lectures/waveEquation2D.ipynb

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    "# Wave equation 2D\n",
    "The acoustic equations of motion in two\n",
    "dimension are\n",
    "\\begin{eqnarray}\n",
    "  \\rho(x,z)\\ddot{u}_x(x,z,t)  & = & \\partial_x \\sigma(x,z,t),\\\\\n",
    "  \\rho(x,z)\\ddot{u}_z(x,z,t)   & = & \\partial_z\\sigma(x,z,t).\n",
    "                                        \\label{eq:ch4-motion}\n",
    "\\end{eqnarray}\n",
    "and the constitutive equation is\n",
    "\\begin{eqnarray}\n",
    "  \\sigma(x,z,t) & = & \\kappa(x,z)\\left[\\partial_x u_x(x,z,t)+ \\partial_z u_z(x,z,t)\\right] +s(x,z,t)\\nonumber\\\\\n",
    "                                              \\label{eq:ch4-stress}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Here:\n",
    "\n",
    "  - $\\ddot{u} = \\partial^2_t u$\n",
    "  - $x,z$ : Horisontal and vertical coordinates\n",
    "  - $t$ : time\n",
    "  - $u_x(x,z,t)$ : Horizontal component of displacement\n",
    "  - $u_z(x,z,t)$ : Vertical component of displacement\n",
    "  - $\\sigma(x,z,t)$ : Stress\n",
    "  - $\\kappa(x,z)$ : Bulk modulus\n",
    "  - $\\rho(x,z)$ : Density\n",
    "  - $s(x,z,t)$ : Source function\n",
    "\n",
    "##  Numerical Grid in 2D\n",
    "  - $\\Delta z$,$\\Delta x$: Grid interval in horizontal and vertical direction\n",
    "  - $\\Delta t$: Time sampling interval\n",
    "  - $N_x$, $N_z$: No of gridpoints in horizontal and vertical direction\n",
    "  - $N_t$: No of time samples\n",
    "\\begin{eqnarray}\n",
    "    x & = & k\\Delta x,  k  = 0, ..., N_x-1,   \\nonumber\\\\\n",
    "    z & = & l\\Delta z,  l  =  0, ..., N_z-1,   \\nonumber \\\\\n",
    "    t & = & m\\Delta z,  m  =  0, ..., N_t-1.   \\nonumber \\\\\n",
    "                                  \\label{eq:ch4-21b}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "\n",
    "\\begin{eqnarray}\n",
    "    \\ddot{\\sigma}(x,z,t) = \\kappa(z) [\\partial_x \\ddot{u_x}(x,z,t) + \\partial_z \\ddot{u_z}(x,z,t)] +\\ddot{s}(x,z,t).\n",
    "                                                \\label{eq:ch4-500}\n",
    "\\end{eqnarray}\n",
    "\n",
    "The second order time derivative on the left hand side of the constitutive equation for stress is\n",
    "approximated with\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\ddot{\\sigma}(x,z,t)& \\approx &\n",
    "      \\frac{\\sigma(x,z,t+\\Delta t) -2\\sigma(x,z,t) +\\sigma(x,z,t-\\Delta t)}{(\\Delta t)^2}. \\nonumber\\\\\n",
    "                                                         \\label{eq:ch4-501}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "If we insert the above equation  on the left hand side of the previous equation above and solve\n",
    "for $\\sigma(x,z,t+\\Delta t)$, we get\n",
    "\n",
    "\n",
    "\\begin{eqnarray}\n",
    "    \\sigma(x,z,t+\\Delta t)           & = &2\\sigma(x,z,t) - \\sigma(x,z,t-\\Delta t) \\nonumber\\\\\n",
    "                       & + &\\Delta t^2\\kappa(x,z)[\\partial_{x} \\ddot{u}_x(x,z,t) + \\partial_{z} \\ddot{u}_z(x,z,t)] \\nonumber\\\\\n",
    "                         & + &\\Delta t^2 \\ddot{s}(x,z,t)\\nonumber\\\\.\n",
    "                                                       \\label{eq:ch4-502}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "The centered first order derivatives are:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "d^+_x \\sigma(x+\\Delta x/2,z,t) = \\frac{\\sigma(x+\\Delta x,z,t)-\\sigma(x,z,t)}{\\Delta x}\\nonumber\\\\\n",
