From e14ab8c5d51938145705cfc67b5b54efd6d35c03 Mon Sep 17 00:00:00 2001 From: Rui Gong <41764570+gong1999@users.noreply.github.com> Date: Wed, 29 Jan 2025 13:42:45 +0800 Subject: [PATCH] Delete book/tccs/group/group.ipynb --- book/tccs/group/group.ipynb | 2333 ----------------------------------- 1 file changed, 2333 deletions(-) delete mode 100644 book/tccs/group/group.ipynb diff --git a/book/tccs/group/group.ipynb b/book/tccs/group/group.ipynb deleted file mode 100644 index 4ab057504..000000000 --- a/book/tccs/group/group.ipynb +++ /dev/null @@ -1,2333 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "d466ed72", - "metadata": {}, - "source": [ - "# On anelliptic approximations for qP velocities in VTI mediaa\n", - "\n", - "aPublished in Geophysical Prospecting, 52, 247-259, (2004)" - ] - }, - { - "cell_type": "markdown", - "id": "fa8db094", - "metadata": {}, - "source": [ - "## Sergey Fomel1\n", - "\n", - "1Bureau of Economic Geology, The University of Texas, Austin, University Station, Box X, Austin, TX 78713-8972, USA" - ] - }, - { - "cell_type": "markdown", - "id": "ad51b985", - "metadata": {}, - "source": [ - "## ABSTRACT" - ] - }, - { - "cell_type": "markdown", - "id": "d211b97d", - "metadata": {}, - "source": [ - "A unified approach to approximating phase and group velocities of qP seismic waves\n", - "in a transversely isotropic medium with vertical axis of symmetry (VTI) is developed.\n", - "While the exact phase-velocity expressions involve four independent parameters to\n", - "characterize the elastic medium, the proposed approximate expressions use only three\n", - "parameters. This makes them more convenient for use in surface seismic experiments,\n", - "where the estimation of all four parameters is problematic. The three-parameter phase-velocity approximation coincides with the previously published ‘acoustic’ approximation of Alkhalifah. The group-velocity approximation is new and noticeably more\n", - "accurate than some of the previously published approximations. An application of\n", - "the group-velocity approximation for finite-difference computation of traveltimes is\n", - "shown." - ] - }, - { - "cell_type": "markdown", - "id": "5deed67c", - "metadata": {}, - "source": [ - "## INTRODUCTION" - ] - }, - { - "cell_type": "markdown", - "id": "c6239b4c", - "metadata": {}, - "source": [ - "Anellipticity (deviation from ellipse) is an important characteristic of\n", - "elastic wave propagation. One of the simplest and yet practically important\n", - "cases of anellipticity occurs in transversally isotropic media with\n", - "the vertical axis of symmetry (VTI). In this type of media, the phase\n", - "velocities of $qSH$ waves and the corresponding wavefronts are elliptic, while\n", - "the phase and group velocities of $qP$ and $qSV$ waves may exhibit strong\n", - "anellipticity ([Tsvankin 2001][tsvankin]).\n", - "\n", - "The exact expressions for the phase velocities of $qP$ and $qSV$ waves in VTI\n", - "media involve four independent parameters. However, it has been observed that\n", - "only three parameters influence wave propagation \n", - "and are of interest to surface seismic methods ([Alkhalifah and Tsvankin 1995][Alkhalifah1995]). Moreover, the exact expressions for the group\n", - "velocities in terms of the group angle are difficult to obtain and too\n", - "cumbersome for practical use. This explains the need for developing practical\n", - "three-parameter approximations for both group and phase velocities in VTI\n", - "media.\n", - "\n", - "Numerous different successful approximations have been previously developed ([Byun, Corrigan and Gaiser 1989][Byun1989]; [Dellinger, Muir\n", - "and Karrenbach 1993][Dellinger1993]; [Alkhalifah and Tsvankin 1995][Alkhalifah1995]; Alkhalifah [1998][Alkhalifah1998], [2000b][Alkhalifah2000b]; [Schoenberg and de Hoop 2000][Schoenberg2000]; [Stopin 2001][Stopin2001];\n", - "[Zhang and Uren 2001][Zhang2001]). A comparative review of different VTI approximations is provided by [Fowler (2003)][fowler]. In this paper, I attempt to construct a unified approach for deriving\n", - "anelliptic approximations.\n", - "\n", - "The starting point is the anelliptic approximation of Muir\n", - "([Muir and Dellinger 1985][Muir.sep.44.55]; [Dellinger et al. 1993][Dellinger1993]). Although not the most accurate for immediate\n", - "practical use, this approximation possesses remarkable theoretical properties.\n", - "The Muir approximation correctly captures the linear part of anelliptic\n", - "behavior. It can be applied to find more accurate approximations with\n", - "nonlinear dependence on the anelliptic parameter. A particular way of ''unlinearizing'' the linear approximation is the shifted hyperbola approach,\n", - "familiar from the isotropic approximations in vertically inhomogeneous media ([Malovichko 1978][malov]; [Sword 1987][Sword.sep.51.313]; [de Bazelaire 1988][deBazelaire1988]; [Castle 1994][Castle1994]) and from the\n", - "theory of Stolt stretch ([Stolt 1978][Stolt1978]; [Fomel and Vaillant 2001][mystolt]). I show that applying\n", - "this idea to approximate the phase velocity of $qP$ waves leads to the known\n", - "''acoustic'' approximation of Alkhalifah ([1998][Alkhalifah1998], [2000a][Alkhalifah2000a]),\n", - "derived in a different way. Applying the same approach to approximate the\n", - "group velocity of $qP$ waves leads to a new remarkably accurate\n", - "three-parameter approximation.\n", - "\n", - "One practical use for the group velocity approximation is traveltime\n", - "computations, required for Kirchhoff imaging and tomography. In the last part\n", - "of the paper, I show examples of finite-difference traveltime computations\n", - "utilizing the new approximation.\n", - "\n", - "[Dellinger1993]:https://sep.stanford.edu/data/media/public/docs/sep75/martin2.ps.gz\n", - "[Abgrall1999]:https://doi.org/10.1190/1.1444519\n", - "[Alkhalifah1998]:https://doi.org/10.1190/1.1444361\n", - "[Alkhalifah2000a]:https://doi.org/10.1190/1.1444815\n", - "[Alkhalifah2000b]:https://doi.org/10.1190/1.1444823\n", - "[Alkhalifah2001]:https://doi.org/10.1046/j.1365-2478.2001.00245.x\n", - "[Alkhalifah1995]:https://doi.org/10.1190/1.1443888\n", - "[deBazelaire1988]:https://doi.org/10.1190/1.1442449\n", - "[Berryman1979]:https://doi.org/10.1190/1.1440984\n", - "[Bevc1997]:https://doi.org/10.1190/1.1444167\n", - "[Bousquie2001]:https://doi.org/10.1190/1.9781560801771.ch18\n", - "[Byun1984]:https://doi.org/10.1190/1.1441603\n", - "[Byun1989]:https://doi.org/10.1190/1.1442624\n", - "[Cao1994]:https://doi.org/10.1190/1.1443623\n", - "[Castle1994]:https://doi.org/10.1190/1.1443658\n", - "[Dellinger1997]:https://doi.org/10.1190/1.1885780\n", - "[Geoltrain1993]:https://doi.org/10.1190/1.1443439\n", - "[Jones1981]:https://doi.org/10.1190/1.1441199\n", - "[Kim1999]:https://library.seg.org/doi/pdf/10.1190/1.1820911\n", - "[Perez2001]:https://doi.org/10.1190/1.1816312\n", - "[Postma1955]:https://doi.org/10.1190/1.1438187\n", - "[Qin1992]:https://doi.org/10.1190/1.1443263\n", - "[Qin1993]:https://doi.org/10.1190/1.1443517\n", - "[Schoenberg2000]:https://doi.org/10.1190/1.1444788\n", - "[Sethian1999]:https://doi.org/10.1190/1.1444558\n", - "[Stolt1978]:https://doi.org/10.1190/1.1440826\n", - "[Stopin2001]:https://doi.org/10.1190/1.9781560801771.ch20\n", - "[Sun1998]:https://doi.org/10.1190/1.1820321\n", - "[Symes1998]:https://doi.org/10.1190/1.1820320\n", - "[Thomsen1986]:https://doi.org/10.1190/1.1442051\n", - "[vanTrier1991]:https://doi.org/10.1190/1.1443099\n", - "[Tsvankin1996]:https://doi.org/10.1190/1.1443974\n", - "[Versteeg1994]:https://doi.org/10.1190/1.1437051\n", - "[Versteeg1991]:https://doi.org/10.3997/2214-4609.201411201\n", - "[Vidale1990]:https://doi.org/10.1190/1.1442863\n", - "[Zhang2002]:https://doi.org/10.1190/1.1817077\n", - "[Zhang2001]:https://doi.org/10.1190/1.1816267\n", - "[ags]: http://doi.org/10.1007/s00791-006-0016-y\n", - "[sweep]:https://doi.org/10.1137/S0036142901396533\n", - "[sweep2]:https://doi.org/10.1016/j.jcp.2003.11.007\n", - "[fowler]:https://doi.org/10.1016/j.jappgeo.2002.12.002\n", - "[jse]:https://sep.stanford.edu/data/media/public/docs/sep75/martin2.ps.gz\n", - "[malov]:https://www.appliedgeophysics.org/\n", - "[tsvankin]:https://doi.org/10.1190/1.9781560803003.refs\n", - "[mystolt]:https://reproducibility.org/RSF/book/sep/stoltst/paper.pdf\n", - "[gassmann]:https://doi.org/10.1007/BF00879140\n", - "[white]:https://pubs.geoscienceworld.org/seg/books/edited-volume/1017/chapter-abstract/106907830/Underground-SoundApplication-of-Seismic-Waves?redirectedFrom=fulltext\n", - "[backus]:https://doi.org/10.1029/JZ067i011p04427\n", - "[paper]:https://doi.org/10.1073/pnas.93.4.1591\n", - "[osher]:https://doi.org/10.1016/0021-9991(88)90002-2\n", - "[book]:https://hrcak.srce.hr/file/69388?origin=publicationDetail.\n", - "[kim]:https://doi.org/10.1190/1.1500384\n", - "[alex]:https://doi.org/10.1073/pnas.201222998\n", - "[alex2]:https://doi.org/10.1137/S0036142901392742\n", - "[tariq]:https://doi.org/10.1046/j.1365-2478.2002.00322.x\n", - "[schneider]:https://doi.org/10.1190/1.1581079\n", - "[qin]:https://doi.org/10.1190/1.1451438\n", - "[linbin]:https://doi.org/10.1190/1.1817077\n", - "[pratt]:https://doi.org/10.1111/j.1365-246X.1992.tb00075.x\n", - "[Alkhalifah.sep.95.tariq3]:https://sep.stanford.edu/data/media/public/docs/sep95/tariq3.ps.gz\n", - "[Muir.sep.44.55]:http://sepwww.stanford.edu/data/media/public/oldreports/sep44/44_04.pdf\n", - "[Sword.sep.51.313]:http://sepwww.stanford.edu/data/media/public/oldreports/sep51/51_22.pdf\n", - "[Fomel.sep.95.sergey3]:https://reproducibility.org/RSF/book/sep/fmeiko/paper.pdf\n", - "[podvin.gji.91]:https://doi.org/10.1111/j.1365-246X.1991.tb03461.x" - ] - }, - { - "cell_type": "markdown", - "id": "34f7814d", - "metadata": {}, - "source": [ - "## EXACT EXPRESSIONS" - ] - }, - { - "cell_type": "markdown", - "id": "92f8b4f5", - "metadata": {}, - "source": [ - "Wavefront propagation in the general anisotropic media can be\n", - "described with the anisotropic eikonal equation\n", - "

(1)

\n", - "\\begin{equation}\n", - " \\label{eq:eikonal}\n", - " v^2\\left(\\frac{\\nabla T}{|\\nabla T|},\\mathbf{x}\\right)\\,|\\nabla T|^2 = \n", - " 1\\;,\n", - "\\end{equation}\n", - "where $\\mathbf{x}$ is a point in space, $T(\\mathbf{x})$ is the\n", - "traveltime at that point for a given source, and\n", - "$v(\\mathbf{n},\\mathbf{x})$ is the phase velocity in the phase direction\n", - "$\\mathbf{n} = \\frac{\\nabla T}{|\\nabla T|}$.\n", - "\n", - "In the case of VTI media, the three modes of elastic wave propagation\n", - "($qSH$, $qSV$, and $qP$) have the following well-known explicit\n", - "expressions for the phase velocities ([Gassmann 1964][gassmann]):\n", - "

(2)

\n", - "

(3)

\n", - "\\begin{eqnarray}\n", - " \\label{eq:qsh}\n", - " v_{SH}^2(\\mathbf{n},\\mathbf{x}) & = & \n", - " m\\,\\sin^2{\\theta} + l\\,\\cos^2{\\theta}\\;; \\\\\n", - " \\nonumber\n", - " v^2_{SV}(\\mathbf{n},\\mathbf{x}) & = &\n", - " \\frac{1}{2}\\,\\left[(a+l)\\,\\sin^2{\\theta} + (c+l)\\,\\cos^2{\\theta}\\right] - \\\\\n", - " & & \\frac{1}{2}\\,\\sqrt{\\left[(a-l)\\,\\sin^2{\\theta} - \n", - " (c-l)\\,\\cos^2{\\theta}\\right]^2 +\n", - " 4\\,(f+l)^2\\,\\sin^2{\\theta}\\,\\cos^2{\\theta}}\\;; \n", - " \\label{eq:qsv} \\\\\n", - " \\nonumber\n", - " v^2_{P}(\\mathbf{n},\\mathbf{x}) & = &\n", - " \\frac{1}{2}\\,\\left[(a+l)\\,\\sin^2{\\theta} + (c+l)\\,\\cos^2{\\theta}\\right] + \\\\\n", - " & & \\frac{1}{2}\\,\\sqrt{\\left[(a-l)\\,\\sin^2{\\theta} - (c-l)\\,\\cos^2{\\theta}\\right]^2 +\n", - " 4\\,(f+l)^2\\,\\sin^2{\\theta}\\,\\cos^2{\\theta}}\\;,\n", - " \\label{eq:qp}\n", - "\\end{eqnarray}\n", - "

(4)

\n", - "\n", - "where, in the notation of [Backus (1962)][backus] and [Berryman (1979)][Berryman1979],\n", - "$a=c_{11}$, $c=c_{33}$, $f=c_{13}$, $l=c_{55}$, $m=c_{66}$, $c_{ij}(\\mathbf{x})$\n", - "are the density-normalized components of the elastic tensor, and $\\theta$ is\n", - "the phase angle between the phase direction $\\mathbf{n}$ and the axis of\n", - "symmetry.\n", - " \n", - "The group velocity describes the propagation of individual ray trajectories\n", - "$\\mathbf{x}(\\tau)$. It can be determined from the phase velocity using the\n", - "general expression\n", - "

(5)

\n", - "\\begin{equation}\n", - " \\mathbf{V} = \\frac{d \\mathbf{x}}{d \\tau} =\n", - " v \\mathbf{n} + \\left(\\mathbf{I} - \\mathbf{n}\\, \\mathbf{n}^T\\right) \n", - " \\nabla_{\\mathbf{n}} v\\;,\n", - " \\label{eq:group}\n", - "\\end{equation}\n", - "\n", - "where $\\mathbf{I}$ denotes the identity matrix, $\\mathbf{n}^T$ stands for the\n", - "transpose of $\\mathbf{n}$, and $\\nabla_{\\mathbf{n}} v$ is the gradient\n", - " of $v$ with respect to $\\mathbf{n}$. The two terms in\n", - "equation 5 are clearly orthogonal to each other. Therefore, the\n", - "group velocity magnitude is ([Postma 1955][Postma1955]; [Berryman 1979][Berryman1979]; [Byun 1984][Byun1984])\n", - "

(6)

\n", - "\\begin{equation}\n", - " \\label{eq:f}\n", - " V = |\\mathbf{V}| = \\sqrt{v^2 + v_{\\theta}^2}\\;,\n", - "\\end{equation}\n", - "where \n", - "

(7)

\n", - "\\begin{equation}\n", - " \\label{eq:falpha}\n", - " v_{\\theta}^2 = \\left|\\left(\\mathbf{I} - \\mathbf{n}\\,\n", - " \\mathbf{n}^T\\right) \\nabla_{\\mathbf{n}} v\\right|^2 =\n", - " \\left|\\nabla_{\\mathbf{n}} v\\right|^2 - \n", - " \\left|\\mathbf{n} \\cdot \\nabla_{\\mathbf{n}} v\\right|^2\\;.\n", - "\\end{equation}\n", - "\n", - "The group velocity has a particularly simple form in the case of elliptic\n", - "anisotropy. Specifically, the phase velocity squared has the\n", - "quadratic form\n", - "

(8)

\n", - "\\begin{equation}\n", - " \\label{eq:ellips}\n", - " v_{\\mbox{ell}}^2(\\mathbf{n},\\mathbf{x}) = \n", - " \\mathbf{n}^T\\,\\mathbf{A}(\\mathbf{x})\\,\\mathbf{n}\n", - "\\end{equation}\n", - "with a symmetric positive-definite matrix $\\mathbf{A}$, and the group\n", - "velocity is \n", - "

(9)

\n", - "\\begin{equation}\n", - " \\label{eq:ellf}\n", - " \\mathbf{V}_{\\mbox{ell}} = \\mathbf{A}\\,\\mathbf{p}\\;, \n", - "\\end{equation}\n", - "\n", - "where $\\mathbf{p} = \\nabla T = \\mathbf{n}/v(\\mathbf{n},\\mathbf{x})$.\n", - "The corresponding group slowness squared has the explicit expression\n", - "

(10)

\n", - "\\begin{equation}\n", - " \\label{eq:ellv}\n", - " \\frac{1}{V_{\\mbox{ell}}^2(\\mathbf{N},\\mathbf{x})} = \n", - " \\mathbf{N}^T\\,\\mathbf{A}^{-1}(\\mathbf{x})\\,\\mathbf{N}\\;, \n", - "\\end{equation}\n", - "where $\\mathbf{N}$ is the group direction, and $\\mathbf{A}^{-1}$ is the matrix\n", - "inverse of $\\mathbf{A}$. For example, the elliptic expression 2 for\n", - "the phase velocity of $qSH$ waves in VTI media transforms into a completely\n", - "analogous expression for the group slowness\n", - "

(11)

