Computational_Seismology_Igel/Greens_function_acoustic_1-3D.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style='background-image: url(\"../../share/images/header.svg\") ; padding: 0px ; background-size: cover ; border-radius: 5px ; height: 250px'>\n",
    "    <div style=\"float: right ; margin: 50px ; padding: 20px ; background: rgba(255 , 255 , 255 , 0.7) ; width: 50% ; height: 150px\">\n",
    "        <div style=\"position: relative ; top: 50% ; transform: translatey(-50%)\">\n",
    "            <div style=\"font-size: xx-large ; font-weight: 900 ; color: rgba(0 , 0 , 0 , 0.8) ; line-height: 100%\">Computational Seismology</div>\n",
    "            <div style=\"font-size: large ; padding-top: 20px ; color: rgba(0 , 0 , 0 , 0.5)\">Green's functions for the homogeneous acoustic wave equation</div>\n",
    "        </div>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p style=\"width:20%;float:right;padding-left:50px\">\n",
    "<img src=../../share/images/book.jpg>\n",
    "<span style=\"font-size:smaller\">\n",
    "</span>\n",
    "</p>\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "This notebook is part of the supplementary material \n",
    "to [Computational Seismology: A Practical Introduction](https://global.oup.com/academic/product/computational-seismology-9780198717416?cc=de&lang=en&#), \n",
    "Oxford University Press, 2016.\n",
    "\n",
    "##### Authors:\n",
    "* Kristina Garina\n",
    "* Ashim Rijal\n",
    "* Heiner Igel ([@heinerigel](https://github.com/heinerigel))\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Excercise:\n",
    "Initialise Green's function in 1D, 2D and 3D cases of the acoustic wave equation and convolve them with an arbitrary source time function **(see Chapter 2, Section 2.2, Fig. 2.9)**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This exercise covers the following aspects:\n",
    "\n",
    "* Learn how to define a source time function\n",
    "* Calculation of analytical Green's function in the 1D, 2D, and 3D cases \n",
    "* Convolution of Green's function with source time function\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Please, execute first!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "code_folding": [
     0
    ]
   },
   "outputs": [],
   "source": [