    "d^+_z \\sigma(x,z+\\Delta z/2,t) = \\frac{\\sigma(x,z+\\Delta x,t)-\\sigma(x,z,t)}{\\Delta z}\\nonumber\\\\\n",
    "\\end{eqnarray}\n",
    "\\begin{eqnarray}\n",
    "d^-_x \\sigma(x-\\Delta x/2,z,t) = \\frac{\\sigma(x,z,t)-\\sigma(x-\\Delta x,z,t)}{\\Delta x}\\nonumber\\\\\n",
    "d^-_z \\sigma(x,z-\\Delta z/2,t) = \\frac{\\sigma(x,z,t)-\\sigma(x,z-\\Delta z,t)}{\\Delta z}\\nonumber\\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "Using centered derivatives in the above equation for $\\ddot{u}_x$ and $\\ddot{u}_z$ we get\n",
    "\n",
    "\\begin{eqnarray}\n",
    " \\ddot{u}_x(x+\\Delta x/2,z,t) & = & \\rho^{-1}(x+\\Delta x/2,z) d^+_x \\sigma(x,z,t) \\nonumber\\\\\n",
    "                           & = & \\rho^{-1}(x+\\Delta x/2,z)\\left[\\frac{ \\sigma(x+\\Delta x,z) - \\sigma(x,z)}{\\Delta x}\\right]\n",
    "                                      \\label{eq:ch4-504}                           \\nonumber\\\\\n",
    " \\ddot{u}_z(x,z+\\Delta z/2,t) & = & \\rho^{-1}(x,z+\\Delta z/2)d^+_z \\sigma(x,z,t) \\nonumber\\\\\n",
    "                             & = & \\rho^{-1}(x,z+\\Delta z/2)\\left[\\frac{ \\sigma(x,z+\\Delta z) - \\sigma(x,z)}{\\Delta z}\\right] \\nonumber\n",
    "                                      \\label{eq:ch4-505}\n",
    "\\end{eqnarray}\n",
    "\n",
    "$\\ddot{u}_x$ and $\\ddot{u}_z$ are now evaluated at $(x+\\Delta x/2,z)$ and $(x,z+\\Delta z/2)$ and not at $(x,z)$,\n",
    "so that the  equation for the stress becomes:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "    \\sigma(x,z,t+\\Delta t) = 2\\sigma(x,z,t) - \\sigma(x,z,t-\\Delta t) \\nonumber\\\\\n",
    "                        + \\Delta t^2{\\kappa(x,z)}[\\partial_{x} \\ddot{u}_x(x+\\Delta x/2,z,t)+ \\partial_{z} \\ddot{u}(x,z+\\Delta z/2,t)]\\nonumber\\\\\n",
    "                         + \\Delta t^2 \\ddot{s}(z,t).\\nonumber\\\\\n",
    "                                                       \\label{eq:ch4-506}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Using numerical approximations $d^-_x$ and $d^-_z$:\n",
    "\\begin{eqnarray}\n",
    "    \\sigma(x,z,t+\\Delta t)            = 2\\sigma(x,z,t) - \\sigma(x,z,t-\\Delta t) \\nonumber\\\\\n",
    "                        + (\\Delta t)^2{\\kappa(x,z)}[d^-_{x} \\ddot{u}_x(x+\\Delta x/2,z,t)+\n",
    "                                                                  d^-_z \\ddot{u}_z(x,z+\\Delta z/2,t)]\\nonumber\\\\\n",
    "                         + \\Delta t^2 \\ddot{s}(x,z,t)\\nonumber\\\\.\n",
    "                                                       \\label{eq:ch4-507}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "  - Source is fixed at one position $\\mathbf{x}=(x_s,z_s)$\n",
    "  - Source time dependence is the Ricker pulse.\n",
    "  - The boundary conditions for the stress : $\\sigma(x,z,t)=0$\n",
    "       for $t\\le0$.\n",
    "   - $\\sigma(x,z=0,t)=0$ and $\\sigma[x=(N_x-1)\\Delta x,z=(N_z-1)\\Delta z,t]=0$.\n",
    "\n",
    "\n",
    "## Algorithm\n",
    "\n",
    " 1. Set $t=0$, $\\sigma(x,z,t=0)=0$ and $\\sigma(x,z,t=-\\Delta t)=0$\n",
    "    for all $z=l\\Delta z$, $l=0,\\ldots,N_z-1$\n",
    "    and $x=m\\Delta x$ $m=0,\\ldots,N_x-1$.\n",
    "    \n",
    "\n",
    " 2. Compute the accelerations $\\ddot{u}_x(z,t)$ and $\\ddot{u}_z(z,t)$ at time $t$,\n",
    "    and for all $x=m\\Delta x$, $m=0,\\ldots,N_x-2$ and $z=k\\Delta z$,\n",
    "    $l=0,\\ldots,N_z-2$ by using the equations\n",
    "    \n",
    "      \\begin{eqnarray}\n",
    "         \\ddot{u}_x(x+\\Delta x/2,x,t) & = & \\rho^{-1}(x+\\Delta x/2,z)d^+_x \\sigma(x,z,t),\\nonumber\\\\\n",
    "         \\ddot{u}_z(x,z+\\Delta z/2,t)   & = & \\rho^{-1}(x,z+\\Delta z/2)d^+_z \\sigma(x,z,t).\n",
    "         \\label{eq:ch4-508}\n",
    "      \\end{eqnarray}\n",
    "      \n",
    "      \n",
    " 3. Compute the stress $\\sigma{(x,z,t+\\Delta t)}$ at the future time $t+\\Delta t$ and\n",
    "    for all $x=m\\Delta x$, $m=1,\\ldots,N_x-1$\n",
    "    and $z=l\\Delta z$, $l=1,\\ldots,N_z-1$\n",
    "    by using the equation\n",
    "    \n",
    "     \\begin{eqnarray}\n",
    "       \\sigma(x,z,t+\\Delta t) & = &2\\sigma(x,z,t) - \\sigma(x,z,t-\\Delta t) \\\\\n",
    "                & + &\\Delta t^2\\kappa(x,z) [d^-_{x} [\\ddot{u}_x(x+\\Delta z/2,z,t)+\\ddot{u}_z(x,z+\\Delta z/2,z,t)]\n",
    "                                                       \\label{eq:ch4-509}\n",
    "      \\end{eqnarray}\n",
    "      \n",
    "\n",
    " 4. Add the source term for a single grid position $x_s=m_s\\Delta x$ and $z_s=l_s\\Delta z)$\n",
    "    \\begin{eqnarray}\n",
    "      \\sigma(x_s,z_s,t+\\Delta t)= \\sigma(x_s,z_s,t+\\Delta t)+\n",
    "       + \\Delta t^2 \\ddot{s}(x_s,z_s,t).\n",
    "                                                       \\label{eq:ch4-510}\n",
    "    \\end{eqnarray}\n",
    "    \n",
    "\n",
    " 5. set $t=t+\\Delta t$ and go to 2. Stop if $t=(N_t-1)\\Delta t$ is reached.\n",
    "\n",
    "## Stability\n",
    "To obtain a numerically stable solution, the following condition must be\n",
    "approximately fulfilled\n",
    "\n",
    "\\begin{eqnarray}\n",
    "  \\frac{c_0\\Delta t}{\\Delta z} \\leq \\frac{1}{\\sqrt{2}}.\n",
    "                  \\label{eq:ch4-37}\n",
    "\\end{eqnarray}\n",
    "\n",
    "This is the stability condition, and it places restriction on the choice of\n",
    "time sampling interval, spatial sampling interval and velocity.\n",
    "\\begin{eqnarray}\n",
    " \\lambda > \\Delta z/2\n",
    "\\end{eqnarray}\n",
    "where the wavelength $\\lambda$ is given by\n",
    "\\begin{eqnarray}\n",
    " \\lambda = c_0/f.\n",
    " \\label{eq:ch4-37c}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "`` `   \n",
    "\n",
    "\n",
    "\n",
    "\n"
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       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    canvas_div.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    canvas_div.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.canvas_div.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "function getModifiers(event) {\n",
       "    var mods = [];\n",
       "    if (event.ctrlKey) {\n",
       "        mods.push('ctrl');\n",
       "    }\n",
       "    if (event.altKey) {\n",
       "        mods.push('alt');\n",
       "    }\n",
       "    if (event.shiftKey) {\n",
       "        mods.push('shift');\n",
       "    }\n",
       "    if (event.metaKey) {\n",
       "        mods.push('meta');\n",
       "    }\n",
       "    return mods;\n",
       "}\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    // from https://stackoverflow.com/q/1114465\n",
       "    var boundingRect = this.canvas.getBoundingClientRect();\n",
       "    var x = (event.clientX - boundingRect.left) * this.ratio;\n",
       "    var y = (event.clientY - boundingRect.top) * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        modifiers: getModifiers(event),\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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       "\">\n",
       "  Your browser does not support the video tag.\n",
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as pl\n",
    "from matplotlib.pyplot import draw, ion\n",
    "import matplotlib.animation as anim\n",
    "from math import *\n",
    "from IPython.display import HTML\n",
    "from IPython.display import display, Image\n",
    "\n",
    "\n",
    "class wave2d :\n",
    "  \n",
    "  #Source pulse\n",
    "  def ricker(self,fp,tp,M,dt) :\n",
    "    s=np.zeros((M))\n",
    "    for k in range(0,M):\n",
    "      t=k*dt\n",
    "      wp=2.0*3.14159*fp\n",
    "      s[k] =(1-0.5*pow(wp,2)*pow((t-tp),2))*exp(-0.25*pow(wp,2)*pow(t-tp,2))\n",
    "    return(s)\n",
    "\n",
    "\n",
    "  def __init__(self) :\n",
    "    self.dx = 5.0   # Case 1 Grid spacing\n",
    "    self.dt = 0.0005 # (seconds)\n",
    "    self.Tmax = 0.4\n",
    "    self.Nt = 500\n",
    "    self.Nx = 200 # Number of gridpoints in x-direction\n",
    "    self.Ny = 200 # Number of gridpoints in y-direction\n",
    "    self.Ns=100\n",
    "    self.t = 0 \n",
    "\n",
    "    #Source parameter\n",
    "    self.f0=20.0 #Dominant freqiency (Hz)\n",
    "    self.t0=0.05  #Time delay\n",
    "    self.src= self.ricker(self.f0,self.t0,self.Nt,self.dt)\n",
    "    \n",
    "    #Source position\n",
    "    self.ixs = int(self.Nx/2)\n",
    "    self.iys = int(self.Ny/2)\n",
    "    self.kappa  = np.zeros((self.Nx,self.Ny))\n",
    "    self.rho    = np.zeros((self.Nx,self.Ny))\n",
    "    \n",
    "    #Animation parameters\n",
    "    self.cnt=0\n",
    "    self.inc=1\n",
    "    self.animrun=True\n",
    "    self.im=0\n",
    "\n",
    "    #Simple model\n",
    "    self.kappa[:,:] = 6.25e+09\n",
    "    #self.kappa[:,int(self.Nx/2-1):self.Nx] = 7.0e+09\n",
    "    #self.kappa[int(self.Nx/2-1):self.Nx,:] = 7.0e+09\n",
    "    self.rho[:,:]    = 1000.0\n",
    "\n",
    "    self.P0 = np.zeros((self.Nx,self.Ny))  #Past pressure\n",
    "    self.P1 = np.zeros((self.Nx,self.Ny))  #Present pressure\n",
    "    self.P2 = np.zeros((self.Nx,self.Ny))  #Future pressure\n",
    "    self.ax= np.zeros((self.Nx,self.Ny))  #Future pressure\n",
    "    self.ay = np.zeros((self.Nx,self.Ny))  #Future pressure\n",
    "\n",
    "  #Forward derivative in x-direction\n",
    "  def dxplus(self,A,dx) :\n",
    "    nx = A.shape[0]\n",
    "    ny = A.shape[1]\n",
    "    dA = np.zeros((nx,ny))\n",
    "    for j in range(0,ny) :\n",
    "      for i in range(0,nx-1) :\n",
    "        dA[i,j] = (A[i+1,j]-A[i,j])/dx\n",
    "    return dA\n",
    "\n",
    "  #Backward derivative in x-direction\n",
    "  def dxminus(self,A,dx) :\n",
    "    nx = A.shape[0]\n",
    "    ny = A.shape[1]\n",
    "    dA = np.zeros((nx,ny))\n",
    "    for j in range(0,ny) :\n",
    "      for i in range(1,nx) :\n",
