1504_Seismic_petrophysics_1/Seismic_petrophysics_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Seismic petrophysics, part 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to create a synthetic dataset of elastic properties (Vp, Vs, density, etc.) starting from well logs. The idea is that the wells cannot possibly sample all the complexity and variations occurring across a reservoir. So what I do is to use various techniques to synthesize new data and create an _abstraction_ of my reservoir to investigate alternative and plausible scenarios (change of pore fluids; lithological variations) or create a training dataset to calibrate 3D seismic volumes. I think this would make sense if you are a geoscientist working in the oil industry with a keen interest in quantitative studies (at least for the terminology and the basic concepts I use here). \n",
    "\n",
    "What I also want to do is to demonstrate the use of Python to build your own tools and workflows and therefore move away from a \"[black-box](http://en.wikipedia.org/wiki/Black_box) approach\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The plan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea is to show how to do these things:\n",
    "\n",
    "* import well log data and create a new lithology curve log;\n",
    "* data augmentation through fluid-replacement modeling; \n",
    "* description of the reservoir complex under study through statistical analysis;\n",
    "* creation of a synthetic dataset to replicate the overall behaviour of the reservoir complex.\n",
    "\n",
    "And while doing this, I will also show some cool features of Python, using the Pandas library to explore geophysical data, defining evergreen functions like Gassmann and Voigt-Reuss-Hill, fancy plots, interactive tools, and all that jazz."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading (and massaging) well data in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The well log I will use is part of the test datasets available on the Quantitative Seismic Interpretation book website:\n",
    "\n",
    "<https://pangea.stanford.edu/researchgroups/srb/resources/books/quantitative-seismic-interpretation>\n",
    "\n",
    "In particular, I use \"Well 2\", contained in the \"Project Data\" zipfile. Plenty of background information for this particular well is available on Per Avseth's PhD thesis, again available from the Stanford website:\n",
    "\n",
    "<https://pangea.stanford.edu/researchgroups/srb/resources/theses>\n",
    "\n",
    "The actual file I will load now, `qsiwell2.csv` is an elaboration of several other files contained in that zip archive (merged some logs, created others, etc.)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now a few words on the libraries I am using:\n",
    "\n",
    "* numpy\n",
    "* matplotlib\n",
    "* pandas\n",
    "\n",
    "I use [Pandas](http://pandas.pydata.org/index.html) to digest log data; it's a library built to handle big datasets and make your life easier (as we shall see later). This is *my* way to do things. You are welcome to use Python's built-in structures if you're inclined to do so or need to keep things minimal (Matt and Evan at [Agile Geoscience](http://www.agilegeoscience.com) do [wonderful things](https://github.com/agile-geoscience/notebooks) relying on the standard triumvirate numpy/scipy/matplotlib).\n",
    "\n",