    "# Import Libraries\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we introduce the initial parameters: velocity, distance, length of seismogram, frequency, number of samples, time increment and geometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "#Initial parameters\n",
    "c = 1.           # velocity m/s \n",
    "r = 2.           # distance from source\n",
    "tmax = 5.        # length of seismogram (s)\n",
    "f0 = 1          # Frequency (Hz)\n",
    "nt = 3000       # number of time samples\n",
    "dt = tmax/nt    # time increment\n",
    "ts=0            # source time\n",
    "\n",
    "\n",
    "# Geometry\n",
    "xs=0            # coordinates of source\n",
    "ys=0\n",
    "zs=0\n",
    "\n",
    "xr=r            # coordinates of receiver\n",
    "yr=0\n",
    "zr=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Source time function\n",
    "\n",
    "Below we initialise time and calculate source time function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "# Defining time\n",
    "\n",
    "for i in range (nt+1):\n",
    "    t=(np.arange(0,i)*dt)\n",
    "time=np.zeros(nt) \n",
    "time[0:nt]=t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Defining source time function\n",
    "\n",
    "p=1./f0          # period\n",
    "t0 = p/dt        # defining t0\n",
    "sigma=4./p      \n",
    "\n",
    "# Initialization of source-time function\n",
    "src=np.zeros(nt) \n",
    "source=np.zeros(nt)\n",
    "\n",
    "# Initialization of first derivative of gaussian\n",
    "for it in range(nt):\n",
    "    t=(it-t0)*dt\n",
    "    src[it]=-2*sigma*t*np.exp(-(sigma*t)**2)\n",
    "source[0:nt]=src\n",
    "\n",
    "# Plotting of source time function\n",
    "plt.plot(time, src)\n",
    "plt.title('Source time function')\n",
    "plt.xlabel('Time, s')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1D Green's function  \n",
    "\n",
    "Below we calculate the Green's function for the 1D acoustic problem, its convolution with a source time function. Please note, that we center the source time function around t=0.\n",
    "\n",
    "In the 1D case, Green's function is proportional to a Heaviside function. As the response to an arbitrary source time function can be obtained by convolution this implies that the propagating waveform is the integral of the source time function.\n",
    "\n",
    "\n",
    "$G_1=\\dfrac{1}{2c}H(t-\\dfrac{|r|}{c}) $\n",
    "\n",
    "$r=x$\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating Green's function in 1D\n",
