSqIHt6gNnIy79VZ6tJIkwD1OH48Ct9KflYlyr8VEhkukR1smrc6oW2VJBkNPSjuOK5ZZn8sViTRi920lyj0+1LN4UeaH9OStvQ7griXx+ivks6pPUp/CRfTm3qoZzJ1z0FOSTEjYFUyUqHgm7Lx5kA3IdgI051KuV8aLxZCrg94g8JKs6ZYpvNdqfoI8Z8uJurnWE+MFnh3HBonf8ajM9xvtWziZBEEQBEvKYvbggiAIApcY6N0QPbggCIIlZL9n9BaRJ4vIO0TkcyJyTERuEJFXi8jpu6mniPy8iKiI/LeObTe12/LPE2v2vZg9OB3r/VZ3PuVQ6kt7//uMl2+/c5xxfWP812Yrm63T2uQS24ENLpzZLmxQVnFcnU/UnynP3X4inxfVJMtXOzTA23fNMfNts0xs6l3r6olA92gO60/P0kH38JJiiUpP/HlSGurhRzkZF8r/RXsTwNrXKp9E1w1i7Lr/Z++oc4O9CCfNMbvHm1hbXR5xxn1HKoYP5PXsO/Y8SIMtH49kkuXZz2ei5UXAzcDLgCPAw4CXAxeKyPeo6tQqiMh5wC8AXy5ke1+7X8sNNRVczAYuCIIgcDlB4+AuVdWvmOUPi8itwFuARwFXV+zjTcBbgW/Hb49uUdVrZ6lgSJRBEATBrskatx0+2n6fPa28iPww8HDgpfOsl2Uhe3AKDNvO79bQyI3DGTrlhagkNipBaWiBlVOs+7866/MyiSzqrG+Wa9I2ykKKF43Flq8eJuDkAX9owInCE4BmCazd2+u4i0pKsmw6hMGst6tnkIznTSpl+hF1vOcofdzT61ETlNkPyJwfqe5B8OZws/PGjbKHKlU1nUgo2f3oib1W3fvKJXA7j+WgrxP54cCcTC5ovz9dyiQiZwK/BrxEVW+V8st5qYjcRXMZ/gp4jar+SU1lFrKBC4IgCHzmJFHeU0SuM8tXqOoVXmYRORu4HPigql7n5Wt5LfD3wO9NyXcVTa/wRuDewE8D7xSRZ6jqlVPKRgMXBEGwjNROzVTgFlU9vyajiJwGvAsYAs+ekvf7gGcCD1ct6wuq+oKs7DuBa4FXA8vZwKkKW23w4ruMR+StX09jJnzm5q3jaTsfXCrP5dJhtxQ5NK5fuYdXjcQ4Ef0k8Rjrzpf/A/O2bZu62fV5+W1P1ix4r3nBjmeaQ87JU8ssEqOlJDe6Xnr7WJ8kEHQu41WUGTnz2U2UL8xv5+07KT7H84RMlnSi8EzK67sMypx5F9QEZZ58X0w+KyMW3rGeG6C5juRam4V+dj52Od92ohGRwzQ9rfOAC1T1yJQibwZ+BzgiIvdo1w2Afrt8TFU3ugqq6raIvA34FRG5r6p+sXSghWzggiAIggJ6YmxwIrICvB04H3i0qn6yotiD2s9Pdmy7DfgZ4A0V+5l6htHABUEQLBknYpiAiPRoXPwvAi7ZhSv/hR3r3kDjRPIC4DOFYw6ApwI3q+qXph1oYRu4HSXg2Na4G3/70VGWZyxRHl4z3X3jgTQRoNTxfCx6N84gF3qei0mZwnE8idHb10Q9k/K+h5e3721nfb5cK0vOMrjbw5MiS1KbFwy3VGbPylBlUGjvelrvxMn71n1Pk3nvsuPsdWCwOgu5LcjWOw22XNh5TVDmQhDkgo+qmyuZmtGTK/N31G5L9jXOlwcfSPfgyM7Zg9jrTcqX+bOaB7neB94IPAV4FXBURB5hth1R1SMicg7wWeByVb0cQFU/lO9IRL4GDOw2EXk68ATgPcDnaZxMnk8ztODpNRVc2AYuCIIg6EbxI8bMkce235e1H8sraKKPCE3PbJb/gzcC96LxuDwLOApcB1ysqu+r2UE0cEEQBMGuUdVzK/LcRMXAQ1V9VMe6a2nkz5mJBi4IgmDJUGC4/z24uz0L2cCJKP02wKiV4Nc303w9MzPhcNuO/DfBUgsd55Fjjyu67ye2rbphAp7drOReXVNm0gY33eU/LzPL5KU1drd52tygzu5W6/Jv0/nj4Q4n2OPpFCORmLR1qy8Fr/bsc8l1zwqV7HM11F4CL+5wMRi3k2/bseFNXE/HwFiciNQtY4cpZBFXkueobjiCPU7PeQ7zutUME9je+zi4hWchG7ggCILAJ3pwDdHABUEQLBt6MHFg724sZAMnwGobfXRgopBOuMmarv/W0K63Lr/+cbyAxKPsyamJEFLrfl+S9/wy06XH0r5L833VRCXJmWVut5qXsVYGnCWfJ0tOyFYVkucscmXxelZE+xhlx9zr0IITNYGhO7SgNLlZIslVhmmxZdzxEBNCb2cu634/+XyYoUVmYzJvXqaf9hL5tfuY+XF6yb6lM0+woA1cEARBMI3owkUDFwRBsIxE+7aYDZwIrLQ1P7Qyvosr2aRJKybAcslb0lIjyeUekW4kEkfizPfneYVpKf7CDBJnSYqsKbPXqCQHPTdcSW70ZMmJMoX9TVtfYiKiTnKxu/N50iUUolj4gTvo13hezhl3rrtcPrVVOCFyJVDwljy+PrvwybxmXvSSiagkpjrmxHslL0j77Lq/bdHCxYzeQRAEwVKykD24IAiCYAq61+iii89CNnAisNJO075qzmBtJe3SWw/Lfh7htCWfb88uWblQkkCu2eBOxytzuxD8deTIhXbQ5vYor9v+SEXzHrR9IqTIfGC3591YkhtrZMmJoL0VgZhlHtKQDdrrSXcludHJ5g0Uz5fT8/Q9L/eLogS+W7kSXMmyXn0dlx+YfQ8L+axcOaT7NwJg2+jJiUelrbPz++UT4wRgQRu4IAiCYBrRg4sGLgiCYBkJiTKcTIIgCILlZGF7cDuKtA2cvJqdzaqxyVkbXGrTSLXt1M1/vGDd/IfZREvbxiiQBmg26ayMP/noOJ3L7rY+yXAC6T5+boaYpyRfmiR1npyo6Aw1Nrxi+YLdbaZz8C5qjW2OzHZaEQkFfPucrf5EEOTuWu75mZgo7tl/q+xx6XtudzXoVYydKdRuUAq2bN55a7cfZmM47Htu3+u+uYhehBNwni/V6MGxwA1cEARBUCIauGjggiAIlo7owcGCNnCqMOy4d1auBFhbGesUAxvVpCAZpdKhlSiNPLid7mCYbOsuP8zKeHPNbTsSZ75sz2Ho6Jp59JQkcoc9T/YPT6maRbWzQwNqI4zMMrdbiVTK7D67eciq7j4qpMuJTba4TefX0IvcUziMN8QkkU/dmtXjBWW2uHJlVh+7bYj9Xdh9TfNIJvZqe89Kfg2tZCnJMCFjYqnVhoOEhWzggiAIginEOLho4IIgCJaTkCgXtoHbkfysdCiZ9mhlSStXlgIve/O+jRK5Mf1nNDDy49Bof1ZGzaeVt/uQ7W75NJfA7NnZCApJjGlTT820kESqqvxz5wXdLZXf6//GRFZ0ZMnaCCOzzO12d55Xy/OcnJBLa06iUMT1vCwFQa48TuWmujJe0PFCZJfkZz/xvPRND7PUzr7XyfOV2QSszNm33tH2XZ6IajQtukzY4GCBG7ggCIKgQDRwMdA7CIIgWE4Wsgc3UthoNbrUszCVGOxA79XVcVueOFRl/ftEtnL+AE1etELU2+NZMokhkfscb7yCJ1gieXQfsViFkbN+YvBvhSw5D1P23VUWvLvWC6bUbZcDxSeKOI/0hMxb4XlZZI/PVMWbB2RKpDe2O6+09Uh2Xp6JwMnJtu7Ay7nnZc/ovNajsm8q2s/cKLerXJ+jB7eQDVwQBEFQQGM2AYgGLgiCYDkJG1ydDU5E7ici/7eIfERE7hIRFZFzO/IdEpHXisgXReRYm/9/78jXE5GXishNIrIuIp8QkR+cw/kEQRAE0DRwe/ksAbU9uAcCPwR8DPivwA84+X4H+FfAi4F/AJ4PvE9EvltV/9rk+yXgRcBl7T6fBrxNRC5R1fdMq4yqsD5sdOst426/kp3NmWesHU9bDX1za3zzdJgFQU6iitgIJd3rm2U6tyWRUHL3au3e5gVezpe9dBL4OStvRzfY4RA223bm912yz+2WWnNWzdCAkst/zUSmtfXJVZ40Qod1A5/mtj3Jftr3qocTVFSoOLzEOQdvwlWotAzNWV1LTGimzqV6qvNeSr97PRQmPC49h+bFTCIUmQe5nw1NGia/RxwIIvJk4OnA+cC9gJuBPwZ+WVXv2MV+fh54NfAXqvrIbFsP+DngJ4D7ADcAl6vqO2r2XetF+V9U9d6q+jjgbU4lvxP4YeBnVPU/quqf0zSKNwOXm3z3omncXqOqr1PVa1T1J4BrgNdU1icIgiBw0Tl8pvIimkh/LwMuBt4EPA/4QNswTUVEzgN+Afiyk+WXgJcDvwE8FriWpjP0uJr9V/XgVKv6q48HtoA/MuWGIvKHwM+LyJqqbgCPAVaBK7PyVwK/KyIPUNUba+oVBEEQOOy/zHipqn7FLH9YRG4F3gI8Cri6Yh9vAt4KfDtZe5R3htrV14jIA2k6Q1PVvnk6mTwEuFFV78rWX0/ToD2wTT8E2AA+05EP4MFAsYHbVrhzs+nLH9s0UUCySASv+Olrjqd/+c0XHk8fWx/f+PXN9CEYmvAjXuDkXBJIo5zUlfGDMtv1aRkbGSXN1y1L5gGp06gkNu0PBZinLFmS5HYrS+b7qpUl9wstCJ6eLHiipMzSvHFJPlvPyoO6gZyd40N5TrodqiKk7IJ5DvgtDquxsqRZv20jnMzwrOTC7qYxreyYT9J7u/+RTLLGbYePtt9nTysvIj8MPJxG5vzjjix77gzN876fBdzWsf5Ws33n+2s6Ofgrz5cgIs8VketE5LrR1rE9VzYIgiCYOxe0358uZRKRM4FfA16iqrc62Wo6Q0UWZpiAql4BXAGwetq9Y4BHEASBh3LCx8GJyNk0/hYfVNXrpmR/LfD3wO8V8szUGbLMs4G7DTinY/1OJW41+e4hIpJVPM/nsnX0y7ccufbXjwK3HDHrr83y/e4Vdul/TNvtInJP4JaDrsQBcrKfP8Q1gLgGO+c//v3dvP19/MO777nH/R4SEdtQXdF2NCYQkdOAd9HEgX92aaci8n3AM4GHdzRec2WeDdz1wJNE5JTMDvdgYJNxN/N6YA34VtKu505382+nHUhVv0lErlPV8/de7cXlZL8GJ/v5Q1wDiGvQdf6qevEJPP5h4CrgPOACVT0ypcibaYaUHRGRe7TrBkC/XT7WOiTuuTM0TxvcVcAK8JSdFSIyAJ4KvL+tMMB7abwtfyQr/6PAp8KDMgiCYDEQkRXg7TRj4R6nqp+sKPYg4CdpGrCdz/cCj2jTz2vz2c6QpbozVN2Dawf1AfzT9vuxIvIV4Cuq+mFV/SsR+SPgDe1J39hW9AGYxkxVvywirwdeKiJ3AB+naQQvohlqEARBENzNace6vZXmt/sSVc2tRB4Xdqx7A824+xcwVvZsZ+gVJm91Z2g3EmU+wPs32+8P04x5gEZ7fRXwSuAewCeAi1X141nZy4A7gRcyHp3+Q6r6p7uoT6cWfJJxsl+Dk/38Ia4BxDU4qPN/I41i9yrgqIg8wmw7oqpHROQc4LM00UcuB1DVD+U7EpGvAQO7bR6dIdlnG18QBEGwhIjITXQ7FgK8QlVf3sYsvnFnubCvD9E0cHmorj7wUuDHSUN1vb2qjtHABUEQBMvIQs3oLSL3F5G3i8jtIvJ1EfljEfmWg67XfiAiTxaRd4jI59qZGW4QkVeLyOlZvjNF5LdF5BYROSoiHxSRhx5UvfcTEXlvO5PFK7P1S30NRORxIvJfROTO9rm/TkQuMtuX/fy/V0TeLyJfFpE7ROTjIvKcLE/VTCZ3dyRmbpkrC9PAicgpNLHNvgN4FvAM4NtoYpOdepB12yemBjIVEaHxXr2Yxjj7gzSerNeIyP0OotL7hYg8HfjOjvVLfQ1E5Cdoxhd9DHgSjc3jbcAp7fZlP/9/AnyQ5px+HPg/aMJB/Y6IPM9k/Z12+y8ClwBfpJnJ5LtOaIX3zs7MLbfRzNziUXu+ewpWvPCo6kJ8aBxStoEHmnUPoBlY+LMHXb99ON9v6lj3TJoYBRe1y09oly80eb6BZnzIrx/0OczxWpwJfIkmZp0CrzTblvYaAOcCx4B/V8iztOffnssv04yjPS1b/xHgI236O9tr8GyzfUBjr3n3QZ/DLs+3Z9I/1p7XuVmeqvOlmcJmg8b+Zcv/