    "For those interested in using their own `.las` files, there is another library (<http://wiki.scipy.org/Cookbook/LASReader>) that can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is how I load `qsiwell2.csv` into a Pandas _DataFrame_ (that I will call `logs`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "logs = pd.read_csv('qsiwell2.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and to check what's now inside `L`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([u'DEPTH', u'VP', u'VS', u'RHO_OLD', u'GR', u'NPHI', u'RHO', u'SW', u'SWX', u'VPVS', u'IP', u'IS', u'VSH', u'RHOm', u'RHOf', u'PHI'], dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logs.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, I have all the required logs for a quantitative analysis: the elastic logs (compressional and shear velocity `Vp` and `Vs`, density `RHO`) as well as the main petrophysical logs (water saturation `Sw`, shale volume `VSH` and porosity `PHI`).\n",
    "\n",
    "Logs stored into a Pandas DataFrame are easily accessed using the syntax `DataFrame.log`, e.g. `L.VP` is the P-wave velocity log and `L.PHI` the porosity log.\n",
    "\n",
    "To select more than one log, use the syntax `DataFrame.[['log1','log2']]`; an alternative is `DataFrame.ix[':',['log1','log2']]` which means selecting all the rows (indicated by `:`) of `log1` and `log2`. This second syntax allows to all kind of crazy selections and filtering like:\n",
    "\n",
    "* `DataFrame.ix[(DataFrame.Z>=top) & (DataFrame.Z<=bottom)]`: to make a selection on the basis of the Z log (e.g., a depth curve), i.e. to perform a selection on the depth window `top`-`bottom`;\n",
    "* `DataFrame.ix[DataFrame.class==4,['log1','log2']]`: to get `log1` and `log2` when `class` is 4 (assuming that `class` is a [categorical variable](http://en.wikipedia.org/wiki/Categorical_variable), for example a litho-facies log like the `LFC` log I have created earlier);\n",
    "* `DataFrame[pd.notnull(DataFrame.log0)].ix[:,'log1','log2']`: to get `log1` and `log2` only when `log0` is not empty.\n",
    "\n",
    "If I want to remove a specific log (e.g., that `RHO_OLD`) I use the `drop` method with the optional `axis=1` (required otherwise Pandas will search for a _row_ named `TVD` instead of a _column_; ys, Pandas allows):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "logs = logs.drop(['RHO_OLD'], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check if I have really deleted `RHO_OLD`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([u'DEPTH', u'VP', u'VS', u'GR', u'NPHI', u'RHO', u'SW', u'SWX', u'VPVS', u'IP', u'IS', u'VSH', u'RHOm', u'RHOf', u'PHI'], dtype='object')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logs.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To rename a log use the `.rename` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "logs.rename(columns={'RHOf': 'RHOfluid'}, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But what if I need to rename multiple logs? Simply assign a new list of names to the DataFrame columns; for example, if I have a 3 logs called `log1`, `log2`, `log3`, I can rename them all in one go using this syntax:\n",
    "\n",
    "    DataFrame.columns=['newlog1','newlog2','newlog3']\n",
    "    \n",
    "Some other useful functions of Pandas are `DataFrame.describe()`, `DataFrame.log.`.\n",
    "\n",
    "What's great about Pandas however is that it simply is the best way I have ever seen to manage large and complex datasets;  the basic Dataframe is a compact, portable and powerful data structure that allows you to quickly inspect your data, either using standard Python functions (like `min()`, `.max()`, `.mean()`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('min', 2013.2528)\n",
      "('max', 2640.5311999999999)\n",
      "('avg', 2977.0987612339309)\n"
     ]
    }
   ],
   "source": [
    "print(\"min\", logs.DEPTH.min())\n",
    "print(\"max\", logs.DEPTH.max())\n",
    "print(\"avg\", logs.VP.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...or something incredibly useful like the `describe` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VP</th>\n",
       "      <th>VS</th>\n",
       "      <th>RHO</th>\n",
       "      <th>PHI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4117.000000</td>\n",
       "      <td>4117.000000</td>\n",