    "\n",
    "G=np.zeros(nt)      # initialization G with zeros\n",
    "\n",
    "for i in range (nt):\n",
    "    if (((time[i]-ts)-abs(xr-xs)/c)>=0):\n",
    "        G[i]=1./(2*c)\n",
    "    else:\n",
    "        G[i]=0\n",
    "\n",
    "# Plotting Green's function in 1D\n",
    "plt.plot(time, G)\n",
    "plt.title(\"Green's function in 1D\" )\n",
    "plt.xlabel(\"Time, s\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# Convolution of Green's function with the 1st derivative of a Gaussian\n",
    "G1=np.convolve(G, source*dt)[:len(G)]\n",
    "\n",
    "# Plotting convolved Green's function in 1D\n",
    "plt.plot(time-t0*dt, G1)\n",
    "plt.title('After convolution')\n",
    "plt.xlabel('Time, s')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.xlim (0, tmax)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2D Green's function  \n",
    "\n",
    "Below we calculate the Green's function for 2D acoustic problem, its convolution with the source time function. Please note, that we center the source time function around t=0. \n",
    "\n",
    "$G_2=\\dfrac{1}{2\\pi c^2}\\dfrac{H(t-\\dfrac{|r|}{c})}{\\sqrt{t^2-\\dfrac{r^2}{c^2}}}$ \n",
    "\n",
    "$r = \\sqrt{x^2+y^2}$\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UKJKW+gZHONY1kLQrFICqknzaNMmWyLQpUCQtNSVhlOHxqorzaO9RoIhMlwJF0tLoMyjJDJQFJXm09QwQDCEnIolSoEhaSuYzKKOqi4PhV7oGhpO2T5H5RIEiaelAey9FedlUFeclbZ8Lwn216z6KyLQoUCQtNYWjDJtNNEv09FSVBIHS1qOeXiLToUCRtNTU3kddZfKauwCqioPxvNTTS2R6FCiSdtydA0maB2WsBSevUBQoItOhQJG009o9SN/QCMuT+FAjcPJ+jLoOi0yPAkXSzoEUdBkGKMjNpjgvW3OiiEyTAkXSzr7WHgBWVhcnfd9VJfm6QhGZJgWKpJ39bT1kGSxL8k15CLoO66a8yPQoUCTt7G3rZWllIXk5yf/xrS7J0015kWlSoEja2d/Ww8qq5Dd3wegViu6hiEyHAkXSiruztzV1gVJVks/x3kGN5yUyDQoUSSvHe4fo6h9mRVXy759A0HV4aMQ50a/xvEQSpUCRtLKvLejhtSoFPbxgzPAravYSSZgCRdLKaJfhFSm7hxIMv6KuwyKJmzJQzKzIzP7SzL4Yvl9rZjekvjSRM+1r6w26DCf5KflRo0/Lt6rrsEjC4rlCeQAYAK4I3zcDf5OyikQmsa+1hyUVheTnZKdk/6NNXrpCEUlcPIGy2t0/DQwBuHsfkLwxw0USkMouw3BqThTdQxFJXDyBMmhmhYADmNlqgisWkVm3r62XldWp6eEFkJ+TTWl+jh5uFJmGnDjW+QTwI2CZmT0IXAX8fiqLEpnI8Z5BOvuGUnqFAqNzyytQRBI1ZaC4+5Nm9hzwWoKmrnvcvTXllYmMszfsMpzqQKkqzqNdszaKJOysgWJml4z76HD473IzW+7uz6WuLJEz7WrpBmD1wpKUHmdBcT7Nx3tTegyRTDTZFcrfh/8WAJcCWwiuUF4NbAJel9rSRE63u6WbvOwsllWmpsvwqOqSPLY0d6T0GCKZ6Kw35d39ane/GtgPXOLul7r7bwAXA7tmq0CRUbtaullVXUxOdmqfx11QnMfxnkFiMY3nJZKIeP7PXOfu20bfuPuLwEWpK0lkYruPdbN6YWrvn0AwQORwzDnRP5TyY4lkkngCZYeZfcnMGszsjeET8zuScXAzu87MdprZLjP76ATLzcw+Fy7fOnpfx8yWmdlTZrbDzLab2T3JqEfmrv6hEQ6097KmJrX3T+DU0/Lq6SWSmHgC5TZgO3AP8AHgpfCzGTGzbOBe4HpgPXCLma0ft9r1wNrw63bgC+Hnw8AH3f08gt5nd06wrWSQfW09xDz1N+Rh7ACRChSRRMTTbbgf+MfwK5kuA3a5+x4AM3sIuIkgsEbdBHzNg8kpNppZhZnVuvthwl5n7t5lZjuApeO2lQwy2sNrzSwEip6WF5meKQPFzPYSPiU/lrufM8NjLwWaxrxvBi6PY52lnOrCjJmtJOgosGmig5jZ7QRXN9TU1NDY2DizqjNEd3d3Wp2LH+8axIDmHc9x7JXkjvwz/lwc748B8MvnX6SwbWdSjzXXpdvPRSrpXCQuniflLx3zugB4F7AgCcee6LfC+OCadB0zKwG+DXzA3U9MdBB3vx+4H6C+vt4bGhqmVWymaWxsJJ3OxbcPP8/SyuNc++ark77v8edicDjGnzf+kOqlK2loWJv0481l6fZzkUo6F4mb8h6Ku7eN+Tro7p8F3pSEYzcDy8a8rwMOxbuOmeUShMmD7v6dJNQjc9iulu5Zae4CyMvJoqwgR01eIgmKp8lr7BPzWQRXLKVJOPZmYK2ZrQIOAjcD7x63zqPAXeH9lcuBTnc/bGYGfBnY4e7/kIRaZA4bHomxu6Wb16+tnrVjVpfk06peXiIJiafJ6+/HvB4G9gK/O9MDu/uwmd0FPA5kA19x9+1mdke4/D5gA/A2ggcpeznVu+wq4H3ANjN7Ifzsf7j7hpnWJXPPntYeBkdinFebjL9j4rOgOI929fISSUg8gfKHoz2xRoVXFTMWBsCGcZ/dN+a1A3dOsN3TaE6WeWPH4eD22LrFZbN2zKqSPPaG0w2LSHzieQ7lW3F+JpISOw53kZttrJ6FhxpHLSjO16yNIgmabLThdcD5QLmZ/daYRWUEvb1EZsWOwydYs7CUvJzUjuE1VnVJHu09g4zEnOwsXQyLxGOyJq964AagArhxzOddwB+nsiiRsV4+coKrVs/eDXkIhl+JOXT0DlJVkj+rxxZJV2cNFHf/HvA9M7vC3X85izWJnNTeM8jREwOcVzt7908AFoQh0t6jQBGJ12RNXh92908D7zazW8Yvd/f/ltLKRICXR2/Iz2IPL4DqcPiV1u5B1i6a1UOLpK3JmrxGRxR+ZjYKEZnIS2GgzPYVyuhVSZumAhaJ22RNXo+F//7r7JUjcroXmjpYWlFI9Sw3O40OEKmeXiLxm6zJ6zEmGBRylLu/IyUViYyxpbmDC5eVz/pxK4tyMQuavEQkPpM1eX1m1qoQmUBb9wBN7X289/IVs37snOwsKovyaFeTl0jcJmvy+q/R12aWB6wjuGLZ6e76s01SbmtzJwAXLquI5PgLivM0yZZIAuIZHPLtwH3AboLhTlaZ2Z+4+w9TXZzMby80dZBl8Kqls9/kBcGzKAoUkfjFOzjk1e6+C8DMVgM/ABQoklJbmjtYu7CU4vx4fkyTr6okj51HuiI5tkg6imcsi5bRMAntAVpSVI8IALGY80JTBxdF1NwFUFWcT5t6eYnELZ4//bab2QbgYYJ7KO8CNo+O76XJrSQVdh7toqN3iMtWJWNy0OmpKsmjo3eI4ZEYOdmzN46YSLqKJ1AKgKPAG8P3xwimAL6RIGAUKJJ0m/a0AXD5OREGyuizKL2DLCzVeKgiU5kyUNz9tqnWEUm2jXvaqasspK6yKLIaTj4t361AEYlHPL28VgF3AyvHrq8HGyVVYjHnV/vaubp+YaR1VOlpeZGExNPk9V2C+dsfA2KpLUcEXmnpor1nMNLmLgjuoQC0duvhRpF4xBMo/e7+uZRXIhL6r53HAHjdmtmdA2W8quJTQ9iLyNTiCZR/MrNPAE8AJ/9Uc/fnUlaVzGs/ebmFdYtLWVJRGGkd5YW5ZGeZHm4UiVM8gfIq4H3AmzjV5OXhe5Gk6uwb4pn9x/mTN5wTdSlkZRmVRXkawl4kTvEEym8C52j8LpkNP/v1MUZizpvWRXtDflR1iYZfEYlXPE9rbSGYV14k5TZsO0x1SV6kT8iPtaA4T0/Li8QpniuURcDLZraZU/dQ3N1vSl1ZMh919Q/x4x0t3PyaZXPmyfSqkny2NXdEXYZIWognUD4x5rUBrwPOmGNeZKaefOkoA8MxbrxwSdSlnFSlKxSRuE35Z2A4L0on8Hbgq8CbCYazF0mqR54/yNKKQi5ZXhl1KSdVFefR1T/MwPBI1KWIzHmTTQF8LnAzwdVIG/BNwNz96lmqTeaRPce6+dmvW/ngW84lK8uiLuek0eFXjvcMsbg8O+JqROa2ya5QXia4GrnR3V/n7v8M6M80SYl/27if3Gzj5suWR13KafS0vEj8JguU3waOAE+Z2RfN7M0E91BEkqqjd5D/eKaZ6y+opaY0P+pyTjM6npfuo4hM7ayB4u6PuPvvEcwl3wj8ObDIzL5gZm+dpfpkHrj/p3voGRzmzqvXRF3KGUabvNr1cKPIlOK5Kd/j7g+6+w1AHfAC8NGUVybzQsuJfr76i328/VW11C8ujbqcMywYvULRw40iU0qos7+7t7v7/3N3DbsiSfHJx15iOOb897fWR13KhMoKcsjNNjV5icRhbjw9JvPSD7Ye5gfbDnPPm9eysro46nImZGbB3PK6KS8yJQWKROKVo118+FtbuGhZBX/8+ugHgpzMgmKN5yUSDwWKzLrdx7p575c2UZiXw33v/Q3ycub2j2FViZ6WF4nH3P4/WTLOUztb+J0v/IKRmPPgH13O4vK5P1d7dUm+nkMRiUOkgWJm15nZTjPbZWZn9ByzwOfC5VvN7JJ4t5W5Zc+xbu7+xvPc9sBmFpUV8K0/vXJO9uqaSHVJHq3dA7h71KWIzGnxDA6ZEmaWDdwLvAVoBjab2aPu/tKY1a4H1oZflwNfAC6Pc1uJ0In+IXa1dLNpTztP7WzhV3vbKcjN4u43reHPGtZQmJc+w5gsLC2gfyhG18AwZQW5UZcjMmdFFijAZcAud98DYGYPATcBY0PhJuBrHvxpuNHMKsysFlgZx7ZnOD7g/P0TOwEY+8emc+rN6Z9zls8nXun09afeZ7x1nL7+mHUS3M/Y9Q8dHODx9m1MtPS0beLYb8yDoec7+4Kv1u4BWsfcxK5fVMqHrq3nXZfWsbB07jdxjTf69P6xrgEFisgkogyUpUDTmPfNBFchU62zNM5tATCz24HbAfIWreHzP9k1ZtmY9c5SpJ3ljc1knTNqnPrYca0TRx2j79xjWEtTwudgojoMKMyBolyjONdYX2EsXpLL4uIsVldkU54fA5p56dnmyRM/It3d3TQ2Np51+aG2YAi7J366ifOq0ufKajqmOhfzic5F4qIMlIl+f43/u/xs68SzbfCh+/3A/QD19fW+81NvT6TGjNXY2EhDQ0PUZcwJU52LupYuPr35pyxZvY6Gi5bOXmER0M/FKToXiYsyUJqBZWPe1wGH4lwnL45tRZKipiRopjvWpZ5eIpOJMlA2A2vNbBVwkGDulXePW+dR4K7wHsnlQKe7HzazY3FsK5IUZYU55OVkKVDS3OBwjJ6BYbrDr56BYbrCf3sGhunqH6ZnYISeweB9XWyEhqiLTjORBYq7D5vZXcDjQDbwFXffbmZ3hMvvAzYAbwN2Ab3AbZNtG8G3IfOAmVFTkq9AiZi70zM4QkfvIB29Q5zoG6Kjb4iO3qAzSEffIJ2jr3uDZd0DQ/QMjNDdP8zgSCyu4xTkZlGSn8ONK1L8DWWgKK9QcPcNBKEx9rP7xrx24M54txVJlYVl+bQoUJLO3ensG+LIiX5auwbDHoJBL8HW7gHaTns9OGko5GVnUV6US3lhLhWFuSwpL6C0oISSghyK83Moycs5+bo0P/ysIIeS/OCrOD+H4rxscrKDx/N0Qz5xkQaKSLqoKclnX1tP1GWknYHhEZra+2g63suRzn4Od/RxqLOfw519HO7o53BnP31DZ04Em5ttVJfkU1WSR3VJPucuKqW6NI8FRXlUFuVRVphLxWh4FOVSUZhHQW4WdrbukDIrFCgicVhYls/mfe1RlzEnDY/E2NfWy+5j3exv62FfW2/wb2svhzr7TntmKcuCB0VrKwpYV1vK1esWUltewOLyAmpK8qkuzae6OJ+ywhyFQxpSoIjEoaakgOO9QwwOx+b8YJap1HKin+2HTvDykS5eOdrFy0e62N3SfVpTVGVRLiuqinnNykpWVNWxsrqIZZVF1FYUsrA0n9zs+Xv+Mp0CRSQOC8uCp+VbuwdYUlEYcTWzo3tgmK3NHWxp6mRLUwdbmjs43Nl/cnlteQHnLirlDWurOXdRKWsWlrCyqpjyIo0mMF8pUETisDAcfqWlK3MDpW9whO2tI2x+/GV+sbuNrc2djMSC9qqVVUVctmoBF9ZVcMHScuoXl1JeqOCQ0ylQROIwdjyvTHKoo48f7zjKEy8dZdOedgZHYuRk7eHCZRX86RtXc+nKSi6sq6CyOC/qUiUNKFBE4jA6qGVLV/8Ua859Rzr7+e4LB/n+1kO8ePAEAOdUF3PrlSso7T3EH7yjgZJ8/WqQxOmnRiQOVSV5mEHLifS8QhkYHuGH247w7eeaeXpXK+5w0bIKPnLdOt6yfhFrFpYA0NjYojCRadNPjkgccrOzWFCUx7E0m7mxtXuABzce4N827qe1e4C6ykLuvnoNv3lJHauqi6MuTzKMAkUkTjWl+bScSI8mr9buAf