    "        dA[i,j] = (A[i,j]-A[i-1,j])/dx\n",
    "    return dA\n",
    "\n",
    "  #Forward derivative in y-direction\n",
    "  def dyplus(self,A,dx) :\n",
    "    nx = A.shape[0]\n",
    "    ny = A.shape[1]\n",
    "    dA = np.zeros((nx,ny))\n",
    "    for i in range(0,nx) :\n",
    "      for j in range(0,ny-1) :\n",
    "        dA[i,j] = (A[i,j+1]-A[i,j])/dx\n",
    "    return dA\n",
    "\n",
    "#Backward derivative in y-direction\n",
    "  def dyminus(self,A,dx) :\n",
    "    nx = A.shape[0]\n",
    "    ny = A.shape[1]\n",
    "    dA = np.zeros((nx,ny))\n",
    "    for i in range(0,nx) :\n",
    "      for j in range(1,ny) :\n",
    "        dA[i,j] = (A[i,j]-A[i,j-1])/dx\n",
    "    return dA\n",
    "\n",
    "#Compute one timestep\n",
    "  def tstep(self,t):\n",
    "    #print(\"Timestep: \", k)\n",
    "    #Compute accelerations\n",
    "    self.ax = self.dxplus(self.P1,self.dx)\n",
    "    self.ax = (1.0/self.rho)*self.ax\n",
    "    self.ay = self.dyplus(self.P1,self.dx)\n",
    "    self.ay = (1.0/self.rho)*self.ay\n",
    "\n",
    "    self.ax = self.dxminus(self.ax,self.dx)\n",
    "    self.ay = self.dyminus(self.ay,self.dx)\n",
    "\n",
    "    self.P2 = 2*self.P1 - self.P0 + (self.dt*self.dt)*self.kappa*(self.ax+self.ay)\n",
    "    self.P2[self.ixs,self.iys] = self.P2[self.ixs,self.iys] + (self.dt*self.dt)*self.src[t]/(self.dx*self.dx)\n",
    "\n",
    "    self.P0=self.P1\n",
    "    self.P1=self.P2\n",
    "    return self.P2\n",
    "\n",
    "  def updatefig(self,*args):\n",
    "    ''' Callback function for updating each frame\n",
    "\n",
    "    Arguments:\n",
    "        *args: provided by callback\n",
    "\n",
    "    Returns\n",
    "        None\n",
    "    '''\n",
    "    \n",
    "    im=self.im\n",
    "    img = self.tstep(self.t) #Get the next frame\n",
    "    im.set_array(img)        #Plot the frame \n",
    "    self.t =  self.t+1\n",
    "    return(im,)\n",
    "\n",
    "\n",
    "  def movie(self):\n",
    "    #Plot frame no 0\n",
    "    fig = pl.figure()\n",
    "    img = self.tstep(0)\n",
    "    self.t=1\n",
    "    o1=0\n",
    "    o2=0\n",
    "    d1=self.dx\n",
    "    d2=d1\n",
    "    n1=self.Nx\n",
    "    n2=self.Ny\n",
    "    cmin=-1.0e-08\n",
    "    cmax= 1.0e-08\n",
    "    colormap=\"gray\"\n",
    "    self.im=pl.imshow(img,interpolation='nearest',clim=(cmin,cmax),\n",
    "                 cmap=colormap,extent=[o1,o1+d1*n1,o2+d2*n2,o2],animated=True)\n",
    "    #self.im=pl.imshow(img,interpolation='nearest',\n",
    "     #       cmap=colormap,extent=[o1,o1+d1*n1,o2+d2*n2,o2],animated=True)\n",
    "    ax=pl.gca()\n",
    "    ar=1.0\n",
    "    asr = 1.0/(ax.get_data_ratio()*ar)\n",
    "    pl.Axes.set_aspect(ax,asr)\n",
    "    #Animation loop\n",
    "    ani = anim.FuncAnimation(fig, self.updatefig, frames=self.Nt-2, repeat=True, interval=100, blit=True)\n",
    "    #pl.close(ani.fig)\n",
    "    display(HTML(ani.to_html5_video()))\n",
    "    \n",
    "   \n",
    "#Test the wave2d class\n",
    "wave = wave2d()\n",
    "wave.movie()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a59e583",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0825e42",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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