       "      <td>2701.000000</td>\n",
       "      <td>2701.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2977.098761</td>\n",
       "      <td>1371.293952</td>\n",
       "      <td>2.225045</td>\n",
       "      <td>0.291759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>449.355552</td>\n",
       "      <td>297.056552</td>\n",
       "      <td>0.061961</td>\n",
       "      <td>0.032196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1439.900000</td>\n",
       "      <td>688.800000</td>\n",
       "      <td>2.036616</td>\n",
       "      <td>0.106844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2594.500000</td>\n",
       "      <td>1141.600000</td>\n",
       "      <td>2.185285</td>\n",
       "      <td>0.276218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3036.100000</td>\n",
       "      <td>1415.300000</td>\n",
       "      <td>2.223544</td>\n",
       "      <td>0.297311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3251.100000</td>\n",
       "      <td>1595.000000</td>\n",
       "      <td>2.264000</td>\n",
       "      <td>0.310519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4431.000000</td>\n",
       "      <td>2427.800000</td>\n",
       "      <td>2.545268</td>\n",
       "      <td>0.376396</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                VP           VS          RHO          PHI\n",
       "count  4117.000000  4117.000000  2701.000000  2701.000000\n",
       "mean   2977.098761  1371.293952     2.225045     0.291759\n",
       "std     449.355552   297.056552     0.061961     0.032196\n",
       "min    1439.900000   688.800000     2.036616     0.106844\n",
       "25%    2594.500000  1141.600000     2.185285     0.276218\n",
       "50%    3036.100000  1415.300000     2.223544     0.297311\n",
       "75%    3251.100000  1595.000000     2.264000     0.310519\n",
       "max    4431.000000  2427.800000     2.545268     0.376396"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logs[['VP','VS','RHO','PHI']].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculation of litho-facies log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to calculate a facies log, where by facies I mean a group of data identified not just by similar lithological properties but through a combination of properties such as lithology and pore fluids; for example brine sand and oil sand will be different facies. For this reason I like to use the term _Litho-Fluid Classes_ -- this is why my facies log will be called LFC:\n",
    "\n",
    "* LFC=0: undef\n",
    "* LFC=1: brine sand\n",
    "* LFC=2: oil sand\n",
    "* LFC=3: gas sand\n",
    "* LFC=4: shale\n",
    "\n",
    "First I restrict my analysis on a smaller depth window because the petrophysical logs are not computed everywhere. Tthen I create \"flag\" logs (i.e., logs made of samples that can only be 1 or 0, i.e. _True_ or _False_) using cut-off values on `VSH` (shale volume) and `SW` (water saturation): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "logs = logs.ix[(logs.DEPTH>=2100) & (logs.DEPTH<=2400)]\n",
    "\n",
    "sand_cutoff = 0.20\n",
    "brine_sand = ((logs.VSH <= sand_cutoff) & (logs.SW >= 0.9))\n",
    "oil_sand = ((logs.VSH <= sand_cutoff) & (logs.SW < 0.9))\n",
    "shale = (logs.VSH > sand_cutoff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that there is no `gas_sand` log (occurrence of gas sands) yet, as the insitu log did not record any gas sand. We will deal with that later.\n",
    "\n",
    "I use the above flag logs to create the `LFC` log and store it into the `logs` DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "temp_lfc = np.zeros(np.shape(logs.VSH))\n",
    "temp_lfc[brine_sand.values] = 1    # LFC will be 1 when ssb (brine sand flag) is True\n",
    "temp_lfc[oil_sand.values] = 2      # LFC will be 2 when sso (oil sand flag) is True\n",
