From 47e7132f26c77326093ee676f0f94c22e010f322 Mon Sep 17 00:00:00 2001
From: GudniRos <gkrosen@gmail.com>
Date: Thu, 29 Jan 2015 08:28:50 -0800
Subject: [PATCH] Wrote 1D codes, both analytic and FV solutions. \n Made test
 notebooks for 1D and worked on the 3D notebook

---
 MT 1D code test.ipynb                | 191 +++++++++++++++++++++++++++
 MT Script - 3D.ipynb                 | 156 +++++++++++++++-------
 simpegMT/Analytics/MT1Danalytic.py   | 101 ++++++++++++++
 simpegMT/Analytics/MT1Danalytic.pyc  | Bin 0 -> 3435 bytes
 simpegMT/Analytics/MT1Dsolutions.py  |  43 ++++++
 simpegMT/Analytics/MT1Dsolutions.pyc | Bin 0 -> 1471 bytes
 simpegMT/Analytics/__init__.py       |   1 +
 simpegMT/Analytics/__init__.pyc      | Bin 0 -> 161 bytes
 simpegMT/Base.pyc                    | Bin 0 -> 2770 bytes
 simpegMT/FDEM/SurveyFDEM.pyc         | Bin 0 -> 5322 bytes
 simpegMT/FDEM/__init__.pyc           | Bin 0 -> 237 bytes
 simpegMT/Utils/MT1Danalytic.py       | 100 ++++++++++++++
 simpegMT/Utils/MT1Danalytic.pyc      | Bin 0 -> 3564 bytes
 simpegMT/Utils/MT1Dsolutions.py      |  42 ++++++
 simpegMT/Utils/MT1Dsolutions.pyc     | Bin 0 -> 1557 bytes
 simpegMT/Utils/__init__.py           |   2 +
 simpegMT/Utils/__init__.pyc          | Bin 0 -> 233 bytes
 simpegMT/__init__.py                 |   2 +-
 simpegMT/__init__.pyc                | Bin 0 -> 204 bytes
 19 files changed, 586 insertions(+), 52 deletions(-)
 create mode 100644 MT 1D code test.ipynb
 create mode 100644 simpegMT/Analytics/MT1Danalytic.py
 create mode 100644 simpegMT/Analytics/MT1Danalytic.pyc
 create mode 100644 simpegMT/Analytics/MT1Dsolutions.py
 create mode 100644 simpegMT/Analytics/MT1Dsolutions.pyc
 create mode 100644 simpegMT/Analytics/__init__.py
 create mode 100644 simpegMT/Analytics/__init__.pyc
 create mode 100644 simpegMT/Base.pyc
 create mode 100644 simpegMT/FDEM/SurveyFDEM.pyc
 create mode 100644 simpegMT/FDEM/__init__.pyc
 create mode 100644 simpegMT/Utils/MT1Danalytic.py
 create mode 100644 simpegMT/Utils/MT1Danalytic.pyc
 create mode 100644 simpegMT/Utils/MT1Dsolutions.py
 create mode 100644 simpegMT/Utils/MT1Dsolutions.pyc
 create mode 100644 simpegMT/Utils/__init__.pyc
 create mode 100644 simpegMT/__init__.pyc

diff --git a/MT 1D code test.ipynb b/MT 1D code test.ipynb
new file mode 100644
index 00000000..cae26cb7
--- /dev/null
+++ b/MT 1D code test.ipynb	
@@ -0,0 +1,191 @@
+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:f84d7f6fac432ae58377d9da7313463a2286c599c51cd1ac6b9a6ad5cb6ebd91"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Test 1D solution of MT problem and compare to a analytic solution\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# import the simpegMT module\n",
+      "from simpegMT.Utils import MT1Danalytic, MT1Dsolutions\n",
+      "\n",
+      "def omega(freq):\n",
+      "    \"\"\"Change frequency to angular frequency, omega\"\"\"\n",
+      "    return 2.*np.pi*freq"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Set up the mesh.\n",
+      "freq = 10.0\n",
+      "hz = [(100.,50)]\n",
+      "M = simpeg.Mesh.TensorMesh([hz],'C')\n",
+      "sig = np.zeros(M.nC) + 1e-8\n",
+      "sig[M.vectorCCx<=0] = 1.0\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Get the fields\n",
+      "anaEd, anaEu, anaHd, anaHu = MT1Danalytic.getEHfields(M,sig,freq,M.vectorNx)\n",
+      "anaEtemp = anaEd+anaEu\n",
+      "# Scale the solution\n",
+      "anaE = anaEtemp/anaEtemp[-1]\n",
+      "\n",
+      "solE = MT1Dsolutions.get1DEfields(M,sig,freq)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plot(solE.real,M.vectorNx,'r*--',anaE.real,M.vectorNx,'b+:')"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 5,
+       "text": [
+        "[<matplotlib.lines.Line2D at 0x7f5b370f1a50>,\n",
+        " <matplotlib.lines.Line2D at 0x7f5b370f1cd0>]"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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B3MiGWo2UgxCR0FAOIgSyIxGaDxvG9vzDlYMQkdDQCCLJYjmIXd/8msN31VAO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\nIiIJKUCIiEhC/w8ZM2f6EBPGOgAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f5b379ae790>"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plot(solE.imag,M.vectorNx,'r*--',-anaE.imag,M.vectorNx,'b+:')"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 6,