\n", - "\\begin{equation}\n", - " \\label{eq:ellsh}\n", - " \\frac{1}{V_{SH}^2(\\mathbf{N},\\mathbf{x})} = \n", - " M\\,\\sin^2{\\Theta} + L\\,\\cos^2{\\Theta}\n", - "\\end{equation}\n", - "where $M=1/m$, $L=1/l$, and $\\Theta$ is the angle between the group direction\n", - "$\\mathbf{N}$ and the axis of symmetry.\n", - "\n", - "The situation is more complicated in the anelliptic case.\n", - "Figure 1 shows the $qP$ and $qSV$ phase velocity profiles in a\n", - "transversely isotropic material -- Greenhorn shale ([Jones and Wang 1981][Jones1981]),\n", - "which has the parameters $a=14.47\\,\\mbox{km}^2/\\mbox{s}^2$,\n", - "$l=2.28\\,\\mbox{km}^2/\\mbox{s}^2$, $c=9.57\\,\\mbox{km}^2/\\mbox{s}^2$, and\n", - "$f=4.51\\,\\mbox{km}^2/\\mbox{s}^2$. Figure 2 shows the\n", - "corresponding group velocity profiles. The non-convexity of the $qSV$ phase\n", - "velocity causes a multi-valued (triplicated) group velocity profile. The\n", - "shapes of all the surfaces are clearly anelliptic.\n", - "\n", - "A simple model of anellipticity is suggested by the Muir approximation\n", - "([Muir and Dellinger 1985][Muir.sep.44.55]; [Dellinger et al. 1993][jse]), reviewed in the next section.\n", - "\n", - "[gassmann]:https://doi.org/10.1007/BF00879140\n", - "[backus]:https://doi.org/10.1029/JZ067i011p04427\n", - "[Berryman1979]:https://doi.org/10.1190/1.1440984\n", - "[Postma1955]:https://doi.org/10.1190/1.1438187\n", - "[Berryman1979]:https://doi.org/10.1190/1.1440984\n", - "[Byun1984]:https://doi.org/10.1190/1.1441603\n", - "[Jones1981]:https://doi.org/10.1190/1.1441199\n", - "[Muir.sep.44.55]:http://sepwww.stanford.edu/data/media/public/oldreports/sep44/44_04.pdf\n", - "[jse]:https://sep.stanford.edu/data/media/public/docs/sep75/martin2.ps.gz" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "f1a81747", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "# Material parameters (km^2/s^2)\n", - "a = 14.47\n", - "l = 2.28\n", - "c = 9.57\n", - "f = 4.51\n", - "\n", - "# Function to compute qP wave phase velocity\n", - "def velocity_qP(theta):\n", - " term1 = 0.5 * ((a + l) * np.sin(theta)**2 + (c + l) * np.cos(theta)**2)\n", - " term2 = 0.5 * np.sqrt(((a - l) * np.sin(theta)**2 - (c - l) * np.cos(theta)**2)**2 + 4 * (f + l)**2 * np.sin(theta)**2 * np.cos(theta)**2)\n", - " return np.sqrt(term1 + term2)\n", - "\n", - "# Function to compute qSV wave phase velocity\n", - "def velocity_qSV(theta):\n", - " term1 = 0.5 * ((a + l) * np.sin(theta)**2 + (c + l) * np.cos(theta)**2)\n", - " term2 = 0.5 * np.sqrt(((a - l) * np.sin(theta)**2 - (c - l) * np.cos(theta)**2)**2 + 4 * (f + l)**2 * np.sin(theta)**2 * np.cos(theta)**2)\n", - " return np.sqrt(term1 - term2)\n", - "\n", - "# Create an array of angles from 0 to 360 degrees\n", - "theta = np.linspace(0, 2 * np.pi, 500)\n", - "\n", - "# Calculate phase velocities for qP and qSV waves\n", - "v_qP = velocity_qP(theta)\n", - "v_qSV = velocity_qSV(theta)\n", - "\n", - "# Convert polar coordinates to Cartesian, but swap x and y to match paper's figure\n", - "x_qP = v_qP * np.sin(theta) # Swapping cos and sin\n", - "y_qP = v_qP * np.cos(theta)\n", - "\n", - "x_qSV = v_qSV * np.sin(theta)\n", - "y_qSV = v_qSV * np.cos(theta)\n", - "\n", - "# Cartesian plot for phase velocity profiles\n", - "plt.figure(figsize=(6, 6))\n", - "plt.plot(x_qP, y_qP, label='qP Wave', color='blue')\n", - "plt.plot(x_qSV, y_qSV, label='qSV Wave', color='green')\n", - "\n", - "# Set axis limits and labels\n", - "plt.xlim(-4, 4)\n", - "plt.ylim(-4, 4)\n", - "plt.xlabel('Horizontal velocity (km/s)', fontsize=12)\n", - "plt.ylabel('Vertical velocity (km/s)', fontsize=12)\n", - "\n", - "# Add black axes\n", - "plt.axhline(0, color='black', lw=1)\n", - "plt.axvline(0, color='black', lw=1)\n", - "\n", - "# Set aspect ratio to be equal\n", - "plt.gca().set_aspect('equal', adjustable='box')\n", - "\n", - "# Show the plot\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "bbadac0b", - "metadata": {}, - "outputs": [], - "source": [ - "from sage.all import *" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "b4132fba", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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J9evDSy/BiBFqBtTo0TIDSghheeHhakHOP/8EDw81tm/IELhwQe/IhLEkuRE25exZ6NtXrfkUGqrG2Xzyiao6KoQQ1tSypUpwvvpKTWSoVQs+/ljq49gDSW6ETcjJUf3cdeqoKZo//aRmMtSrp3dkQghn5uKiuqeOHlVFQcePV7M1N27UOzJxK5LcCN1t3w7Nm6uBfCNGqMrCAwbIuBohhO0IClLj/nbuVGNzOnRQ71fx8XpHJooiyY3QTWIijBmjmn5dXFSS8+mnanVfIYSwRU2awJYtaomXRYtUa/O8eVLl2NZIciOsTtNUt1Pt2vDdd6o76q+/1KwEIYSwdS4uqojo4cOqBWfQIOjVC2Ji9I5M5JPkRlhVXBzcc49aubtVK/XmMG4cuLnpHZkQQhRP+fLqi9qSJbBvH0RGqgkQUhtHf5Lc/EPWlrIsTVNTK+vVU33WixfDwoVqRpQQQtiz3r3h0CFVbPSZZ6B1a7UsjNCPJDf/kLWlLOfSJejfHx58ELp3h4MHVSE+IYRwFKVKweefw+bNkJCgZlR98gnk5ekdmXOS5EZY1IIFULeumjb5889qLagyZfSOSgghLKN1a9izB0aOVF3uXbrAmTN6R+V8JLkRFhEfD4MHqxabdu1Ua03//npHJYQQlufjo1pt1q6FU6egQQP4+muZUWVNktwIs1u1SrXWrFwJP/ygWm+Cg/WOSgghrKtzZ9i/X32xe/RRNTZHlnCwDkluhNlkZsKECdCzJzRqpFprHnxQivEJIZxXQIBaXXzJElXLq2FD9cVPWJYkN8Isjh1Tfc2ffQYffaRW8a5YUe+ohBDCNvTuDQcOqCKAd92lvghmZuodleOS5EaU2HffqQs2JQW2bVOD6FzklSWEEIUEB6svfh9+qL4Itm6txuQI83Ooj6ApU6bQvHlz/P39CQ4Opm/fvhw9elTvsBxWerpaUG7oULUW1K5dKskRQghRNBcXVQtn2za1BE2TJrB0qd5ROR6HSm42bNjAmDFj2LZtG2vWrCEnJ4du3bqRmpqqd2gO5+RJ9a1jzhyYPRu++UYtJieEEOL2mjRRBU07dVJ1v158EXJy9I7KcRg0rWST0y5dukR0dDSXL18mPT2dsmXLUq5cOWrVqoWrq6u54jTJ5cuXCQ4OZsOGDbRv396oxyQlJREQEEBiYiKlZAXHIi1ZolprypVTM6EaNNA7IiGKJtezsHWaBu+/Dy+9BG3bqkU4y5fXOyrbZew1bdKKPmvWrGH+/Pls3LiRkydPFrmPj48PLVu2pHv37gwZMoSQkBBTTlUiiYmJAAQFBd10n8zMTDKvG9WVlJRk8bjsVW4uvPIKvPMO9O2rWmwCAvSOSggh7JfBAM89B3fcodbca9wY5s8HI7+Pi5swuuUmIyODzz77jGnTphEdHU3+w7y9vQkODiYoKAhvb2/i4+OJj4/n0qVL6gQGA25ubvTq1YuXX36Zpk2bWu7ZXEfTNPr06cO1a9fYtGnTTfebNGkSkydPvuF2+aZXWGKiWvl29WqYOhWefVameAvbJy03wp5cuAADB8KWLfDppzB6tN4R2R5jr2mjkptZs2YxceJEYmNj8fT0pEePHvTq1YsWLVpQt25dXIqYGhMfH8/27dvZvHkzP/30EydOnMBgMHD//fczdepUKleuXLJneBtjxoxh+fLlbN68mdBbrM5YVMtNWFiYvBle5+RJtZJ3XJxaAbdbN70jEsI4ktwIe5OTo6aJf/opjBqlfrq76x2V7TBrcuPi4kJERATPP/88AwcONOlNYteuXXz66afMnTuX//3vf7z22mvFPoaxxo4dy+LFi9m4cSNVq1Yt1mPlzbCwDRvgvvugdGn49VeoXVvviIQwnlzPwl59+SWMGaMmbvzyC5Qtq3dEtsHYa9qo2VLffvstR48eZeTIkSa/QTRt2rTgOJ06dTLpGLejaRpPPvkkCxcu5I8//ih2YiMK+/pruPNONWD4r78ksRFCCGt57DG1NtXBg9C8ORw6pHdE9sWo5GbIkCFmm/lUtWpV2rVrZ5Zj/deYMWP44YcfmDNnDv7+/ly4cIELFy6Qnp5ukfM5qtxcGD9erYXyyCNqnM0txmQLIYSwgHbt1HRxPz/VgrNund4R2Q+HqnMzbdo0EhMT6dixIxUqVCjY5s+fr3dodiM1VdVc+OQT1dc7bZr09wohhF4qV4bNm1XrTffuajFicXsmTQW/naSkJFauXElcXBxNmjShQ4cOljjNDUpYssfpxcfD3Xer9U+WL4cePfSOSAghREAArFgBI0fCkCFw5owqyyEzVm/O5ORm/vz5vPPOOzzxxBM8+uijBbcfOXKEbt26ERsbW3DbkCFDmD17dokCFZZ17pz6VnDpkmr6bN5c74iEEELkc3dXq4tXrQqvvgqxsfD556BzrVybZXK31Pz589m3b98NlX/HjRvHuXPniIiIoE+fPvj5+fH999+zYsWKEgcrLOPIEdWfm5r6b/OnEEII22IwwGuvwVdfwcyZ8NBDkJ2td1S2yeTkZt++fQQFBVGzZs2C286fP8+aNWsIDw/nwIEDLFy4kF9//RVN04iKijJLwMK8tm9XJb9LlVKFo2rV0jsiIYQQt/LII6qK8YIFqlp8WpreEdkek5Oby5cvEx4eXui2devWoWkagwcPxsvLC4D27dtTuXJlDh8+XLJIhdmtWQOdO6uEZuNGqFRJ74iEEEIYo39/VXts/Xo1PvKf1YbEP0xObrKyssjNzS1026ZNmzAYDDfUsQkJCeH8+fOmnkpYwMqV0KsXdOigkhyZ6i2EEPale3f1/n3ggPqievmy3hHZDpOTm0qVKnHy5EnSrmsPW7VqFW5ubrRp06bQvsnJyQTICos2Y9Uq6NcPevaERYvAx0fviIQQQpiidWtVST42VhKc65mc3Nx5552kpaUxduxY/v77byZNmkR0dDSdO3fG57pPy/T0dI4fP05YWJhZAraUqKgoIiMjae7go2lXrVJ9tN27q3WiPDz0jkgIIURJNGiguqcuX4YuXSTBgWKsCv5fMTExNG3alPj4eEDVmHF3d2fTpk20aNGiYL+ffvqJgQMHMm7cOD788EPzRG1BjrwWzerVqkBft25qrRJJbISjc+TrWYj/OnwYOnaEkBD44w/HXI/KrGtLFSU8PJydO3fyxBNP0K1bNx599FG2b99eKLEBWL9+PQ0bNqRPnz6mnkqYQX5i07Ur/PyzJDZCCOFo6tRRdcouXlQtOFev6h2RfkxuuXFUjvhN77ffoHdvtQjmggXg6al3REJYhyNez0LczsGD0KmTmgG7bh0EBuodkfmYveWmfv36vPzyy2zZskWWObAj69apFhtJbIQQwjnUrau6paKj4Z57nLMOjtHJzYkTJ5g6dSrt27cnODiYhx9+mPnz55Mok+tt1s6dqsWmXTtJbIQQwpnUq6fWo9q9G+6/3/kqGRud3MTHx7N48WJGjBiBp6cnP/zwA4MHD6ZcuXJ07tyZDz/8kKNHj1oyVlEMR46oqd716sHChZLYCCGEs2nZUr3///YbjBgBeXl6R2Q9Jo+52b17N7/++ivLli1j9+7daJqGwWAgIiKCe+65h7vvvpsOHTrg5maRhcctxhH66C9eVC9qX19VeVgK9Aln5QjXsxAlNX8+DBoEY8fCxx/b92rixl7TZhlQfPHiRZYtW8ayZctYu3YtKSkpGAwG/P396datG7169aJnz56UK1eupKeyOHt/M0xLUwPJYmLgr7/gPytkCOFU7P16FsJcpk2DJ56AN9+EV17ROxrTWTW5uV52djbr1q3j119/ZcWKFZw+fRqDwYDBYKB58+bcc889vPzyy+Y8pVnZ85thXp7qW125UrXYNG2qd0RC6Muer2chzG3yZJg0CebOhYED9Y7GNLolN/916NChgu6rbdu2kZeXd8OaVLbEnt8MX3gB3ntPLakgZYWEuWTlZpGVm0VOXg65ebloaPi6++Ll5oXBxtu37el61jSNPC1P/Z61XHLzcnF1ccXbzdvmf8/CPmgaPPywqnW2bh20aqV3RMVn7DVt8QExkZGRREZG8sILL3Dt2jVWrVpl6VM6pS+/hHffhQ8/lMRGGE/TNM6nnOfQ5UMcunyIo1eOEpcSx6XUSwVbUmZSkY91Mbjg5+GHn4cfAZ4BVPSvSEX/ilTyr0SlUpWIKB1B9aDqVAmsgoer81aNTM1K5djVYxy9epSziWe5mHqRCykXuJByoeDf19KvkasV/aXP09WTsj5lKeNThjLeZSjnW46IwAhqla1FnbJ1aFi+IV5uXlZ+VsIeGQzw1Vdw+rT6nNi+HapU0Tsqy5Aifv+IiooiKiqK3Nxcjh07Zhff9PKtWaNmRj3+OHz+uX0PFhOWd/raaVaeWMnvp35n27ltnE85D4CHqwc1y9QkPCCccj7lCPYNJtg3mLI+ZfFy88LNxQ1XgysAqdmppGalkpKVQkpWCvHp8ZxPOU9cchyxybHEJceRlZsFgKvBlepB1WkQ0qDQVjmgssVbJKzZcpOenc6BSwfYfX43By8d5OjVoxy5coSzSWcL9inlWYryfuULthDfEMr7lSfIOwg3F7eC37GriytuLm5k52YTnx7PlbQrXE2/ypW0K1xKvcSJ+BMFx3VzcaNhSEPuqHQHXSK60DWiK/6e/hZ9rsK+Xb6sJp14e8OWLWBP61pbrVvqyJEjrF69mlOnTpGSknLTAn8Gg4Gvv/66JKeyCntqxgb4+29o00ZtS5eCnU1OE1agaRrbY7cz7+95rDixgmNXj+Hm4kbrsNa0Dm1Ni0otqBdcj6qlq+LmYp4XUJ6WR2xSLCfiT3Ds6jEOXj7I/ov72X9xP9cyrgHqg75+cH0ahjSkacWmNKnQhLrl6uLu6m6WGMBy13NqVip7L+xl9/nd7L6wuyChydVycXNxo2aZmtQqU4vaZWtTq0wtapWtRa0ytSjtXdpsMaRlp3Ho8iG2x25ne+x2tp7dyvH447i7uNOhSgfuqXkPg+oNopyv7U/kENZ3+LDqlmrZEpYts5/PDosnN9nZ2YwcOZLvvvsO4LZViw0Gg02PtclnT8lNfDw0awb+/rB5s/opRL749Hhm7ZnFl7u/5NjVY1Twq0Cvmr3oWb0nXSK6UMrT+q9vTdOITY4tSHT2X9zPngt7OHrlKBoanq6eNAhpQJMKTWhaQSU89YLr4elmWqEmc1zP19Kvsf/ifnaf382u87vYfX43R64cQUPDw9WD+sH1C2JtWrEp9YLr6dZNdOraKZYfW86y48tYd3odAP3q9OOxJo/RuWpnXAwmLycoHNDvv0OPHvDsszB1qt7RGMfiyc1LL73EO++8g4eHB/feey+NGzemXLlyt2xmHjp0qCmnsip7SW7y8qBXLzXde9cux+03FcUXmxTLlM1T+HrP1+Rpedxf936GNhxKpyqdcHVx1Tu8IqVkpRS0hOw6v4tdcbs4fOUweVoe7i7u1A+pT5PyTWgQ0oA65eoQWS6SCn4VbtutVZzrOTMnkyNXjnDg0gEOXDzA/kv7OXDxALHJsQB4uXnRqHwjmpRvUpDIRJaLtNnxRFfSrvD9vu/5cveXHL5ymGqlq/Fs62cZ3mi4ycmicDzvvw/PPacmovTtq3c0t2fx5CYsLIzz58/zxx9/0L59e5MDtTX2ktxMnqy2FStU5i3EhZQLTN08lek7p+Pj7sMzLZ/h8WaPE+wbrHdoJknLTmPfhX2FWkwOXzlcMJYnwDOAiNIRVA6sTOWAylT0r0gZ7zKU9SlLae/SeLl5cTn+Mr0a9OK3g7+BpxorlD9O6HzyeaITo4lJjCn4mZOXA0B4QDj1g+vTIKQB9YPrUz+kPrXL1jZbt501aZrG1rNb+XT7p/xy6BfCSoUxqeMkhjQYYrPJrrAeTYMBA9TYzR07oGZNvSO6NYsnNz4+PlSpUoVDhw6ZHKQtsofkZsUK1WozeTK8+qre0Qi9Zedm88lfnzBp/SRcXVyZ0GoC41qO06XbydJy8nI4fe00hy4f4vCVw5y+dproxGjOJJzhYupFEjISCj8gA5gKvAhc11PkYnChvF95wgPCqRxQmfCAcCJKR1A/uD71gusR4GVHIyyL4fDlw7y67lUWHF5A4/KNiborilZhdjgfWJhVUhK0aAHu7rBtm6pub6ssntzUq1cPgL///tu0CG2UrSc3p0+r4nytW6sBxC7She7U9l/cz0MLH+Lg5YOMaT6GyR0nm3XQqr3JycshPj2ea+nXyMzN5GjsUe5vej/bTmyjfJny+Hr44ufhh6erp1PXjtl2bhtjVoxh9/ndjGo6ive6vYefh5/eYQkdHTyoEpy+feGHH2x31q2xn9EmfzQOHz6cw4cPc+DAAVMPIYopKwseeAACA+H77yWxcWaapvHZX5/R4ssWGAwGdj62k097furUiQ2oadHBvsHUKluLBiEN6F69OwB1ytWhcmDlgmntzpzYALQMbcn2R7fzWc/P+G7/dzSa3oi/zv2ld1hCR3Xrwtdfw5w5aqkGe2fyx+MzzzxD79696dWrF7/++qs5YxI38fLLsHevWgSttHN/hjm1K2lX6DW3F0+teopRzUbx16N/0bhCY73DEnbG1cWVJ1s8yd7H91LWpyztZ7fnq91f6R2W0NHAgWr9qQkTwN5HnJSozo2madx3330sWbKEoKAgqlWrho+PT9EnMhhYu3atyYFai612S61ZA926wQcfwPjxekcj9HLs6jHu+vEuEjMT+bbvt9xV4y69Q7Jptno925qs3CyeWvkUM3bNYFTTUXzS8xObnQUmLCstTZUY8fRUs3E9bOxlYPExNykpKfTr148//vjjtjVuQOrclMS1a1C/PkRGwqpV0h3lrDZFb6LPvD6U9yvP8sHLqVq6qt4h2TxbvJ5t2Ze7vmTMijG0r9yeRQ8skkrHTmr3blXcb/x426t/Y/G1pV555RXWrl1LmTJlGDlyJI0aNbptnRthmjFjIDUVZs2SxMZZrT+znrt+vIuWoS1ZcP8Cpx9bIyzjsaaPUbNMTe6Zew93fn8nKx9cSZB3kN5hCStr0gTeeANeekkt7dOhg94RFZ/JLTehoaFcvnyZPXv2EBkZae64rM5W15aaP1/1g/74IwwerHc0Qg+bojfR48cetAlrw9JBS2WRxGKQlhvT7IrbRY8fe1CtdDV+f/h3mUnlhHJzoXNnOHMG9u1TE1lsgcW7pXx9falevTr79u0zOUhbZEtvhnFxUK8e3HmnSnKkUcz5bD27lW7fd+OO0Dv4ddCv+LgXPaZNFM2Wrmd7sytuF52+7USrsFb8OuhXGYPjhKKjoUEDuOceNT3cFlh8KnitWrVIT0839eHiNjQNRoxQg7qmTZPExhmdunaKXnN60bRiU5YOXCqJjbCqphWbsnjgYtafWc/QxUPJ0/L0DklYWeXK8MUXqudg/ny9oykek5ObJ554ghMnTrB+/XozhiPyzZoFq1ern2XK6B2NsLaUrBT6zOtDGZ8yLH5gMb4eNlwyVDiszlU7M+feOfx08Cf+98f/9A5H6GDwYOjfH8aOVYs12wuTk5tHH32U8ePHc++99/LZZ5+RkpJizric2qVLaiGzhx9Wg7mEc9E0jWGLh3Em4QyLH1gsg4eFru6LvI+3O7/NlM1T+PWo1DRzNgYDfPqpKiL73HN6R2M8k8fcREREAHDu3LmCKd7lypW7ZZ2bkydPmhim9dhCH/3DD8Py5XDkCJQrp0sIQkfvbnmXF35/gcUPLKZP7T56h2PXbOF6dgSaptFvfj82RG9g18hdRJSO0DskYWUzZ8Ljj8Mff0CnTvrFYfEBxS7FnJMsdW6Ms3atGkD89ddqzI1wLgcuHqDpzKY80/IZ3un6jt7h2D29r2dHkpCRQNOZTQnxDWHT8E2yoriTyctTU8IvXoT9+8FLp0mbFk9uoqOji/2YypUrm3Iqq9LzzTAjQ41ML18eNmyQQcTOJjs3mzu+uoOs3Cx2jdyFp5un3iHZPUluzGtT9CY6zO7AR90/4umWT+sdjrCyw4ehYUN44QVVB0cPFi/iZw+Jir2ZOlXVFFi8WBIbZzRl8xT2X9zPX4/+JYmNsEntKrfjyRZP8tLal+hVsxfVgqrpHZKwojp11BqHb72lBhrXqaN3RDdn8oDis2fPFmv/pUuXmnoqp3D0KEyZAs8/r5ZZEM4lJjGGKZun8Fzr52hasane4QhxU293eZsQvxCeXiUtN87opZcgPNz21zg0Obnp0qULly9fNmrfn3/+mQEDBph6KqcwYQJUqgSvvKJ3JEIPL/7+IoFegbzc7mW9QxHilvw8/Hj3zndZfnw5f5z+Q+9whJV5esL776t1Dles0DuamzM5uTlx4gRdu3YlISHhlvvNmTOHwYMHG7W4prNau1bNjnrnHfD21jsaYW1bz25l7t9zebvz27JQobAL/SP70yq0FRN+myDF/ZxQ375qxtT48ZCdrXc0RTM5uXnyySfZv38/d911F6mpqUXu88033zB06FBcXFyYN2+eyUE6stxc1WrTqpUqlCScz4u/v0jj8o0Z2mio3qEIYRSDwcAH3T5g74W9/LDfRuryC6sxGODjj+H4cYiK0juaopmc3Hz66acMHTqUbdu20adPH7KysgrdP336dB599FFcXV355ZdfuPfee0scrCVFRUURGRlJ8+bNrXre779Xi5J98IEMInZGW89uZVPMJiZ2mIiLQZZ8F/ajVVgr+tXux1ub3iI3z/bLfAjzatAAHnsMJk+GK1f0juZGJk8FB8jLy+P+++9n4cKF3HPPPSxcuBBXV1c+/fRTxo0bh5eXF4sWLaJ79+7mjNmirDl1NDUVataEtm3tb90OYR595vXh+NXj/P3E35LcWIBMBbesv879RcuvW7Lw/oX0q9NP73CElV2+DDVqqMKzn35qnXNafOFMUIX85s6dS7du3Vi2bBlDhw5l6tSpjBs3Dh8fH5YtW2ZXiY21ffCByninTtU7EqGHg5cOsvToUp5v87wkNsIu3RF6B+0rt+fdre/KuEonVK6cmuE7YwbExOgdTWElfkd1d3dn0aJFtG7dmjlz5vDKK6/g5+fHihUr6Ny5szlidEiXL8O776rFyKpW1TsaoYf3/3yf0FKhDK4/WO9QhDDZc62fY9u5bWw5u0XvUIQOnnoKAgL0K+p3M2b5uujt7c3y5ctp0qQJpUqV4rfffqN9+/bmOLTDeu89cHFRNQOE87mWfo15f89jTPMxeLh66B2OECa7q8Zd1AiqwbSd0/QORejAz099jn3zjRpgbCuMSm5cXV1vu5UuXZo9e/aQlJREmzZtbrjfzc3kYsgO5+JF+PxzGDcOypTROxqhhzkH5pCdm82wRsP0DkWIEnExuPBYk8dYcGgBCRkJeocjdDB6tFo2aNIkvSP5l1HJjaZpJd7y8qQWQr533gEPD3jmGb0jEXr5bv933F3zbsr7ldc7FCFK7MEGD5Kdl82CQwv0DkXowMsLXn0V5s6Fv//WOxrFqOQmLy/PLJuA8+dh2jSV2JQurXc0Qg/RCdFsj93OwLoD9Q5FCLOo6F+RzlU788MBqXnjrIYPhypV1NRwW+BwUzQ2btzIPffcQ8WKFTEYDCxevFjvkAr56CPVajNunN6RCL0sPLwQT1dP7q55t96hCGE2g+sNZv2Z9VxMuah3KEIHHh7w4ouwYIFtjL1xuOQmNTWVhg0b8vnnn+sdyg2uXVOtNk88oUaXC+e04PACulXrRilPqbsiHEd+sr7qxCqdIxF6efhhCA5Wa0/pzajkJi0tzawnNffxrtezZ0/efPNNm6yIPG2aWofjaVlM12mdTz7PlrNb6B8pa20IxxLsG0zzis1ZeWKl3qEInXh5qc+3b7+FCxf0jcWo5KZKlSq88847pKSklOhkW7dupUePHnzwwQclOo45ZWZmkpSUVGizhPR0tRbH8OFqVLlwTmtPrwXU9FkhHE3P6j1ZfXI1OXk5eocidDJ6NLi7W69i8c0YldxERETw0ksvERYWxiOPPMKaNWvIzTVuLZG4uDg++ugjmjVrRrt27di8eTP16tUrUdDmNGXKFAICAgq2sLAwi5xnzhxVjXjCBIscXtiJP07/QYOQBpT1Kat3KEKY3V017iIhI4Ft57bpHYrQSWAgPP44fPEFWKitwChGry31888/88orr3DixAkMBgNeXl40btyYpk2bUqFCBYKCgvD09CQhIYH4+HgOHz7Mzp07iY6ORtM03NzcGD58OJMnT6a8lZouDAYDixYtom/fvjfdJzMzk8zMzIL/JyUlERYWZta1aDQNmjSB0FD49VezHFLYqaqfVKVvrb581OMjvUNxCrK2lHXl5uUS/H4wY1uMZVLHSXqHI3Ry7hxERKilhcaPN++xjb2mja6sN2DAAPr378+qVauYOXMmK1asYOvWrWzduhVDEctZ5+dMVatWZcSIEYwYMYIKFSqY8FQsy9PTE09PT4ueY+tW2LtX1pBydqevneZMwhk6Ve2kdyhCWISriyt3VLqD7bHb9Q5F6Cg0FO6/X7XejBunqvFbW7HKBhsMBnr27EnPnj1JS0vjzz//ZOvWrURHR3PlyhUyMjIICgoiODiYRo0a0bZtW6pXr26p2O3G55+rlVO7dtU7EqGnv2L/AqBNWBudIxHCclpUasHn2z9H07Qiv/gK5zB6NPz4I/z+O3TrZv3zm7wmgo+PD126dKFLly7mjKfEUlJSOHHiRMH/T58+zd69ewkKCiI8PNzq8Zw/D7/8oqbG6ZG9Ctux78I+QkuFUsZH1twQjqt5xeZcTb/KmYQzVC0tqwI7q9atoX59NUtYj+TG4T5ud+7cSePGjWncuDEA48ePp3Hjxrz22mu6xDNjBnh6wtChupxe2JC9F/fSqHwjvcMQwqKaV2oOIF1TTs5gUK03S5fC2bPWP7/DJTcdO3Yscm2r2bNnWz2W7GyV3AwZokaQC+e278I+GoY01DsMISwq2DeYKoFV2BG3Q+9QhM4eegh8fODLL61/bodLbmzJ6tWqkNHIkXpHIvR2MeUi51POS8uNcAoNQhpw6PIhvcMQOvP3V1/uv/xSfdm3JkluLOi771SfY6NGekci9Lb/4n4AabkRTqF66eqciD9x+x2Fw3vsMfUlf80a655XkhsLuXZN9TU+/LDqexTO7eS1k7gaXGWApXAK1YOqczrhtFQqFjRqBHXrwvffW/e8ktxYyM8/q2a4Bx/UOxJhC84knCEsIAw3F5MnKAphN6oHVScnL4fohGi9QxE6MxhU19TixdatWCzJjYV8952a/maDdQuFDqITo6kcUFnvMISwiupBqr7Z8fjjOkcibMHgwZCZCQsWWO+cktz8IyoqisjISJo3b17iY508CVu2qC4pIQCiE6KpHCjJjXAOYQFqjb5zSed0jkTYgrAw6NjRul1TJic306ZNIyEhwYyh6GvMmDEcOnSIHTtKPn1xzhzw84M+fcwQmHAIMYkxhJeyfhFJIfTg5uJGGe8yXEq9pHcowkYMGQLr16t1p6zB5ORmzJgxVKhQgYEDB7Jq1SqMXH/TKSxcCL16qfn9QgBcTb9KOd9yeochhNUE+wZLciMK9OsHrq5q7I01mJzc3HXXXeTm5vLTTz9x9913Exoayosvvsjhw4fNGZ/dOX1aLZLZr5/ekQhbkZadRkZOBmW8ZdkF4TxC/EIkuREFAgOhc2dYtMg65zM5uVm2bBnnzp3j/fffp169epw/f553332XevXq0bJlS6ZPn+5Q3VbGWrIEPDygZ0+9IxG2Ij49HoAg7yCdIxHCeoJ9g7mYelHvMIQN6dcPNmyAq1ctf64SDSgODg5m/Pjx7Nu3jz179vD0009Trlw5tm/fXqjbauXKlU7TbbVoEdx5p6rMKAT8m9zIgpnCmQR6BpKUacW5v8Lm9ekDeXmwbJnlz2W22VINGzbko48+IjY2liVLltC3b180TePnn3+mV69eBd1WR44cMdcpbc7ly7B5s3RJicISMhIACPQK1DUOIazJ292b9Ox0vcMQNqRCBWjZ0jpdU2afCu7q6so999zD119/zSuvvIKrqyuaphV0W9WtW5cuXbqwbds2c59ad7/+CpoGvXvrHYmwJZk5mQB4unrqHIkQ1uPj7kNadpreYQgb06+fWncxzcIvDbMmN3l5eSxfvpz777+fChUqMGnSJHJycmjQoAEffvghzz//POXLl2fdunW0a9eOxdYaNm0ly5ZBq1YQHKx3JMKWZOVmAeDh6qFzJEJYjyQ3oii9ekFGBmzcaNnzmCW52b9/PxMmTKBSpUr07t2bX375BW9vb0aNGsWOHTvYu3cv48aNY+rUqURHR/Pee++Rm5vLxIkTzXF6m5CTA2vXQo8eekcibE12nloO193VXedIhLAebzdvSW7EDWrXhkqVLL+QpskL3Vy+fJkff/yRb7/9lv3796NpGgaDgc6dOzNixAjuvfdePD1vbIZ3c3NjwoQJfPvttxw9erREwduSHTvUuhldu+odibA10nIjnJG3uzfpOTLmRhRmMKjPSZtNbkJDQ8nJyUHTNKpUqcLQoUMZPnw44eHGVWENCgoiOzvb1NPbnDVrICAAmjXTOxJha/KTG3cXabkRzsWAQe8QhA3q2hVmz4bz5y23/qLJyY2LiwsDBw5kxIgRdOnSpdiPnz9/PhkZGaae3ub89ht06QJusuiz+I/sXOmWEs4nT8vDxSDLF4ob3Xmn+vn772pZBksw+aP4woULBAQEmHzikJAQkx9rCVFRUURFRZGbm1vsx6alwV9/wSefWCAwYfcMBvXt1VlqPQkBktyImwsOhkaNVI+HpZIbk195zzzzDO+8845R+77zzjuMGDHC1FNZRUkWzty+XQ0obtvWAoEJu5c/BTwzN1PnSISwHkluxK106mTZGVMmv/Jmz57N8uXLjdp31apVfPvtt6aeyuZt3QqlSkHdunpHImyRp9s/yU2OJDfCeWiaJsmNuKk2bSA6GmJjLXN8q7zycnJycHFx3Bf5li2q6qKrq96RCFvk5eYFQEaO44wxE+J2crVcSW7ETbVurX5u3WqZ41v8lZebm8upU6cIDAy09Kl0kZcHf/6pslAhiiLdUsIZpWen4+3urXcYwkZVqABVq6rGAUswekDxxo0bWb9+faHbYmJieP3112/6mPT