notebooks/00_Synthetic_wedge_model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### X lines of Python\n",
    "\n",
    "# Wedge model\n",
    "\n",
    "This is part of [an Agile blog series](http://ageo.co/xlines00) called **x lines of Python**.\n",
    "\n",
    "We start with the usual preliminaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make an earth model\n",
    "\n",
    "We'll start off with an earth model --- an array of 'cells', each of which has some rock properties.\n",
    "\n",
    "Line 1 sets up some basic variables, then in line 2 I've used a little matrix-forming trick, `np.tri(m, n, k)`, which creates an *m* &times; *n* matrix with ones below the *k*th diagonal, and zeros above it. The `dtype` specification just makes sure we end up with integers, which we need later for the indexing trick.\n",
    "\n",
    "Then line 3 just sets every row above `depth//3` (the `//` is integer division, because NumPy prefers integers for indexing arrays), to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "length, depth = 40, 100\n",
    "model = 1 + np.tri(depth, length, -depth//3, dtype=int)\n",
    "model[:depth//3,:] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll have a quick look with some very basic plotting commands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11466aa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(model, cmap='viridis', aspect=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[60]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can make some Vp-rho pairs (rock 0, rock 1, rock 2) and select from those with `np.take`. This works like `vlookup` in Excel --- it says \"read this array, `model` in this case, in which the values *i* are like 0, 1, ... n, and give me the *i*th element from this other array, `rocks` in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rocks = np.array([[2700, 2750],  # Vp, rho\n",
    "                  [2400, 2450],\n",
    "                  [2800, 3000]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Edit:** I was using `np.take` here, but ['fancy indexing'](http://docs.scipy.org/doc/numpy/user/basics.indexing.html) is shorter and more intuitive. We are just going to index `rocks` using the integers in `model`. That is, if `model` has a `1`, we take the second element, `[2400, 2450]`, from `rocks`. We'll end up with an array containing the rocks corresponding to each element of `earth`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "earth = rocks[model]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now apply `np.product` to those Vp-rho pairs to get impedance at every sample.\n",
    "\n",
    "This might look a bit magical, but we're just telling Python to apply the function `product()` to every set of numbers it encounters on the last axis (index `-1`). The array `earth` has shape (100, 40, 2), so you can think of it as a 100 row x 40 column 'section' in which each 'sample' is occupied by a Vp-rho pair. That pair is in the last axis. So product, which just takes a bunch of numbers and multiplies them, will return the impedance (the product of Vp and rho) at each sample location. We'll end up with a new 100 x 40 'section' with impedance at every sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "imp = np.apply_along_axis(np.product, -1, earth)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could have saved a step by taking from `np.product(rocks, axis=1)` but I like the elegance of having an earth model with a set of rock properties at each sample location. That's how I think about the earth --- and it's similar to the concept of a geocellular model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model seismic reflections\n",
    "\n",
    "Now we have an earth model — giving us acoustic impedance everywhere in this 2D grid — we define a function to compute reflection coefficients for every trace.\n",
    "\n",
    "I love this indexing trick though I admit it looks weird the first time you see it. It's easier to appreciate for a 1D array. Let's look at the differences:\n",
    "\n",
    "    >>> a = np.array([1,1,1,2,2,2,3,3,3])\n",
    "    >>> a[1:] - a[:-1]\n",
    "    array([0, 0, 1, 0, 0, 1, 0, 0])\n",
    "\n",
    "This is equivalent to:\n",
    "\n",
    "    >>> np.diff(a, axis=0)\n",
    "    \n",
    "But I prefer to spell it out so it's analogous to the sum on the denominator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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f7+7uks/nmZmZIZ/P+9J9rtC+mI76pP0F4Jpz7l+aWQxIAZ8BXnTOfd7MngY+DTxzSu0U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\noS0iEiIKbRGREFFoi4iEyP8Hut1Zi7YrJlsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f42fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rc =  (imp[1:,:] - imp[:-1,:]) / (imp[1:,:] + imp[:-1,:])\n",
    "\n",
    "plt.imshow(rc, cmap='Greys', aspect=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use a wavelet function from [`bruges`](https://github.com/agile-geoscience/bruges). This is not cheating! Well, I don't think it is... we could use `scipy.signal.ricker` but I can't figure out how to convert frequency into the 'width' parameter that function wants. Using the Ricker from `bruges` keeps things a bit simpler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import bruges\n",
    "\n",
    "w = bruges.filters.ricker(duration=0.100, dt=0.001, f=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make sure it looks OK:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UHkkUxwtXx47Qpw+sXh3PDm7wgw9+8xvfQfzii3DEEVGXSMKmmoG0ybHHwvvvw7x5MH58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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106d0ec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(w)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now one more application of `apply_along_axis`. We could use a loop to step over the traces, but the rule of thumb in Python is \"if you are using a loop, you're doing it wrong.\". So, we'll use `apply_along_axis`.\n",
    "\n",
    "It looks a bit more complicated this time, because we can't just pass a function like we did with `product` before. We want to pass in some more things, not just the trace that `apply_along_axis` is going to send it. So we use Python's 'unnamed function creator', `lambda` (in keeping with all things called `lambda`, it's a bad name that no-one can quite explain)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4onfp4VxCHllHLoV8apulCU9LyL2xKI1Lz7BZjrzy9re/HaWUKw7uOu2FKH+R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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111932e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "synth = np.apply_along_axis(lambda t: np.convolve(t, w, mode='same'),\n",
    "                            axis=0,\n",
    "                            arr=rc)\n",
    "\n",
    "plt.imshow(synth, cmap=\"Greys\", aspect=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "That's it! And it only needed 9 lines of Python! Not incldung boring old imports and plotting stuff.\n",
    "\n",
    "Here they are so you can count them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "length, depth = 40, 100\n",
    "model = 1 + np.tri(depth, length, -depth//3)\n",
    "model[:depth//3,:] = 0\n",
    "rocks = np.array([[2700, 2750], [2400, 2450], [2800, 3000]])\n",
    "earth = np.take(rocks, model.astype(int), axis=0)\n",
    "imp = np.apply_along_axis(np.product, -1, earth)\n",
    "rc =  (imp[1:,:] - imp[:-1,:]) / (imp[1:,:] + imp[:-1,:])\n",
    "w = bruges.filters.ricker(duration=0.100, dt=0.001, f=40)\n",
    "synth = np.apply_along_axis(lambda t: np.convolve(t, w, mode='same'), axis=0, arr=rc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr />\n",
    "\n",
    "<div>\n",
    "<img src=\"https://avatars1.githubusercontent.com/u/1692321?s=50\"><p style=\"text-align:center\">© Agile Geoscience 2016</p>\n",
    "</div>"
   ]
  }
 ],
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