+       "text": [
+        "[<matplotlib.lines.Line2D at 0x7f5b36fded50>,\n",
+        " <matplotlib.lines.Line2D at 0x7f5b36fdefd0>]"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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E7Gzeu/IlPq7fN2/Wzuuvw4wZ8NoFY+H113l3WyKfbjuNx856C2rWJPDbW1gQ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\nYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f5b379c6810>"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "semilogx(abs(solE),M.vectorNx,'r*--',abs(anaE),M.vectorNx,'b+:')"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 7,
+       "text": [
+        "[<matplotlib.lines.Line2D at 0x7f5b36fcda50>,\n",
+        " <matplotlib.lines.Line2D at 0x7f5b36f1fd50>]"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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UKCRuSqs7AOR+2ICPnv2cr3PmwqBBrFizmt/c0ZJ/fPQ2vbKzyc/Lo5ZeuSKV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\ngg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f5b370013d0>"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "anaE[1].conj()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 8,
+       "text": [
+        "(-1.2220068301411678e-08-1.5509245597740526e-09j)"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 8
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file
diff --git a/MT Script - 3D.ipynb b/MT Script - 3D.ipynb
index 65b6b8b3..16907ac2 100644
--- a/MT Script - 3D.ipynb	
+++ b/MT Script - 3D.ipynb	
@@ -1,6 +1,7 @@
 {
  "metadata": {
-  "name": ""
+  "name": "",
+  "signature": "sha256:5ff50687aa6b5eff8d9f077fee29dfb14e6eaa12563cbe8511b1dddc2ba76e23"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -22,7 +23,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 35
+     "prompt_number": 1
     },
     {
      "cell_type": "code",
@@ -33,7 +34,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 18
+     "prompt_number": 2
     },
     {
      "cell_type": "code",
@@ -61,12 +62,13 @@
        ]
       }
      ],
-     "prompt_number": 25
+     "prompt_number": 3
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
+      "# Setup the model\n",
       "conds = [1e-2,1]\n",
       "sig = Utils.ModelBuilder.defineBlock(M.gridCC,[0,0,-300],[500,500,-100],conds)\n",
       "sig[M.gridCC[:,2]>0] = 1e-8\n",
@@ -80,26 +82,28 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 34,
+       "prompt_number": 4,
        "text": [
-        "<matplotlib.colorbar.Colorbar instance at 0x10b57b7e8>"
+        "<matplotlib.colorbar.Colorbar instance at 0x7f55faf27290>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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gdeum3HtvM9LS8s2SgyHm+qx8fe/loYc6MHLkRlOHLOyVGarjyJEjGTlyZJX1Hh4e+iIO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\nx8g+dgyAoClTrBVmndWW1+aIiErtD73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3qKq7gf7AG263N4DL3eXLgLdU9bCqZgEbgR4i0gSoq6qL3H6TfLYxxpio+Tk8\ns/N04CcReR3oBCwB7gLSVLXkcTHbOXYVU1PA9xlaOTg3hjlM2UtPc912Y4yJqngaI69qIU8CugK3\nq+piEXkGdxilhKqq80CI0PjSZ7kVzl8SY4yBzUAWAJmZoXtQTjwV8qqOkefg3Ipxsfv+XZzCni8i\njQHcYZOSG8GUvwlMc3cfue6yb3uu1wde4POyIm6MOeZ0SqpDZmZmyPZa48fIVTUfyBaRs9ymPsAq\nYCYw2G0bDEx3l2cAA0UkRUROB1oDi9z97HFnvAgwyGcbY4yJmp/DGDnAHcBkEUkB/gNcj/N8uWki\nMhTnu87VAKq6WkSm4dwA5ggwTI89LHQY8A+gFs4smI+rEZMxxoRErEwtDEaVC7mqLgfO8VjVx0//\nx4DHPNqXAB2qGocxxoRDrAybBMNuY2uMMR7CObQiIveKyFERaehn/SgRWeVeLDlFRFID7c8KuTHG\neCgmMahXZYlIC6Av4Pm8OPeBEjcCXVW1A86Q9cBA+4yNkXoTVmNeCLx+7O2RiSPUampeJjaEcfrh\nU8AI4AM/6/fgXGNTW0SKgdr4mc1Xwgq5McZ4CEchF5HLcKZu/yB+ngGrqgUi8jdgK3AA+ERVPwu0\nXyvkxhjj4RABh6X9EpE5QGOPVaOBUcBFvt09tk/HuVK+FbAbeEdE/qCqk/19phVyY4zx4O+IfP/c\nxeyf+53f7VS1r1e7iLTHuXppuXs03hxYIiLdVfVHn67dgG9Udae73XvA+YAVcmOMqQx/hTy197mk\n9j639H3B2JeD2p+qruTY/acQkc3A2apaUK7rWuBhEakFHMSZ0r2IAGzWijHGeIjAJfqlN4YRkaYi\nMgtKr9GZBHwH/OB2mRBoR3ZEbowxHsJ9+b2qnuGzvA24xOf9OGBcsPuyQm6MMR7i6e6HVsiNMcaD\nFXITU2rqhTE1NS8TGw4V/QxummWMMTVZ8ZH4KY/xE6kxxkRQ8REbWjHGmLhmhdwYY+LckcNWyI0x\nJq4dLY6f8hg/kRpjTCTZ0IoxxsS5g/FTHuMnUmOMiaQj0Q4geFbIjTHGixVyY4yJc3FUyO02tsYY\n4+VwkK9KEJFMEckRkaXuK8NPvwYi8q6IrBGR1SJyrle/ElbIq+je/HyadO0KwJ/mzaP9wGMPue40\neDCPFBcf92