0dLZu3cqFCxfo6aDLZB89Cteu/ZuFCvFf0i0lnFFqdio+7j56hyFsWJs2NpDcrFu3jsmTJ2MwGApmfcTExDBp0qTbPrZ06dK3TILs2ZYt4OICd9yhdyTCVknLjXBGqVmp+Lr76h2GsGEtW8L8+ZCVBR5mrnFqdHLTsWPHgn9rmsbrr79OeHg4w4cPL3J/g8GAt7c3ERERdOvWDX9//xIHa4t27FADiR306QkzyG+5kTE3wpmkZafh6yHJjbi5xo0hOxsOHVJTw83J6OSmQ4cOdOjQoeD/+cmNI60PZYq9e9UfSIibyW+aT8+WUvTCeaRmS8uNuLUGDdRyDHv2mD+5MXlAcV5eHhstvaynjcvJgf37zf9HEY4lwFMVu0zMTNQ5EiGsJzU7VVpuxC35+UHNmiq5MTeZp1cCx4+rpdul5UbcSoDXP8lNhiQ3wnkkZybj5+GndxjCxjVubJnkxqhuqfwWGh8fH5r9szKkKa027du3L/ZjbNm+fepngwb6xiFsm4erB95u3iRkJOgdihBWk5iZSKRnpN5hCBvXqBEsWwaaprqozMWo5KZjx44YDAZq1arFoUOHCt1mLIPBQE5OjmlRWoEpa0sdPgzly0NQkAUDEw4hwCtAuqWEU0nMSCzokhXiZurWhZQUiIuDSpXMd1yjkpv27dtjMBgIDw+/4TZHMWbMGMaMGUNSUpLRC4IePgy1a1s4MOEQAjwDpFtKOJWkzCRKeZbSOwxh42rWVD+PHtUhuflv8b6b3eZsjhyRxTKFcQK9AqVbSjgNTdNIzEwsGG8mxM1UrQpubnDsGHTubL7jyoBiE+Xmqj+GtNwIYwR6BZKQmaB3GEJYRXpOOjl5OdItJW7L3R0iItTnqTlJcmOiuDjIzIRq1fSORNiDQK9A6ZYSTiP/tS4tN8IYNWuqbilzMjm52bhxI507d2bGjBm33G/69Ol07tyZLZZaQEInp0+rn1Wr6huHsA+BXoFcy7imdxhCWEVSZhKAjLkRRrGp5Oarr75iw4YNtGrV6pb7tWrVivXr1zNr1ixTT2WT8pObKlV0DUPYCRlzI5xJ/sxA6ZYSxqhaFc6ehbw88x3T5ORm27ZtBAUF0eA2RV4aNmxImTJlHLLlJiQEfGTRW2GE0l6lJbkRTkO6pURxhIaqxTOvXDHfMU1ObmJjY6liZLNFlSpViI2NNfVUNik2FsLC9I5C2Iv8lhtN0/QORQiLk5YbURyhoernuXPmO6bJyY2HhwfJyclG7ZucnIyLi2ONXb54UbXcCGGMQK9A8rQ8krOMu2aEsGf5Y278Pf11jkTYg/z6NuZsAzE546hduzbHjx/n2G3mbx07doxjx45RM79Sj4OQ5EYUR6BXIIB0TQmnkJiRiK+7L24uRpVSE04uOFjVurGJlpv77rsPTdN4+OGHSUhIKHKfhIQEhg4disFgYMCAAaaeyiZduCDJjTBeae/SgCQ3wjlIAT9RHK6uULGieZMbk9PqMWPGMGvWLHbs2EGdOnV45JFHuOOOOwgMDCQhIYFt27Yxa9YsLl68SO3atRk7dqz5oraA4qwtpWmq5aZ8eSsEJhyCtNwIZ5KYkSjTwEWxhITA5cvmO57JyY23tzerV6+mX79+7N69mylTptywj6ZpNGvWjAULFuDt7V2iQC2tOGtLJSWpAn7SciOMlZ/cXEuXWjfC8SVlJslgYlEsQUEQH2++45WoQzQsLIzt27ezcOFClixZwuHDh0lKSsLf35+6devSt29f+vbt65CDiUGSG2E8abkRzkS6pURxBQWp4R7mUuLRXi4uLvTv35/+/fubIx67kD/EqHRpXcMQdsTD1QNPV0+ZLSWcQmJmIqW95A1SGC8oCA4dMt/xHKtJxUryZ8D7yyxHUQxebl5k5GToHYYQFidjbkRxBQXB1avmO55Z5umdPn2aNWvWcOzYMZKTk/H396dmzZp07dqVqg64+JIkN8IUktwIZyFjbkRx+flBaqr5jlei5ObatWs88cQT/PzzzwWVVzVNw2AwAGAwGHjggQf4/PPPKe1AfTj5yU0p+WIiikGSG+EsZMyNKC4fH0hLM9/xTE5u0tPT6dKlC/v27UPTNFq1akXdunUJCQnh4sWLHDx4kD///JN58+Zx5MgRtmzZgpeXl/ki11Fysio45OmpdyTCnkhyI5xFYkaitNyIYvHxUbOQc3NV3ZuSMnnMzUcffcTevXupVasW27dvZ8uWLcycOZM33niDmTNnsmXLFrZv307t2rXZu3cvH3/8ccmjNdIXX3xB1apV8fLyomnTpmzatMmsx8/MBAfJ04QVSXIjnIGmaaTnpOPjLqsKC+PlL0Kdnm6e45mc3Pz000+4urqybNkymjVrVuQ+zZo1Y+nSpbi4uDBv3jyTgyyO+fPnM27cOF555RX27NlDu3bt6NmzJzExMWY7R06OarkRoji83LxIzzbTlSuEjcrT8gBwdTHD12/hNPIbDDLM9P3P5OTmxIkT1KtXj4iIiFvuV61aNerVq8eJEydMPVWxfPjhhzzyyCM8+uij1KlTh48//piwsDCmTZtmtnNIciNM4eXmRXqOJDfCsRUkNwZJboR+TE5uXF1dyc7ONmrf7OxsqxTyy8rKYteuXXTr1q3Q7d26dWPr1q1mO092Nri7m+1wwkm4ubgVvPEL4ajyX+MuBqk0Ioz3z5wk/pmPVGImtz/UqlWLXbt2sW/fPho2bHjT/fbu3cuhQ4do3ry5qacy2pUrV8jNzSXkP6WDQ0JCuHCT0oeZmZlkZmYW/D8pKanQz6Kkpqo/wC12EeIGOek5ZJN9y9eWMC9jrmdhXmnZaZABmWmZ8nsXRsufBp6cfOvGA6NfU5qJPv30U81gMGihoaHa0qVLi9xnyZIlWlhYmObi4qJ99tlnpp7KaLGxsRqgbd26tdDtb775plarVq0iHzNx4kQNkE022WSTTTbZ7GRLTEy8ZT5g0LT8xqDiycnJoXv37qxbtw6DwUB4eDi1a9cmODiYS5cucfjwYc6ePYumaXTu3JnVq1fjao75XbeQlZWFj48PP//8M/369Su4/emnn2bv3r1s2LDhhscU1XITFhbG2bNnKXWTQjbvvQfTp8PJk+Z/DsJx3TP3Hsr5lGNWn1l6h+I0jLmehXmlZKVQ6YNKfN3na/pHOs+yPKJkFi+GoUMhOhoCA2++X/41nZiYeMtr2uRuKTc3N5YvX87//vc/pk+fTnR0NNHR0YX28fHxYfTo0bzxxhsWT2wAPDw8aNq0KWvWrCmU3KxZs4Y+ffoU+RhPT088iyhYU6pUqZv+4vz91aBiea8UxWHwNODp6ykfsjq41fUszMsr1wu8wM3bTX7nwmje3upnqVLm+Wwt0ZwfLy8v3n//fSZOnMjmzZs5duwYKSkp+Pn5UbNmTdq2bYu/ldcoGD9+PEOGDKFZs2a0atWKmTNnEhMTw6hRo8x2Dnd3NahYiOJIyUrB30PW7BCOzd1FDZjIys3SORJhT2xmQPH1/P396dmzJz179jTH4UrkgQce4OrVq7z++uucP3+eevXqsWLFCipXrmy2c3h4QJZct6KYkjKTZDFB4fAMBgMerh5k5mTefmch/pGbq36aq5PHIau1PPHEEzzxxBMWO35+y42mmS/LFI5PkhvhLDxdPaXlRhRL/rpS+d1TJWVUcmOu6r7h4eFmOY7eri8T7SMVxoWRJLkRzsLD1YPMXGm5EcZLS1NViq3aclOlSpWClb5NZTAYyMnJKdExbEX+SO7EREluhHGyc7NJz0mX5EY4BU83T1lHTRRLaqp5P0+NSm7Cw8NLnNw4kvzkJiEBKlTQMxJhL5KzkgEkuRFOwd/Dn5SsFL3DEHYkIeHWU8CLy6jk5syZM+Y7owO4PrkRwhhJmaqqpiQ3whkEeAWQmJGodxjCjsTHQ1CQ+Y4ni3+YQJIbUVyS3AhnUsqzFElZsvSCMN61a1C6tPmOJ8mNCSS5EcUlyY1wJgGe0nIjiufaNRtrubl48SJvvfUW3bp1o27dulSrVq3Q/YsXL2bmzJlkZNj24LKoqCgiIyONWuDT11fVurlyxQqBCYcgyY1wJqU8S5GYKcmNMN7ly1CmjPmOV6I6N4sXL2bYsGEkJyeTv0TVfwceHzp0iFdffZVy5coVWhLB1owZM4YxY8aQlJREQEDALfc1GKBSJYiNtVJwwu5JciOcSYBnQMFrXghjxMZCaKj5jmdyy83evXt54IEHSEtLY/z48WzYsIGmTZvesN+gQYPQNI0FCxaUKFBbExoK587pHYWwF8mZyRgw4Ovuq3coQlhcKc9S0i0ljJaeDlevmje5Mbnl5u233yYnJ4evvvqK4cOHA2qtqf+qWrUqISEh7N+/3/QobVClSpLcCOPlF/CTkgrCGQR4ScuNMF5+L4hNtNxs3LiRMmXKFCQ2txIWFsY5B8sEQkOlW0oYT6oTC2dSyrMUyVnJ5Obl6h2KsAP56YFNJDfXrl0zejkFTdPIzHSsUtz53VL5K5kKcSuS3AhnEugVCCCtN8Io+clNpUrmO6bJyU25cuWIjo6+7X65ubkcO3aMihUrmnoqmxQaChkZqvCQELcjyY1wJgGealKGzJgSxjh3Tk0DN+fyCyYnN23btiU+Pp4lS5bccr/Zs2eTnJxM586dTT2VTQoLUz+NyO+EICkrCX9Pf73DEMIq8ltuEjISdI1D2IezZ83bagMlSG4mTJgAwMiRI1m+fHmR+3z33Xc8/fTTuLm58fTTT5t6KptUo4b6efSovnEI+yAtN8KZBHj903IjM6aEEY4fh+rVzXtMk5Ob5s2b8/7773PlyhV69+5NhQoV+PvvvwFo37495cqVY/jw4aSnp/PJJ58QGRlptqBtQenSEBICR47oHYmwB0mZSZTykORGOAdpuRHFcfQo1Kpl3mOWqELxM888w/Lly2nUqBEXL14kMTERTdPYvHkzV69epW7duixbtozRo0ebK16bUqeOJDfCONJyI5yJjLkRxkpNhZgY8yc3JapQDNCjRw969OhBTEwMBw4cIDExET8/PyIjI6lu7nYmG1O7NmzdqncUwh5IciOciaebJ15uXtJyI27r+HH10+aSm3zh4eFGTw13FLVrw+zZkJsLrq56RyNsmSQ3wtkEegXKmBtxW/njVm2mW+rZZ59l9+7d5oxFV8VZODNf7dpqOnhMjAUDE3YvT8sjOTNZkhvhVAI8A6TlRtzWwYMQHGzeFcGhBMnNhx9+SPPmzalVqxaTJ0/m2LFj5ozL6saMGcOhQ4fYsWOH0Y+pU0f9PHjQQkEJh5CalYqGJsmNcCqBXoEy5kbc1v790LCh+Y9rcnLzzDPPULFiRY4fP87rr79OnTp1aNasGR9++CGxTrIuQViYyjYdqAFLWEB+lVapcyOcSYCXtNyI29u3z8aSmw8++ICzZ8+yfv16HnvsMYKCgti9ezfPPfcclStXplOnTsycOZN4By7hazBA06awa5fekQhblpadBoCfh5/OkQhhPdJyI27nyhU4c0Z9jppbiaaCg6ppM336dC5cuMDy5csZPHgwvr6+bNiwgdGjR1OhQgV69erF3LlzzRGvzWnWDHbu1DsKYcvykxsfdzPWFhfCxsmYG3E7+Z+dzZqZ/9glTm7yubq60rNnT77//nsuXrzIvHnz6NOnDy4uLqxYsYIhQ4aY61Q2pWlTiIuDCxf0jkTYqtTsVECSG+FcAjwDZOFMcUs7dqiCuNWqmf/YZpsKfj0vLy/69OmDwWAgMTGRdevWoTno8tn5zWk7dsA99+gbi7BN0nIjnJGHqwdZuVl6hyFs2I4dqtXGYDD/sc2a3OTm5rJmzRrmzp3L4sWLSUlJQdM03Nzc6N69uzlPZTMqV4YKFWDLFkluRNEkuRHOyM3FjZy8HL3DEDZK0+Cvv+CxxyxzfLMkN5s2bWLu3Ln88ssvXL16FU3TMBgMtGnThsGDBzNgwADKlCljjlPZHIMB2rWDTZv0jkTYqoycDAC83Lx0jkQI63F3dZfkRtzUsWNw6ZL6/LQEk5Ob3bt3M3fuXObPn09sbGxBt1PDhg0ZNGgQgwYNIiwszGyB2rK2bWHCBEhPB29vvaMRtiZPywPAxWC2IW5C2DxpuRG3smkTuLhAq1aWOb7JyU2zZs0wGAxomkZERASDBg1i8ODB1MmvbOdE2rWD7GzVf9i+vd7RCFuTn/gbsEDHshA2SpIbcSubNkGjRlDKQrVNTU5ugoODeeCBBxg8eDB33HGHOWOyO/Xrqz/Qxo2S3IgbaajkRlpuhDOR5EbcyqZN0Lu35Y5vcnITFxeHi4vjvFlHRUURFRVFbm5usR/r6godOsDvv8P//meB4IRdy++WMlhiSoAQNkqSG3EzJ0/C6dPQubPlzmFyduJIiQ2YtrbU9bp3VzOmkpPNHJiwe9ItJZyRm4sb2bnZeochbNCaNeDmBh07Wu4cjpWh6Kh7d8jJgXXr9I5ECCH0l5OXg5uLRUqpCTv3229qILGlxtuAJDdmU706RESoP5oQ18ufAp4/JVwIZ5CZk4mnm6feYQgbk5MDa9dC166WPY8kN2bUrRusXq13FMLW+Hr4Av8uwyCEM8jMzcTTVZIbUdjWrZCUpD4vLUmSGzPq0QNOnIDjx/WORNiS/MrE+ZWKhXAGGTkZeLh66B2GsDGLFqmq/s2bW/Y8ktyYUdeuqojfokV6RyJsiSQ3whklZCQQ6BWodxjChmia+nzs108V8LMkSW7MyMdHtd5IciOu5+v+T7dUlnRLCedxLeMaQd5BeochbMjevRAdrZIbS5Pkxsz69YNt2yA2Vu9IhK3I//Yanx6vbyBCWFF8erwkN6KQRYugdGlVF87SJLkxs1691Pz9JUv0jkTYimDfYAwYuJByQe9QhLCaa+nSciMKW7hQfUa6u1v+XEYlN66uriXe3Nyco95B6dLQqRMsWKB3JMJWuLu6U9anrCQ3wqnEp8dT2qu03mEIG3H8OBw8CPfea53zGZXcaJpW4i0vL8/Sz8VmDBgA69fD+fN6RyJsRXm/8pxPkReEcB6XUi9R1qes3mEIG7FggZpwY+kp4PmMSm7y8vLMstmyqKgoIiMjaW6G+Wn9+6uuqXnzzBCYcAjl/cpLy41wGilZKVzLuEZ4QLjeoQgboGnw/ffQt6+aeGMNMubmHyVdW+p6pUurfsUffjBDYMIhVPCvIC03wmnEJMYAUDmwss6RCFuwaxccOgRDh1rvnJLcWMhDD8Hu3eoPKkTlgMqcvnZa7zCEsIrohGgAabkRAHz7rSrcd+ed1junJDcWctddEBgorTdCqV22NudTzpOYkah3KEJY3MlrJ3F3caeif0W9QxE6y8qCuXPVF35XV+udt8RTmDZt2sSPP/7Ivn37iI+PJzu76CXuDQYDJ0+eLOnp7IanJwweDLNnw+TJ1pn6JmxXnbJ1ADhy5Qh3hN6hczRCWNbBSwepVbaWrAouWLECrl61bpcUlDC5GTNmDNOnT0fTtNvuazAYSnIquzRyJHzxBSxfrgZSCedVs0xNQJIb4RwOXj5I3XJ19Q5D2IDZs6FpU6hr5ZeDyd1SP/zwA9OmTaNOnTr8/vvvNGvWDIPBwPHjx/njjz/46KOPqFy5Mt7e3kyfPp1Tp06ZM2670LAh3HEHzJihdyRCb74evoQHhHP4ymG9QxHCojRNk+RGABATA7/+Co88Yv1zm5zcfPXVVxgMBubNm0fnzp3x9FRL21erVo2OHTvy9NNPc/z4ce6++26eeuopLl++bLag7cnIkbB6NZw5o3ckQm/1g+uz98JevcMQwqLOp5wnPj2eusGS3Di7adPA3x+GDLH+uU1Obvbv3094eDj16tUD/u12ur6Lys3NjS+//BJXV1feeuutEoZ6e2+99RatW7fGx8eHwMBAi5/PGA88oP64X32ldyRCb61CW7Ht3DbyNNuu+SRESeyIVeU0mlcsec0wYb/S0+HLL2H4cPDzs/75TU5u0tPTCQ4OLvi/t7c3AAkJCYX2CwgIIDIykq1bt5p6KqNlZWUxYMAARo8ebfFzGcvXFx5+WP2RMzL0jkboqXVYaxIzEzl0WeoDCMf1V+xflPcrT2ipUL1DETqaN08NJH7iCX3Ob3JyU758ea5du1bw/woVKgBwqIjCLpcvXyYpKcnUUxlt8uTJPPPMM9SvX9/i5yqOsWPh8mWYM0fvSISeWlRqgavBlS0xW/QORQiL2Ri9kdZhrZ1yEolQNA0++wx69oQaNfSJweTkplatWsTFxRV0Q7Vt2xZN03jnnXcKTQf//vvviYmJISIiouTR2qmaNeGee+DDD9UfXTgnXw9fGldozNZzlm/FFEIPSZlJbDu3ja4RXfUOReho61bYs0d9sdeLycnN3XffTVpaGhs3bgRg4MCBVKhQgeXLl1OrVi0GDBhA+/btGTZsGAaDgVGjRpktaHPKzMwkKSmp0GYJ48erFVHXrLHI4YWdaB3amo3RG40qnyCEvVl/Zj25Wq4kN07us89Ui0337vrFYHJyc//99/PGG2/g/k91Oj8/P5YtW0ZERARnzpxhwYIFbN68GVdXVyZMmMBYE1O4SZMmYTAYbrnt3LnT1KfBlClTCAgIKNjCwsJMPtattG8PTZrABx9Y5PDCTnSr1o0zCWc4dvWY3qEIYXZrTq6hamBVqgVV0zsUoZNTp+CXX1SrjYuOayAYNDN/hczLy2P79u2cOXMGb29vWrZsSUhIiMnHu3LlCleuXLnlPlWqVMHLy6vg/7Nnz2bcuHE3DG4uSmZmJpmZmQX/T0pKIiwsjMTEREqVKmVy3EX58UdVgnrfPmjQwKyHFnYiLTuNoHeCmNJlCs+0ekbvcBxeUlISAQEBFrmexY1qfV6LjpU7MuMeKe7lrEaOhCVL4PRpy6wAbuw1bfba2C4uLrRs2ZKWLVua5Xhly5albNmyZjlWUTw9PQtq9Fja/ffD//4Hb74JP/1klVMKG+Pj7kOXiC4sPLJQkhvhUI5eOcqxq8eY2mWq3qEIncTEqIrEb71lmcSmOBxq4cyYmBj27t1LTEwMubm57N27l71795KSkqJ3aIBaX+rll1WT3cGDekcj9DKo3iA2x2wuWDlZCEcw9++5+Hv406N6D71DETp55x0oVQpsoRqLycnN0qVLiYiI4IPbDCL54IMPiIiIYMWKFaaeymivvfYajRs3ZuLEiaSkpNC4cWMaN25cojE55jZ0KISFqcxWOKe+tfvi4+7DnANSG0A4Bk3TmPv3XPrV6Ye3u7fe4QgdxMXB11/DM8/oU7Tvv0xObr777juio6Pp16/fLffr06cPZ86c4bvvvjP1VEabPXs2mqbdsHXs2NHi5zaWhwe89JIqcHTkiN7RCD34efjRr3Y/vt//vcyaEg5hz4U9HLt6jMH1BusditDJe++Btzc8+aTekSgmJzd79uwhODj4tvVrqlevTkhIiE21nuht+HCoVEmNvRHO6cH6D3L4ymFZa0o4hG/3fks5n3J0ieiidyhCB5cuqQWin3oKAgL0jkYxObmJi4sjPDzcqH3DwsI4f/68qadyOJ6eauzNnDmwf7/e0Qg9dK3WlfJ+5fly95d6hyJEiaRlp/Hd/u8Y0XgEbi5mn6Mi7MDUqeDqCk8/rXck/zI5ufH19TV6pe8rV65YbUaSvXj0UaheHV54Qe9IhB7cXNwY3Ww03+77lvj0eL3DEcJk3+/7nqTMJB5v+rjeoQgdnDoFn3+uPsuCgvSO5l8mJzf169cnOjr6tt1NO3fu5MyZMwWrhwvF3R2mTIFVq2DtWr2jEXoY1WwUOXk5fLlLWm+EfcrNy+X9P9/nvjr3UbV0Vb3DETp46SUoV05V4bclJic3gwcPRtM0HnzwQU6dOlXkPqdPn+bBBx/EYDAweLAMNPuve++Fli3h+echL0/vaIS1BfsGM6TBED7+62PSstP0DkeIYlt8ZDEn4k/wXOvn9A5F6GDbNlWz7c039a9r818mVyjOzc2lQ4cObN26FS8vL+69917uuOMOAgMDSUhIYNu2bSxevJj09HRat27Nhg0bcHV1NXf8ZmftiqabNqmlGebMgUGDLH46YWNOXTtFzc9q8m7Xdxnfysa++jgAqVBsOXlaHo2mN6KcbznWPizNz85G06BdO0hOht271ZgbazD2mi7R8gsJCQkMHz6cJUuWqINdt8R9/mH79evH119/TWBgoKmnsYqoqCiioqLIzc3l2LFjVn0z7NNHDSw+dEhNpRPO5bGlj7Hk6BJOPX0KPw8bKBDhQCS5sZw5B+bw4MIH+fORP2kZap6K9MJ+LFqkeh9++w26WnGdVKskN/l27tzJkiVLOHz4MElJSfj7+1O3bl369u1LkyZNSnp4q9LjzfDoUahfH155BSZOtMophQ2JToim1ue1mNBqAm91keqO5iTJjWVk5GRQ94u61C1Xl6WDluodjrCyrCyoVw8iItS4UWuy6tpSzZo1o1mzZuY4lFOqVQsmTFADjIcMUS8Y4TwqB1bm+TbP886WdxjeeDjVg6rrHZIQt/T+1vc5m3iWFYMtX3le2J4PP1SzpBYs0DuSm3OotaXs2f/+B8HBtlUnQFjPi21fpLxfecatGidVi4VNO5Nwhrc3vc0zLZ+hVtlaeocjrOzMGXj9dfVZVb++3tHcnCQ3NsLXFz76CJYtg19/1TsaYW0+7j583P1jlh9fLmtOCZuVp+UxbPEwyvmW43/t/6d3OMLKNA3GjoUyZWDSJL2juTWjuqXyl1ioXr06v/32W6HbjGUwGDh58mQxw3Mu994L3bqpEtZ33imDi51Nvzr9eLD+gzyx4gnahrelcmBlvUMSopCP/vyIDdEb+OPhP/D39Nc7HGFlS5aoL+ALFoC/jf/5jRpQ7OKiGnhq167NoUOHCt1m9IkMBnJzc00I0br0HoB47Jhq6nv+eXjjDaufXugsISOBBtMaEFE6grUPr8XVxfbLJ9gyva9nR/L3pb9pOrMpTzZ/kg+6f6B3OMLKUlIgMlJ9Pi1bBtdNjrYqsw4oPn36NADu7u433CbMq2ZNePFFePtt6N8fGjbUOyJhTYFegXzX7zs6f9uZtze9zasdXtU7JCFIyUrhgV8eoEZQDZnR56QmT4bLl+Gzz/RLbIrDqOSmcuUbm8eLuk2YxyuvqGa/Rx5RFSDdZC06p9KxSkcmdpjIa+tfo0FIA/rU7qN3SMKJ5Y+ziUmMYfuj2/Fy89I7JGFl27apGVJvvWU/s3lNHlC8ceNG9u3bZ9S++/fvZ+PGjaaeyul4eMCsWbBnD3wgrb9O6dUOr3Jfnft4aNFD7L2wV+9whBN76feXWHh4Id/3+5465eroHY6wsrQ0GDoUmjWDZ5/VOxrjmZzcdOzYkaeeesqofZ9++mk6d+5s6qmcUosWaiGyiRPh8GG9oxHW5mJwYXbf2dQuW5seP/TgRPwJvUMSTujz7Z/z7tZ3+bD7h/St3VfvcIQOXnkFYmLg22/tqxehRFPBi1OPQ2p3FN/rr0PVqqqwX3a23tEIa/Pz8GPF4BUEegXS9fuunL4m49yE9czcNZOxK8cyodUExrUcp3c4QgcbN8Inn6juqNq19Y6meKxS5+bq1at42/i85qioKCIjI2nevLneoRTw9obvv4d9+2TmlLMq51uONUPW4Gpwpe03bfn70t96hyScwPSd03l82eOMbTGW97q+p3c4QgcpKTBsGLRpY5/FZY1uZEpKSiIhIaHQbZmZmZw9e/amrTLp6els2LCBv//+m4Y2Pu1nzJgxjBkzpmCama1o1gxefVW14vToAa1b6x2RsLawgDA2j9hMjx960P6b9iwfvJxWYa30Dks4IE3TeH3D60zaMImnWjzFxz0+LrQgsnAe48fDxYuwZo31Vvw2J6OTm48++ojXX3+90G07d+6kSpUqRj3+kUceKVZg4l8vvwyrV8PAgWqQcZkyekckrK28X3nWD1tP77m9ufP7O/m277f0j+yvd1jCgaRmpTJi6Qh+OvgTb3Z6k5fbvSyJjZOaPx++/BJmzoRq1fSOxjRGJzeBgYGEh4cX/D8mJgYPDw/Kly9f5P4GgwFvb28iIiJ44IEHeOihh0oerZNyc4N586BRIzVqfelSKGYNReEAAr0CWf3QaoYvGc6AnwcwodUEpnSZgrur++0fLMQtnIw/yX0/3ceJ+BP8POBnSZyd2IkT8Nhj6sv0o4/qHY3pjKpQXBQXFxfatm3rcFO8bbmi6YoVcPfd8N579jUlT5iXpml8+tenPLvmWZpUaMI3fb4hslyk3mHZJFu+nm2Bpml8uftLxq8eT4hfCIsfWEz9EBteDVFYVGamGvqQlAS7doEtXjLGXtMmf///5ptveOWVV0x9uDDBXXfBCy+oCsZbt+odjdCLwWDg6ZZPs2n4JpIyk2g8ozFvb3qb7FyZUieMd+raKXrN7cXjyx5ncP3B7H18ryQ2Tu755+Hvv1W3lC0mNsVhcstN1apVKVWqFDt27MDDw8PccenG1r/pZWdDp06q7oCMvxEZORlMXj+Zd7e+S60ytXi7y9v0qdXHqcZK5Gl5XEi5QHRCNNcyrpGUmURiRiKJmYkkJSXx1l1v8frq1/H198XLzYvSXqUJ8g4itFQooaVCKeVZyql+XwkZCby96W0++esTyvmUY0avGdxd8269wxI6W7RILd782Wfw5JN6R3Nzxn5Gm5zc+Pr6UrduXbZv325ykLbI1pMbgLNnoXFjaNlSxt8IZc/5Pbzw+wusObWGlqEtmdplKh2qdNA7LLO6knaFAxcPsP/ifo5ePcrphNOcvnaaMwlnyMzNLLSvi8GFUp6lcM925/KrlwmYFECeRx7pOenk5OUU2tfPw4/KAZVpENKARuUbFWzBvsHWfHoWl5adxle7v+KNjW+Qlp3Gi21eZELrCfi4++gdmtDZiRPQvDl07gy//GLba0dZPLlp0KABGRkZHDt2zOQgbZE9JDcAK1eqbqq334aXXtI7GmEr1p5ay4trX2Rn3E6aV2zO6GajeaDeA3b1AZan5XEy/iS7z+9mz4U97L2wlwOXDhCXHAeAl5sXNcvUpGpgVbWVVj8rB1amjHcZArwC8HX3xWAw3HA9a5pGWnYaV9KucC7pXMF26top9l3cx76L+0jJSgGggl+FQslOo/KNqFa6mt2t1B6XHMeXu77ks+2fcS3jGkMbDuXNzm9S0b+i3qEJG5CcrL4o5+TAX39BYKDeEd2axZObd999l5deeok///yTFi1amByorbGX5AZU/Zu33oLFi6F3b72jEbZC0zSWHVvGFzu/YPWJ1QR4BTCs4TAebvgwjco3sqkumOzcbI5cOcLu87sLJTPJWckAhJYKpVH5RjQMaUiDkAY0CGlA9aDquLkYN9GzuNdznpbHqWun2Hthb6EtNjkWAF93XxqENKBhSMOChKd+SH2bSx7TstNYeXwls/fNZsXxFXi6evJI40cY32o8VUtX1Ts8YSPy8lRX1Lp1KrGxhyrEFk9ucnNz6du3Lzt37mT69On07t3bpt40TWVPyU1eHgwYoGrgbN0KDRroHZGwNaeunWLGzhnM2juLK2lXqBJYhT61+nBnxJ20C29HgJf1ClamZ6dz4NIB9pzfU5DI7L+4v6BLqUZQDRpXaEyT8k1oXKExjcs3ppxvuRKd01zX8+XUy+y7uK9QwnPkyhFytVxcDC7ULFNTJTshjagbXJc6ZetQJbCK1Vp58rQ8jlw5wpaYLSw7vow1J9eQnpNOi0otGNFoBAPrDbTq31rYh0mTVIHYpUuhVy+9ozGOxZObzp07o2kamzdvJi8vj4CAAGrUqIGvr2/RJzIYWLt2rSmnsip7Sm4AUlOhXTu4ehW2b4eQEL0jErYoOzebDdEbWHh4Ib8e+5VzSedwMbjQMKQhDcs3pH5wfeoF16NecD3K+5XHxWDaQK707HSiE6M5GX+SE/EnOHntJCev/fPv+JPkarm4GlyJLBdZkMg0qdCEhuUbUsrT/NebJa/n9Ox0Dl4+WJDs5Cc/+d1aXm5e1CpTizrl6lCnbB1qlalFeEA4oaVCqeBfwejWp/9Kzkzm1LVTnLp2iv0X9/PnuT/5K/YvEjISMGCgdVhr+tTqQ5/afahZpqY5n7JwIIsXQ79+8OabanFMe2Hx5MalmKNYDQYDubm5ppzKquwtuQE4d04NBouIgLVrwctL74iELdM0jZPXTrL+zHq2nt3K35f+5uDlg6RlpwHg5uJGBb8KVPSvSIBXAB6uHgWbp6snHq4eZORkcC3jGtfSrxGfHl/w7+sH9nq6ehJROoLqQdWpVroatcvWpkmFJtQLroe3u3XWmrP29axpGueSznH4ymEOXT7E4cuHOXxFbVfSrhTs52JwIcQ3hDI+ZSjlWapg8/fwx8XgQp6WR56WR66WS3JmMtcy1O85Ljmu0HGCvINoGdqSlpVa0iqsFS0qtbBIkigcy+7d0L499OwJP/1k2wOI/8viyc2GDRuK/ZgOHWx39kZUVBRRUVHk5uZy7Ngxu0puQLXadOiguqm+/da+XqxCf3laHqevnebg5YOcSzpHXHIcscmxpGSlkJWbVWjLzMnE082T0l6lKe1dWv38Z3p1ae/ShJYKpXpQdSr6VzS5BchcbOnLSkJGAmcTzxYayJw/df36TUPD1eCKi8EFF4MLfh5+BHkHEeQdRIhvCNWCqhFROoKI0hGU8ynnEMMBhPWcPQt33AGVKsH69XCTzhabZfHkxlHZ0pthcc2bB4MGwZQpqtCfEM7Onq9nIcwtKUkNY0hIUAOIb7J6kk0z9po2rdNX2KSBA+HwYTU1vFIlGDJE74iEEELYgqwsuP9+OHNGTUCxx8SmOMyS3GzZsoUNGzYQGxtLRkYGX3/9dcF9Z86cISsri5o1ZWCbNUyaBLGxMGIElC2r+lSFEEI4r7w8GD5cTflesQLq1tU7IssrUXJz4sQJHnzwQXbu3AmowXQGg6FQcvPuu+8yY8YM1q9fT7t27UoWrbgtgwGmT4crV6B/fzXAuGVLvaMSQgihB02DCRNg7ly1ZlSXLnpHZB0mj/a7ePEiHTp0YMeOHTRr1oxJkyZRvXr1G/YbNmwYmqaxYMGCEgUqjOfmpl7ITZuqVcQPH9Y7IiGEEHp45x34+GOIilITTpyFycnN22+/zfnz5xkzZgzbtm3j1VdfJaSIIistWrTA39+frbKMtVV5e6vCTJUqQdeucOqU3hEJIYSwpk8+UWMwJ06E0aP1jsa6TE5uli1bhq+vL++///5tpyJGRERw9uxZU08lTBQYqKoX+/iolcSjo/WOSAghhDVERcG4cfDCCyq5cTYmJzexsbHUqFEDT0/P2+7r6enJtWvXTD2VKIEKFeCPP1RXVadOquCfEEIIxzV9Ojz5pBprM2WKc9Y9Mzm58fPz4/Lly0btGxMTQ5kyZUw9lSih0FCV4OTlqSXt4+L0jkgIIYQlfPml6oJ6+ml47z3nTGygBMlN48aNiYuL48CBA7fcb8OGDVy4cIGWMmVHV5UrqwQnPV2Nlr9wQe+IhBBCmNOsWTByJIwZAx995LyJDZQguXnkkUfQNI0RI0Zw/vz5Ivc5efIkI0aMwGAw8Nhjj5kcpDCPiAiV4CQlqXVFZBiUEEI4hu++g0cfhVGj4LPPnDuxgRIkNwMHDqR///7s2rWLyMhIBg4cSExMDACvvfYa9957L3Xr1uX06dM89NBD9OjRw2xBW0JUVBSRkZE0b95c71AsqkYN2LhRVats1w5OntQ7IiGEECUxa5Yq0vfII2ogsbMnNlDCtaVycnJ49dVX+fjjj8nM/Hc1YIPBgKZpeHh4MG7cON566y1cXV3NErClOctaNGfPwp13QnIy/P47REbqHZEQ5ucs17NwXh9/DM88A48/Dl98AS76rlVrcVZdOPPKlSusWLGCAwcOkJiYiJ+fH5GRkdx9991UqFChpIe3Kmd6M7x4UdXAOX9eTRlv0kTviIQwL2e6noVz0TR44w01zfv552HqVOdosZFVwU3kbG+G8fHQowccOwZLlkCHDnpHJIT5ONv1LJxDbq6aDRUVBW+/rQr1OQtjr+kSFfHLyckx9eHCRgQFqW6pZs2gWzf4+We9IxJCCHEzqanQr5+qZTNzpnMlNsVhcnLTu3dvKlSowKhRo1i/fr0ZQxLWVqqUWin2vvvggQfUSHshhBC25eJFVYz1jz/g119BJiHfXInq3Fy9epWZM2fSpUsXQkNDefbZZ9m1a5c54xNW4uEBP/wA48fDU0+pPtzcXL2jEkIIAXD0KLRqpSaDbNwIPXvqHZFtMzm52bVrF0ePHmXixInUqlWLuLg4PvzwQ1q0aEGtWrWYPHkyR48eNWeswsJcXOD991Xxpw8+UE2fycl6RyWEEM5t82Zo3VotiLxtm0z+MEaJJo3VqFGDiRMncujQIXbv3s2zzz5LWFgYx48f5/XXXycyMpKmTZvywQcfcM7CixqdOXOGRx55hKpVq+Lt7U21atWYOHEiWVlZFj2vIxo3DpYtgw0b1AV1+rTeEQkhhHP66SdVtqNBA9iyRVWbF7dnthnxjRo14t133+XMmTNs2rSJxx9/nLJly7Jnzx6ef/55qlataq5TFenIkSPk5eUxY8YMDh48yEcffcT06dN5+eWXLXpeR9Wzp/qGkJ4OzZurZlAhhBDWoWlqJtQDD0D//rBqFQQG6h2V/bDoVPBz584xcuRIVq1ahcFgINfKgzjee+89pk2bxqlTp4x+jEwdLezqVbj/fpXcTJumynsLYS/kehb2KDkZhg2DhQtVHZuJE52jho0xjL2m3cx94sTERBYuXMicOXNYv349eXl5AJQuXdrcpzIqlqCgoFvuk5mZWai6clJSkqXDsitlyqhvDE8/rUbm//23GpfjZvZXjhBCiOPHoW9fNXB48WLo00fviOyTWbqlMjIy+Omnn+jXrx/ly5fn0UcfZe3atXh4eDBgwAAWL15808U1LeXkyZN89tlnjBo16pb7TZkyhYCAgIItLCzMShHaD3d3VdY7Kgo+/xzuvlu16AghhDCf5cvVMIDcXNi+XRKbkjC5WyonJ4fVq1czd+5cli5dSmpqKpqm4ebmxp133sngwYPp168fvr6+JQpw0qRJTJ48+Zb77Nixg2bNmhX8Py4ujg4dOtChQwe++uqrWz62qJabsLAwaca+iT/+UN1Uvr6q4F+LFnpHJMTNSbeUsAd5eWp8zWuvwT33qBW+AwL0jso2WXz5hbJly3Lt2jU0TcNgMNC6dWsGDx7M/fffT5kyZUwO/L+uXLnClStXbrlPlSpV8PLyAlRi06lTJ+644w5mz56NSzFXEZM3w9s7e1YlOLt2wYcfwpgx0h8sbJNcz8LWxcer8TW//gqTJ8P//uf