7lqd18fdN+BodjNNTXcNtVq3j9mmqysvR8h6SGAkUkTrXlBad1m52LegeH+ZendvPlp/cyMDzCb11Sxx1vXH2ySUsklRQoInGqrShkS3Nn1GVMyN154qWjfPLR7Rzq7OfGC5fwgWvWsrpGQSKzR4EiEqfasgLaewbpHxqhIHfuzNzY2TvExx7ZyoZtR6hfVMp/3HIxr1m5IOqyZB5SoIjEqTZ8oPFIZz8r52GWRWAAAAwJSURBVMgN7U172vjAN1/gWNcAH7q2ntvfcI6GNpHIKFBE4lRbHjyLcqizb04EyoOb9vO/vredZZWFfOfPruTVdRVRlyTznAJFJE6jgXIk4hvzsZjztxt28OWn99JQX8M/33IxpQUaBkWip0ARiVNtedDkFWVPr1jM+R+PbOOhzU3cesUK/vKG9ScnhBKJmgJFJE6FedlUFOVyuLMvkuPHYs7HvrONbz7TxF1Xr+GDbz1Xc4bInKJAEUnA4rICDndEc4XyD0++wjefaeLuN63hL96iMJG5R9fKIglYUlEYSZPXNzcf4PNP7eLm1yxTmMicpUARScDi8oJZb/J67sBxPv7Ii7zh3Br+9zsvUJjInKVAEUnAkvJgKuD+oZFZOV5H7yB3//vz1FYU8M+3XKxnTGRO00+nSAIWz2JPL3fnQ9/aSktXP/e++xLNkChzngJFJAFLKoJnUQ4eT32z1/deOMSTLx3lI9et00OLkhYUKCIJWL6gCICm470pPU5b9wCffGw7Fy+v4LarVqX0WCLJokARSUBteSE5WcaB9tQGyv/+/kv0DIzw6d9+Ndmav0TShAJFJAHZWUZdZWFKA+XZ/e1894VD3PHGc1i7qDRlxxFJNgWKSIKWLSiiKUWBEos5f/39HSwqy+eOhtUpOYZIqihQRBK0fEFRyq5QHtt6iC1NHXzo2nUU5WkgC0kvChSRBC1fUERH7xAn+oeSut/B4Rif/tFOLlhaxm9dvDSp+xaZDQoUkQSd7OmV5KuUbz/XzMGOPj741nqydCNe0pACRSRBy1IQKEMjMe59ahcX1pXTcG5N0vYrMpsUKCIJWl4VBEoy76M88txBmo/3cc81azVWl6QtBYpIgsoKcqkoymVva3ICZXgkxuef2sWr68q5un5hUvYpEgUFisg0rKkpYfex7qTs64mXjnKgvZc7r16jqxNJawoUkWlYs7CEXS3JCZSvPL2X5QuKuOa8RUnZn0hUIgkUM1tgZk+a2a/DfyvPst51ZrbTzHaZ2UfHfP5/zexlM9tqZo+YmUbOk1m1ZmEJ7T2DtPcMzmg/W5s7eGb/cW69cqWGWJG0F9UVykeBH7v7WuDH4fvTmFk2cC9wPbAeuMXM1oeLnwQucPdXA68AH5uVqkVCaxaWAMz4KuWBn++jJD+H3720LhlliUQqqkC5CfjX8PW/Au+cYJ3LgF3uvsfdB4GHwu1w9yfcfThcbyOg/xtlVo0Gyq9buqa9j5YT/Xx/6yF+5zfqKC3QXCeS/qIKlEXufhgg/Heiri1LgaYx75vDz8b7A+CHSa9QZBJLygspzM2e0RXK1zfuZzjm/P6VK5NXmEiEUjZYkJn9J7B4gkUfj3cXE3zm447xcWAYeHCSOm4HbgeoqamhsbExzsNntu7ubp2L0HTPxcJC51cvH6Cx9FjC2w6OOA883cuF1dnse3Ez+xLeQ2ro5+IUnYvEpSxQ3P2asy0zs6NmVuvuh82sFmiZYLVmYNmY93XAoTH7uBW4AXizuztn4e73A/cD1NfXe0NDQ0LfR6ZqbGxE5yIw3XPxmmNbaNzZwhvf+MaEu/s+/EwTXYNb+dBNl3LVmuqEj50q+rk4RecicVE1eT0K3Bq+vhX43gTrbAbWmtkqM8sDbg63w8yuAz4CvMPdUzvTkchZvGppOa3dgxw5kdj88u7OAz/fR/2iUq5cXZWi6kRmX1SB8ingLWb2a+At4XvMbImZbQAIb7rfBTwO7AAedvft4fafB0qBJ83sBTO7b7a/AZFX1ZUDsLW5M6HtNu5pZ8fhE9x21Uo9yCgZJZIJF9y9DXjzBJ8fAt425v0GYMME661JaYEicVhfW0Z2lrGtuZNrz5/oduHEHvj5XiqLcnmnhqiXDKMn5UWmqSA3m7ULS9h2MP4rlP1tPTy54yjvuXwFBbnZKaxOZPYpUERm4NV15Wxp7iAWO2u/kNN89Rf7yMky3nfFihRXJjL7FCgiM3D5qio6eofYeXTqBxxP9A/x8OYmbnj1EhaVFcxCdSKzS4EiMgNXhL20frG7bcp1H97cRM/gCH9w1apUlyUSCQWKyAwsqShkVXUxv9zdOul6g8MxHvj5Pl6zsvJk7zCRTKNAEZmhK1dX8cvdbfQPjZx1ne+E88X/WYM6KErmUqCIzNB1FyymZ3CExp0TD8EyNGZGxoZ6zRcvmUuBIjJDV5xTRVVxHo9tPTTh8m/86kAwX/ybNV+8ZDYFisgM5WRnceOFS3hi+xGOdJ4+DEtb9wCfeXwnV66u4k3rNF+8ZDYFikgS/OHrVjESc77QuOvkZ+7Oxx95kd7BET75jvN1dSIZT4EikgTLFhTxnstX8LWN+3nq5RaGR2L83YYd/Gj7ET5y3TrWLiqNukSRlItkLC+RTPSR69fx7P7j/MG/bqaiMJfjvUO877Ur+KPX67kTmR8UKCJJUpKfw0N/8loeeHofB9p7ecv6RVx7/iI1dcm8oUARSaKyglzuuWZt1GWIREL3UEREJCkUKCIikhQKFBERSQoFioiIJIUCRUREkkKBIiIiSaFAERGRpFCgiIhIUpi7R13DrDGzLmBn1HXMEdXA5NMMzh86F6foXJyic3FKvbtPOSDdfHtSfqe7Xxp1EXOBmT2jcxHQuThF5+IUnYtTzOyZeNZTk5eIiCSFAkVERJJivgXK/VEXMIfoXJyic3GKzsUpOhenxHUu5tVNeRERSZ35doUiIiIpokAREZGkmBeBYmbXmdlOM9tlZh+Nup4omdlXzKzFzF6MupYomdkyM3vKzHaY2XYzuyfqmqJiZgVm9isz2xKei09GXVPUzCzbzJ43s+9HXUuUzGyfmW0zsxfi6Tqc8fdQzCwbeAV4C9AMbAZucfeXIi0sImb2BqAb+Jq7XxB1PVExs1qg1t2fM7NS4FngnfPx58KCOYqL3b3bzHKBp4F73H1jxKVFxsz+ArgUKHP3G6KuJypmtg+41N3jesBzPlyhXAbscvc97j4IPATcFHFNkXH3nwLtUdcRNXc/7O7Pha+7gB3A0mirioYHusO3ueFXZv+lOQkzqwPeDnwp6lrSzXwIlKVA05j3zczTXxwyMTNbCVwMbIq2kuiETTwvAC3Ak+4+b88F8Fngw0As6kLmAAeeMLNnzez2qVaeD4FiE3w2b//6ktOZWQnwbeAD7n4i6nqi4u4j7n4RUAdcZmbzsjnUzG4AWtz92ahrmSOucvdLgOuBO8Mm87OaD4HSDCwb874OOBRRLTKHhPcLvg086O7fibqeucDdO4BG4LqIS4nKVcA7wnsHDwFvMrOvR1tSdNz9UPhvC/AIwS2Es5oPgbIZWGtmq8wsD7gZeDTimiRi4Y3oLwM73P0foq4nSmZWY2YV4etC4Brg5Wirioa7f8zd69x9JcHvip+4+3sjLisSZlYcdljBzIqBtwKT9g7N+EBx92HgLuBxghuvD7v79mirio6ZfQP4JVBvZs1m9odR1xSRq4D3EfwF+kL49baoi4pILfCUmW0l+APsSXef191lBYBFwNNmtgX4FfADd//RZBtkfLdhERGZHRl/hSIiIrNDgSIiIkmhQBERkaRQoIiISFIoUEREJClyoi5AJJ2ZWRXw4/DtYmAEOBa+73X3KyMpTCQC6jYskiRm9ldAt7t/JupaRKKgJi+RFDGz7vDfBjP7LzN72MxeMbNPmdl7wjlItpnZ6nC9GjP7tpltDr+ummL/tWb20/ChzBfN7PWz8X2JnI2avERmx4XAeQRTB+wBvuTul4UTe90NfAD4J+Af3f1pM1tOMLrDeZPs893A4+7+t+G8P0Up/Q5EpqBAEZkdm939MICZ7QaeCD/fBlwdvr4GWB8MMwZAmZmVhvO1TLhP4CvhIJffdfcXUlO6SHzU5CUyOwbGvI6NeR/j1B92WcAV7n5R+LV0kjAZnSztDcBB4N/M7P0pqFskbgoUkbnjCYKBTAEws4vCfy8zs6+NX9nMVhDM3fFFgpGTL5mtQkUmokARmTv+G3CpmW01s5eAO8LPlwN9E6zfALxgZs8Dv01wD0YkMuo2LDLHmdn/Bf7N3bdGXYvIZBQoIiKSFGryEhGRpFCgiIhIUihQREQkKRQoIiKSFAoUERFJCgWKiIgkxf8HB5Ma5b2XIVIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculation of Green's function for 2D\n",
    "\n",
    "G=np.zeros(nt)                    # initialization G with zeros\n",
    "r=np.sqrt((xs-xr)**2+(ys-yr)**2)\n",
    "\n",
    "for i in range (nt):\n",
    "    if (((time[i]-ts)-abs(xr-xs)/c)>0):\n",
    "        G[i]=(1./(2*np.pi*c**2))*(1./np.sqrt((time[i]-ts)**2-(r**2/c**2)))\n",
    "    else:\n",
    "        G[i]=0\n",