p1wQXRCjcogXICSKpVi9/85S8M37SJ0QcPcnd2Nr9+6KFohFopgfIa/OWXnr+rUXv3\nRivcoFQxLH+hAAAbJElEQVT0u+p+++0MW7WKUfv2cU9uLpe9/jq1TzklGqFWSn7+vXTt2gSAefP+\nxMCB7UvXJSYK999/PmvW3Mb+/Q+ybt3t3Hprt/AFUxzkq3IUeEpVu7ivj/30exb4SFXbAB2BNYF2\nWq2hFRFJxLn5eY6qXioiDYG3gdOALOBqVS10+44ChuCkPlxVP3Xbzwb+AZzgBn5ndWKKhJPS00mu\nXZu8pUtJSE6mabdubP3qqzJ9jhYX81TTpuDzgNWDu3ZFOtSgVZSTJCTw+1mzSKlThw9vuokd69ZR\nu1Ejap98chSjrlhFeb09YAAJycml7yUhgRsXL+Y/H/v7/yv6Ksqp/cCBXPS3v/HhLbew6bPPqN+i\nBZe8/DIDJk1i8sUXRzHywNLTT6J27WSWLs0jOTmBbt2a8tVXW0vXjx17ATfe2JUbb5zJ8uX5nH9+\nCyZMuJSiomJee21p6AMK39CK91OXS1aK1Ad+paqDAVT1CM6zO/2q7hj5ncBqoK77fiQwR1XHicgD\n7vuRItIWuAZoCzQDPhOR1qqqwEvAUFVdJCIfiUhGgL9SMaFlz57kLlwIqjQ75xz279zJnpyc4/rt\n37EjCtFVTUU5dbruOpp07cpz6ekc2LkTgD3Z2dEKN2gV5XWwsLBM/zP69KFes2Z893Jwj++Khopy\natajB9t/+IFlr78OOL+n7ydMoPfYsdEKOSg9e7Zk4cJcVOGcc5qxc+d+cnL2lK4fPLgTf/3rN8yY\nsQ6ALVt20717M0aP/lV4CvnB0O/SdYeIXIdzEHxvycGuj9OBn0TkdaATsAS4U1X3+9thlQu5iDQH\n+gF/Bu5xm/sDvdzlN4C5OMX8MuAtVT0MZInIRqCHiGwB6qpqyfPoJgGXAzFZyB/YtQtVJSk1FUlI\nYERBAYnJySSmpjKioABUGdeoEQAJiYncsXEjybVqsWPdOr7961/Z8NFHUc7geMHm1OaKK8hdtIjz\n7r6bjoMGUXz4MJs//5zPRo6MyW8alfld+Tr7llvI+/578r7/PgpRBxZsThtnz6bL0KGc9utfs2X+\nfE5MS6PtVVex/sMPo52Cp127HkBVSU1NIiFBKCgYQXJyIqmpiRQUjEAVGjUaR2pqIocOlR3LOHjw\nCKed1oDmzeuVKfohUcUjchGZAzT2WDUa58D1Uff9/wF/A4aW65cEdAVuV9XFIvIMTh19xN9nVueI\n/GngfqCeT1uaqm53l7dz7EGjTYEFPv1ycI7MD7vLJXLd9pj0UseOiAhDFyxg1i23kL9sGVdMncrK\nKVNY+8EHpf12rF3LB9dfT/7y5SSlptLu6qu5duZMZtxwQ+lRUqwINqeT0tNp0KoVWlzMtCuvJKVO\nHX779NMMnD6df/TqFeAToiPYvHzVadyYX1x6KR/ddluEow1OsDn959NP+eSuu/jjJ58gCQkkJCWx\n/sMPmXHDDVGM3r+OHV9CRFiwYCi33DKLZcvymTr1CqZMWckHH6wt7Td79kaGD+/O559vYtWqn+je\nvRlDhnRBVWnatG7kCvmKubByrt/NVLVvMLsXkVeBmR6rcnCGqxe779/FKeR+VamQi8jvgB9VdamI\n9Pbqo6oqIuq1riq+9FluhfPdI9L2ZGdzaocOJCYns27mTFLq1KFx585M7d+/zDBK7sKFzlffkveL\nFnFCw4b0fOCBmCvkweYkCc558XcHDuTQbme4bsaQIdy4eDFpnTqxffnyqMTvT7B5+eoyZAiHDxxg\nxZQpEY42OMHmdNall/Lbp5/mk7vvZsu//0295s3p++STXDZxIu8PGhTFDLxlZ++hQ4dTSU5OZObM\nddSpk0Lnzo3p338qO3YcG024886PefnlS1i27BZUldzcvbz66veMHNmTo0cXA+vIzAxZyfFfyNv0\ndl4lpgY/ZCUiTVQ1z307AFhRvo+q5otItoicparrgT7AqkD7reoR+flAfxHph3OSsp6IvAlsF5HG\nbiBNgB/d/rlAC5/tm+P81cl1l33bc70+MNrzPW5duZL6LVuSkJREYnIyI3fvRhISSEpNZfimTQCM\nb9OGvbme4ZO7cCEdfv/7SIZcocrktC8vj8Tk5NIiDvDT6tUANDjttJgq5FX6XYnQ9cYbWTF5Mof3\n+x2KjJrK5PSrBx/kh3/+s3Sc/6dVqyjat4/r58/ny0ceoXDz5mimUsbKlbfSsmV9kpISSE5OZPfu\nkSQkCKmpSWzaNByANm3Gk5u7l8LCgwwc+C8SE9/j1FNPJC9vnztrRdi0KR1oSmbmGMaG6lxAJacW\nBukJEemMM3tlM3AzgIg0Bf6uqiUPYL4DmCwiKcB/gOsD7bRKhVxVHwQedAPoBdynqoNEZBwwGHjC\n/e90d5MZwBQReQpn6KQ1sMg9at8jIj2ARcAg4LmqxBRukzMySExJof/EiWycPZtV06bRa8wYig8d\n4qvHHwdgX16e3+2bdO3K7q1b/a6PhsrktGX+fHqOGEFK3boUuVPzGv3iFwAUZmVFJX5/qvK7OjMj\ng/otW7LklVeiEXKFKpWTCFpcdixZjx51VwWcMBFxGRmTSUlJZOLE/syevZFp01YxZkwvDh0q5vHH\nnZk4eXn7ymxTXKylbdde255587IoKDgQ+uAqP7WwQqp6nZ/2bcAlPu+XA+cEu99QzSMv+T7zONBX\nRNYDF7rvUdXVwDScGS6zgWHujBWAYcCrwAZgY6zOWNmTk0NhVhZpHTuy9v33Kdy8mbQOHVj/4YcU\nbt5M4ebNpf+z9BozhjMzMjgpPZ1T2ral1yOP0GXIEBY89VSUsyirMjktfvFFDu/fz4BJkzilbVua\nnnMOl/7972TNncv2H36IciZlVSavEmfffDO5ixbFXC4lKpPT2vfeo/OQIXQcNIgGrVrR8n/+h4uf\nf5785cvZ5R69x4qcnD1kZRXSsWMa77+/ls2bC+nQIY0PP1zP5s2FbN5cyNGjTqk4++wmXHllW844\n4yTOPbc577xzFR07pjF8eJhKxpEgXzGg2pfoq+o8YJ67XIAznuPV7zHgMY/2JUCH6sYRCY27dKH4\n0CF2rl9Par16nNKuHVvmzz+uX2rduvQbP546jRtz+MABdqxZwztXXcXa6dM99hpdweb03+3beePC\nC/ntU09x4+LFHCgoYMOsWcx54IEoRF2xYPMCqNu0Ka379ePDm26KcJSVE2xOX48bh6ryP6NGUf+l\nlzhYWMjmL77g81GjohB1xbp0acyhQ8WsX7+TevVSadfuFObP33Jcv9TUJB555NekpzekqKiYefOy\nOP/8iaxe/VN4Agvf9MOQk2MHxrFLRDQz2kGE2Bj35z42xr7qVkdNzAlqZl4lOYnE9tzyylIdg4ig\nqtX6ZYmIMj7I2nhb9T+vuuymWcYY4yVGhk2CYYXcGGO8WCE3xpg4F57ph2ERN2Pk8RCnMSb6QjZG\n/ucga85oGyM3xpjYFEezVuKmkNekGQNQs2dC1KScoGbmVRNzgmN5hYSNkRtjTJyLozFyK+TGGOMl\nDJfoh4sVcmOM8WJDK8YYE+eskBtjTJyLozHyUN390BhjapZDQb4qSUTuEJE1IrJSRJ4I0C9RRJaK\niNdThMqwI3JjjPEShqEVEbkA59nGHVX1sIicEqB7+Yfb+2VH5MYY4+VwkK/KuRX4i/sgelTV8x68\nPg+3fxWocLK/FXJjjPFSHOSrcloDvxaRBSIyV0S6+elX8nD7o37Wl2FDK8YY48Xf0MqOubBzrt/N\nRGQO0Nhj1WicmnuSqp4rIufgPDntjHLbV/hw+/KskBtjjBd/hbxBb+dVYn3Zh3Ooal9/uxSRW4H3\n3H6LReSoiDRS1Z0+3bwebj/J3/M+wYZWjDHGW3jGyKfjPM8YETkLSClXxFHVB1W1haqeDgwEvghU\nxMEKuTHGeAvP9MOJwBkisgJ4C7gOQESaisgsP9tUeCcwG1oxxhgvYZh+6M5WGeTRvg24xKO99OH2\ngVghN8YYL3F0ZacVcmOM8WJ3PzTGmDgXRzfNqtLJThFpISJfisgq934Bw932hiIyR0TWi8inItLA\nZ5tRIrJBRNaKyEU+7WeLyAp33bPVT8kYY0LgSJCvGFDVWSuHgbtVtR1wLnCbiLQBRgJzVPUs4HP3\nPSLSFrgGaAtkAC+KlD5j6iVgqKq2BlqLSEaVszHGmFAJz/TDsKhSIVfVfFVd5i7vA9YAzXBuBvOG\n2+0N4HJ3+TLgLVU9rKpZwEagh4g0Aeqq6iK33ySfbYwxJnrCdPfDcKj2GLmItAK6AAuBNFXd7q7a\nDqS5y02BBT6b5eAU/sPucolct90YY6IrRoZNglGtQi4idYB/AXeq6l7xeSK3qqqIhOyR1l/6LLcC\nTg/Vjo0xcW0zkOUua2Zm6HYcI8MmwajylZ0ikoxTxN9U1elu83YRaeyubwL86LbnAi18Nm+OcySe\n6y77tud6fd4FPi8r4saYEqdzrDZkhrKQh+fuh2FR1VkrArwGrFbVZ3xWzQAGu8uDce4rUNI+UERS\nROR0nFs5LlLVfGCPiPRw9znIZxtjjImeOJq1UtWhlZ7AH4EfRGSp2zYKeByYJiJDcb7tXA2gqqtF\nZBrO0y6OAMNUtWTYZRjwD6AW8JGqflzFmIwxJnRipEgHo0qFXFW/wv/RfB8/2zwGPObRvgToUJU4\njDEmbOJojNyu7DTGGC81/YjcGGNM5YnIVOAX7tsGQKGqdinXpwXONTWn4tzCdoKqPhdov1bIjTEm\nQlR1YMmyiPwVKPToVnLl/DJ3ivcSEZmjqmv87dcKuTHGRJg7S+9qnFmTZbiz+fLd5X0isgbnokor\n5MYYUzlhPdv5K2C7qv4nUKdyV877ZYXcGGM8+TvbOd99eROROUBjj1UPqupMd/laYEqgT3eHVd7F\nuXJ+X6C+VsiNMcaTvyPy89xXibKzqlW1b6C9ikgSMADoGqBPyZXz//S5ct4vK+TGGOPpQLh23AdY\n4z6n8zgBrpz3q8r3WjHGmJotbDckvwZ4y7dBRJqKyCz3bcmV8xeIyFL3FfA5DXZEbowxnsJzRZCq\nXu/Rtg24xF0OdOW8JyvkxhjjKX6u0bdCbowxnuLnGn0r5MYY4yl+jsjtZGcV3JufT5OuzsyhP82b\nR/uBA8usb9a9O0O+/poH9+/nntxcLvzzn8Hn6UmxKlBep7Rty5XTpnH7unU8fOQIl06YEK0wKy1Q\nXp2vv57rvviC+378kZG7d3Pj4sW0v/baaIUatEA5pV90EUO++Yb7fvyRB/fv544NG7jg0UdJSIr9\n47aK/t8qcXKbNozat4+HiorCGM2BIF/RF/u/2RhzUno6ybVrk7d0KQnJyTTt1o2tX31Vur5e8+YM\nmjOH1e+8w4yhQ2l01ln0nzgREeHzBx+MYuSBVZRXUq1a7M7KYt0HH3DePfdw7Hbysa2ivFpdcAFr\n33+fOffdx4GCAn45YAADJk3i6JEjrH7nnShG7l9FOR3cvZsFTz/NjytXUrR3L026duV3EyaQUrcu\nn9x9dxQjD6yivEok1arFVdOmsfnzzzkzI+BkjmqyoZUaq2XPnuQuXAiqNDvnHPbv3MmenGPPj+52\n660cLCxkxg03ALBj7Vq+fPhh+o4bx7xHH+XIwYPRCj2givLKW7KEvCVLAOgydGi0wqy0ivKaft11\nZfovePppTuvVi3ZXXx2zhbyinHIXLnTWu/bk5NCqd29O69UrGuEGraK8SvQbP54t8+eTu3AhZ158\ncRgjip+hFSvkQXpg1y5UlaTUVCQhgREFBSQmJ5OYmsqIggJQZVyjRrTo2ZP/fPppmW3/88kn9Hvh\nBRp36ULOt99GKQNvweYVb6qTV62TTmLXpk0RjrhiVc2p0S9+QXpGBmvfey8KUVesMnl1HDSIpmef\nzd/POScCQ2B2RF7jvNSxIyLC0AULmHXLLeQvW8YVU6eycsoU1n7wQWm/Oo0bs/Xf/y6z7b78fADq\nNmkS0ZiDEWxe8aaqeXX4wx9o1qMHs4cPj2C0walsTndnZ1P75JNJTElh2euv88VDD0Uh6ooFm9fJ\nv/wlF/31r/yjd2+Kwzo2XiJ+jsjtZGeQ9mRnk1q/PonJyaybOZMDu3bRuHNnVk6dyp7sbPZkZ0c7\nxCqxvI75Rf/+XDphAjOGDGH78uVRiDqwyuY0sWdPXunShfcHDSL9t78l49lnoxR5YMHklZiSwlXv\nvMMXDz3EjjV+7+YaYvHz9GU7Ig/CrStXUr9lSxKSkkhMTmbk7t1IQgJJqakMd7+Cj2/Thr25uezL\nyzvuyPvEtDQA9ublRTz2QCqTVzypSl7trrmGy15/nZk33MCKKQFvShcVVclp99atgHOe5mhxMf87\neTKfjxrF4f37o5KDl2DzSkhK4pS2bek3fjz9xo8HQESQhAQeKiriy4cf5usnnghxdPFzRG6FPAiT\nMzJITEmh/8SJbJw9m1XTptFrzBiKDx3iq8cfB2CfW6Szv/6ajoMGldn+zIwMiv77X/KXLo147IFU\nJq94Utm8ut5wAxnPPcf0665j9bvvRivsgKr7u0pITARA3P/GiqDzEuHF9u3LbPvLyy+n99ixvNyp\nE//98ccwRBcbUwuDYYU8CHtycpCEBNI6duTDm26icPNm0jp0YG5mJoWbN5fpu/illzjn9tu59O9/\nZ8HTT3NSejoXPPooi55/PuZmrFQmr4SkJE5p1w6A1Lp1qdWoEWmdOlFcVBTBr7rBqUxe5951F33G\njeOj225jy7//XfrtqbioiIO7dkUjfE+Vyem8e+7hpzVrKNiwAVWlabdu9HniCdZOn07R3r1RysBb\nZfIq/+9sb/funu2hY0fkNU7jLl0oPnSInevXk1qvHqe0a8eW+cffXH5vbi7/vOgiLnrqKW787jsO\nFhay5JVXYvZEU7B51W3WjJu//x4AVaVJ1660GTCAwqwsnktPj3TYFQo2r+7DhyMJCfzu5Zf53csv\nl7ZnzZ3LpN/8JpIhVyjYnBKSkug7bhwNWrVCjx6lMCuLRS+8wIJngrojasQFm5ensF7PEBvj38GQ\nWLiww71F4zNAIvCqqj5Rbr1mRiOwMBrj/tzHxsEVn8GqiTlBzcyrJuYETl4igqpWKzERUXgxyN7D\ngv48EekOvAAk4/ylGKaqiz36BayJ5UV91oqIJOIklgG0Ba4VkTbRjcrb5oq7hF0sxACxEUcsxACx\nEUcsxACxE0dohGXWyjjgYVXtAjzivi+jKjUx6oUc6A5sVNUsVT0MTAUui3JMnrKiHQCxEQPERhxZ\n0Q7AlRXtAIiNGCB24giNsDxYIg+o7y43ALymhFW6JsbCGHkzwHcCbA7QI0qxGGOMKyxj5COBr0Tk\nrzgH0ud59Kl0TYyFQh7UIP2YGBjL18xMxmRmhnSflc0rHDFURaA4IvW7ivTPwl9esfA7qWoMof5d\nxcLPInSqNv1QROYAjT1WjQaGA8NV9X0RuQqYCJR/WHOlfylRP9kpIucCmaqa4b4fBRz1Hdx3TjwY\nY0xwQnOyM/SfJyJ7VLWeuyxAoarWL9enwppYXiwckX8HtBaRVsA2nAeTlrkbTnV/KcYYUxlhrDkb\nRaSXqs4DLgTWe/SpsCaWF/VCrqpHROR24BOcqTavqWpsXWFijDGhcRMwXkRSccZubgIQkabA31X1\nkqrUxKgPrRhjjKmeWJh+GJCIZIjIWhHZICIPhHjfLUTkSxFZJSIrRWS4295QROaIyHoR+VREGvhs\nM8qNZa2IXOTTfraIrHDXVfo2cyKSKCJLRWRmFGNoICLvisgaEVktIj0iHYe7z1Xu9lNEJDUSMYjI\nRBHZLiIrfNpC9rluHm+77QtE5LQgY3jS/X0sF5H3RKS+z7qQx+AvDp9194rIURFpGOmfhdt+h/vz\nWCkivufRwvKziBuqGrMvnK8VG4FWOFdCLQPahHD/jYHO7nIdYB3QBmeS/gi3/QHgcXe5rRtDshvT\nRo59q1kEdHeXPwIyKhnLPcBkYIb7PhoxvAEMcZeTcOa7RiwOdz+bgFT3/dvA4EjEAPwK6AKs8GkL\n2ecCw4AX3eVrgKlBxtAXSHCXHw93DP7icNtbAB/jXPfTMAo/iwuAOUCy+/6UcP8s4uUV9QACBufM\nsfzY5/1IYGQYP2860AdYC6S5bY2Bte7yKOABn/4fA+cCTYA1Pu0DgZcr8bnNgc/cf6gz3bZIx1Af\n2OTRHrE4gIY4