4i1+WhMXH3MTHx1O/fn0GDx7MoEGDCA8PN/VQt1S2bFnKli1r1L6xsbF06tSJpk2b8s033xQ7sRHGCQtT08Sffx7GjlU1GL78Evz99Y5MCCHsx59/wsCBkJKiym/cfbfeETkOk5Obv//+m8jISHPGUiJxcXF07NiR8PBw3n//fS5fvlxwX/ny5XWMzDF5eMDHH0ObNvDII2ptqrlzpbiUEELcTl6eavV+6SXVtT9vnvrSKMzH5KYNW0psAH777TdOnDjBH3/8QWhoKBUqVCjYhOUMGAA7d4KfH7RsqSob/zNBTgghxH+cP69aaJ57Ti13s369JDaW4DD9NsOGDUPTtCI3YVk1a8LWrWpNqmefVQUAL1zQOyohhLAtCxdC/fqwd69arPidd9RsVGF+DpPcCH15eqr6N6tXw759qlT48uV6RyWEEPpLSoLhw+G++6B9ezhwQBa+tDRJboRZdesG+/erfuRevVThP6mLKIRwVps2QcOG8MsvMGsWLFgARs6RESUgyY0wu+BgNa1x5kw1UK5BA1i3Tu+ohBDCerKy1IDhDh2gUiXVoj18uJTNsBZJboRFGAyq1Wb/frWKbefOarXxtDS9IxNCCMvat09NsHj/fXjrLVU6IyJC76iciyQ3wqKqVlWtNh9+CNOnq1ac9ev1jkoIIcwvIwNeeUWVxsjKgr/+Uq03rq56R+Z8JLkRFufiAs88o77NVKwInTrB449DYqLekQkhhHls2gSNGsF778Grr8Lu3VL3S0+S3PwjKiqKyMhImjdvrncoDqtWLdVqExUFc+ZA3bqwdKneUQkhhOmSkuCJJ9QsqNKlYc8etUaUh4fekTk3SW7+MWbMGA4dOsSOHTv0DsWhubioN4KDB1UXVZ8+0Ls3nD6td2RCCFE8y5apL2nffQeffKKWoqlbV++oBEhyI3QSHq7q4Pzyi/qmExkJb7yh+qyFEMKWnT2ratbcc49KZg4eVEVMZWyN7ZDkRujGYFBvEIcPw9NPw+uvq+qdq1bpHZkQQtwoO1vNgKpTR1VlnzMHVq5UM0KFbZHkRujOzw+mTlXTxsPCVOXO++6DmBi9IxNCCOX336FxY3jhBbVY8JEjMGiQ1K2xVZLcCJtRpw6sXatWF//zT/X/qVPVlEohhNDD8eNqXGDXrhAYqBYK/uQTCAjQOzJxK5LcCJtiMMDAgepb0ahR8L//qYHHa9boHZkQwpkkJMCECWpMzf79MH++mu7duLHekQljSHIjbFKpUvDBB2r13JAQtWZV794q6RFCCEvJyYFp06BGDZgxAyZNUuMC779fuqDsiSQ3wqbVq6dq48ybp1bSrVcPxoyBy5f1jkwI4Wjyx9U88YRa+Pf4cXj5ZfD21jsyUVyS3AibZzDAAw+ob09Tp8KPP0K1aurfMnVcCFFSRY2r+eYbqFBB78iEqSS5EXbDywuefRZOnFCr6776qqp6PGcO5OXpHZ0Qwt5cvQrjx/87ruann2DjRmjaVO/IRElJciPsTtmyarbCwYPqTejBB9UKvGvX6h2ZEMIepKXBlCmqBfjLL/8dVzNggIyrcRSS3PxD1payPzVrwsKFsGGDekO6807o3FkV1xJCiP/KzlaDhKtXh4kTYehQOHlSxtU4Iklu/iFrS9mv9u1h2zZYskQ1M7dpA3ffrVblFUKIvDw1KaFePRg9Wn0JOnJEtQAHB+sdnbAESW6EQzAY1IDAPXvUm9iJE6rLqn9/OHRI7+iEEHrIy4MFC1StrEGDVIvN7t3www8QEaF3dMKSJLkRDsXFRc2sOnhQzXbYtUt9WxsyRDU/CyEcn6bB0qXQpIn6glOxoqp6vnw5NGqkd3TCGiS5EQ7JzQ2GDYOjRyEqCv74A2rXhscfVyv6CiEcj6aphSxbtIA+faB0aTX76bff1KQD4TwkuREOzcND9bGfOAHvvKMGINeoAePGwcWLekcnhDAHTVMF+Nq0gbvuUtf92rWwbh20a6d3dEIPktwIp+DtrepZnDql1quaPRuqVlVrx1y4oHd0QghTbdgAHTuqAny5ubBqFWzerAYNC+clyY1wKv7+Krk5fRqeew6+/lolOePGQVyc3tEJIYyhabB6tWqV6dgRkpPh11/VrMnu3aVWjZDkRjip0qVh8mQ4cwZeegm+/VbNnhgzBqKj9Y5OCFGUvDxYvBiaN4cePSArS5WA2LVLrQUlSY3IJ8mNcGqBgfDaayqhee01mD9fTRcdPlxWIBfCVuTmwty50LAh9OsHfn6wZo1qqendW5IacSNJboQASpVSVUrPnIF331WzKyIjVTn2PXv0jk4I55SVBbNmQZ06MHgwhIbCpk2wfr2qSC5JjbgZSW6EuI6fHzzzjBp4PGOGKvjVpImagbF5s97RCeEcMjLgiy/UzMZHHlELW+7YoaZ5t22rd3TCHkhyI0QRPD3hscdUnZwff4SYGDV4sX17NRtD0/SOUAjHc+0avP02VKkCY8eqqd0HDsCiRdCsmd7RCXsiyc0/ZOFMURQ3N9Ucvn+/GriYmQk9e6py7t9+q5rNhRAlExOjSjWEhcHrr6sCfEeOwJw5qsK4EMVl0DT5Dnq9pKQkAgICSExMpFSpUnqHI2yMpqmKp++/D8uWqbLuTz8NI0eqwcnCtsj1bNsOHID33lODhf381GzFsWMhJETvyIStMvaalpYbIYrBYIAOHVRNjYMHVSvOq6+qb5zjx8s0ciFuR9NU5eC77lItoBs2qAQnJgbefFMSG2EektwIYaLISPjqK5XQPP20qnpcrRo8+KAaiCyE+FduLvz8s1r3qXNniI1Vq3OfOKGKaPr76x2hcCSS3AhRQuXLq2+cZ8/CRx+p1YebNoUuXdTsDun4Fc4sKQk+/hhq1oT771dlF1atgr171RcBd3e9IxSOSJIbIczE11eNFzh2DH76SZWEv+suqF9ftepkZuodoRDWc/w4PPUUVKqkljpp2VJN5167VpZIEJYnyY0QZubmpor//fWXGnwcEaEqHletCm+8IauRC8elaapycK9eUKuWGig8bpzquv3xR5nOLaxHkhshLMRgULVxli6Fw4dVmfgpUyA8HIYOhZ079Y5QCPNIS4OZM9W07W7dVBftV1+pn2+8oWYVCmFNktwIYQW1a8P06WoQ5dtvqxad5s2hdWuYNw+ys/WOUIjiO3sWXnxRzRYcNUqNq1m3To2nGTECvLz0jlA4K0luhLCi0qVhwgQ1Q2TxYvD2hkGDVEXWN9+ES5f0jlCIW9M02LJFDQ6uWhWmTYNhw+DkSVVJuGNHGU8j9CfJjRA6cHVVVVjXrlWFzHr1Ui06oaEq2dmwQWZZCduSlKQSmcaN1fpOe/eqWVDnzsEHH6hERwhbIcmNEDqrV08t0nnuHLzzjqqR07GjWizw00/VejtC6EHT1AynRx+FChXUbMAqVWDFCrU8wpNPSn0aYZskufmHrC0l9BYUpFYkP3IE/vhDTSGfMEFNpR0xArZvl9YcYR3JySrhbtpUFd377Td44QU162nxYlWZ20U+PYQNk7Wl/kPWohG25MIFmDVLzUSJjlYJz4gR8NBDULas3tHZPrmei2f3bpXUzJmjZkDdfTc8/jj06KG6UoXQm6wtJYQDKF8eXn5ZDdZcsULVDnn+eTW1dsAAVek1N1fvKIU9u3ABPvwQGjVSLTXLl6sWwzNnVBmDu++WxEbYHze9AxBC3J6rq+oK6NkTLl9WBdG+/lr9PzRUlbEfMkSN0xHidjIyYMkS+O47WL1avb7uuUfVpOnZUxWiFMKeScuNEHamXDlV9XX/fjUOp1evfwuoNWmi1re6cEHvKIWt0TTYvBlGjlQtggMHQnw8fP45nD8Pv/yiEhxJbIQjkDE3/yF99MIeZWaqRTq//x6WLYOcHOjaFR54QE05DwrSO0J9OPv1rGmq1MAvv6jWvlOnVIXshx9WLX01a+odoRDFY+w1LcnNfzj7m6Gwf/Hx8PPPalDopk2qy6FzZ+jfH/r2VS0/zsIZr2dNUwODf/lFbSdOQGAg9Ounkpr27WWmk7BfktyYyBnfDIXjunBBVY39+WdVGBBUDZ3+/dWHXfnyuoZncc5yPWua6qLMT2jOnFGtdf36qb91587g4aF3lEKUnFPOlurduzfh4eF4eXlRoUIFhgwZQlxcnN5hCaGb8uVh9GhVN+f8eVVh1tVVFWOrWBE6dFCFAk+f1jtSUVzZ2WqNsmeegcqVoWVLNUC4Rw+1MveFC2rxyh49JLERzsehWm4++ugjWrVqRYUKFYiNjeXZZ58FYOvWrUYfw1m+6QnndvWqmi3zyy/w++/qgzIyUk37vftutaCnu7veUZaco13PsbFq+v/KlSqBSUpSlYPvu0+10LRtK9O2hWOTbilg6dKl9O3bl8zMTNyNfKd2tDdDIW4nKUl9UC5frmrpXLwIAQGqK+POO9VWo4Z9LoZo79dzdrZapHLlSrUdOKDGy9xxx7+lAZo0kTE0wnkYe0077KS/+Ph4fvzxR1q3bn3LxCYzM5PMzMyC/yclJVkjPCFsRqlS6pv/ffdBXp4ajLpihVrUc9w49QEbGvpvotOhg/q/ML/sbNi1C9avV2OkNm+GlBQICVHdSy+/DN26Oe/sNyGM5XAtNy+88AKff/45aWlptGzZkmXLllGmTJmb7j9p0iQmT558w+32+k1PCHNKSVEzrn7/XW3796vbw8NV11Xr1tCmDTRoYJv1UWy95ebKFZXM7Nypxs9s2QKpqeDnp7qYOnRQyUyjRtI6IwQ4ULfUzZKP6+3YsYNmzZoBcOXKFeLj44mOjmby5MkEBASwbNkyDDdpUy+q5SYsLMxm3wyF0NOlS+oDeMsW2LpVfTBnZYGvr+oqad0amjdXXSWVKunflWVLyc2lS+r3tWuXah3btQtiYtR9pUr9m8x07Kh+f7aYLAqhN4dJbq5cucKVK1duuU+VKlXw8vK64fZz584RFhbG1q1badWqlVHns6U3QyFsXUaG+pDeuvXfhOfyZXVfuXJqraJ69dSaWLVrq59ly1ov6dHrej5//t8EJn+LjVX3BQaq5KVp03+3iAhpmRHCGA4z5qZs2bKUNXH54/y87fqWGSGE+Xh5qW6pNm3guedUvZXY2H8/2HfvVnV2Tp9W43lAjRfJT3byE57atdUHvL3M0NI01RJz4oRa1PTkyX//feKEmo0G6rk2bapWcc9PZKpW1b9FSwhHZ/PJjbG2b9/O9u3badu2LaVLl+bUqVO89tprVKtWzehWGyFEyRgMarBxaCj07v3v7ZmZ6kP/yBG1HT0Kf/8NCxao2VqgpjBXqqS20NB/f1aooJKE67eAAMtMec7JgWvXVJXn/O3iRYiLU0lbXBxER6skJiXl38dVqADVqqkkrVcvqFNHJTKVK0siI4QeHCa58fb2ZuHChUycOJHU1FQqVKhAjx49mDdvHp6ennqHJ4RT8/RUK5b/d9VyTVPF5o4eVdvZs3DunNr271c/U1NvPJ7BoBKc/ETHy+vGTdMgLU3tf9996jHZ2YW3nBz1MyNDJTI3mywZHKyKHlasqIrlPfQQVK+uEpqICDXmSAhhOxwmualfvz5//PGH3mEIIYrBYFCtHhUqqIG0/6VpKrn5b2vK9f9PTFQtQxkZ/24JCYXHsHh5gY+PGqTr7v7vlv9/T0+VKJUpU7iFqHRpNUZIKvwKYV8cJrkRQjgeg0FNi/bzg7Cw4j8+KUm17Pz4o5qRJIRwDjI+XwghhBAORZIbIYQQQjgUSW6EEEII4VAkuRFCCCGEQ5HkRgghhBAORWZL/SMqKoqoqChycnIAWR1cCEeQfx3L9SyEY8i/lm+3cpTNry1lbfnrUQkhhBDCNp09e5bQ0NCb3i/JzX/k5eURFxeHv7//TVcSB2jevDk7duwo1rGL+xhLnyN/BfSzZ88avaigLT7v4u5vjedta78nU56zpWOyxjls9XnLtW2ZczjK85b3tJvTNI3k5GQqVqyIyy1Wm5Vuqf9wcXG5ZTaYz9XVtdirDBf3MdY4B0CpUqWMfowtPm9TYgLLPm9b/D1B8Z6ztWJyxuct17blzgH2/7zlPe3WAgICbruPDCg20ZgxYyz+GGucwxrHt/TztvRzNuUctvh7MoU8b9vY39THWPr48rxtY39T2OLfzpzPW7qlnFhSUhIBAQEkJiaa9C3BXjnj83bG5wzyvOV5Owdnfd63Ii03TszT05OJEyc63arpzvi8nfE5gzxved7OwVmf961Iy40QQgghHIq03AghhBDCoUhyI4QQQgiHIsmNEEIIIRyKJDcCgN69exMeHo6XlxcVKlRgyJAhxMXF6R2WRZ05c4ZHHnmEqlWr4u3tTbVq1Zg4cSJZWVl6h2Zxb731Fq1bt8bHx4fAwEC9w7GYL774gqpVq+Ll5UXTpk3ZtGmT3iFZ1MaNG7nnnnuoWLEiBoOBxYsX6x2SxU2ZMoXmzZvj7+9PcHAwffv25ejRo3qHZXHTpk2jQYMGBbVtWrVqxcqVK/UOy2ZIciMA6NSpEz/99BNHjx5lwYIFnDx5kv79++sdlkUdOXKEvLw8ZsyYwcGDB/noo4+YPn06L7/8st6hWVxWVhYDBgxg9OjReodiMfPnz2fcuHG88sor7Nmzh3bt2tGzZ09iYmL0Ds1iUlNTadiwIZ9//rneoVjNhg0bGDNmDNu2bWPNmjXk5OTQrVs3UlNT9Q7NokJDQ5k6dSo7d+5k586ddO7cmT59+nDw4EG9Q7MJMltKFGnp0qX07duXzMxM3N3d9Q7Hat577z2mTZvGqVOn9A7FKmbPns24ceNISEjQOxSzu+OOO2jSpAnTpk0ruK1OnTr07duXKVOm6BiZdRgMBhYtWkTfvn31DsWqLl++THBwMBs2bKB9+/Z6h2NVQUFBvPfeezzyyCN6h6I7abkRN4iPj+fHH3+kdevWTpXYACQmJhIUFKR3GKKEsrKy2LVrF926dSt0e7du3di6datOUQlrSExMBHCq6zg3N5d58+aRmppKq1at9A7HJkhyIwq88MIL+Pr6UqZMGWJiYliyZIneIVnVyZMn+eyzzxg1apTeoYgSunLlCrm5uYSEhBS6PSQkhAsXLugUlbA0TdMYP348bdu2pV69enqHY3EHDhzAz88PT09PRo0axaJFi4iMjNQ7LJsgyY0DmzRpEgaD4Zbbzp07C/Z/7rnn2LNnD7/99huurq48/PDD2GOvZXGfN0BcXBw9evRgwIABPProozpFXjKmPG9HZzAYCv1f07QbbhOO48knn2T//v3MnTtX71CsolatWuzdu5dt27YxevRohg4dyqFDh/QOyybIquAO7Mknn2TgwIG33KdKlSoF/y5btixly5alZs2a1KlTh7CwMLZt22Z3zZzFfd5xcXF06tSJVq1aMXPmTAtHZznFfd6OrGzZsri6ut7QSnPp0qUbWnOEYxg7dixLly5l48aNhIaG6h2OVXh4eFC9enUAmjVrxo4dO/jkk0+YMWOGzpHpT5IbB5afrJgiv8UmMzPTnCFZRXGed2xsLJ06daJp06Z88803uLjYb2NmSf7ejsbDw4OmTZuyZs0a+vXrV3D7mjVr6NOnj46RCXPTNI2xY8eyaNEi1q9fT9WqVfUOSTeaptnle7YlSHIj2L59O9u3b6dt27aULl2aU6dO8dprr1GtWjW7a7Upjri4ODp27Eh4eDjvv/8+ly9fLrivfPnyOkZmeTExMcTHxxMTE0Nubi579+4FoHr16vj5+ekbnJmMHz+eIUOG0KxZs4JWuZiYGIceU5WSksKJEycK/n/69Gn27t1LUFAQ4eHhOkZmOWPGjGHOnDksWbIEf3//gta6gIAAvL29dY7Ocl5++WV69uxJWFgYycnJzJs3j/Xr17Nq1Sq9Q7MNmnB6+/fv1zp16qQFBQVpnp6eWpUqVbRRo0Zp586d0zs0i/rmm280oMjN0Q0dOrTI571u3Tq9QzOrqKgorXLlypqHh4fWpEkTbcOGDXqHZFHr1q0r8u86dOhQvUOzmJtdw998843eoVnUiBEjCl7b5cqV07p06aL99ttveodlM6TOjRBCCCEciv0OMBBCCCGEKIIkN0IIIYRwKJLcCCGEEMKhSHIjhBBCCIciyY0QQgghHIokN0IIIYRwKJLcCCGEEMKhSHIjhBBCCIciyY2wS/mrXNsSW4xJT7b++6hSpQoGg4EzZ87ocv6OHTtiMBhYv369Lue/mZYtW1K2bFlSUlIK3W7rf09TfPfddxgMBr766iu9QxFmJsmNEE5s7969TJo0icWLF+sdivjH+vXrmTRpki5Jz88//8xff/3F+PHj7WKNsbS0NLy9valbt65Jjx88eDARERFMnDiRtLQ0M0cn9CTJjRBmUqtWLWrVqqV3GMWyd+9eJk+eLMmNDsLDw6lVqxY+Pj6Fbl+/fj2TJ0+2enKTl5fHK6+8QqlSpXjyySetem5TrVmzhoyMDHr16mXS493c3Hj++eeJi4vjs88+M3N0Qk+S3AhhJkeOHOHIkSN6hyHsxHfffceRI0do0aKF3qEAsHr1ao4fP06/fv0oVaqU3uEYZdmyZQAmJzcAAwcOxNPTk2nTppGXl2eu0ITOJLkRQgjBzJkzARg0aJDOkRhH0zRWrFhBUFAQrVu3Nvk4AQEB9OjRg+joaNasWWPGCIWeJLkRdm/lypW0b98ef39/AgIC6NmzJ3v27Lnp/levXuX555+nVq1aeHt7U7p0aTp27MiPP/6Ipmk37D979mwMBgPDhg0jNTWVl19+mZo1a+Ll5UXHjh0L9itqwOWwYcMKbr/ZVqVKlRvOGRMTw+jRo6latSqenp6ULVuWnj17snLlyiKf06RJkzAYDEyaNInExETGjRtHeHg4np6eVK9enTfeeIOcnJxCj6lSpQrDhw8H4Ntvvy0U0/XP68KFC3z22Wd0796dKlWq4OXlRenSpenQoQPff//9TX/PxZGbm0v58uUxGAzs3LnzpvtNmDABg8HA+PHjb7hv+/btDBw4kEqVKuHh4UFISAgDBgy45WvhZrKzs/nss89o0aIFpUqVwtfXl4YNG/LWW2/dcmxGWloa77//Pi1btiQwMBAfHx9q1KjBkCFD2LBhQ6F9ixpQbDAYmDx5MgCTJ08u9DcZNmwYCQkJeHt74+7uzsWLF28aR69evTAYDERFRRn1fFNTU1m+fDleXl507tzZqMfk0zSNp556CoPBQPXq1YmOjgbgzJkzhV7fX331FY0bN8bHx4dKlSrx1FNPkZycDKi//wcffEDdunXx9vYmNDSUF198kaysrJued/fu3cTFxdGjRw9cXV0Lbo+Ojubxxx8nIiICT09P/P39iYiIoF+/fsybN6/IY+W3/MyfP79Yz13YME0IOwRogDZt2jTNYDBoFSpU0Jo0aaL5+vpqgObn56cdPnz4hscdP35cCwsL0wDNw8NDa9KkiRYREVFwvIcffljLy8sr9JhvvvlGA7T7779fa9KkiWYwGLQ6depojRs31rp163ZDTNd76623tDZt2hS5Va5cWQO0ypUrF3rMtm3btMDAQA3QfH19taZNm2qhoaEFx3/11VdveF4TJ07UAG3cuHFanTp1NDc3N61Ro0ZalSpVCh736KOPFnpM//79tRo1amiAFhwcXCi2J598smC/N954QwM0b29vrVq1alqzZs208PDwguOOGjXqln8jY40dO1YDtPHjxxd5f15enlapUiUN0LZv317ovg8//FAzGAwaoAUFBWmNGzfWypQpowGau7u7tmDBghuOl//7P336dKHb09LStM6dOxfEX6dOHa1Bgwaai4uLBmiNGjXSrly5csPxoqOjtTp16hQ8rkaNGlqTJk20oKAgDdA6dOhQaP8OHTpogLZu3bqC29q0aVPw+gwLCyv0N3nrrbc0TdO0QYMGaYD2wQcfFPl7unDhgubm5qZ5eHhoV69eLXKf/1qzZo0GaK1atbrpPkX9PXNycrRhw4ZpgFavXj3t/PnzBfedPn264PU9fvx4DdCqVaum1atXT3Nzc9MArXPnzlpubq7Wt2/fgt91rVq1Cv6WDz/88E3jmTRpkgZoc+bMKXTOsmXLaoDm4+Oj1a9fX2vUqFHB36Bhw4ZFHmvfvn0F8QnHIMmNsEv5b7Q+Pj7aN998U3B7UlKS1qVLFw3QHnjggUKPycvL05o1a1bwQXPhwoWC+1auXFmQGH3xxReFHpef3Li6umo1a9bUDh06VHBfenr6DTEZ4+LFiwUfYlOnTi24PTU1tSBxuP/++7WkpKSC+2bPnq25urpqgLZixYpCx8tPbtzd3bX27dtrsbGxBfctXbq04HH/Tfjyn9vQoUNvGuumTZu0P/74Q8vJySl0+759+wo+zNevX3/D44qb3Pz5558aoFWqVEnLzc294f7169drgFa9evVCt69cuVIzGAxa2bJlb0hivvrqK83NzU3z9/fX4uLiCt13s+RmwoQJGqBVrFhR27VrV8Htx48f12rXrl3wt7leTk6O1rRpUw3QmjVrVug1ommatmfPnhteV0UlN5r2799y4sSJN/wONO3fRKRBgwZF3v/BBx9ogNa/f/8i7y/K5MmTNaBQUvtf//17ZmZmavfdd58GaC1atLghkcpPbtzc3LSAgADt999/L7jvwIEDBcln3759tdDQUG3Pnj0F969bt07z8PDQAO3gwYNFxtOsWTPN1dVVi4+PL7jtySefLHg9JycnF9r/8OHD2owZM4o8Vk5Ojubt7a0BhRI0Yb8kuRF2Kf+NduzYsTfct3//fg3QAgICCt2e/6Hg6elZ5BvYu+++W/BN8/rWm/wEACj0YXezmG4nKytLa9eunQZoAwcOLHTfl19+qQFaSEhIocQp3xNPPKEBWrt27Qrdnv+B6O3trZ09e/aGx917770aoH344YeFbjcmubmV33//XQO0xx577Ib7ipvcaJpW0IpWVLL0+OOPF9ly1aRJEw3QlixZUuQx85OV119/vdDtRSU3iYmJmo+PjwZoixYtuuFY27dv1wDNYDBoJ06cKLj9p59+KmgBK6pVpyimJjd5eXkFLXLXJwT5GjRooAHasmXLjIpD0zRtxIgRGlDQOlSU6/+eqampWvfu3TVA69ixY6EkPF9+cgNoH3300Q33v/TSSwX3F/W7HjhwYJGvWU3TtPPnz2sGg0Fr3759odvzY9q3b99tnvGN8l8P27ZtK/Zjhe2RMTfCrj366KM33Fa/fn28vLxITEzk6tWrBbf/9ttvAAwYMIDy5cvf8LhRo0bh6elJdHQ0R48eveH+unXr0qRJkxLHPHbsWDZt2kSTJk2YNWtWofvyY3zsscfw8vK64bFPP/00AFu3biU1NfWG+3v06EFoaOgNtzdv3hyAU6dOmRRzcnIyX375JUOHDqVbt260a9eOtm3b8uKLLwKwb98+k477X/mDWefOnVvo9pycHH755RdA1SbJFx0dze7duwkODqZ3795FHjP/9v+OeSnK5s2bSUtLIzw8nD59+txwf/PmzWnVqhWaphUafLpkyRIARowYQZkyZW57npIwGAwMHToUUGOlrrd37172799P+fLl6dGjh9HHvHLlCgBBQUG33TcxMZHu3buzevVq7r77blauXIm/v/8tHzNixIgbbmvUqFHBOfv27XvD/Y0bNwaKfs0uX74cTdNumCUVFhYGwC+//FLk+LlbyX/uly9fLtbjhG2S5EbYtWrVqhV5e7ly5QAKVVk9duwYAJGRkUU+xt/fv+DNMX/f69WpU6dEsQJMmzaNGTNmEBwczOLFi/H29i50/+1irFGjBh4eHuTm5nLy5Mkb7r/Z7yM4OBjghqqzxtizZw+1a9dm5MiRfPfdd6xZs4bNmzezZcuWgsG/8fHxxT5uUfITl19++YXs7OyC23/77TeuXr1Ko0aNqF27dsHtBw4cACAjI4O2bdsWueUPPo6Njb3t+fN//7Vr175pNd78gnHXv0YOHz4MqOq+1jB8+HAMBgNz5swpNFA8P9l56KGHCg2yvZ2MjAwAPD09b7tv586d2bx5MwMHDmTRokVFJuHXK1euXJFTy/Ov0eJcw/luNgV8zJgxuLu788Ybb1C1alVGjRrFjz/+SFxc3G2fV/61mJ6eftt9he2T5EbYNV9f3yJvd3FRL+3rv73lv0nmf9AXJSQkBKBgFocx5zLWpk2bePrpp3F3d2fBggUFidT1bhejwWAoeNMvToxF/T6MkZuby/33309cXBx33XUXGzZs4MqVK+Tk5KBpGsePHwcolIiURGRkJA0bNuTq1auFWkbyW3Kub7UB1YoAkJSUxJYtW4rcdu3aBRj3oWXqayQpKQmAwMDA257DHCpXrkznzp25dOlSwQy6nJwc5syZA6hZesWR32qRkJBw231PnDgBqBZSd3f32+7/3yKF+fKTx9vd/9/XbFZWFr///jsRERE3fOFo1KgRGzdupFu3bsTGxjJjxgweeughQkND6d69e0ESWpT8BL1s2bK3fU7C9klyI5xGfjn5S5cu3XSf/Om1t2tmL66YmBjuu+8+srOz+fzzz2nbtq1JMWqaVtBsbu4Yi7J9+3ZOnDhB5cqVWbhwIe3bt6dMmTIFrQJnz541+zn/2zWVnp7OkiVLMBgMDBw4sNC++b+vNm3aoKkxhDfdjFlDytTXSP6/jUkOzCW/qye/tWblypVcunSJZs2aFXs5gvxkzpgWuJUrV+Ln58crr7zCxx9/XLygzWDdunWkpKTctHBfy5YtWb16NdeuXWPVqlW88MILhIaG8ttvv9G1a9eb/o3yn3v+lwdh3yS5EU6jZs2aABw6dKjI+5OTkws+rPP3NYf09HT69u3L5cuXeeKJJxg5cqTJMR4/fpysrCxcXV1v2pxfHLdbCDE/IWjatGmRXRbmGmtzvUGDBmEwGFi8eDHp6en8+uuvJCcn07Zt2xtau/K77w4fPmyW6rL5v//Dhw/ftJXr4MGDhfaFf7uqtm3bVuIYjF2c8t577yUwMJBff/2V+Ph4Zs+eDRS/1Qb+Hf9yq5aNfK1bt2bZsmX4+PjwzDPP8MUXXxT7fCVhbFViPz8/unfvztSpUzly5AjVqlUjNja2yFpRV69e5dKlS/j4+NjdEiqiaJLcCKfRvXt3QC0OeOHChRvunzFjBpmZmVSuXNmsb3AjRoxgz549dOjQgU8++cSoGL/88suCcRDX+/TTTwHVUlHSbjK4/TiD/PuLKhiXnZ1tkW/u4eHhtGnThpSUFH799deCFpyiKufWqFGDevXqER8fz3fffVfic7dt2xYfHx/Onj1bMEj4ejt37uTPP//EYDDQtWvXgtvzB8TOmjWrxOOPjB374eXlxaBBg8jKyuLzzz9n2bJleHh4mFRhOL8l8VYFFK/XoUMHlixZgpeXF08++SRff/11sc9pquXLl+Pv70+HDh2MfoyPjw/169cHKHL8zfbt2wHV6mNMV5uwfZLcCKfRuXNnmjdvTmZmJoMGDSrU9fDbb78VVIZ98cUXjf72fDtTp05l3rx5VK5cmV9++QU3N7db7j9o0CDCw8O5ePEiw4YNKzSY8ocffmDGjBkFMZpDREQEADt27Ciy8m7Lli1xc3Njy5YthZKHxMREHnzwwVtWyS2J/LE106dPZ+XKlbi5uTFgwIAi933nnXcwGAyMGTOGr7766oZKzKdOneKtt95i4cKFtz1vqVKlGD16NABPPvlkoerGJ0+eLJildP/99xdqOevbty/NmjXj0qVL3HXXXTfMttu3bx/Tpk0z4pn/+zfZunXrDc/lv/K7pt544w2ysrLo3bu3UTOe/qtGjRpUrVqV6Ohozp07Z9Rj7rzzThYuXIi7uzsjR47khx9+KPZ5i+vgwYOcPn2arl274uHhccP9o0ePZv78+Te8ljdu3MjatWsBipzxuGXLFgC6detmgaiFLqw++VwIM+A2NVRuVqDt+PHjBdV+PT09tSZNmmjVq1cvON6QIUNuWqH4drVgioopP44qVarctFLxf4utbdu2TQsICNBAVShu1qxZQcE/QPvf//53w7lvVxvlZs8hNze3oEpxmTJltFatWmkdOnTQnn766YJ9nn322YJzh4eHa02bNtW8vb01d3d3bdq0aQW1gYz5fRjr8uXLBVVsAa1nz5633P/zzz8vKFTo7++vNW3aVGvWrJkWEhJScIxp06YVesytKhR36tSp4HGRkZFaw4YNC47fsGHDm1YorlWrVsHjatasqTVt2rSgWJ0xFYo1TdXaKV26tAZoFSpU0Nq0aaN16NBBmzJlSpHPPb+uDcWsbfNf+ZWo33///SLvv9nfc/HixZq7u7vm6uqqzZ8/v+D26ysUF2XdunVF/l7yFfWanTp1qgZos2bNKvIxDRs2LCgcWKdOHa1FixYFf2dAe+ihh4p8XI0aNTQ3N7cbCj0K+yXJjbBLpiY3mqY+OJ999lmtRo0amqenp1aqVCmtffv22vfff39DYqNp5klubrUV9eZ/5swZ7fHHH9cqV66seXh4aKVLl9a6deumLV++vMhzm5rcaJqmHTt2TOvfv78WHBxc8AF+/QdOXl6e9vHHH2u1a9fWPDw8tLL/b++OQZIJ4ziO/zWJ0iCIipoCoUkaMmlJaIyCcAq0xUVaXRqEpiKICAJb2wwadGtqCtJFcdSlpanQpSaDKOL3Tq/UWxpiL+nx/az38Ofg7rgfzz3P/8bHtb6+rmKx2PYF1k24kaS1tbVmjbOzs2/HVyoVJRIJ+f1+DQ0NaXR0VIFAQLFYTLlcTk9PTx/Gt7tHXl5elE6nFQqF5PP5NDw8rLm5Oe3v73+q816j0dDBwYGCwaBGRkbk9Xo1OzureDyufD7/YWyrcCNJ5XJZq6urGhsba/72odX9d3x8LDPT1NTUpy7Snbi/v5fH49H8/PyXx9tdz1wup4GBAXk8nmZDvv8RbsLhsFwu14fu4u9dXV0pmUwqGAxqYmJCg4ODmpmZ0crKii4uLr58vsvlssxMkUjky5roTy6pw72hAICekUql7PDw0La3t+3o6KirWltbW3Z6emqFQqHljr7f8vj4aJOTk7awsGClUunH6sbjcctkMlYqlWxxcfHH6uJ3seYGAPrU6+trcy3U3z+8d2N3d9e8Xq/t7e11XeunXV5e2tvb27e7pDpxe3tr5+fntrGxQbBxmParGwEAPevk5MRqtZotLy+37GrdienpactkMlatVq3RaDT7/vSCzc3NT00cu3V3d2c7OzvNheJwDj5LAUAfqdfrFo1G7eHhwarVqrndbsvn87a0tPTbpwb0DD5LAUAfeX5+tuvra7u5ubFAIGDZbJZgA/yDmRsAAOAozNwAAABHIdwAAABHIdwAAABHIdwAAABHIdwAAABHIdwAAABHIdwAAABHIdwAAABHIdwAAABH+QPxg1UTMruOZwAAAABJRU5ErkJggg==", - "text/plain": [ - "Graphics object consisting of 2 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c11, c12, c13, c22, c23, c33, c44, c55, c66 = var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - " [c11, c12, c13, 0, 0, 0],\n", - " [c12, c22, c23, 0, 0, 0],\n", - " [c13, c23, c33, 0, 0, 0],\n", - " [0, 0, 0, c44, 0, 0],\n", - " [0, 0, 0, 0, c55, 0],\n", - " [0, 0, 0, 0, 0, c66]\n", - "])\n", - "\n", - "n1, n2, n3 = var('n1,n2,n3') # components of the normal vector\n", - "A = matrix([\n", - " [n1, 0, 0, 0, n3, n2],\n", - " [0, n2, 0, n3, 0, n1],\n", - " [0, 0, n3, n2, n1, 0]\n", - "])\n", - "\n", - "V = M.substitute(c12=c11-2*c66, c22=c11, c23=c13, c44=c55)\n", - "C = A * V * A.transpose()\n", - "\n", - "# Convert map object to a list\n", - "e3 = list(map(lambda x: x.full_simplify(), C.eigenvalues()))\n", - "\n", - "# Substitute and simplify expressions\n", - "vp(n1) = e3[1].substitute(n2=0, n3=sqrt(1-n1^2))\n", - "vsv(n1) = e3[2].substitute(n2=0, n3=sqrt(1-n1^2))\n", - "\n", - "# Switch vp and vsv due to a Sage bug\n", - "vptrue = vsv\n", - "vsvtrue = vp\n", - "\n", - "# Parametric plot for P-wave and SV-wave velocities\n", - "ppx = (sqrt(vptrue(sin(x))) * sin(x)).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "ppz = (sqrt(vptrue(sin(x))) * cos(x)).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "pp = parametric_plot([ppx, ppz], (x, 0, 2*pi))\n", - "\n", - "psvx = (sqrt(vsvtrue(sin(x))) * sin(x)).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "psvz = (sqrt(vsvtrue(sin(x))) * cos(x)).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "psv = parametric_plot([psvx, psvz], (x, 0, 2*pi), color='green')\n", - "\n", - "# Combine the plots\n", - "p = pp + psv\n", - "\n", - "# Show the plot\n", - "p.show(frame=True, axes_labels=['horizontal velocity (km/s)', 'vertical velocity (km/s)'])" - ] - }, - { - "cell_type": "markdown", - "id": "bfd6773c", - "metadata": {}, - "source": [ - "