    "           \n",
    "# Plotting Green's function in 2D\n",
    "plt.plot(time, G)\n",
    "plt.title(\"Green's function in 2D\" )\n",
    "plt.xlabel(\"Time, s\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.xlim((0, tmax))\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# Convolution of Green's function with the 1st derivative of a Gaussian\n",
    "G2=np.convolve(G, source*dt)[:len(G)]\n",
    "\n",
    "# Plotting convolved Green's function in 1D\n",
    "plt.plot(time-t0*dt,G2)\n",
    "plt.title('After convolution')\n",
    "plt.xlabel('Time, s')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.xlim((0, tmax))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D Green's function  \n",
    "\n",
    "Below we calculate the Green's function for 3D acoustic problem, its convolution with the source time function. Please note, that we center the source time function around t=0. \n",
    "\n",
    "$G_3=\\dfrac{1}{4 \\pi c^2 r}\\delta(t-r/c)$ \n",
    "\n",
    "$r = \\sqrt{x^2+y^2+z^2}$\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculation of Green's function for 3D case\n",
    "\n",
    "G=np.zeros(nt)                               # initialization G with zeros\n",
    "\n",
    "# Defining time\n",
    "for i in range (nt+1):\n",
    "    t=(np.arange(0,i)*dt)\n",
    "new_time=np.zeros(nt) \n",
    "new_time[0:nt]=t\n",
    "new_time=t[2]-t[1]\n",
    "\n",
    "r=np.sqrt((xs-xr)**2+(ys-yr)**2+(zs-zr)**2)     # defining the distance to receiver\n",
    "amp=1./(4*np.pi*(c**2)*r)                       # defining amplitudes\n",
    "t_arr=ts+(r/c)                               # time arrival\n",
    "i_arr=t_arr//new_time\n",
    "b=int(i_arr)\n",
    "G[b]= amp/dt\n",
    "\n",
    "# Plotting Green's function in 3D\n",
    "plt.plot(time, G)\n",
    "plt.title(\"Green's function in 3D\" )\n",
    "plt.xlabel(\"Time, s\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.xlim((0, tmax))\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# Convolution of Green's function with the 1st derivative of a Gaussian\n",
    "G3=np.convolve(G, source)[:len(G)]\n",
    "\n",
    "# Plotting convolved Green's function in 1D\n",
    "plt.plot(time-t0*dt, G3)\n",
    "plt.title('After convolution')\n",
    "plt.xlabel('Time, s')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.xlim (0, tmax)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}