f0xPwvlDMhOnkEUkBrcIrAhH7m6fHu5yEvBTMDGUWzcA+Ge4Y/AXB/AO0JGyhTxi\nPwtgGnChR7+w/izi4RXrQyteE+ObheODxDlD3AVYiPM/73Z31XYgzV1u6sZQPp7y7bmVjPNp4H7g\nqE9bpGM4HfhJRF4Xke9F5O8icmIk41DVAuBvwFacs/WFqjonkjGUE8rPLf23rKpHgN2+wxNBGoJz\nVBnxGETkMiBHVX8otyqScbQGfu0OhcwVkW5RiCEmxXohj8iZWBGpA/wLuFNVy9znU50/2WGLQ0R+\nB/yoqksBzylP4Y7BlQR0xfm62RX4L843oIjFISLpwF04R2JNgToi8sdIxuBPtD63hIiMBopUNeJP\nvRCR2sCDwBjf5kjHgfNv9CRVPRfnwGdaFGKISbFeyHNxxuVKtKDsX9hqE5FknCL+pqpOd5u3i0hj\nd30ToOSu9eXjae7Gk+su+7YH+1id84H+IrIZeAu4UETejHAMuPvI0WN3YnsXp7DnRzCObsA3qrrT\nPUp6D2d4LZIx+ArF7yDHZ5uW7r6SgPruN5AKicifgH7AH3yaIxlDOs4f1+Xuv9PmwBIRSYtwHDk4\n/yZw/50eFZGTIxxDTIr1Ql46MV5EUnBOSswI1c5FRIDXgNWq6nuz5hk4J9lw/zvdp32giKSIyOk4\nX/UWqWo+sEecWR4CDPLZJiBVfVBVW6jq6ThjeF+o6qBIxuDGkQ9ki8hZblMfYBXOOHWk4lgLnCsi\ntdxt+wCrIxyDr1D8Dj7w2NeVwOfBBCDO7UzvBy5TVd8nk0QsBlVdoappqnq6++80B+jqDjtFLA6c\nn/+F7s/lLCBFVXdEOIbYFO1B+opewMU4J8A2AqNCvO//wRmXXgYsdV8ZOCfdPsO56upToIHPNg+6\nsawFfuvTfjawwl33XBXj6cWxWSsRjwHoBCwGluMc+dSPdBzACJw/ICtwZtEkRyIGnG9D24AinLHT\n60P5uUAqzlDABmAB0CqIGIa4/bf4/Pt8MZwxlIvjUMnPotz6TbgnOyPwsyiNwf238Ka7zyVA73D/\nLOLlZRcEGWNMnIv1oRVjjDEVsEJujDFxzgq5McbEOSvkxhgT56yQG2NMnLNCbowxcc4KuTHGxDkr\n5MYYE+f+P/pjeYweur3BAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x10ae16e90>"
+        "<matplotlib.figure.Figure at 0x7f55de17de90>"
        ]
       }
      ],
-     "prompt_number": 34
+     "prompt_number": 4
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
+      "# Get the mass matrix \n",
+      "# The model\n",
       "Msig = M.getEdgeInnerProduct(sig)\n",
       "MsigBG = M.getEdgeInnerProduct(sigBG)\n",
       "\n",
@@ -108,7 +112,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 38
+     "prompt_number": 5
     },
     {
      "cell_type": "code",
@@ -122,78 +126,128 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 39
+     "prompt_number": 6
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "def get1Dfields(sigHalf, freq):\n",
-      "    hz = [(100.,18)]\n",
-      "    M = Mesh.TensorMesh([hz],'C')\n",
-      "    sig = np.zeros(M.nC) + 1e-8\n",
-      "    sig[M.vectorCCx<=0] = sigHalf\n",
-      "    G = M1D.nodalGrad\n",
-      "    Mmu = Utils.sdiag(M.vol*(1.0/mu_0))\n",
-      "    Msig = M.getFaceInnerProduct(sig)\n",
-      "    A = G.T*Mmu*G - 1j*omega(freq)*Msig\n",
-      "    Aii = A[1:-1,1:-1]\n",
-      "    Aio = A[1:-1,[0,-1]]\n",
-      "    bc = np.r_[0.0,1.0]\n",
-      "    rhs = -Aio*bc\n",
-      "    eii = Solver(Aii).solve(rhs)\n",
-      "    e = np.r_[bc[0],eii,bc[1]]\n",
-      "    return e"
+      "# Need to solve x and y polarizations of the source.\n",
+      "from simpegMT.Utils import get1DEfields\n",
+      "# Get a 1d solution for a halfspace background\n",
+      "mesh1d = simpeg.Mesh.TensorMesh([M.hz],np.array([M.x0[2]]))\n",
+      "e0_1d = get1DEfields(mesh1d,M.r(sigBG,'CC','CC','M')[0,0,:],freq)\n",
+      "# Setup x (east) polarization (_x)\n",
+      "ex_x = np.zeros(M.vnEx,dtype=complex)\n",
+      "ey_x = np.zeros((M.nEy,1),dtype=complex)\n",
+      "ez_x = np.zeros((M.nEz,1),dtype=complex)\n",
+      "# Assign the source to ex_x\n",
+      "for i in arange(M.vnEx[0]):\n",
+      "    for j in arange(M.vnEx[2]):\n",
+      "        ex_x[i,j,:] = e0_1d\n",
+      "eBG_x = np.vstack((simpeg.Utils.mkvc(M.r(ex_x,'Ex','Ex','V'),2),ey_x,ez_x))\n",
+      "rhs_x = ABG.dot(eBG_x)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 89
+     "prompt_number": 50
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "x0 = -h1.sum()/2"
+      "# Setup y (north) polarization (_y)\n",
+      "ex_y = np.zeros((M.vnEx,1))\n",
+      "ey_y = np.zeros(M.vnEy)\n",
+      "ez_y = np.zeros((M.vnEz,1))\n",
+      "# Assign the source to ex_x\n",
+      "for i in arange(M.vnEy[0]):\n",
+      "    for j in arange(M.vnEy[2]):\n",
+      "        ey_y[i,j,:] = e0_1d\n",
+      "eBG_y = np.vstack((ex_y,simpeg.Utils.mkvc(M.r(ey_y,'Ey','Ey','V'),2),ez_y))\n",
+      "rhs_y = ABG.dot(eBG_y)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 87
+     "prompt_number": 12
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "sigs = np.logspace(-3,1,4)\n",
-      "for s in sigs:\n",
-      "    e = get1Dfields(s,1e1)\n",
-      "    plot(e.imag,M.vectorNx)\n",