Figure 1 Phase-velocity profiles for qP (outer curve) and qSV (inner curve) waves in a transversely isotropic material (Greenhorn shale).

" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "28320f1c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "Graphics object consisting of 2 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c11, c12, c13, c22, c23, c33, c44, c55, c66 = var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - " [c11, c12, c13, 0, 0, 0],\n", - " [c12, c22, c23, 0, 0, 0],\n", - " [c13, c23, c33, 0, 0, 0],\n", - " [0, 0, 0, c44, 0, 0],\n", - " [0, 0, 0, 0, c55, 0],\n", - " [0, 0, 0, 0, 0, c66]\n", - "])\n", - "\n", - "n1, n2, n3 = var('n1,n2,n3') # components of the normal vector\n", - "A = matrix([\n", - " [n1, 0, 0, 0, n3, n2],\n", - " [0, n2, 0, n3, 0, n1],\n", - " [0, 0, n3, n2, n1, 0]\n", - "])\n", - "\n", - "V = M.substitute(c12=c11-2*c66, c22=c11, c23=c13, c44=c55)\n", - "C = A * V * A.transpose()\n", - "\n", - "# Convert map object to list\n", - "e3 = list(map(lambda x: x.full_simplify(), C.eigenvalues()))\n", - "\n", - "# Define normal vector and compute phase velocities\n", - "nv = vector([n1, n2, n3]).column()\n", - "vsphase = sqrt(e3[2])\n", - "vpphase = sqrt(e3[1])\n", - "\n", - "# Compute group velocities\n", - "vsgroup = vsphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector([diff(vsphase, n1), diff(vsphase, n2), diff(vsphase, n3)]).column()\n", - "vsgroup = [vsgroup[0][0].full_simplify(), vsgroup[1][0].full_simplify(), vsgroup[2][0].full_simplify()]\n", - "vsgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1-n1^2)).full_simplify(), vsgroup))\n", - "\n", - "vpgroup = vpphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector([diff(vpphase, n1), diff(vpphase, n2), diff(vpphase, n3)]).column()\n", - "vpgroup = [vpgroup[0][0].full_simplify(), vpgroup[1][0].full_simplify(), vpgroup[2][0].full_simplify()]\n", - "vpgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1-n1^2)).full_simplify(), vpgroup))\n", - "\n", - "# Compute group velocity magnitudes\n", - "vgs(n1) = (vsgroup[0]**2 + vsgroup[1]**2 + vsgroup[2]**2).full_simplify()\n", - "vgp(n1) = (vpgroup[0]**2 + vpgroup[1]**2 + vpgroup[2]**2).full_simplify()\n", - "\n", - "# Sage bug workaround: switch expressions\n", - "vgptrue = vgs\n", - "vgstrue = vgp\n", - "\n", - "# Compute sn12 and pn12\n", - "sn12(n1) = (vsgroup[0]**2 / vgs).full_simplify()\n", - "pn12(n1) = (vpgroup[0]**2 / vgp).full_simplify()\n", - "\n", - "# Switch sn12 and pn12 due to bug\n", - "pn12true = sn12\n", - "sn12true = pn12\n", - "\n", - "# Parametric plots for group velocities\n", - "vsx = (sqrt(vgstrue(sin(x))) * sign(sin(x)) * sqrt(sn12true(sin(x)))).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "vsz = (sqrt(vgstrue(sin(x))) * sign(cos(x)) * sqrt(1 - sn12true(sin(x)))).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "pgs = parametric_plot([vsx, vsz], (x, 0, 2*pi), color='green')\n", - "\n", - "vpx = (sqrt(vgptrue(sin(x))) * sign(sin(x)) * sqrt(pn12true(sin(x)))).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "vpz = (sqrt(vgptrue(sin(x))) * sign(cos(x)) * sqrt(1 - pn12true(sin(x)))).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "pgp = parametric_plot([vpx, vpz], (x, 0, 2*pi))\n", - "\n", - "# Combine the plots\n", - "p = pgp + pgs\n", - "\n", - "# Show the plot\n", - "p.show(frame=True, axes_labels=['horizontal velocity (km/s)', 'vertical velocity (km/s)'])" - ] - }, - { - "cell_type": "markdown", - "id": "277343c7", - "metadata": {}, - "source": [ - "