    "temp_lfc[shale.values] = 4         # LFC will be 4 when sh (shale flag) is True\n",
    "logs['LFC'] = temp_lfc             # Copy the temporary log temp_lfc into the DataFrame with name `LFC`\n",
    "\n",
    "logs.to_csv('qsiwell2_lfc.csv',index=False) # save the data for use in Part 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's see if this is all ok; the total number of samples after zooming in the 2100-2400 m depth window is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1968,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(logs.VSH)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the following prints out how many samples each facies is made of:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "brine sst=706, oil sst=134, shale=1128\n"
     ]
    }
   ],
   "source": [
    "string = \"brine sst={0}, oil sst={1}, shale={2}\"\n",
    "data = (np.count_nonzero(brine_sand),\n",
    "        np.count_nonzero(oil_sand),\n",
    "        np.count_nonzero(shale))\n",
    "print(string.format(*data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a final check to make this newly defined `LFC` log only has values within the range 1 to 4 (there will be no undefined samples in this particular depth interval, i.e. classes with `LFC=0`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LFC min: 1.0, LFC max: 4.0\n"
     ]
    }
   ],
   "source": [
    "print(\"LFC min: {0}, LFC max: {1}\".format(logs.LFC.min(), logs.LFC.max()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is very easy to do plots of all types with `pandas`, and to show that here's a one-liner that plots $V_\\mathrm{P}$ histograms for each class (remember that at this point we only have classes 1, 2 and 4, i.e. brine sand, oil sand and shales):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
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       "co5OubT3KbOkbmdzyZFZO5tNlpylaldyac8SthmVlJuqTai63FT7e8p2ZtTjt7F2BM3MJo2k04AX\n",
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       "zMzMzMysYf4/VgH3qPEn4JYAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x55a4990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logs.IP.hist(bins=50, color='black', by=logs.LFC, figsize=(15,2), layout=(1,3), lw=0)\n",
    "#plt.savefig(\"histograms.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First I need a custom colormap for my classes, i.e. a discrete colormap with following classes-colors association:\n",
    "\n",
    "* LFC=0: undef, GRAY\n",
    "* LFC=1: brine sand, BLUE\n",
    "* LFC=2: oil sand, GREEN\n",
    "* LFC=3: gas sand, RED\n",
    "* LFC=4: shale, BROWN\n",
    "\n",
    "This is the way to define this colormap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.colors as colors\n",
    "#      0=undef   1=bri  2=oil   3=gas 4=shale\n",
    "ccc = ['#B3B3B3','blue','green','red','#996633',]\n",
    "cmap_facies = colors.ListedColormap(ccc[0:len(ccc)], 'indexed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now display a summary view of all the logs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "IpFIJDqc/wfMWj+WaUKvbgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5ba7b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ztop=2100; zbot=2400\n",
    "ll=logs.ix[(logs.DEPTH>=ztop) & (logs.DEPTH<=zbot)]\n",
    "\n",
    "cluster=np.repeat(np.expand_dims(ll['LFC'].values,1), 100, 1)\n",
    "\n",
    "f, ax = plt.subplots(nrows=1, ncols=4, figsize=(8, 12))\n",
    "ax[0].plot(ll.VSH, ll.DEPTH, '-g', label='Vsh')\n",
    "ax[0].plot(ll.SW, ll.DEPTH, '-b', label='Sw')\n",
    "ax[0].plot(ll.PHI, ll.DEPTH, '-k', label='phi')\n",
    "ax[1].plot(ll.IP, ll.DEPTH, '-', color='0.5')\n",
    "ax[2].plot(ll.VPVS, ll.DEPTH, '-', color='0.5')\n",
    "im=ax[3].imshow(cluster, interpolation='none', aspect='auto',cmap=cmap_facies,vmin=0,vmax=4)\n",
    "\n",
    "cbar=plt.colorbar(im, ax=ax[3])\n",