OfA3B32uJ+KzMD04Gq+Za1X1+OBwbdxE/4LmJV8qtC6Q6eOBL6jq8ajSqno7zT/6Zbomv0LjFvwHHduW+Ro8hybK7m8V8izz+UMTbHeLpqG33M5YgeqcyQT4Q+AxIrLGgqB7mLmFyfMtBSt+qIg8YO81vnuzSA3cQ4BPday/noqgm0tCHsi0dE2+RZrwOQuNiDySpuf6fCfLMl+DRwJ/BzxNRD4rIkMR+YyI2GuxzOcP41iFvy4i3ywi9xCRHwe+nyZYL9TNZLJM1J7vnoMVLzqL1MCVZis48wTX5YQj3YFMp83gsNDXRURWacL6vE5Vb3CyLfM1+GYaO/Nraea/+gHgA8BviMgL2zzLfP6o6qdoxtk+AfhHmnN9I/CTqvqHbbbamUyWhX2duWWZWJjZBE5mZBeBTJeMlwCHaQaSnoz0gNOBf62qO/NlXd161b1URH79wGp2ghCRbwPeQdPr+EkaqfIJwG+JyLqqvvUg6xfcvVmkBu42uv+Nev9mlgIpBzItXZOd7QtJO/zjMhpD+1pmR1mTJijrHSzxNQC+StOD+0C2/v00XpP3ZbnPHxonky2aUFBb7bo/F5FvBP6DiPwB9TOZLAsnbOaWRWeRJMqd2cBzHkxF0M1FRKYHMi1dk5tV9c59ruJ+ch5wiMYgboOyQjOE4jbgoSz3Nbh+yvYRy33+0NzjT5jGbYe/BL6RxlPweuAB7VAiSz6TybJQe757Dla86CxSA/du4BEict7Oilaq+d5221IhaSDTJ2p3INN3A2eLyAWm3BnApSz+NflrmqCs+QeaRu9Cmhd5ma/BO9vvx2TrL6aJ9fcllvv8oRke8l2tPdbyL4B1ml5I7Uwmy0LM3FLLQY9TqP0Ap9L8oH2SRoN/PE0w538gGyOzDB+agd1KE7j6Ednnfm2eHvDfgc8DT6P5IfwQzUt//4M+h326Lvk4uKW9BoDQBDf4Ko396QeA/9heg3+97Offnt+T2/N9X/ve/wDNoGUFXm/y/SFNr/7HaDws307TAD78oM9hxnN+svkNeF67fMFuz5fGOWkd+FkaZ5030fT8Lzno8zwh1/KgK7DLG/8tNAbnr9PYX/6EbBDksnyAm9qHu+vzcpPvLOB32x+0u2gGcX7nQdd/H69L0sAt+zUAzqDxGvxfNPLT3wA/fLKcf3t+j20b7a+07/1fAz8F9E2ew8DraXp868D/AB510HWf8Xy99/5Duz1fmilofgH4HM2Qgb8BnnzQ53iiPhFsOQiCIFhKFskGFwRBEATVRAMXBEEQLCXRwAVBEARLSTRwQRAEwVISDVwQBEGwlEQDFwRBECwl0cAFQRAES0k0cEEQBMFSEg1cEARBsJT8/1KnOI8mUmWLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vp = 1.0/np.sqrt(result['x'].reshape(true_model.shape))\n",
    "plot_image(vp,vmin=2.4, vmax=2.8, cmap=\"cividis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] _Feng, B., and H. Wang, 2012, Reverse time migration with source wavefield reconstruction strategy: Journal of Geophysics and Engineering, 9, 69–74_\n",
    "\n",
    "[2] _Dussaud E, Symes W W, Williamson P, Lemaistre L, Singer P, Denel B and Cherrett A 2008. Computational strategies for reverse-time migration 78th Ann. Int. Mtg. Soc. Expl. Geophys. pp 2267–71 (expanded abstract)_"
   ]
  }
 ],
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