Figure 2 Group-velocity profiles for qP (outer curve) and qSV (inner curve) waves in a transversely isotropic material (Greenhorn shale).

" - ] - }, - { - "cell_type": "markdown", - "id": "debad10b", - "metadata": {}, - "source": [ - "## MUIR APPROXIMATION" - ] - }, - { - "cell_type": "markdown", - "id": "908266cf", - "metadata": {}, - "source": [ - "[Muir and Dellinger (1985)][Muir.sep.44.55] suggested representing anelliptic $qP$ phase\n", - "velocities with the following approximation:\n", - "

(12)

\n", - "\\begin{equation}\n", - "\\label{eq:muph}\n", - " v_P^2(\\theta) \\approx e(\\theta) + \n", - "\\frac{(q-1)\\,a\\,c\\,\n", - "\\sin^2{\\theta}\\,\\cos^2{\\theta}}{e(\\theta)}\n", - "\\;,\n", - "\\end{equation}\n", - "where $e(\\theta)$ is the elliptical part of the velocity, defined by\n", - "

(13)

\n", - "\\begin{equation}\n", - "\\label{eq:muel}\n", - "e(\\theta) = a\\,\\sin^2{\\theta} + c\\,\\cos^2{\\theta}\\;,\n", - "\\end{equation}\n", - "and $q$ is the anellipticity coefficient ($q=1$ in case of elliptic\n", - "velocities). Approximation 12 uses only three parameters to\n", - "characterize the medium ($a$, $c$, and $q$) as opposed to the four parameters\n", - "($a$, $c$, $l$, and $f$) in the exact expression.\n", - "\n", - "There is some freedom in choosing an appropriate value for the coefficient\n", - "$q$. Assuming near-vertical wave propagation and the vertical axis of symmetry\n", - "(a VTI medium) and fitting the curvature ($d^2 v_P/d \\theta^2$) of the exact\n", - "phase velocity 4 near the vertical phase angle ($\\theta = 0$),\n", - "leads to the definition ([Dellinger et al. 1993][jse]),\n", - "

(14)

\n", - "\\begin{equation}\n", - " \\label{eq:qpdef}\n", - " q = \\frac{l\\,(c-l) + (l+f)^2}\n", - " {a\\,(c-l)}\\;.\n", - "\\end{equation}\n", - "\n", - "In terms of Thomsen's elastic parameters $\\epsilon$ and $\\delta$ ([Thomsen 1986][Thomsen1986]) and the elastic parameter $\\eta$ of\n", - "[Alkhalifah and Tsvankin (1995)][Alkhalifah1995],\n", - "

(15)

\n", - "\\begin{equation}\n", - " \\label{eq:eta2q}\n", - " q = \\frac{1 + 2\\,\\delta}{1 + 2\\epsilon}\n", - "= \\frac{1}{1 + 2\\,\\eta}\\;.\n", - "\\end{equation}\n", - "This confirms the direct relationship between $\\eta$ and anellipticity. If we\n", - "were to fit the phase velocity curvature near the horizontal axis\n", - "$\\theta=\\pi/2$ (perpendicular to the axis of symmetry), the appropriate value\n", - "for $q$ would be\n", - "

(16)

\n", - "\\begin{equation}\n", - " \\label{eq:qpdefhat}\n", - " \\hat{q} = \\frac{l\\,(a-l) + (l+f)^2}\n", - " {c\\,(a-l)}\\;.\n", - "\\end{equation}\n", - "\n", - "[Muir and Dellinger (1985)][Muir.sep.44.55] also suggested approximating the VTI\n", - "group velocity with an analogous expression\n", - "

(17)

\n", - "\\begin{equation}\n", - " \\label{eq:muir2}\n", - "\\frac{1}{V^2_{P}(\\Theta)} \\approx E(\\Theta) + \n", - "\\frac{(Q-1)\\,A\\,C\\,\n", - "\\sin^2{\\Theta}\\,\\cos^2{\\Theta}}{E(\\Theta)}\n", - "\\end{equation}\n", - "where $A=1/a$, $C=1/c$, $Q = 1/q$, $\\Theta$ is the group angle, and\n", - "$E(\\Theta)$ is the elliptical part:\n", - "

(18)

\n", - "\\begin{equation}\n", - "\\label{eq:muel2}\n", - "E(\\Theta) = A\\,\\sin^2{\\Theta} + C\\,\\cos^2{\\Theta}\\;.\n", - "\\end{equation}\n", - "Equations 12 and 17 are consistent in the sense\n", - "that both of them are exact for elliptic anisotropy ($q=Q=1$) and\n", - "accurate to the first order in $(q-1)$ or $(Q-1)$ in the general case of\n", - "transversally isotropic media.\n", - "\n", - "To the same approximation order, the connection between the phase and group directions is\n", - "

(19)

\n", - "\\begin{equation}\n", - "\\label{eq:t2T}\n", - "\\tan{\\Theta} = \\tan{\\theta}\\,\\frac{a}{c}\\, \n", - "\\left(1 - (q-1)\\,\\frac\n", - " {a\\,\\sin^2{\\theta} - c\\,\\cos^2{\\theta}}\n", - " {a\\,\\sin^2{\\theta} + c\\,\\cos^2{\\theta}}\\right)\\;.\n", - "\\end{equation}\n", - "\n", - "[Muir.sep.44.55]:http://sepwww.stanford.edu/data/media/public/oldreports/sep44/44_04.pdf\n", - "[jse]:https://sep.stanford.edu/data/media/public/docs/sep75/martin2.ps.gz\n", - "[Thomsen1986]:https://doi.org/10.1190/1.1442051\n", - "[Alkhalifah1995]:https://doi.org/10.1190/1.1443888\n" - ] - }, - { - "cell_type": "markdown", - "id": "8b58f719", - "metadata": {}, - "source": [ - "## SHIFTED-HYPERBOLA APPROXIMATION FOR THE PHASE VELOCITY" - ] - }, - { - "cell_type": "markdown", - "id": "394251bb", - "metadata": {}, - "source": [ - "Despite the beautiful symmetry of Muir's approximations 12 and 17, they are less accurate in practice than some other\n", - "approximations, most notably the weak anisotropy approximation of [Thomsen (1986)][Thomsen1986], which can be written as ([Tsvankin 1996][Tsvankin1996])\n", - "

(20)

\n", - "\\begin{equation}\n", - " \\label{eq:thoms}\n", - " v_P^2(\\theta) \\approx c\\,\\left(1 + 2\\,\\epsilon\\,\\sin^4{\\theta} + \n", - " 2\\,\\delta\\,\\sin^2{\\theta}\\,\\cos^2{\\theta}\\right)\\;,\n", - "\\end{equation}\n", - "where\n", - "

(21)

\n", - "\\begin{equation}\n", - " \\label{eq:epsdelta}\n", - " \\epsilon = \\frac{a-c}{2\\,c}\\quad\\mbox{and}\\quad\n", - " \\delta = \\frac{(l + f)^2 - (c - l)^2}{2\\,c\\,(c - l)}\\;.\n", - "\\end{equation}\n", - "\n", - "Note that both approximations involve the anellipticity factor ($q-1$ or\n", - "$\\epsilon-\\delta$) in a linear fashion. If the anellipticity effect is\n", - "significant, the accuracy of Muir's equations can be improved by\n", - "replacing the linear approximation with a nonlinear one. There are, of\n", - "course, infinitely many nonlinear expressions that share the same\n", - "linearization. In this study, I focus on the shifted hyperbola approximation,\n", - "which follows from the fact that an expression of the form\n", - "

(22)

\n", - " \\begin{equation}\n", - " \\label{eq:lin}\n", - " x + \\frac{\\alpha}{x} \n", - " \\end{equation}\n", - "is the linearization (Taylor series expansion) of the form\n", - "

(23)

\n", - "\\begin{equation}\n", - " \\label{eq:nonlin}\n", - " x\\,(1-s) + s\\,\\sqrt{x^2 + \\frac{2\\,\\alpha}{s}}\n", - "\\end{equation}\n", - "\n", - "for small $\\alpha$. Linearization does not depend on the parameter $s$, which\n", - "affects only higher-order terms in the Taylor expansion.\n", - "Expression 23 is reminiscent of the shifted hyperbola\n", - "approximation for normal moveout in vertically heterogeneous media ([Malovichko 1978][malov]; [Sword 1987][Sword.sep.51.313]; [de Bazelaire 1988][deBazelaire1988]; [Castle 1994][Castle1994]) and the\n", - "Stolt stretch correction in the frequency-wavenumber migration ([Stolt 1978][Stolt1978]; [Fomel and Vaillant 2001][mystolt]). It is evident that Muir's\n", - "approximation 12 has exactly the right form 22 to be\n", - "converted to the shifted hyperbola approximation 23. \n", - "\n", - "Thus, we seek an approximation of the form\n", - "

(24)

\n", - "\\begin{equation}\n", - " \\label{eq:shiftm}\n", - " v_P^2(\\theta) \\approx e(\\theta)\\,(1-s) + s\\,\\sqrt{e^2(\\theta) + \n", - " \\frac{2\\,(q-1)\\,a\\,c\\,\n", - " \\sin^2{\\theta}\\,\\cos^2{\\theta}}{s}}\n", - "\\end{equation}\n", - "with $e(\\theta)$ defined by equation 13. The plan is to select a\n", - "value of the additional parameter $s$ to fit the exact phase velocity\n", - "expression 4 and then to constrain $s$ so that it depends only on\n", - "the three parameters already present in the original\n", - "approximation 12.\n", - "\n", - "One can verify that the velocity curvature $d^2 v_P/d \\theta^2$ around the\n", - "vertical axis $\\theta=0$ for approximation 24 depends on the\n", - "chosen value of $q$ but does not depend on the value of the shift parameter\n", - "$s$. This means that the velocity profile $v_P(\\theta)$ becomes sensitive to\n", - "$s$ only further away from the vertical direction. This separation of\n", - "influence between the approximation parameters is an important and attractive\n", - "property of the shifted hyperbola approximation. I find an appropriate value\n", - "for $s$ by fitting additionally the fourth-order derivative $d^4 v_P/d\n", - "\\theta^4$ at $\\theta=0$ to the corresponding derivative of the exact\n", - "expression. The fit is achieved when $s$ has the value\n", - "

(25)

\n", - "\\begin{equation}\n", - " \\label{eq:sval}\n", - " s = \\frac{c-l}{2}\\,\\frac{(a-l)\\,(c-l) - (l+f)^2}\n", - " {a\\,(c-l)^2 - c\\,(l+f)^2}\\;. \n", - "\\end{equation}\n", - "It is more instructive to express it in the form\n", - "

(26)

\n", - "\\begin{equation}\n", - " \\label{eq:sval2}\n", - " s = \\frac{1}{2}\\,\\frac{(a-c)\\,(q-1)\\,(\\hat{q}-1)}\n", - " {a\\,\\left(1 - \\hat{q} - q\\,(1-q)\\right) - \n", - " c\\,\\left((\\hat{q}-1)^2+\\hat{q}\\,(q-\\hat{q})\\right)}\\;, \n", - "\\end{equation}\n", - "where $q$ and $\\hat{q}$ are defined by equations 14 and 16. In this form of the expression, $\\hat{q}$ appears as\n", - "the extra parameter that we need to eliminate. This parameter was defined by\n", - "fitting the velocity profile curvature around the horizontal axis, which would\n", - "correspond to infinitely large offsets in a surface seismic experiment. One\n", - "possible way to constrain it is to set $\\hat{q}$ equal to $q$, which implies\n", - "that the velocity profile has similar behavior near the vertical and the\n", - "horizontal axes. Setting $\\hat{q} \\approx q$ in equation 26 yields\n", - "

(27)

\n", - "\\begin{equation}\n", - " \\label{eq:sappr}\n", - " s \\approx \\lim_{\\hat{q} \\rightarrow q} s = \\frac{1}{2}\\;.\n", - "\\end{equation}\n", - "Substituting 27 in equation 24 produces the final approximation\n", - "

(28)

\n", - "\\begin{equation}\n", - " \\label{eq:shiftm2}\n", - " v_P^2(\\theta) \\approx \\frac{1}{2}\\,e(\\theta) + \n", - " \\frac{1}{2}\\,\\sqrt{e^2(\\theta) + \n", - " 4\\,(q-1)\\,a\\,c\\,\\sin^2{\\theta}\\,\\cos^2{\\theta}}\\;.\n", - "\\end{equation}\n", - "\n", - "Approximation 28 is exactly equivalent to the acoustic\n", - " approximation of Alkhalifah ([1998][Alkhalifah1998], [2000a][Alkhalifah2000a]),\n", - "derived with a different set of parameters by formally setting the $S$-wave\n", - "velocity ($l=v_S^2$) in equation 4 to zero. A similar\n", - " approximation is analyzed by [Stopin (2001)][Stopin2001].\n", - "Approximation 28 was proved to possess a remarkable accuracy\n", - "even for large phase angles and significant amounts of anisotropy.\n", - "Figure 3 compares the accuracy of different approximations using\n", - "the parameters of the Greenhorn shale. The acoustic approximation appears\n", - "especially accurate for phase angles up to about 25 degrees and does not\n", - "exceed the relative error of 0.3\\% even for larger angles.\n", - "\n", - "[Thomsen1986]:https://doi.org/10.1190/1.1442051\n", - "[Tsvankin1996]:https://doi.org/10.1190/1.1443974\n", - "[malov]:https://www.appliedgeophysics.org/\n", - "[Sword.sep.51.313]:http://sepwww.stanford.edu/data/media/public/oldreports/sep51/51_22.pdf\n", - "[deBazelaire1988]:https://doi.org/10.1190/1.1442449\n", - "[Castle1994]:https://doi.org/10.1190/1.1443658\n", - "[mystolt]:https://reproducibility.org/RSF/book/sep/stoltst/paper.pdf\n", - "[Stolt1978]:https://doi.org/10.1190/1.1440826\n", - "[Alkhalifah1998]:https://doi.org/10.1190/1.1444361\n", - "[Alkhalifah2000a]:https://doi.org/10.1190/1.1444815\n", - "[Stopin2001]:https://doi.org/10.1190/1.9781560801771.ch20" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "308edb00", - "metadata": {}, - "outputs": [ - { - "data": 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", - "text/plain": [ - "Graphics object consisting of 3 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c11, c12, c13, c22, c23, c33, c44, c55, c66 = var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - " [c11, c12, c13, 0, 0, 0],\n", - " [c12, c22, c23, 0, 0, 0],\n", - " [c13, c23, c33, 0, 0, 0],\n", - " [0, 0, 0, c44, 0, 0],\n", - " [0, 0, 0, 0, c55, 0],\n", - " [0, 0, 0, 0, 0, c66]\n", - "])\n", - "\n", - "n1, n2, n3 = var('n1,n2,n3') # components of the normal vector\n", - "A = matrix([\n", - " [n1, 0, 0, 0, n3, n2],\n", - " [0, n2, 0, n3, 0, n1],\n", - " [0, 0, n3, n2, n1, 0]\n", - "])\n", - "\n", - "V = M.substitute(c12=c11-2*c66, c22=c11, c23=c13, c44=c55)\n", - "C = A * V * A.transpose()\n", - "\n", - "# Convert map object to list\n", - "e3 = list(map(lambda x: x.full_simplify(), C.eigenvalues()))\n", - "\n", - "# Substitute and simplify expressions for phase velocities\n", - "vp(n1) = e3[1].substitute(n2=0, n3=sqrt(1-n1^2))\n", - "vsv(n1) = e3[2].substitute(n2=0, n3=sqrt(1-n1^2))\n", - "\n", - "# Sage bug workaround: switch vp and vsv expressions\n", - "vptrue = vsv\n", - "\n", - "# Muir-Dellinger approximation\n", - "q = var('q')\n", - "el(n1) = c11*n1^2 + c33*(1-n1^2)\n", - "md(n1) = el(n1) + (q-1) * c11 * c33 * n1^2 * (1-n1^2) / el(n1)\n", - "qz = ((2*c13 + c33)*c55 + c13^2) / (c11*c33 - c11*c55)\n", - "mdplot = plot(100*abs(sqrt(md(sin(x*pi/180)) / vptrue(sin(x*pi/180))) - 1)\n", - " .substitute(q=qz)\n", - " .substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51), \n", - " (x, 0, 90), linestyle='--')\n", - "\n", - "# Shifted hyperbola approximation\n", - "s = var('s')\n", - "sh(n1) = (1-s) * el(n1) + s * sqrt(el(n1)^2 + 2*(q-1) * c11 * c33 * n1^2 * (1-n1^2) / s)\n", - "shplot = plot(100*abs(sqrt(sh(sin(x*pi/180)) / vptrue(sin(x*pi/180))) - 1)\n", - " .substitute(q=qz)\n", - " .substitute(s=0.5)\n", - " .substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51), \n", - " (x, 0, 90))\n", - "\n", - "# Weak anisotropy approximation\n", - "epsilon, delta = var('epsilon,delta')\n", - "epsilon = (c11 - c33) / (2 * c33)\n", - "delta = ((c55 + c13)^2 - (c33 - c55)^2) / (2 * c33 * (c33 - c55))\n", - "th(n1) = c33 * (1 + 2*epsilon*n1^4 + 2*delta*n1^2*(1-n1^2))\n", - "weakplot = plot(100*abs(sqrt(th(sin(x*pi/180)) / vptrue(sin(x*pi/180))) - 1)\n", - " .substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51), \n", - " (x, 0, 90), linestyle=':')\n", - "\n", - "# Combine the plots\n", - "p = shplot + mdplot + weakplot\n", - "\n", - "# Display the plot\n", - "p.show(axes_labels=['phase angle (degrees)', 'relative error (%)'], aspect_ratio=50, frame=True, axes=False)" - ] - }, - { - "cell_type": "markdown", - "id": "2afd89ce", - "metadata": {}, - "source": [ - "

Figure 3 Relative error of different phase velocity\n", - " approximations for the Greenhorn shale anisotropy. Short dash: Thomsen's\n", - " weak anisotropy approximation. Long dash: Muir's approximation. Solid line:\n", - " suggested approximation (similar to Alkhalifah's acoustic approximation.)

" - ] - }, - { - "cell_type": "markdown", - "id": "009872b9", - "metadata": {}, - "source": [ - "## SHIFTED-HYPERBOLA APPROXIMATION FOR THE GROUP VELOCITY" - ] - }, - { - "cell_type": "markdown", - "id": "6ee215bb", - "metadata": {}, - "source": [ - "A similar strategy is applicable for approximating the group velocity. Applying\n", - "the shifted hyperbola approach to ''unlinearize'' Muir's\n", - "approximation 17, we seek an approximation of the form\n", - "

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\n", - "\\begin{equation}\n", - " \\label{eq:shiftM}\n", - " \\frac{1}{V_P^2(\\Theta)} \\approx E(\\Theta)\\,(1-S) + S\\,\\sqrt{E^2(\\Theta) + \n", - " \\frac{2\\,(Q-1)\\,A\\,C\\,\n", - " \\sin^2{\\Theta}\\,\\cos^2{\\Theta}}{S}}\n", - "\\end{equation}\n", - "\n", - "An approximation of this form with $S$ set to $1/2$ was proposed earlier by [Zhang and Uren (2001)][Zhang2001]. Similarly to the case of the phase velocity\n", - "approximation, I constrain the value of $S$ by Taylor fitting of the velocity\n", - "profiles near the vertical angle.\n", - "\n", - "Although there is no simple explicit expression for the transversally\n", - "isotropic group velocity, we can differentiate the parametric representations\n", - "of $V_P$ and $\\Theta$ in terms of the phase angle $\\theta$ that follow from\n", - "equation 5. The group velocity is an even function of the angle\n", - "$\\Theta$ because of the VTI symmetry. Therefore, the odd-order derivatives are\n", - "zero at the axis of symmetry ($\\Theta=\\theta=0$). Fitting the second-order\n", - "derivative $d^2 V_P/d\\Theta^2$ at $\\theta=0$ produces $Q=1/q=1+2\\,\\eta$,\n", - "consistent with Muir's approximation 17. Fitting additionally\n", - "the fourth-order derivative $d^4 V_P/d\\Theta^4$ at $\\theta=0$ produces\n", - "

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\n", - "\\begin{equation}\n", - " \\label{eq:Sval}\n", - " S = \\frac{1}{2}\\,\\frac{\n", - " \\left[(l+f)^2 + l\\,(c-l)\\right]^2\\,\\left[(c-l)\\,(a-l) - (l+f)^2\\right]}{\n", - " a^2\\,c\\,(c-l)\\,(l+f)^2 - \\left[l\\,(c-l) + (l+f)^2\\right]^3}\n", - "\\end{equation}\n", - "or, equivalently,\n", - "

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\n", - "\\begin{equation}\n", - " \\label{eq:Sval2}\n", - " S = \\frac{1}{2}\\,\\frac{(C-A)\\,(Q-1)\\,(\\hat{Q}-1)}\n", - " {C\\,\\left(\\hat{Q}\\,(Q^2-Q-1) + 1\\right) + \n", - " A\\,\\left(\\hat{Q}-Q^3+Q^2-1\\right)}\\;,\n", - "\\end{equation}\n", - "where $\\hat{Q}=1/\\hat{q}$. As in the\n", - "previous section, I approximate the optimal value of $S$ by setting $\\hat{Q}$\n", - "equal to $Q$, as follows:\n", - "

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\n", - "\\begin{equation}\n", - " \\label{eq:Sappr}\n", - " S \\approx \\lim_{\\hat{Q} \\rightarrow Q} S = \\frac{1}{2\\,(1+Q)} = \n", - " \\frac{1}{4\\,(1 + \\eta)}\\;.\n", - "\\end{equation}\n", - "\n", - "Selected in this way, the value of $S$ depends on the anelliptic parameter $Q$\n", - "(or $\\eta$) and, for small anellipticity, is close to $1/4$, which is\n", - "different from the value of $1/2$ in the approximation of\n", - "[Zhang and Uren (2001)][Zhang2001].\n", - "\n", - "The final group velocity approximation takes the form\n", - "

(33)

\n", - "\\begin{equation}\n", - " \\label{eq:shiftM2}\n", - " \\frac{1}{V^2_{P}(\\Theta)} \\approx \\frac{1+2\\,Q}{2\\,(1+Q)}\\,E(\\Theta) + \n", - "\\frac{1}{2\\,(1+Q)}\\,\n", - "\\sqrt{E^2(\\Theta) + 4\\,(Q^2-1)\\,A\\,C\\,\\sin^2{\\Theta}\\,\\cos^2{\\Theta}}\\;.\n", - "\\end{equation}\n", - "\n", - "In Figure 4, the accuracy of approximation 33 is compared with the accuracy of Muir's approximation 17 and the\n", - "accuracy of the weak anisotropy approximation ([Thomsen 1986][Thomsen1986]) for the\n", - "elastic parameters of the Greenhorn shale. The weak anisotropy approximation,\n", - "used in this comparison, is\n", - "

(34)

