{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### x lines of Python\n", "# Amplitude-vs-offset plot\n", "\n", "This notebook accompanies [a blog post at Agile*](http://ageo.co/xlines03).\n", "\n", "In the first **x lines** we made a 2D synthetic seismogram. A major simplification in that model was normal incidence at 0 degrees of offset: the ray of seismic energy was assumed to be perfectly vertical. In this notebook, we'll model non-vertical incidence.\n", "\n", "When the reflection is not perpendicular to the geological interface, we have to use the Zoeppritz equation, or simplications of it, to model the angle-dependent reflectivity. Agile's library [`bruges`](http://github.com/agile-geoscience/bruges) (Bag of Really Useful Geophysical Equations and Stuff) has lots of different reflectivity formulations to compare; we'll look at three.\n", "\n", "The data is from Blangy, JP, 1994, AVO in tranversely isotropic media—An overview. *Geophysics* **59** (5), 775–781. Blangy conveniently defined his model rocks very fully and clearly (take not would-be authors!). Related blog post: [The Blangy equation](http://www.agilegeoscience.com/blog/2014/8/7/the-blangy-equation.html?rq=blangy)\n", "\n", "Before we start, the usual prelims:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll initiate some variables with some of Blangy's test data: the Type 3 AVO rocks from his Table 1. We only need the acoustic properties at first, but we'll define the elastic and anisotropic parameters as well, just in case we need them later (we will!)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Upper layer: shale.\n", "vp0, vs0, ρ0, δ0, ε0 = 2307, 1108, 2150, 0.15, 0.30 # Line 1\n", "\n", "# Lower layer: wet sand.\n", "vp1, vs1, ρ1, δ1, ε1 = 1951, 930, 2200, 0.00, 0.00 # Line 2\n", "\n", "# Lower layer: gas sand.\n", "vp1g, vs1g, ρ1g, δ1g, ε1g = 1951, 1301, 1950, 0.00, 0.00 # Line 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For peace of mind, or just for fun, we can make a plot of these properties. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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uvQHLPrAMXZnauSlhVsgfVniPNAPZONGhlDA8d0gpZ3QDcCWAvQBeBqADuC7G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\nlwzSf0I/Y/vHKB4pklmU0TzeUt3gIPT3+4HUikX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 3))\n", "\n", "z = np.arange(0, 20)\n", "\n", "ax0 = fig.add_subplot(1, 3, 1)\n", "ax0.plot(np.append(np.repeat(vp0, 10), np.repeat(vp1, 10)), z, 'ob', markeredgecolor='none')\n", "ax0.plot(np.append(np.repeat(vp0, 10), np.repeat(vp1g, 10)), z, 'ob', alpha=0.4, markeredgecolor='none')\n", "ax0.set_xlim(1900, 2400)\n", "ax0.axhline(9.5, c='k')\n", "ax0.invert_yaxis()\n", "ax0.set_title('Vp')\n", "ax0.text(2000, 5, 'SHALE')\n", "ax0.text(2200, 15, 'SANDSTONE')\n", "ax0.text(1980, 13, 'wet')\n", "ax0.text(1980, 17, 'gas', alpha=0.4)\n", "\n", "ax1 = fig.add_subplot(1, 3, 2)\n", "ax1.plot(np.append(np.repeat(vs0, 10), np.repeat(vs1, 10)), z, 'og', markeredgecolor='none')\n", "ax1.plot(np.append(np.repeat(vs0, 10), np.repeat(vs1g, 10)), z, 'og', alpha=0.4, markeredgecolor='none')\n", "ax1.set_xlim(850, 1350)\n", "ax1.axhline(9.5, c='k')\n", "ax1.invert_yaxis()\n", "ax1.set_title('Vs')\n", "ax1.text(950, 5, 'SHALE')\n", "ax1.text(1050, 15, 'SANDSTONE')\n", "ax1.text(950, 13, 'wet')\n", "ax1.text(1220, 17, 'gas', alpha=0.4)\n", "\n", "ax2 = fig.add_subplot(1, 3, 3)\n", "ax2.plot(np.append(np.repeat(ρ0, 10), np.repeat(ρ1, 10)), z, 'or', markeredgecolor='none')\n", "ax2.plot(np.append(np.repeat(ρ0, 10), np.repeat(ρ1g, 10)), z, 'or', alpha=0.4, markeredgecolor='none')\n", "ax2.set_xlim(1800, 2500)\n", "ax2.axhline(9.5, c='k')\n", "ax2.invert_yaxis()\n", "ax2.set_title('rho')\n", "ax2.text(1900, 5, 'SHALE')\n", "ax2.text(2250, 15, 'SANDSTONE')\n", "ax2.text(2100, 13, 'wet')\n", "ax2.text(2000, 17, 'gas', alpha=0.4)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Shuey equation\n", "\n", "Let's start with a bit of maths — [the 2-term Shuey approximation](http://subsurfwiki.org/wiki/Shuey_equation). I'm using the formulation given by Avesth, P, T Mukerji and G Mavko (2005). *Quantitative seismic interpretation.* Cambridge University Press, Cambridge, UK. \n", "\n", "$$R(\\theta) \\approx R(0) + G \\sin^2 \\theta$$\n", "\n", "where\n", "\n", "$$R(0) = \\frac{1}{2} \\left( \\frac{\\Delta V_\\mathrm{P}}{V_\\mathrm{P}} + \\frac{\\Delta \\rho}{\\rho} \\right)$$\n", "\n", "and\n", "\n", "$$G = \\frac{1}{2} \\frac{\\Delta V_\\mathrm{P}}{V_\\mathrm{P}} - 2 \\frac{V^2_\\mathrm{S}}{V^2_\\mathrm{P}} \\left( \\frac{\\Delta \\rho}{\\rho} + 2 \\frac{\\Delta V_\\mathrm{S}}{V_\\mathrm{S}} \\right)$$\n", "\n", "In these equations, $\\Delta V_\\mathrm{P}$ means the difference in the velocity of the two layers, and $V_\\mathrm{P}$ means the mean of the two layers. Let's make a function to help with this 'difference over mean':" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# I'm on a tight line budget so I'm defining a function on a\n", "# single line. Don't do this, it makes your code less readable.\n", "def dom(upper, lower): return np.subtract(lower, upper) / np.mean((lower, upper))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First term:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "R0 = 0.5 * (dom(vp0, vp1) + dom(ρ0, ρ1))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.072113074510185018" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, that looks reasonable, but the second term $G$ is going to take some really fiddly math... and I'm on a budget, I don't have enough lines for all that. Besides, I might easily make a mistake.\n", "\n", "Luckily, our library `bruges` has all these equations. There's a `bruges.reflection.shuey2` function that returns the 2-term Shuey reflectivity for a given interface and angle range." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import bruges" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# I have to use 31 because `arange()` goes up to but not including.\n", "θ = range(0, 31) # Line 4\n", "\n", "shuey = bruges.reflection.shuey2(vp0, vs0, ρ0, # Line 5\n", " vp1, vs1, ρ1,\n", " θ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I now have an array of the reflection coefficients corresponding to the angles I passed in (0 to 40 degrees of offset)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.07211307, -0.07209299, -0.07203278, -0.0719325 , -0.07179227,\n", " -0.07161228, -0.07139274, -0.07113391, -0.07083612, -0.07049972,\n", " -0.07012512, -0.06971278, -0.06926321, -0.06877695, -0.06825459,\n", " -0.06769678, -0.06710418, -0.06647752, -0.06581757, -0.06512512,\n", " -0.06440103, -0.06364618, -0.06286148, -0.06204788, -0.06120639,\n", " -0.06033803, -0.05944385, -0.05852495, -0.05758244, -0.05661747,\n", " -0.05563122])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shuey" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "shuey_g = bruges.reflection.shuey2(vp0, vs0, ρ0, # Line 6\n", " vp1g, vs1g, ρ1g,\n", " θ)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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bv23rVj82JBhEXnoJ7r/f72vRwtcNBpGBA/20XhGRCFHoEDmYNW0Kxx3nS9D6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\ngQP3vf7www+dmbkXXnghrN7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(shuey, label='Brine case') # Line 7\n", "plt.plot(shuey_g, 'red', label='Gas case') # Line 8\n", "plt.legend(loc='best'); # Line 9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's the 10 lines of Python used up, but we already got a useful plot. \n", "\n", "Weith a few more lines, we can make the plot a bit prettier." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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WGrn719I9oJn9FLiilSYODGvtEKQ/VyduH3e/IWbb62bWHfgB8MvWDjJ58mR6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\ncvr1ayq77x5Cn0KPiHQSKV9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axhline(0, color='k', alpha=0.3)\n", "plt.plot(θ, shuey, 'b', lw=2, label='Brine case')\n", "plt.plot(θ, shuey_g, 'r', lw=2, label='Gas case')\n", "plt.axhline(0, color='k', alpha=0.4)\n", "plt.ylim(-0.25, 0.1)\n", "plt.xlabel('theta [deg]')\n", "plt.ylabel('reflectivity [unitless]')\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare to Zoeppritz and Aki-Richards\n", "\n", "We could also replace that 2-term Shuey evaluation with another algorithm. For example, let's compute the Aki-Richards approximation and the full Zoeppritz solution, and compare the three results. \n", "\n", "First, we'll make a wider angle range, so we can compare them outside the reliability 'window' of Shuey's approximation (up to about 25 degrees or so for most interfaces)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "θ = np.arange(0, 51)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "shuey = bruges.reflection.shuey2(vp0, vs0, ρ0,\n", " vp1, vs1, ρ1,\n", " θ)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "zoeppritz = bruges.reflection.zoeppritz_rpp(vp0, vs0, ρ0,\n", " vp1, vs1, ρ1,\n", " θ)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "akirichards = bruges.reflection.akirichards(vp0, vs0, ρ0,\n", " vp1, vs1, ρ1,\n", " θ)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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/9u7d6/c6MzOT119/Pef10aNHeeONN2jQoEG+/xzvvfceBw8eW11j5syZ7Nix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\niIhIxFKQERERkYilICMiIiIR6/8AXOXH3Pz1VD4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(shuey, label='Shuey')\n", "plt.plot(zoeppritz, 'r', lw=2, label='Zoeppritz')\n", "plt.plot(akirichards, label='Aki-Richards')\n", "plt.axhline(0, color='k', alpha=0.4)\n", "plt.xlabel('theta [deg]')\n", "plt.ylabel('reflectivity [unitless]')\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see how Shuey breaks down at about 25 degrees, whereas Aki-Richards is quite reliable even to wide offsets. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Isotropic and anisotropic approximations\n", "\n", "We can go further still. Blangy's paper gives us an AVO approximation for weakly anisotropic rocks. We can use another `bruges` function to compute that response. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# The function returns the isotropic and the anisotropic reponses.\n", "# Since we don't need the isotropic response (it's the same as the\n", "# Aki-Richards solution), we can assign it to _, a sort of throwaway.\n", "_, blangy = bruges.rockphysics.blangy(vp0, vs0, ρ0, δ0, ε0,\n", " vp1, vs1, ρ1, δ1, ε1,\n", " θ)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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C8/wVzrnvgdW+/gD6AwY0M7MlZvazmb1oZk0r+wuIiIhI5Qll6GgEbAiscM4VApt8+0o6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\ndcyaNYuhQ4ce8uf7tWnThpkzZxIVFcW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(akirichards, label='Aki-Richards')\n", "plt.plot(blangy, label='Blangy')\n", "plt.axhline(0, color='k', alpha=0.4)\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "

© Agile Geoscience 2016

\n", "
" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 1 }