examples: Minor edits

Author: George Bisbas

examples/seismic/tutorials/03_fwi.ipynb

@@ -173,7 +173,7 @@
     "from examples.seismic import AcquisitionGeometry\n",
     "\n",
     "t0 = 0.\n",
-    "tn = 1000. \n",
+    "tn = 1000.\n",
     "f0 = 0.010\n",
     "# First, position source centrally in all dimensions, then set depth\n",
     "src_coordinates = np.empty((1, 2))\n",
@@ -419,11 +419,10 @@
    "outputs": [],
    "source": [
     "# Create FWI gradient kernel \n",
-    "from devito import Function, TimeFunction, norm\n",
+    "from devito import Function, norm\n",
     "from examples.seismic import Receiver\n",
     "\n",
-    "import scipy\n",
-    "def fwi_gradient(vp_in):    \n",
+    "def fwi_gradient(vp_in):\n",
     "    # Create symbols to hold the gradient\n",
     "    grad = Function(name=\"grad\", grid=model.grid)\n",
     "    # Create placeholders for the data residual and data\n",
@@ -440,19 +439,19 @@
     "    for i in range(nshots):\n",
     "        # Update source location\n",
     "        geometry.src_positions[0, :] = source_locations[i, :]\n",
-    "        \n",
+    "\n",
     "        # Generate synthetic data from true model\n",
     "        _, _, _ = solver.forward(vp=model.vp, rec=d_obs)\n",
-    "        \n",
+    "\n",
     "        # Compute smooth data and full forward wavefield u0\n",
     "        _, u0, _ = solver.forward(vp=vp_in, save=True, rec=d_syn)\n",
-    "        \n",
+    "\n",
     "        # Compute gradient from data residual and update objective function \n",
     "        compute_residual(residual, d_obs, d_syn)\n",
-    "        \n",
+    "\n",
     "        objective += .5*norm(residual)**2\n",
     "        solver.gradient(rec=residual, u=u0, vp=vp_in, grad=grad)\n",
-    "    \n",
+    "\n",
     "    return objective, grad"
    ]
   },
@@ -571,11 +570,11 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Objective value is 39292.605833 at iteration 1\n",
-      "Objective value is 24506.628229 at iteration 2\n",
-      "Objective value is 14386.573665 at iteration 3\n",
-      "Objective value is 7907.616850 at iteration 4\n",
-      "Objective value is 3960.106497 at iteration 5\n"
+      "Objective value is 39293.304688 at iteration 1\n",
+      "Objective value is 24506.697266 at iteration 2\n",
+      "Objective value is 14386.468750 at iteration 3\n",
+      "Objective value is 7907.354492 at iteration 4\n",
+      "Objective value is 3959.922607 at iteration 5\n"
      ]
     }
    ],
@@ -590,19 +589,19 @@
     "    # Compute the functional value and gradient for the current\n",
     "    # model estimate\n",
     "    phi, direction = fwi_gradient(model0.vp)\n",
-    "    \n",
+    "\n",
     "    # Store the history of the functional values\n",
     "    history[i] = phi\n",
-    "    \n",
+    "\n",
     "    # Artificial Step length for gradient descent\n",
     "    # In practice this would be replaced by a Linesearch (Wolfe, ...)\n",
     "    # that would guarantee functional decrease Phi(m-alpha g) <= epsilon Phi(m)\n",
     "    # where epsilon is a minimum decrease constant\n",
     "    alpha = .05 / mmax(direction)\n",
-    "    \n",
+    "\n",
     "    # Update the model estimate and enforce minimum/maximum values\n",
     "    update_with_box(model0.vp , alpha , direction)\n",
-    "    \n",
+    "\n",
     "    # Log the progress made\n",
     "    print('Objective value is %f at iteration %d' % (phi, i+1))"
    ]

examples/seismic/tutorials/05_staggered_acoustic.ipynb

@@ -15,12 +15,14 @@
    },
    "outputs": [],
    "source": [
-    "from devito import *\n",
+    "from devito import (SpaceDimension, Grid, TimeFunction, Constant, solve,\n",
+    "                    Operator, Eq, VectorTimeFunction, norm)\n",
+    "from devito.types import NODE\n",
     "from examples.seismic.source import DGaussSource, TimeAxis\n",
     "from examples.seismic import plot_image\n",
     "import numpy as np\n",
     "\n",
-    "from sympy import init_printing, latex\n",
+    "from sympy import init_printing\n",
     "init_printing(use_latex='mathjax')"
    ]
   },
@@ -32,7 +34,7 @@
    },
    "outputs": [],
    "source": [
-    "# Initial grid: 1km x 1km, with spacing 100m\n",
+    "# Set up initial grid: 1km x 1km, with spacing 100m\n",
     "extent = (2000., 2000.)\n",
     "shape = (81, 81)\n",
     "x = SpaceDimension(name='x', spacing=Constant(name='h_x', value=extent[0]/(shape[0]-1)))\n",