\n", - "\\begin{equation}\n", - " \\label{eq:thoms2}\n", - " V_P^2(\\Theta) \\approx c\\,\\left(1 + 2\\,\\epsilon\\,\\sin^4{\\Theta} + \n", - " 2\\,\\delta\\,\\sin^2{\\Theta}\\,\\cos^2{\\Theta}\\right)\\;,\n", - "\\end{equation}\n", - "\n", - "where $\\epsilon$ and $\\delta$ are Thomsen's parameters, defined in\n", - "equations 21. A similar form (in a different\n", - "parameterization) was introduced by [Byun et al. (1989)][Byun1989].\n", - "\n", - "[Zhang2001]:https://doi.org/10.1190/1.1816267\n", - "[Thomsen1986]:https://doi.org/10.1190/1.1442051\n", - "[Byun1989]:https://doi.org/10.1190/1.1442624" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "5f3c1ed0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "Graphics object consisting of 3 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Define constants and matrix\n", - "c11, c12, c13, c22, c23, c33, c44, c55, c66 = var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - " [c11, c12, c13, 0, 0, 0],\n", - " [c12, c22, c23, 0, 0, 0],\n", - " [c13, c23, c33, 0, 0, 0],\n", - " [0, 0, 0, c44, 0, 0],\n", - " [0, 0, 0, 0, c55, 0],\n", - " [0, 0, 0, 0, 0, c66]])\n", - "\n", - "n1, n2, n3 = var('n1,n2,n3') # components of the normal vector\n", - "nv = vector([n1, n2, n3]).column()\n", - "\n", - "A = matrix([\n", - " [n1, 0, 0, 0, n3, n2],\n", - " [0, n2, 0, n3, 0, n1],\n", - " [0, 0, n3, n2, n1, 0]])\n", - "\n", - "V = M.substitute(c12=c11 - 2 * c66, c22=c11, c23=c13, c44=c55)\n", - "C = A * V * A.transpose()\n", - "e3 = list(map(lambda x: x.full_simplify(), C.eigenvalues())) # Convert map to list\n", - "\n", - "vsphase = sqrt(e3[2])\n", - "vpphase = sqrt(e3[1])\n", - "\n", - "# Compute vsgroup and vpphase\n", - "vsgroup = vsphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector([diff(vsphase, n1), diff(vsphase, n2), diff(vsphase, n3)]).column()\n", - "vsgroup = [vsgroup[0][0].full_simplify(), vsgroup[1][0].full_simplify(), vsgroup[2][0].full_simplify()]\n", - "vsgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1 - n1^2)).full_simplify(), vsgroup)) # Convert map to list\n", - "\n", - "vpgroup = vpphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector([diff(vpphase, n1), diff(vpphase, n2), diff(vpphase, n3)]).column()\n", - "vpgroup = [vpgroup[0][0].full_simplify(), vpgroup[1][0].full_simplify(), vpgroup[2][0].full_simplify()]\n", - "vpgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1 - n1^2)).full_simplify(), vpgroup)) # Convert map to list\n", - "\n", - "# Further calculations\n", - "vgs(n1) = (vsgroup[0]^2 + vsgroup[1]^2 + vsgroup[2]^2).full_simplify()\n", - "vgp(n1) = (vpgroup[0]^2 + vpgroup[1]^2 + vpgroup[2]^2).full_simplify()\n", - "\n", - "vgptrue(n1) = vgs(n1)\n", - "vgstrue(n1) = vgp(n1)\n", - "\n", - "sn12(n1) = (vsgroup[0]^2 / vgs).full_simplify()\n", - "pn12(n1) = (vpgroup[0]^2 / vgp).full_simplify()\n", - "\n", - "pn12true(n1) = sn12(n1)\n", - "\n", - "# Thomsen's weak anisotropy\n", - "epsilon = (c11 - c33) / (2 * c33)\n", - "delta = ((c55 + c13)^2 - (c33 - c55)^2) / (2 * c33 * (c33 - c55))\n", - "TH(n1) = c33 * (1 + 2 * epsilon * pn12true(n1)^2 + 2 * delta * pn12true(n1) * (1 - pn12true(n1)))\n", - "\n", - "gpx = (arcsin(sqrt(pn12true(sin(x * pi / 180)))) * 180 / pi).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51) # Group angle\n", - "\n", - "# Calculate relative error for weak anisotropy\n", - "WEAKgpz = 100 * abs(sqrt((TH(sin(x * pi / 180)) / vgptrue(sin(x * pi / 180)))) - 1).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "WEAKgplot = parametric_plot([gpx, WEAKgpz], (x, 0, 90), linestyle=':')\n", - "\n", - "# Muir-Dellinger calculations\n", - "Q, N1 = var('Q,N1')\n", - "ELp(n1) = (1 / c11) * pn12(n1) + (1 / c33) * (1 - pn12(n1))\n", - "MDp(n1) = (ELp(n1) + (Q - 1) * (1 / c11) * (1 / c33) * pn12(n1) * (1 - pn12(n1)) / ELp(n1))^-1\n", - "\n", - "ELs(n1) = (1 / c11) * sn12(n1) + (1 / c33) * (1 - sn12(n1))\n", - "MDs(n1) = (ELs(n1) + (Q - 1) * (1 / c11) * (1 / c33) * sn12(n1) * (1 - sn12(n1)) / ELs(n1))^-1\n", - "\n", - "MDptrue(n1) = MDs(n1)\n", - "\n", - "qz = ((2 * c13 + c33) * c55 + c13^2) / (c11 * c33 - c11 * c55)\n", - "QZ = 1 / qz\n", - "\n", - "# Calculate relative error for Muir-Dellinger\n", - "MDgpz = 100 * abs(sqrt((MDptrue(sin(x * pi / 180)) / vgptrue(sin(x * pi / 180)))) - 1).subs(Q=QZ).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "MDgplot = parametric_plot([gpx, MDgpz], (x, 0, 90), linestyle='--')\n", - "\n", - "# Shifted hyperbola calculations\n", - "S = var('S')\n", - "SHp(n1) = ((1 - S) * ELp(n1) + S * sqrt(ELp(n1)^2 + 2 * (Q - 1) * (1 / c11) * (1 / c33) * pn12 * (1 - pn12) / S))^-1\n", - "SHs(n1) = ((1 - S) * ELs(n1) + S * sqrt(ELs(n1)^2 + 2 * (Q - 1) * (1 / c11) * (1 / c33) * sn12 * (1 - sn12) / S))^-1\n", - "\n", - "SHptrue(n1) = SHs(n1)\n", - "\n", - "# Calculate relative error for shifted hyperbola\n", - "SHgpz = 100 * abs(sqrt((SHptrue(sin(x * pi / 180)) / vgptrue(sin(x * pi / 180)))) - 1).subs(S = 1 / (2 * (1 + QZ)), Q = QZ).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51)\n", - "SHgplot = parametric_plot([gpx, SHgpz], (x, 0, 90))\n", - "\n", - "# Final plot\n", - "p = WEAKgplot + MDgplot + SHgplot\n", - "p.show(axes_labels=['phase angle (degrees)', 'relative error (%)'], aspect_ratio=25, frame=True, axes=False)" - ] - }, - { - "cell_type": "markdown", - "id": "f4b847f0", - "metadata": {}, - "source": [ - "

Figure 4 Relative error of different group velocity\n", - " approximations for the Greenhorn shale anisotropy. Short dash: Thomsen's\n", - " weak anisotropy approximation. Long dash: Muir's approximation. Solid line:\n", - " suggested approximation.

" - ] - }, - { - "cell_type": "markdown", - "id": "a497d5c7", - "metadata": {}, - "source": [ - "Approximation 33 turns out to be remarkably accurate\n", - "for this example. It appears nearly exact for group angles up to 45\n", - "degrees from vertical and does not exceed 0.3\\% relative error even at\n", - "larger angles. It is compared with two other approximations in\n", - "Figure 5. These are the Zhang-Uren approximation ([Zhang and Uren 2001][Zhang2001]) and the Alkhalifah-Tsvankin approximation, which\n", - "follows directly from the normal moveout equation suggested by\n", - "[Alkhalifah and Tsvankin (1995)][Alkhalifah1995]:\n", - "

(35)

\n", - "\\begin{equation}\n", - " \\label{eq:talts}\n", - " t^2(x) \\approx t_0^2 + \\frac{x^2}{V_n^2} - \n", - " \\frac{2\\,\\eta\\,x^4}{V_n^2\\,\\left[t_0^2\\,V_n^2 + (1+ 2\\,\\eta)\\,x^2\\right]}\n", - "\\;,\n", - "\\end{equation}\n", - "where $t(x)$ is the moveout curve, $t_0$ is the vertical traveltime, and $V_n\n", - "= \\sqrt{a/(1 + 2\\,\\eta)}$ is the NMO velocity. In a homogeneous medium,\n", - "equation 35 corresponds to the group velocity approximation\n", - "

(36)

\n", - "\\begin{equation}\n", - " \\label{eq:valts}\n", - " \\frac{1}{V_P^2(\\Theta)} \\approx \\frac{\\cos^2{\\Theta}}{V_z^2} + \n", - " \\frac{\\sin^2{\\Theta}}\n", - " {V_n^2} - \\frac{2\\,\\eta\\,\\sin^4{\\Theta}}\n", - " {V_n^2\\,\\left[\\cos^2{\\Theta}\\,V_n^2/V_z^2 + \n", - " (1+ 2\\,\\eta)\\,\\sin^2{\\Theta}\\right]}\n", - "\\;,\n", - "\\end{equation}\n", - "where $V_z = \\sqrt{c}$. In the notation of this paper, the Alkhalifah-Tsvankin\n", - "equation 36 takes the form\n", - "

(37)

\n", - "\\begin{equation}\n", - " \\label{eq:valts2}\n", - " \\frac{1}{V_P^2(\\Theta)} \\approx E(\\Theta) + \n", - " \\frac{(Q-1)\\,A\\,C\\,\n", - " \\sin^2{\\Theta}\\,\\cos^2{\\Theta}}{E(\\Theta) + (Q^2-1)\\,A\\,\\sin^2{\\Theta}}\n", - "\\end{equation}\n", - "and differs from approximation 17 by the correction term in the\n", - "denominator. Approximation 33 is noticeably more accurate\n", - "for this example than any of the other approximations considered here.\n", - "\n", - "[Alkhalifah1995]:https://doi.org/10.1190/1.1443888\n", - "[Zhang2001]:https://doi.org/10.1190/1.1816267" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "6fdc718f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "Graphics object consisting of 3 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c11, c12, c13, c22, c23, c33, c44, c55, c66 = var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - " [c11, c12, c13, 0, 0, 0],\n", - " [c12, c22, c23, 0, 0, 0],\n", - " [c13, c23, c33, 0, 0, 0],\n", - " [0, 0, 0, c44, 0, 0],\n", - " [0, 0, 0, 0, c55, 0],\n", - " [0, 0, 0, 0, 0, c66]\n", - "])\n", - "\n", - "n1, n2, n3 = var('n1,n2,n3') # components of the normal vector\n", - "nv = vector([n1, n2, n3]).column()\n", - "\n", - "A = matrix([\n", - " [n1, 0, 0, 0, n3, n2],\n", - " [0, n2, 0, n3, 0, n1],\n", - " [0, 0, n3, n2, n1, 0]\n", - "])\n", - "\n", - "V = M.substitute(c12=c11 - 2 * c66, c22=c11, c23=c13, c44=c55)\n", - "C = A * V * A.transpose()\n", - "e3 = list(map(lambda x: x.full_simplify(), C.eigenvalues()))\n", - "\n", - "vsphase = sqrt(e3[2])\n", - "vpphase = sqrt(e3[1])\n", - "\n", - "vsgroup = vsphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector(\n", - " [diff(vsphase, n1), diff(vsphase, n2), diff(vsphase, n3)]).column()\n", - "vsgroup = [vsgroup[0][0].full_simplify(), vsgroup[1][0].full_simplify(), vsgroup[2][0].full_simplify()]\n", - "vsgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1 - n1^2)).full_simplify(), vsgroup))\n", - "\n", - "vpgroup = vpphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector(\n", - " [diff(vpphase, n1), diff(vpphase, n2), diff(vpphase, n3)]).column()\n", - "vpgroup = [vpgroup[0][0].full_simplify(), vpgroup[1][0].full_simplify(), vpgroup[2][0].full_simplify()]\n", - "vpgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1 - n1^2)).full_simplify(), vpgroup))\n", - "\n", - "vgs(n1) = (vsgroup[0]^2 + vsgroup[1]^2 + vsgroup[2]^2).full_simplify()\n", - "vgp(n1) = (vpgroup[0]^2 + vpgroup[1]^2 + vpgroup[2]^2).full_simplify()\n", - "\n", - "vgptrue(n1) = vgs(n1)\n", - "vgstrue(n1) = vgp(n1)\n", - "\n", - "sn12(n1) = (vsgroup[0]^2 / vgs).full_simplify()\n", - "pn12(n1) = (vpgroup[0]^2 / vgp).full_simplify()\n", - "\n", - "pn12true(n1) = sn12(n1)\n", - "\n", - "gpx = (arcsin(sqrt(pn12true(sin(x * pi / 180)))) * 180 / pi).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51) # Group angle\n", - "\n", - "# Thomsen's weak anisotropy\n", - "epsilon = (c11 - c33) / (2 * c33)\n", - "delta = ((c55 + c13)^2 - (c33 - c55)^2) / (2 * c33 * (c33 - c55))\n", - "TH(n1) = c33 * (1 + 2 * epsilon * pn12true(n1)^2 + 2 * delta * pn12true(n1) * (1 - pn12true(n1)))\n", - "\n", - "# Alkhalifah-Tsvankin\n", - "TS(n1) = 1 / ((1 - sn12(n1)) / c33 + (sn12(n1) * (-c55 + c33) * (sn12(n1) * c33 * (-c55 + c33) + (1 - sn12(n1)) * (c13^2 + c55 * (c33 + 2 * c13)))) / (c11 * sn12(n1) * (c55 - c33)^2 * c33 + (1 - sn12(n1)) * (c13^2 + c55 * (c33 + 2 * c13))^2))\n", - "\n", - "TSgpz = 100 * abs(sqrt((TS(sin(x * pi / 180)) / vgptrue(sin(x * pi / 180)))) - 1).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51) # Relative error\n", - "TSgplot = parametric_plot([gpx, TSgpz], (x, 0, 90), linestyle=':')\n", - "\n", - "# Muir-Dellinger\n", - "Q, N1 = var('Q,N1')\n", - "\n", - "ELp(n1) = (1 / c11) * pn12(n1) + (1 / c33) * (1 - pn12(n1))\n", - "MDp(n1) = (ELp(n1) + (Q - 1) * (1 / c11) * (1 / c33) * pn12(n1) * (1 - pn12(n1)) / ELp(n1))^-1\n", - "\n", - "ELs(n1) = (1 / c11) * sn12(n1) + (1 / c33) * (1 - sn12(n1))\n", - "MDs(n1) = (ELs(n1) + (Q - 1) * (1 / c11) * (1 / c33) * sn12(n1) * (1 - sn12(n1)) / ELs(n1))^-1\n", - "\n", - "MDptrue(n1) = MDs(n1)\n", - "\n", - "qz = ((2 * c13 + c33) * c55 + c13^2) / (c11 * c33 - c11 * c55)\n", - "QZ = 1 / qz\n", - "\n", - "# Shifted hyperbola\n", - "S = var('S')\n", - "SHp(n1) = ((1 - S) * ELp(n1) + S * sqrt(ELp(n1)^2 + 2 * (Q - 1) * (1 / c11) * (1 / c33) * pn12 * (1 - pn12) / S))^-1\n", - "SHs(n1) = ((1 - S) * ELs(n1) + S * sqrt(ELs(n1)^2 + 2 * (Q - 1) * (1 / c11) * (1 / c33) * sn12 * (1 - sn12) / S))^-1\n", - "\n", - "SHptrue(n1) = SHs(n1)\n", - "\n", - "# Zhang-Uren\n", - "URgpz = 100 * abs(sqrt((SHptrue(sin(x * pi / 180)) / vgptrue(sin(x * pi / 180)))) - 1).subs(S=1 / 2, Q=QZ).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51) # Relative error\n", - "URgplot = parametric_plot([gpx, URgpz], (x, 0, 90), linestyle='--')\n", - "\n", - "SHgpz = 100 * abs(sqrt((SHptrue(sin(x * pi / 180)) / vgptrue(sin(x * pi / 180)))) - 1).subs(S=1 / (2 * (1 + QZ)), Q=QZ).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51) # Relative error\n", - "SHgplot = parametric_plot([gpx, SHgpz], (x, 0, 90))\n", - "\n", - "p = TSgplot + URgplot + SHgplot\n", - "p.show(axes_labels=['phase angle (degrees)', 'relative error (%)'], aspect_ratio=25, frame=True, axes=False)" - ] - }, - { - "cell_type": "markdown", - "id": "cdf9d5df", - "metadata": {}, - "source": [ - "

Figure 5 Relative error of different group velocity\n", - " approximations for the Greenhorn shale anisotropy. Short dash:\n", - " Alkhalifah-Tsvankin approximation. Long dash: Zhang-Uren \n", - " approximation. Solid line: suggested approximation.

" - ] - }, - { - "cell_type": "markdown", - "id": "d002e315", - "metadata": {}, - "source": [ - "Another accurate group velocity approximation was suggested by\n", - "[Alkhalifah (2000b)][Alkhalifah2000b]. However, the analytical expression is\n", - "complicated and inconvenient for practical use. The accuracy of Alkhalifah's\n", - "approximation for the Greenhorn shale example is depicted in\n", - "Figure 6.\n", - "\n", - "[Alkhalifah2000b]:https://doi.org/10.1190/1.1444823" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "e6f6d129", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "Graphics object consisting of 2 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Define constants and matrix\n", - "c11, c12, c13, c22, c23, c33, c44, c55, c66 = var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - " [c11, c12, c13, 0, 0, 0],\n", - " [c12, c22, c23, 0, 0, 0],\n", - " [c13, c23, c33, 0, 0, 0],\n", - " [0, 0, 0, c44, 0, 0],\n", - " [0, 0, 0, 0, c55, 0],\n", - " [0, 0, 0, 0, 0, c66]])\n", - "\n", - "n1, n2, n3 = var('n1,n2,n3') # components of the normal vector\n", - "nv = vector([n1, n2, n3]).column()\n", - "\n", - "A = matrix([\n", - " [n1, 0, 0, 0, n3, n2],\n", - " [0, n2, 0, n3, 0, n1],\n", - " [0, 0, n3, n2, n1, 0]])\n", - "\n", - "V = M.substitute(c12=c11 - 2 * c66, c22=c11, c23=c13, c44=c55)\n", - "C = A * V * A.transpose()\n", - "e3 = list(map(lambda x: x.full_simplify(), C.eigenvalues())) # Convert map to list\n", - "\n", - "vsphase = sqrt(e3[2])\n", - "vpphase = sqrt(e3[1])\n", - "\n", - "vsgroup = vsphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector([diff(vsphase, n1), diff(vsphase, n2), diff(vsphase, n3)]).column()\n", - "vsgroup = [vsgroup[0][0].full_simplify(), vsgroup[1][0].full_simplify(), vsgroup[2][0].full_simplify()]\n", - "vsgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1 - n1^2)).full_simplify(), vsgroup)) # Convert map to list\n", - "\n", - "vpgroup = vpphase * nv + (identity_matrix(3) - nv * nv.transpose()) * vector([diff(vpphase, n1), diff(vpphase, n2), diff(vpphase, n3)]).column()\n", - "vpgroup = [vpgroup[0][0].full_simplify(), vpgroup[1][0].full_simplify(), vpgroup[2][0].full_simplify()]\n", - "vpgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1 - n1^2)).full_simplify(), vpgroup)) # Convert map to list\n", - "\n", - "# Further calculations as in your original code\n", - "vgs(n1) = (vsgroup[0]^2 + vsgroup[1]^2 + vsgroup[2]^2).full_simplify()\n", - "vgp(n1) = (vpgroup[0]^2 + vpgroup[1]^2 + vpgroup[2]^2).full_simplify()\n", - "\n", - "vgptrue(n1) = vgs(n1)\n", - "vgstrue(n1) = vgp(n1)\n", - "\n", - "sn12(n1) = (vsgroup[0]^2 / vgs).full_simplify()\n", - "pn12(n1) = (vpgroup[0]^2 / vgp).full_simplify()\n", - "\n", - "pn12true(n1) = sn12(n1)\n", - "\n", - "gpx = (arcsin(sqrt(pn12true(sin(x * pi / 180)))) * 180 / pi).substitute(c11=14.47, c33=9.57, c55=2.28, c13=4.51) # Group angle\n", - "\n", - "# Thomsen's weak anisotropy\n", - "\n", - "epsilon=(c11-c33)/(2*c33)\n", - "delta=((c55+c13)^2-(c33-c55)^2)/(2*c33* (c33-c55))\n", - "TH(n1)=c33*(1+2*epsilon*pn12true(n1)^2+2*delta*pn12true(n1)*(1-pn12true(n1)))\n", - "\n", - "# Muir-Dellinger\n", - "Q,N1=var('Q,N1')\n", - "\n", - "ELp(n1)=(1/c11)*pn12(n1)+(1/c33)*(1-pn12(n1))\n", - "MDp(n1)=(ELp(n1)+(Q-1)*(1/c11)*(1/c33)*pn12(n1)*(1-pn12(n1))/ELp(n1))^-1\n", - "\n", - "ELs(n1)=(1/c11)*sn12(n1)+(1/c33)*(1-sn12(n1))\n", - "MDs(n1)=(ELs(n1)+(Q-1)*(1/c11)*(1/c33)*sn12(n1)*(1-sn12(n1))/ELs(n1))^-1\n", - "\n", - "MDptrue(n1)=MDs(n1)\n", - "\n", - "qz=((2*c13 + c33)*c55 + c13^2)/(c11*c33 - c11*c55)\n", - "QZ = 1/qz\n", - "\n", - "# Shifted hyperbola\n", - "\n", - "S=var('S')\n", - "SHp(n1)=((1-S)*ELp(n1)+S*sqrt(ELp(n1)^2+2*(Q-1)*(1/c11)*(1/c33)*pn12*(1-pn12)/S))^-1\n", - "SHs(n1)=((1-S)*ELs(n1)+S*sqrt(ELs(n1)^2+2*(Q-1)*(1/c11)*(1/c33)*sn12*(1-sn12)/S))^-1\n", - "\n", - "SHptrue(n1)=SHs(n1)\n", - "\n", - "SHgpz=100*abs(sqrt((SHptrue(sin(x*pi/180))/vgptrue(sin(x*pi/180))))-1).subs(S=1/(2*(1+QZ)),Q=QZ).substitute(c11=14.47,c33=9.57,c55=2.28,c13=4.51) # Relative error\n", - "SHgplot = parametric_plot([gpx,SHgpz],(x,0,90))\n", - "\n", - "# Alkhalifah \n", - "\n", - "v,h,q=var('v,h,q')\n", - "TA(a,b)=1/(b*sqrt((b^2*h^4*q^2*(b^6*h^6*q^3 - 3*a^2*b^4*h^4*(-3 + q)*q^2*v^2 + 3*a^4*b^2*h^2*q*(1 + 2*q)*v^4 + 4*a^6*v^6))/((b^2*h^2*q + a^2*v^2)*(b^6*h^6*q^4 + a^2*b^4*h^4*q^2*(1 + 5*q)*v^2 + a^4*b^2*h^2*q*(-13 + 22*q)*v^4 + 4*a^6*v^6))) + a*v*sqrt((a^2*b^6*h^6*q^3*(1 + 3*(-1 + q)*q)*v^2 - 6*a^4*b^4*h^4*q^2*(2 + (-4 + q)*q)*v^4 + 9*a^6*b^2*h^2*q*(-1 + 2*q)*v^6 + 4*a^8*v^8)/(b^8*h^8*q^4 + a^2*b^6*h^6*q^3*(10 + 3*(-2 + q)*q)*v^2 - 3*a^4*b^4*h^4*q^2*(3 + 2*(-5 + q)*q)*v^4 + a^6*b^2*h^2*q*(-5 + 18*q)*v^6 + 4*a^8*v^8)))^2\n", - "\n", - "TAgpz=100*abs(sqrt((TA(sqrt(1-sn12(sin(x*pi/180))),sqrt(sn12(sin(x*pi/180)))).substitute(v=1/sqrt(c33),h=1/sqrt(c11),q=1/(((c55 + c13)^2 + c55*(c33 - c55))/(c11*(c33 - c55))))/vgptrue(sin(x*pi/180))))-1).substitute(c11=14.47,c33=9.57,c55=2.28,c13=4.51) # Relative error\n", - "TAgplot = parametric_plot([gpx,TAgpz],(x,0,90),linestyle='--')\n", - "\n", - "p = TAgplot+SHgplot\n", - "p.show(axes_labels=['phase angle (degrees)','relative error (%)'],aspect_ratio=200,frame=True,axes=False)" - ] - }, - { - "cell_type": "markdown", - "id": "6fb5213e", - "metadata": {}, - "source": [ - "

Figure 6 Relative error of different group velocity\n", - " approximations for the Greenhorn shale anisotropy. Dashed line:\n", - " Alkhalifah approximation. Solid line: suggested approximation.