-      "ylim([-900,0])\n",
-      "ylabel('Depth, m')\n",
-      "legend(['$\\sigma = 1e%d$'%log10(s) for s in sigs],'best')"
+      "# Solve the systems for each polarization\n",
+      "Ainv = simpeg.SolverCG(A)\n",
+      "e_x = Ainv*rhs_x\n",
+      "\n",
+      "e_y = Ainv*rhs_x"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 28
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 101,
-       "text": [
-        "<matplotlib.legend.Legend at 0x10c40d750>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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XIiMjSUpKIjU1FW9vbwD8/f1Zs2aNFqVbzKG0NNyrV6diCV6YEijCIi5cgG++UVsi/fqp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\nsOIJ/Z33A0v7JjEAAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x10c969890>"
+       "ename": "NameError",
+       "evalue": "name 'e0_1d' is not defined",
+       "output_type": "pyerr",
+       "traceback": [
+        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+        "\u001b[1;32m<ipython-input-36-4c5017fec386>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mM\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvnEx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[1;32min\u001b[0m \u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mM\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvnEx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m         \u001b[0mex_x\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0me0_1d\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+        "\u001b[1;31mNameError\u001b[0m: name 'e0_1d' is not defined"
        ]
       }
      ],
-     "prompt_number": 101
+     "prompt_number": 36
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Get a 1d solution for a halfspace background\n",
+      "mesh1d = simpeg.Mesh.TensorMesh(M.hz,M.x0[2])\n",
+      "e0_1d = get1DEfields(mesh1d,M.r(sigBG,'CC','CC','M')[0,0,:],freq)\n",
+      "# Setup x (east) polarization (_x)\n",
+      "ex_x = np.zeros(M.vnEx)\n",
+      "ey_x = np.zeros(M.vnEy)\n",
+      "ez_x = np.zeros(M.vnEz)\n",
+      "# Assign the source to ex_x\n",
+      "for i in arange(M.vnEx[0]):\n",
+      "    for j in arange(M.vnEx[2]):\n",
+      "        ex_x[i,j,:] = e0_1d\n",
+      "eBG_x = np.vstack(M.r(ex_x,'Ex','Ex','V'),M.r(ex_y)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "ename": "SyntaxError",
+       "evalue": "invalid syntax (<ipython-input-34-f14ef29654fd>, line 12)",
+       "output_type": "pyerr",
+       "traceback": [
+        "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-34-f14ef29654fd>\"\u001b[1;36m, line \u001b[1;32m12\u001b[0m\n\u001b[1;33m    eBG_x = np.vstack(M.r(ex_x,'Ex','Ex','V'),M.r(ex_y)\u001b[0m\n\u001b[1;37m                                                       ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
+       ]
+      }
+     ],
+     "prompt_number": 34
     },
     {
      "cell_type": "code",
diff --git a/simpegMT/Analytics/MT1Danalytic.py b/simpegMT/Analytics/MT1Danalytic.py
new file mode 100644
index 00000000..66db5df5
--- /dev/null
+++ b/simpegMT/Analytics/MT1Danalytic.py
@@ -0,0 +1,101 @@
+# Analytic solution of EM fields due to a plane wave
+
+import numpy as np, SimPEG as simpeg
+
+def getEHfields(m1d,sigma,freq,zd):
+	'''Analytic solution for MT 1D layered earth. Returns E and H fields.
+
+	:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
+	:param numpy.array, vector sigma: Physical property of conductivity corresponding with the mesh.
+	:param float, freq: Frequency to calculate data at.
+	:param numpy array, vector zd: location to calculate EH fields at
+
+	Assumes a halfspace with the same conductive as the last cell below.
+
+	'''
+	# Note add an error check for the mesh and sigma are the same size.
+	# Need make the solution e^-iwt dependent
+
+	# Constants: Assume constant 
+	mu = 4*np.pi*1e-7*np.ones((m1d.nC+1))
+	eps = 8.85*1e-12*np.ones((m1d.nC+1))
+	# Angular freq 
+	w = 2*np.pi*freq
+	# Add the halfspace value to the property
+	sig = np.concatenate((np.array([sigma[0]]),sigma))
+	# Calculate the wave number
+	k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
+
+	# Initiate the propagation matrix, in the order down up.