    "# cbar.set_label('0=undef,1=brine,2=oil,3=gas,4=shale')\n",
    "# cbar.set_ticks(range(0,4+1)); cbar.set_ticklabels(range(0,4+1))\n",
    "cbar.set_label((12*' ').join(['undef', 'brine', 'oil', 'gas', 'shale']))\n",
    "cbar.set_ticks(range(0,1)); cbar.set_ticklabels('')\n",
    "\n",
    "for i in range(len(ax)-1):\n",
    "    ax[i].set_ylim(ztop,zbot)\n",
    "    ax[i].invert_yaxis()\n",
    "    ax[i].grid()\n",
    "    ax[i].locator_params(axis='x', nbins=4)\n",
    "ax[0].legend(fontsize='small', loc='lower right')\n",
    "ax[0].set_xlabel(\"Vcl/phi/Sw\"),    ax[0].set_xlim(-.1,1.1)\n",
    "ax[1].set_xlabel(\"Ip [m/s*g/cc]\"), ax[1].set_xlim(3000,9000)\n",
    "ax[2].set_xlabel(\"Vp/Vs\"),         ax[2].set_xlim(1.5,3)\n",
    "ax[3].set_xlabel('LFC')\n",
    "ax[1].set_yticklabels([]); ax[2].set_yticklabels([]); ax[3].set_yticklabels([]); ax[3].set_xticklabels([])\n",
    "\n",
    "#plt.savefig(\"log.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see the same data in crossplot domain that should be familiar to geophysicists, i.e. acoustic impedance (Ip) versus Vp/Vs ratio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "iuLUCjAZeFFVt6lqCnga+ATFq3efyZvxFJGAiMwFmoEnVXUesJ+qNntNmoH9vPcHACuyTl8BjO1l\n",
       "/0pvf6HxM+AqIJ21r1i1AijwhIjEReQSb18x6p0ArBORu0TkFRG5XUSqKU6tPfkUcJ/3vuj0qupG\n",
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       "q+w8GgOKR2sWH1DVY4FzgMtE5JTsg0WktwSYBtyqqtOAduA/shsUkdbtiEgZMAN4sOexYtErIhOB\n",
       "r+OmJA8AakTkc9ltikUrgKq+DfwEmA08ipuSTfVoUzR6+4O8R9t601yPANOBZhHZH8Ab/q/1mq3E\n",
       "+VYyjMM93az03mfvXznQfe4jJwEXiMh7uCf1D4nIvRSnVgBUdbX3cx3w38BxFKfeFcAKVZ3jbT+E\n",
       "M6ZrilBrNucAL3v3F4rz3jYCz6nqBlVNAn8CTqSI762q3qmqjap6Ks6N9i7FeW/7hXxF247MRG2J\n",
       "SCVwFvAq8DDOKY/383+89w8DnxKRMhGZABwGvKSqa4DNXoSjAJ/POqcgUNVvq+qBqjoBN9X1d1X9\n",
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       "p4nIMyLyF6948G1e+jLDMIYgZjwNY/B4P/BVXCHhibj8oYZhDEHMeBrG4PGSqi5R1TQusfrJ+e6Q\n",
       "YRh7hxlPwxg8sv2fgvlDDWPIYsbTMAaP40RkvIgEgIuAZ/PdIcMw9g4znoYxsGSPLucAv8DVhVxM\n",
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       "iBlPwzAMw+gjZjwNwzAMo4+Y8TQMwzCMPmLG0zAMwzD6iBlPwzAMw+gj/wd2BdUavD9xrQAAAABJ\n",
       "RU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x597dd70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "\n",
    "plt.scatter(logs.IP, logs.VPVS,20, c=logs.LFC,\n",
    "            marker='o', edgecolors='none',\n",
    "            alpha=0.7, cmap=cmap_facies,\n",
    "            vmin=0, vmax=4)\n",
    "plt.xlim(3000, 9000); plt.ylim(1.5, 3);\n",
    "plt.xlabel('Ip'); plt.ylabel('Vp/Vs')\n",
    "plt.grid();\n",
    "\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label((15*' ').join(['undef', 'brine', 'oil', 'gas', 'shale']))\n",
    "cbar.set_ticks(range(0,1)); cbar.set_ticklabels('')\n",
    "\n",
    "#plt.savefig(\"crossplot.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The colors are the same as above; but what about that red color? Well, that points to gas sands -- but so far we don't have gas sands in here. In the next tutorial, I will show how to synthesize gas sands and create an additional _gas sand_ class. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Avseth, P., Mukerji, T. & Mavko, G. Quantitative Seismic Interpretation. (Cambridge University Press, 2005).\n",
    "\n",
    "\n",
    "See also the awesome collection of tutorials curated by Matt Hall for [The Leading Edge](http://library.seg.org/journal/leedff) and available here: <https://github.com/seg/tutorials>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr />\n",
    "<p style=\"color:gray\">©2015 Alessandro Amato del Monte, openly licensed under the terms of <a href=\"https://creativecommons.org/licenses/by-sa/4.0/\">CC-BY-SA</a>. This tutorial appeared in SEG Leading Edge in April 2015. </p>"
   ]
  }
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