" - ] - }, - { - "cell_type": "markdown", - "id": "240bb8a9", - "metadata": {}, - "source": [ - "It is similarly possible to convert a group velocity approximation into the\n", - "corresponding moveout equation. In a homogeneous anisotropic medium, the\n", - "reflection traveltime $t$ as a function of offset $x$ is\n", - "

(38)

\n", - "\\begin{equation}\n", - " \\label{eq:travel}\n", - " t(x) = \\frac{2\\,\\sqrt{(x/2)^2+z^2}}\n", - " {V_P\\left(\\arctan\\left(\\frac{x}{2\\,z}\\right)\\right)}\\;,\n", - "\\end{equation}\n", - "where $z = t_0\\,V_P(0)/2$ is the depth of the reflector. The moveout equation\n", - "corresponding to approximation 33 is\n", - "

(39)

\n", - "\\begin{eqnarray}\n", - " \\nonumber\n", - " t^2(x) & \\approx & \\frac{1+2\\,Q}{2\\,(1+Q)}\\,H(x) + \n", - "\\frac{1}{2\\,(1+Q)}\\,\n", - "\\sqrt{H^2(x) + 4\\,(Q^2-1)\\,\\frac{t_0^2\\,x^2}{Q\\,V_n^2}} \\\\\n", - "& = & \\frac{3+4\\,\\eta}{4\\,(1+\\eta)}\\,H(x) + \n", - "\\frac{1}{4\\,(1+\\eta)}\\,\n", - "\\sqrt{H^2(x) + 16\\,\\eta\\,(1+\\eta)\\,\\frac{t_0^2\\,x^2}{(1+2\\,\\eta)\\,V_n^2}}\n", - "\\;,\n", - " \\label{eq:moveout}\n", - "\\end{eqnarray}\n", - "where\n", - "$H(x)$ represents the hyperbolic part:\n", - "

(40)

\n", - "\\begin{equation}\n", - " \\label{eq:hyper}\n", - " H(x) = t_0^2 + \\frac{x^2}{Q\\,V_n^2} = \n", - " t_0^2 + \\frac{x^2}{(1+2\\,\\eta)\\,V_n^2}\\;.\n", - "\\end{equation}\n", - "For small offsets, the Taylor series expansion of equation 39 is\n", - "

(41)

\n", - "\\begin{eqnarray}\n", - "\\nonumber\n", - "t^2(x) & \\approx & t_0^2 + \\frac{x^2}{V_n^2} - \n", - "(Q-1)\\,\\frac{x^4}{t_0^2\\,V_n^4} +\n", - "(Q-1)\\,(2\\,Q^2-1)\\,\\frac{x^6}{Q\\,t_0^4\\,V_n^6} + O(x^8) \\\\\n", - "& = & t_0^2 + \\frac{x^2}{V_n^2} - 2\\,\\eta\\,\\frac{x^4}{t_0^2\\,V_n^4} +\n", - "2\\,\\eta\\,(1+8\\,\\eta+8\\eta^2)\\,\\frac{x^6}{(1+2\\,\\eta)\\,t_0^4\\,V_n^6} + \n", - "O(x^8)\\;.\n", - "\\label{eq:moveout2} \n", - "\\end{eqnarray}\n", - "\n", - "Figure 7 compares the accuracy of different moveout\n", - "approximations assuming reflection from the bottom of a homogeneous\n", - "anisotropic layer of 1 km thickness with the elastic parameters of Greenhorn\n", - "shale. Approximation 39 appears extremely accurate for\n", - "half-offsets up to 1 km and does not develop errors greater than 5 ms even\n", - "at much larger offsets.\n", - "\n", - "It remains to be seen if the suggested approximation proves to be useful for\n", - "describing normal moveout in layered media. The next section discusses its\n", - "application for traveltime computation in heterogenous velocity models." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "68ade98c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "Graphics object consisting of 3 graphics primitives" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c11,c12,c13,c22,c23,c33,c44,c55,c66=var('c11,c12,c13,c22,c23,c33,c44,c55,c66')\n", - "M = matrix([\n", - "[c11, c12, c13, 0, 0, 0],\n", - "[c12, c22, c23, 0, 0, 0],\n", - "[c13, c23, c33, 0, 0, 0],\n", - "[0, 0, 0, c44, 0, 0],\n", - "[0, 0, 0, 0, c55, 0],\n", - "[0, 0, 0, 0, 0, c66]])\n", - "\n", - "n1,n2,n3=var('n1,n2,n3') # components of the normal vector\n", - "nv=vector([n1,n2,n3]).column()\n", - "\n", - "A = matrix([\n", - "[n1, 0, 0, 0, n3, n2],\n", - "[0, n2, 0, n3, 0, n1],\n", - "[0, 0, n3, n2, n1, 0]])\n", - "V=M.substitute(c12=c11-2*c66,c22=c11,c23=c13,c44=c55)\n", - "C=A*V*A.transpose()\n", - "e3=list(map(lambda x: x.full_simplify(), C.eigenvalues()))\n", - "\n", - "vsphase=sqrt(e3[2])\n", - "vpphase=sqrt(e3[1])\n", - "\n", - "# Ensure vsgroup is a list before simplification\n", - "vsgroup = list(vsgroup) # Convert map object to list\n", - "vsgroup = [vsgroup[0].full_simplify(), vsgroup[1].full_simplify(), vsgroup[2].full_simplify()]\n", - "vsgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1-n1^2)).full_simplify(), vsgroup))\n", - "\n", - "# Ensure vpgroup is a list before simplification\n", - "vpgroup = list(vpgroup) # Convert map object to list\n", - "vpgroup = [vpgroup[0].full_simplify(), vpgroup[1].full_simplify(), vpgroup[2].full_simplify()]\n", - "vpgroup = list(map(lambda x: x.substitute(n2=0, n3=sqrt(1-n1^2)).full_simplify(), vpgroup))\n", - "\n", - "vgs(n1)=(vsgroup[0]^2+vsgroup[1]^2+vsgroup[2]^2).full_simplify()\n", - "vgp(n1)=(vpgroup[0]^2+vpgroup[1]^2+vpgroup[2]^2).full_simplify()\n", - "\n", - "vgptrue(n1)=vgs(n1)\n", - "vgstrue(n1)=vgp(n1)\n", - "\n", - "sn12(n1)=(vsgroup[0]^2/vgs).full_simplify()\n", - "pn12(n1)=(vpgroup[0]^2/vgp).full_simplify()\n", - "\n", - "pn12true(n1) = sn12(n1)\n", - "\n", - "\n", - "# Muir-Dellinger\n", - "Q,N1=var('Q,N1')\n", - "\n", - "ELp(n1)=(1/c11)*pn12(n1)+(1/c33)*(1-pn12(n1))\n", - "ELs(n1)=(1/c11)*sn12(n1)+(1/c33)*(1-sn12(n1))\n", - "\n", - "qz=((2*c13 + c33)*c55 + c13^2)/(c11*c33 - c11*c55)\n", - "QZ = 1/qz\n", - "\n", - "# Shifted hyperbola\n", - "\n", - "S=var('S')\n", - "SHp(n1)=((1-S)*ELp(n1)+S*sqrt(ELp(n1)^2+2*(Q-1)*(1/c11)*(1/c33)*pn12*(1-pn12)/S))^-1\n", - "SHs(n1)=((1-S)*ELs(n1)+S*sqrt(ELs(n1)^2+2*(Q-1)*(1/c11)*(1/c33)*sn12*(1-sn12)/S))^-1\n", - "\n", - "SHptrue(n1)=SHs(n1)\n", - "\n", - "gsin(x)=(sqrt(pn12true(sin(x)))).substitute(c11=14.47,c33=9.57,c55=2.28,c13=4.51) # sine of group angle\n", - "gcos(x)=sqrt(1-gsin(x)*gsin(x)) # cosine of group angle\n", - "\n", - "TS(n1)= (1-sn12(n1))/c33 + (sn12(n1)*(-c55 + c33)*(sn12(n1)*c33*(-c55 + c33) + (1-sn12(n1))*(c13^2 + c55*(c33 + 2*c13))))/(c11*sn12(n1)*(c55 - c33)^2*c33 + (1-sn12(n1))*(c13^2 + c55*(c33 + 2*c13))^2)\n", - "\n", - "SHplot = parametric_plot([gsin(x)/gcos(x),2000/gcos(x)*abs(1/sqrt(SHptrue(sin(x)))-1/sqrt(vgptrue(sin(x)))).subs(S=1/(2*(1+QZ)),Q=QZ).substitute(c11=14.47,c33=9.57,c55=2.28,c13=4.51)],(x,0,1.33))\n", - "ZUplot = parametric_plot([gsin(x)/gcos(x),2000/gcos(x)*abs(1/sqrt(SHptrue(sin(x)))-1/sqrt(vgptrue(sin(x)))).subs(S=1/2,Q=QZ).substitute(c11=14.47,c33=9.57,c55=2.28,c13=4.51)],(x,0,1.33),linestyle='--',color='green')\n", - "TSplot = parametric_plot([gsin(x)/gcos(x),2000/gcos(x)*abs(sqrt(TS(sin(x)))-1/sqrt(vgptrue(sin(x)))).substitute(c11=14.47,c33=9.57,c55=2.28,c13=4.51)],(x,0,1.33),linestyle=':',color='red')\n", - "\n", - "p=SHplot+ZUplot+TSplot\n", - "p.show(frame=True,axes_labels=['offset (km)','absolute time error (ms)'],aspect_ratio=1/4,axes=False)" - ] - }, - { - "cell_type": "markdown", - "id": "018286cd", - "metadata": {}, - "source": [ - "

Figure 7 Traveltime moveout error of different group velocity\n", - " approximations for Greenhorn shale anisotropy. The reflector depth is 1 km.\n", - " Short dash: Alkhalifah-Tsvankin approximation. Long dash: Zhang-Uren\n", - " approximation. Solid line: suggested approximation.

" - ] - }, - { - "cell_type": "markdown", - "id": "fd15e117", - "metadata": {}, - "source": [ - "## APPLICATION: FINITE-DIFFERENCE TRAVELTIME COMPUTATION" - ] - }, - { - "cell_type": "markdown", - "id": "78ae20a6", - "metadata": {}, - "source": [ - "As an essential part of seismic imaging with the Kirchhoff method,\n", - "traveltime computation has received a lot of attention in the geophysical\n", - "literature. Finite-difference eikonal solvers\n", - "([Vidale 1990][Vidale1990]; [Podvin and Lecompte 1991][podvin.gji.91]; [van Trier and Symes 1991][vanTrier1991]) provide an efficient\n", - "and convenient way of computing first arrival traveltimes on regular grids.\n", - "Although they have a limited capacity for imaging complex structures\n", - "([Geoltrain and Brac 1993][Geoltrain1993]), eikonal solvers can be extended in several different\n", - "ways to accommodate multiple arrivals\n", - "([Bevc 1997][Bevc1997]; [Symes 1998][Symes1998]; [Abgrall and Benamou 1999][Abgrall1999]). A particularly\n", - "attractive approach to finite-difference traveltime computation is the fast\n", - "marching method, developed by [Sethian (1996)][paper] in the general context of level\n", - "set methods for propagating interfaces ([Osher and Sethian 1988][osher]; [Sethian 1999][book]). [Sethian and Popovici (1999)][Sethian1999] adopt the fast marching method for computing\n", - "seismic isotropic traveltimes. Alternative implementations are discussed by [Sun and Fomel (1998)][Sun1998], [Alkhalifah and Fomel (2001)][Alkhalifah2001] and [Kim (2002)][kim].\n", - "The fast marching method possesses a remarkable numerical stability, which\n", - "results from a cleverly chosen order of finite-difference evaluation. The\n", - "order selection scheme resembles expanding wavefronts of\n", - "[Qin et al. (1992)][Qin1992] and wavefront tracking of\n", - "[Cao and Greenhalgh (1994)][Cao1994].\n", - "\n", - "While the anisotropic eikonal equation 1 operates with phase\n", - "velocities, the kernel of the fast marching eikonal solver can be interpreted\n", - "in terms of local ray tracing in a constant-velocity background\n", - "([Fomel 1997][Fomel.sep.95.sergey3]) and is more conveniently formulated with the help\n", - "of the group velocity. [Sethian and Vladimirsky (2001)][alex] present a thorough extention of the\n", - "fast marching method to anisotropic wavefront propagation in the form of\n", - "ordered upwind methods. In this paper, I adopt a simplified approach.\n", - "Anisotropic traveltimes are computed in relation to an isotropic background.\n", - "At each step of the isotropic fast marching method, the local propagation\n", - "direction is identified, and the anisotropic traveltimes are computed by local\n", - "ray tracing with the group velocity corresponding to the same direction. This\n", - "is analogous to the tomographic linearization approach in ray tracing, where\n", - "anisotropic traveltimes are computed along ray trajectories, traced in the\n", - "isotropic background ([Chapman and Pratt 1992][pratt]). [Alkhalifah (2002)][tariq] and [Schneider (2003)][schneider]\n", - "present different approaches for linearizing the anisotropic eikonal equation.\n", - "\n", - "Many alternative forms of finite-difference traveltime computation in\n", - "anisotropic media are presented in the literature ([Qin and Schuster 1993][Qin1993]; [Dellinger and Symes 1997][Dellinger1997]; [Kim 1999][Kim1999]; [Bousquie and Siliqi 2001][Bousquie2001]; [Perez and Bancroft 2001][Perez2001]; [Qin and Symes 2002][qin]; [Zhang, Rector and Hoversten 2002][Zhang2002]).\n", - "Although the method of this paper has limited accuracy because of the\n", - "linearization assumption, it is simple and efficient in practice and serves as\n", - "an illustration for the advantages of the explicit group velocity\n", - "approximation 33. For a more accurate and robust extension of\n", - "the fast marching method for anisotropic traveltime calculation, I recommend\n", - "the ordered upwind methods of Sethian and Vladimirsky ([2001][alex], [2003][alex2]).\n", - "\n", - "Figure 8 shows finite-difference wavefronts for an isotropic and\n", - "an anisotropic homogeneous media, compared with the exact solutions. The\n", - "anisotropic media has the parameters of the Greenhorn shale. The\n", - "finite-difference error decreases with finer sampling.\n", - "\n", - "[Dellinger1993]:https://sep.stanford.edu/data/media/public/docs/sep75/martin2.ps.gz\n", - "[Abgrall1999]:https://doi.org/10.1190/1.1444519\n", - "[Alkhalifah1998]:https://doi.org/10.1190/1.1444361\n", - "[Alkhalifah2000a]:https://doi.org/10.1190/1.1444815\n", - "[Alkhalifah2000b]:https://doi.org/10.1190/1.1444823\n", - "[Alkhalifah2001]:https://doi.org/10.1046/j.1365-2478.2001.00245.x\n", - "[Alkhalifah1995]:https://doi.org/10.1190/1.1443888\n", - "[deBazelaire1988]:https://doi.org/10.1190/1.1442449\n", - "[Berryman1979]:https://doi.org/10.1190/1.1440984\n", - "[Bevc1997]:https://doi.org/10.1190/1.1444167\n", - "[Bousquie2001]:https://doi.org/10.1190/1.9781560801771.ch18\n", - "[Byun1984]:https://doi.org/10.1190/1.1441603\n", - "[Byun1989]:https://doi.org/10.1190/1.1442624\n", - "[Cao1994]:https://doi.org/10.1190/1.1443623\n", - "[Castle1994]:https://doi.org/10.1190/1.1443658\n", - "[Dellinger1997]:https://doi.org/10.1190/1.1885780\n", - "[Geoltrain1993]:https://doi.org/10.1190/1.1443439\n", - "[Jones1981]:https://doi.org/10.1190/1.1441199\n", - "[Kim1999]:https://library.seg.org/doi/pdf/10.1190/1.1820911\n", - "[Perez2001]:https://doi.org/10.1190/1.1816312\n", - "[Postma1955]:https://doi.org/10.1190/1.1438187\n", - "[Qin1992]:https://doi.org/10.1190/1.1443263\n", - "[Qin1993]:https://doi.org/10.1190/1.1443517\n", - "[Schoenberg2000]:https://doi.org/10.1190/1.1444788\n", - "[Sethian1999]:https://doi.org/10.1190/1.1444558\n", - "[Stolt1978]:https://doi.org/10.1190/1.1440826\n", - "[Stopin2001]:https://doi.org/10.1190/1.9781560801771.ch20\n", - "[Sun1998]:https://doi.org/10.1190/1.1820321\n", - "[Symes1998]:https://doi.org/10.1190/1.1820320\n", - "[Thomsen1986]:https://doi.org/10.1190/1.1442051\n", - "[vanTrier1991]:https://doi.org/10.1190/1.1443099\n", - "[Tsvankin1996]:https://doi.org/10.1190/1.1443974\n", - "[Versteeg1994]:https://doi.org/10.1190/1.1437051\n", - "[Versteeg1991]:https://doi.org/10.3997/2214-4609.201411201\n", - "[Vidale1990]:https://doi.org/10.1190/1.1442863\n", - "[Zhang2002]:https://doi.org/10.1190/1.1817077\n", - "[Zhang2001]:https://doi.org/10.1190/1.1816267\n", - "[ags]: http://doi.org/10.1007/s00791-006-0016-y\n", - "[sweep]:https://doi.org/10.1137/S0036142901396533\n", - "[sweep2]:https://doi.org/10.1016/j.jcp.2003.11.007\n", - "[fowler]:https://doi.org/10.1016/j.jappgeo.2002.12.002\n", - "[jse]:https://sep.stanford.edu/data/media/public/docs/sep75/martin2.ps.gz\n", - "[malov]:https://www.appliedgeophysics.org/\n", - "[tsvankin]:https://doi.org/10.1190/1.9781560803003.refs\n", - "[mystolt]:https://reproducibility.org/RSF/book/sep/stoltst/paper.pdf\n", - "[gassmann]:https://doi.org/10.1007/BF00879140\n", - "[white]:https://pubs.geoscienceworld.org/seg/books/edited-volume/1017/chapter-abstract/106907830/Underground-SoundApplication-of-Seismic-Waves?redirectedFrom=fulltext\n", - "[backus]:https://doi.org/10.1029/JZ067i011p04427\n", - "[paper]:https://doi.org/10.1073/pnas.93.4.1591\n", - "[osher]:https://doi.org/10.1016/0021-9991(88)90002-2\n", - "[book]:https://hrcak.srce.hr/file/69388?origin=publicationDetail.\n", - "[kim]:https://doi.org/10.1190/1.1500384\n", - "[alex]:https://doi.org/10.1073/pnas.201222998\n", - "[alex2]:https://doi.org/10.1137/S0036142901392742\n", - "[tariq]:https://doi.org/10.1046/j.1365-2478.2002.00322.x\n", - "[schneider]:https://doi.org/10.1190/1.1581079\n", - "[qin]:https://doi.org/10.1190/1.1451438\n", - "[linbin]:https://doi.org/10.1190/1.1817077\n", - "[pratt]:https://doi.org/10.1111/j.1365-246X.1992.tb00075.x\n", - "[Alkhalifah.sep.95.tariq3]:https://sep.stanford.edu/data/media/public/docs/sep95/tariq3.ps.gz\n", - "[Muir.sep.44.55]:http://sepwww.stanford.edu/data/media/public/oldreports/sep44/44_04.pdf\n", - "[Sword.sep.51.313]:http://sepwww.stanford.edu/data/media/public/oldreports/sep51/51_22.pdf\n", - "[Fomel.sep.95.sergey3]:https://reproducibility.org/RSF/book/sep/fmeiko/paper.pdf\n", - "[podvin.gji.91]:https://doi.org/10.1111/j.1365-246X.1991.tb03461.x" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "2e38951b", - "metadata": {}, - "outputs": [], - "source": [ - "from m8r import view" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "0db60341", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Writing 1_const.scons\n" - ] - } - ], - "source": [ - "%%file 1_const.scons \n", - "\n", - "import math\n", - "\n", - "def spike(mag):\n", - " return '''\n", - " spike n1=201 n2=201 n3=1 d1=0.05 d2=0.05 d3=0.05 mag=%g\n", - " label1=Z label2=X unit1=km unit2=km\n", - " ''' % mag\n", - "\n", - "vm = math.sqrt(math.sqrt(14.47*9.57))\n", - "\n", - "Flow('vm',None,spike(vm))\n", - "Flow('vx',None,spike(3.80395))\n", - "Flow('vz',None,spike(3.09354))\n", - "Flow('et',None,spike(0.340859))\n", - "\n", - "def contour(title):\n", - " return '''\n", - " contour screenratio=1 nc=24 c0=0 dc=0.1 \n", - " title=\"%s\"\n", - " ''' % title\n", - "\n", - "Flow('ciso','vm','eikonalvti order=1 zshot=5 yshot=5')\n", - "Plot('ciso',contour('Isotropic'))\n", - "\n", - "def rgraph(title):\n", - " return '''\n", - " window j1=25 | transp |\n", - " graph screenratio=1 title=\"%s\"\n", - " min1=0 min2=0 max1=10 max2=10\n", - " transp=y yreverse=y\n", - " label1=Z label2=X unit1=km unit2=km\n", - " ''' % title\n", - "\n", - "Flow('iray','vm','rays2a zshot=5 yshot=5 nr=361 nt=600 dt=0.004')\n", - "Plot('iray',rgraph('Isotropic'))\n", - "\n", - "da = math.pi/180\n", - "graph = '''\n", - "graph wanttitle=n wantaxis=n dash=1\n", - "min1=-5 max1=5 min2=-5 max2=5 screenratio=1\n", - "'''\n", - "\n", - "Flow('tiso',None,\n", - " '''\n", - " spike n1=361 d1=%g o1=0 n2=24 d2=0.1 o2=0 |\n", - " rtoc |\n", - " math output=\"%g*x2*exp(I*x1)\"\n", - " ''' % (da,vm))\n", - "Plot('tiso',graph)\n", - "\n", - "Plot('iso','ciso tiso','Overlay')\n", - "Plot('isor','iray tiso','Overlay')\n", - "\n", - "Flow('cane','vz vx et',\n", - " 'eikonalvti vx=${SOURCES[1]} eta=${SOURCES[2]} order=1 zshot=5 yshot=5')\n", - "Plot('cane',contour('VTI Anelliptic'))\n", - "\n", - "Flow('aray','vz vx et',\n", - " '''\n", - " rays2a vx=${SOURCES[1]} eta=${SOURCES[2]}\n", - " zshot=5 yshot=5 nr=361 nt=600 dt=0.004\n", - " ''')\n", - "Plot('aray',rgraph('VTI Anelliptic'))\n", - "\n", - "Flow('tane',None,\n", - " '''\n", - " exgr - |\n", - " spray axis=2 n=24 d=0.1 o=0 |\n", - " math output=\"input*x2\"\n", - " ''')\n", - "Plot('tane',graph)\n", - "\n", - "Plot('ane','cane tane','Overlay')\n", - "Plot('aner','aray tane','Overlay')\n", - "\n", - "Result('const','iso ane','SideBySideIso')\n", - "Result('constr','isor aner','SideBySideIso')" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "adab2b06", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "view(\"const\")" - ] - }, - { - "cell_type": "markdown", - "id": "5bd9894e", - "metadata": {}, - "source": [ - "

Figure 8 Finite-difference wavefronts in an isotropic (left) and an anisotropic (right) homogeneous medium. The anisotropic medium has the\n", - "parameters of the Greenhorn shale. The finite-difference sampling is 100 m. The contour sampling is 0.1 s. Dashed curves indicate the exact\n", - "solution. The finite-difference error will be reduced at finer sampling.

" - ] - }, - { - "cell_type": "markdown", - "id": "f71e3b67", - "metadata": {}, - "source": [ - "Figure 9 shows the first arrival wavefronts (traveltime contours)\n", - "computed in the anisotropic Marmousi model created by\n", - "[Alkhalifah (1997)][Alkhalifah.sep.95.tariq3] in comparison with wavefronts for the\n", - "isotropic Marmousi model ([Versteeg and Grau 1991][Versteeg1991]; [Versteeg 1994][Versteeg1994]). The model\n", - "parameters are shown in Figure 10. The observed significant\n", - "difference in the wavefront position suggests a difference in the positioning\n", - "of seismic images when anisotropy is not properly taken into account.\n", - "\n", - "[Alkhalifah.sep.95.tariq3]:https://sep.stanford.edu/data/media/public/docs/sep95/tariq3.ps.gz\n", - "[Versteeg1991]:https://doi.org/10.3997/2214-4609.201411201\n", - "[Versteeg1994]:https://doi.org/10.1190/1.1437051" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "daf8c31b", - "metadata": {}, - "outputs": [ - { - "data": { - "application/javascript": [ - "Jupyter.notebook.kernel.restart()" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from IPython.display import display, Javascript\n", - "display(Javascript('Jupyter.notebook.kernel.restart()'))" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "99cf435e", - "metadata": {}, - "outputs": [], - "source": [ - "from m8r import view" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "ae34f24a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Writing 1_marmmod.scons\n" - ] - } - ], - "source": [ - "%%file 1_marmmod.scons \n", - "\n", - "\n", - "for comp in ('vx','vz','eta'):\n", - " src = 'marm%s.HH' % comp\n", - " Fetch(src,'marm')\n", - " Flow(comp,src,'dd form=native')\n", - "\n", - "grey = '''\n", - "grey allpos=y scalebar=y\n", - "screenratio=0.325644 screenht=8 pclip=100\n", - "label1=Depth unit1=m label2=Lateral unit2=m\n", - "'''\n", - "\n", - "Plot('vz','scale dscale=0.001 | %s bias=1.3 title=\"Vertical velocity\" barlabel=\"km/s\" ' % grey)\n", - "Plot('eta',grey + ' title=\"\\F10 h\\F3 \"')\n", - "Result('marmmod','vz eta','OverUnderIso')" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "4b661d03", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Writing 2_marm.scons\n" - ] - } - ], - "source": [ - "%%file 2_marm.scons \n", - "\n", - "Flow('iso','vz','window | eikonalvti order=1 yshot=3000')\n", - "Flow('ane','vz vx eta',\n", - " '''\n", - " window | eikonalvti order=1 yshot=3000\n", - " vx=${SOURCES[1]} eta=${SOURCES[2]}\n", - " ''')\n", - "\n", - "def contour(title):\n", - " return '''\n", - " contour title=\"%s\" \n", - " screenratio=0.325644 screenht=8 nc=30 c0=0 dc=0.1\n", - " label1=Depth unit1=m label2=Lateral unit2=m\n", - " ''' % title\n", - "\n", - "Plot('iso',contour('Isotropic'))\n", - "Plot('ane',contour('VTI Anelliptic'))\n", - "\n", - "Result('marm','iso ane','OverUnderIso')" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "b2aff45f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "view(\"marm\")" - ] - }, - { - "cell_type": "markdown", - "id": "35d35ebb", - "metadata": {}, - "source": [ - "

Figure 9 Finite-difference wavefronts in the isotropic (top) and anisotropic (bottom) Marmousi models. A significant shift in the wavefront\n", - "position suggests a possible positioning error when seismic imaging does not take anisotropy into account.

" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "a9a52ee0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "view(\"marmmod\")" - ] - }, - { - "cell_type": "markdown", - "id": "3d3f7146", - "metadata": {}, - "source": [ - "

Figure 10 Alkhalifah's anisotropic Marmousi model.\n", - " Top: vertical velocity. Bottom: anelliptic $\\eta$ parameter. The\n", - " vertical velocity is taken equal to the NMO velocity $V_n$.

" - ] - }, - { - "cell_type": "markdown", - "id": "d18b24f1", - "metadata": {}, - "source": [ - "## CONCLUSIONS" - ] - }, - { - "cell_type": "markdown", - "id": "28bbdfc0", - "metadata": {}, - "source": [ - "A general approach to approximating both phase and group velocities in a VTI medium has been developed. The suggested approximations use three elastic\n", - "parameters as opposed to the four parameters in the exact phase velocity\n", - "expression. The phase velocity approximation coincides with the acoustic\n", - "approximation of Alkhalifah ([1998][Alkhalifah1998], [2000a][Alkhalifah2000a]) but is derived\n", - "differently. The group velocity approximation has an analogous form and\n", - "similar superior approximation properties. It is important to stress that the\n", - "two approximations do not correspond exactly to each other. The exact group\n", - "velocity corresponding to the acoustic approximation is different from the\n", - "approximation derived in this paper and can be too complicated for practical\n", - "use ([Alkhalifah 2000b][Alkhalifah2000b]). The suggested phase and group approximations match\n", - "each other in the sense that they have analogous approximation accuracy in the\n", - "dual domains.\n", - "\n", - "The group velocity approximation is useful for approximating normal moveout\n", - "and diffraction traveltimes in applications to non-hyperbolic velocity\n", - "analysis and prestack time migration. It is also useful for traveltime\n", - "computations that require ray tracing in locally homogeneous cells. I have\n", - "shown examples of such computations utilizing an anisotropic extension of the\n", - "fast marching finite-difference eikonal solver.\n", - "\n", - "[Alkhalifah1998]:https://doi.org/10.1190/1.1444361\n", - "[Alkhalifah2000a]:https://doi.org/10.1190/1.1444815\n", - "[Alkhalifah2000b]:https://doi.org/10.1190/1.1444823" - ] - }, - { - "cell_type": "markdown", - "id": "8ebd61c6", - "metadata": {}, - "source": [ - "## ACKNOWLEDGEMENTS" - ] - }, - { - "cell_type": "markdown", - "id": "ef894238", - "metadata": {}, - "source": [ - "The paper was improved by helpful suggestions from Tariq Alkhalifah and Paul Fowler." - ] - }, - { - "cell_type": "markdown", - "id": "4b866b4e", - "metadata": {}, - "source": [ - "## REFERENCES" - ] - }, - { - "cell_type": "markdown", - "id": "ec6c8717", - "metadata": {}, - "source": [ - "[Abgrall R. and Benamou J.D. 1999. 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