+	UDp = np.zeros((2,m1d.nC+1),dtype=complex)
+	UDp[1,0] = 1 # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
+	# Loop over all the layers, starting at the bottom layer
+	for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
+		# Calculate 
+		yp1 = k[lnr]/(w*mu[lnr]) # Admittance of the layer below the current layer
+		zp = (w*mu[lnr+1])/k[lnr+1] # Impedance in the current layer 
+		# Build the propagation matrix
+		
+		# Convert fields to down/up going components in layer below current layer
+		Pj1 = np.array([[1,1],[yp1,-yp1]]) 
+		# Convert fields to down/up going components in current layer
+		Pjinv = 1./2*np.array([[1,zp],[1,-zp]])
+		# Propagate down and up components through the current layer
+		elamh = np.array([[np.exp(-1j*k[lnr+1]*h),0],[0,np.exp(1j*k[lnr+1]*h)]])
+
+		# The down and up component in current layer.
+		UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
+
+	# Calculate the fields
+	Ed = np.zeros((zd.size,),dtype=complex)
+	Eu = np.zeros((zd.size,),dtype=complex)
+	Hd = np.zeros((zd.size,),dtype=complex) 
+	Hu = np.zeros((zd.size,),dtype=complex)
+
+	# Loop over the layers and calculate the fields
+	for ki,mui,epsi,dlow,dup,Up,Dp in zip(k[1::],mu[1::],eps[1::],m1d.vectorNx[:-1],m1d.vectorNx[1::],UDp[0,1::],UDp[1,1::]):
+		dind = np.logical_and(dup >= zd, zd > dlow)
+		Ed[dind] = Dp*np.exp(-1j*ki*(dup-zd[dind]))
+		Eu[dind] = Up*np.exp(1j*ki*(dup-zd[dind]))
+		Hd[dind] = (ki/(w*mui))*Dp*np.exp(-1j*ki*(dup-zd[dind]))
+		Hu[dind] = -(ki/(w*mui))*Up*np.exp(1j*ki*(dup-zd[dind]))
+
+	# Return return the fields
+	return Ed, Eu, Hd, Hu
+
+def getImpedance(m1d,sigma,freq):
+	"""Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
+
+	:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
+	:param numpy.array, vector sigma: Physical property corresponding with the mesh.
+	:param numpy.array, vector freq: Frequencies to calculate data at.
+
+
+	"""
+
+	# Define constants
+	mu0 = 4*np.pi*1e-7
+	eps0 = 8.85e-12
+
+	# Initiate the impedances
+	Z1d = np.empty(len(freq) , dtype='complex')
+	h = m1d.hx   #vectorNx[:-1]
+	# Start the process
+	for nrFr, fr in enumerate(freq):
+		om = 2*np.pi*fr
+		Zall = np.empty(len(h)+1,dtype='complex')
+		# Calculate the impedance for the bottom layer
+		Zall[0] = (mu0*om)/np.sqrt(mu0*eps0*(om)**2 - 1j*mu0*sigma[0]*om) 
+
+		for nr,hi in enumerate(h):
+			# Calculate the wave number
+			# print nr,sigma[nr]
+			k = np.sqrt(mu0*eps0*om**2 - 1j*mu0*sigma[nr]*om)
+			Z = (mu0*om)/k
+			
+			Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
+
+		#pdb.set_trace()
+		Z1d[nrFr] = Zall[-1]
+
+	return Z1d
\ No newline at end of file
diff --git a/simpegMT/Analytics/MT1Danalytic.pyc b/simpegMT/Analytics/MT1Danalytic.pyc
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diff --git a/simpegMT/Analytics/MT1Dsolutions.py b/simpegMT/Analytics/MT1Dsolutions.py
new file mode 100644
index 00000000..a2900240
--- /dev/null
+++ b/simpegMT/Analytics/MT1Dsolutions.py
@@ -0,0 +1,43 @@
+import numpy as np, SimPEG as simpeg
+from MT1Danalytic import getEHfields
+from scipy.constants import mu_0
+
+def get1DEfields(m1d,sigma,freq,sourceAmp=1.0):
+	"""Function to get 1D electrical fields"""
+	
+	# Get the gradient
+	G = m1d.nodalGrad
+	# Mass matrices
+	# Magnetic permeability
+	Mmu = simpeg.Utils.sdiag(m1d.vol*(1.0/mu_0))
+	# Conductivity
+	Msig = m1d.getFaceInnerProduct(sigma)
+	# Set up the solution matrix
+	A = G.T*Mmu*G - 1j*2.*np.pi*freq*Msig
+	# Define the inner part of the solution matrix
+	Aii = A[1:-1,1:-1]
+	# Define the outer part of the solution matrix
+	Aio = A[1:-1,[0,-1]]
+
+	# Set the boundary conditions
+	Ed_low, Eu_low, Hd_low, Hu_low = getEHfields(m1d,sigma,freq,np.array([m1d.vectorNx[0]]))
+	Etot_low = Ed_low + Eu_low
+	## Note: need to use conjugate of the analytic solution. It is derived with e^iwt
+	bc = np.r_[Etot_low.conj(),sourceAmp]
+	# The right hand side
+	rhs = -Aio*bc
+	# Solve the system
+	Aii_inv = simpeg.Solver(Aii)
+	eii = Aii_inv*rhs
+	# Assign the boundary conditions
+	e = np.r_[bc[0],eii,bc[1]]
+	# Return the electrical fields
+	return e
+
+
+if __name__ == '__main__':
+
+	hz = [(100.,18)]
+	M = simpeg.Mesh.TensorMesh([hz],'C')
+	sig = np.zeros(M.nC) + 1e-8
+	sig[M.vectorCCx<=0] = sigHalf
\ No newline at end of file
diff --git a/simpegMT/Analytics/MT1Dsolutions.pyc b/simpegMT/Analytics/MT1Dsolutions.pyc
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diff --git a/simpegMT/Analytics/__init__.py b/simpegMT/Analytics/__init__.py
new file mode 100644
index 00000000..92f785d8
--- /dev/null
+++ b/simpegMT/Analytics/__init__.py
@@ -0,0 +1 @@
+from MT1Dsolutions import *  # Add the names of the functions
diff --git a/simpegMT/Analytics/__init__.pyc b/simpegMT/Analytics/__init__.pyc
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diff --git a/simpegMT/Utils/MT1Danalytic.py b/simpegMT/Utils/MT1Danalytic.py
new file mode 100644
index 00000000..f5605125
--- /dev/null
+++ b/simpegMT/Utils/MT1Danalytic.py
@@ -0,0 +1,100 @@
+# Analytic solution of EM fields due to a plane wave
+
+import numpy as np, SimPEG as simpeg
+
+def getEHfields(m1d,sigma,freq,zd):
+	'''Analytic solution for MT 1D layered earth. Returns E and H fields.
+
+	:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
+	:param numpy.array, vector sigma: Physical property of conductivity corresponding with the mesh.
+	:param float, freq: Frequency to calculate data at.
+	:param numpy array, vector zd: location to calculate EH fields at
+
+	Assumes a halfspace with the same conductive as the last cell below.
+
+	'''
+	# Note add an error check for the mesh.
+
+	# Constants: Assume constant 
+	mu = 4*np.pi*1e-7*np.ones((m1d.nC+1))
+	eps = 8.85*1e-12*np.ones((m1d.nC+1))
+	# Angular freq 
+	w = 2*np.pi*freq
+	# Add the halfspace value to the property
+	sig = np.concatenate((np.array([sigma[0]]),sigma))
+	# Calculate the wave number
+	k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
+
+	# Initiate the propagation matrix, in the order down up.
+	UDp = np.zeros((2,m1d.nC+1),dtype=complex)
+	UDp[1,0] = 1 # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
+	# Loop over all the layers, starting at the bottom layer
+	for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
+		# Calculate 
+		yp1 = k[lnr]/(w*mu[lnr]) # Admittance of the layer below the current layer
+		zp = (w*mu[lnr+1])/k[lnr+1] # Impedance in the current layer 
+		# Build the propagation matrix
+		
+		# Convert fields to down/up going components in layer below current layer
+		Pj1 = np.array([[1,1],[yp1,-yp1]]) 
+		# Convert fields to down/up going components in current layer
+		Pjinv = 1./2*np.array([[1,zp],[1,-zp]])
+		# Propagate down and up components through the current layer
+		elamh = np.array([[np.exp(-1j*k[lnr+1]*h),0],[0,np.exp(1j*k[lnr+1]*h)]])
+
+		# The down and up component in current layer.
+		UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
+
+	# Calculate the fields
+	Ed = np.zeros((zd.size,),dtype=complex)
+	Eu = np.zeros((zd.size,),dtype=complex)
+	Hd = np.zeros((zd.size,),dtype=complex) 
+	Hu = np.zeros((zd.size,),dtype=complex)
+
+	# Loop over the layers and calculate the fields
+	for ki,mui,epsi,dlow,dup,Up,Dp in zip(k[1::],mu[1::],eps[1::],m1d.vectorNx[:-1],m1d.vectorNx[1::],UDp[0,1::],UDp[1,1::]):
+		dind = np.logical_and(dup >= zd, zd > dlow)
+		Ed[dind] = Dp*np.exp(-1j*ki*(dup-zd[dind]))
+		Eu[dind] = Up*np.exp(1j*ki*(dup-zd[dind]))
+		Hd[dind] = (ki/(w*mui))*Dp*np.exp(-1j*ki*(dup-zd[dind]))
+		Hu[dind] = -(ki/(w*mui))*Up*np.exp(1j*ki*(dup-zd[dind]))
+
+	# Return return the fields
+	return Ed, Eu, Hd, Hu
+
+def getImpedance(m1d,sigma,freq):
+	"""Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
+
+	:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
+	:param numpy.array, vector sigma: Physical property corresponding with the mesh.
+	:param numpy.array, vector freq: Frequencies to calculate data at.
+
+
+	"""
+
+	# Define constants
+	mu0 = 4*np.pi*1e-7
+	eps0 = 8.85e-12
+
+	# Initiate the impedances
+	Z1d = np.empty(len(freq) , dtype='complex')
+	h = m1d.hx   #vectorNx[:-1]
+	# Start the process
+	for nrFr, fr in enumerate(freq):
+		om = 2*np.pi*fr
+		Zall = np.empty(len(h)+1,dtype='complex')
+		# Calculate the impedance for the bottom layer
+		Zall[0] = (mu0*om)/np.sqrt(mu0*eps0*(om)**2 - 1j*mu0*sigma[0]*om) 
+
+		for nr,hi in enumerate(h):
+			# Calculate the wave number
+			# print nr,sigma[nr]
+			k = np.sqrt(mu0*eps0*om**2 - 1j*mu0*sigma[nr]*om)
+			Z = (mu0*om)/k
+			
+			Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
+
+		#pdb.set_trace()
+		Z1d[nrFr] = Zall[-1]
+
+	return Z1d
\ No newline at end of file
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diff --git a/simpegMT/Utils/MT1Dsolutions.py b/simpegMT/Utils/MT1Dsolutions.py
new file mode 100644
index 00000000..3b1149b8
--- /dev/null
+++ b/simpegMT/Utils/MT1Dsolutions.py
@@ -0,0 +1,42 @@
+import numpy as np, SimPEG as simpeg
+from MT1Danalytic import getEHfields
+from scipy.constants import mu_0
+
+def get1DEfields(m1d,sigma,freq,sourceAmp=1.0):
+	"""Function to get 1D electrical fields"""
+	
+	# Get the gradient
+	G = m1d.nodalGrad
+	# Mass matrices
+	# Magnetic permeability
+	Mmu = simpeg.Utils.sdiag(m1d.vol*(1.0/mu_0))
+	# Conductivity
+	Msig = m1d.getFaceInnerProduct(sigma)
+	# Set up the solution matrix
+	A = G.T*Mmu*G - 1j*2.*np.pi*freq*Msig
+	# Define the inner part of the solution matrix
+	Aii = A[1:-1,1:-1]
+	# Define the outer part of the solution matrix
+	Aio = A[1:-1,[0,-1]]
+
+	# Set the boundary conditions
+	Ed_low, Eu_low, Hd_low, Hu_low = getEHfields(m1d,sigma,freq,np.array([m1d.vectorNx[0]]))
+	Etot_low = Ed_low + Eu_low
+	bc = np.r_[Etot_low,sourceAmp]
+	# The right hand side
+	rhs = -Aio*bc
+	# Solve the system
+	Aii_inv = simpeg.Solver(Aii)
+	eii = Aii_inv*rhs
+	# Assign the boundary conditions
+	e = np.r_[bc[0],eii,bc[1]]
+	# Return the electrical fields
+	return e
+
+
+if __name__ == '__main__':
+
+	hz = [(100.,18)]
+	M = simpeg.Mesh.TensorMesh([hz],'C')
+	sig = np.zeros(M.nC) + 1e-8
+	sig[M.vectorCCx<=0] = sigHalf
\ No newline at end of file
diff --git a/simpegMT/Utils/MT1Dsolutions.pyc b/simpegMT/Utils/MT1Dsolutions.pyc
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diff --git a/simpegMT/Utils/__init__.py b/simpegMT/Utils/__init__.py
index e69de29b..4414cd54 100644
--- a/simpegMT/Utils/__init__.py
+++ b/simpegMT/Utils/__init__.py
@@ -0,0 +1,2 @@
+from MT1Dsolutions import *  # Add the names of the functions
+from MT1Danalytic import * 
diff --git a/simpegMT/Utils/__init__.pyc b/simpegMT/Utils/__init__.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..4ca335f2074aa00c6f94804b2e41df03b1d75bcb
GIT binary patch
literal 233
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diff --git a/simpegMT/__init__.py b/simpegMT/__init__.py
index a18e6230..1fc4b26e 100644
--- a/simpegMT/__init__.py
+++ b/simpegMT/__init__.py
@@ -1,4 +1,4 @@
 # from EM import *
 import Utils
-import FDEM
+# import FDEM
 import Base
diff --git a/simpegMT/__init__.pyc b/simpegMT/__init__.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..90172de163c4a7264da5e90ad543c6b829dfafa3
GIT binary patch
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literal 0
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