├── .gitignore ├── LICENSE ├── README.md ├── docs ├── Makefile ├── make.bat └── source │ ├── api_GPRTD.rst │ ├── api_license.rst │ ├── conf.py │ ├── examples │ ├── raypaths.html │ └── shotgather.png │ ├── index.rst │ └── simpeg-logo.png ├── notebooks ├── 2DGPRTEzmode.ipynb ├── 2DGPRTEzmode_pml.ipynb ├── 2DGPRTMzmode.ipynb ├── 2DGPRTMzmode_pml.ipynb ├── RayPaths.ipynb ├── shot_raypaths.npy └── time.npy ├── requirements.txt └── simpeggpr ├── GPRTimeSurvey.py ├── GPRTimeTEz.py ├── GPRTimeTMz.py └── __init__.py /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Folders 9 | docs/build/* 10 | 11 | # Distribution / packaging 12 | .Python 13 | env/ 14 | build/ 15 | develop-eggs/ 16 | dist/ 17 | downloads/ 18 | eggs/ 19 | lib/ 20 | lib64/ 21 | parts/ 22 | sdist/ 23 | var/ 24 | *.egg-info/ 25 | .installed.cfg 26 | *.egg 27 | *.ipynb_checkpoints/ 28 | 29 | # PyInstaller 30 | # Usually these files are written by a python script from a template 31 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 32 | *.manifest 33 | *.spec 34 | 35 | # Installer logs 36 | pip-log.txt 37 | pip-delete-this-directory.txt 38 | 39 | # Unit test / coverage reports 40 | htmlcov/ 41 | .tox/ 42 | .coverage 43 | .cache 44 | nosetests.xml 45 | coverage.xml 46 | 47 | # Translations 48 | *.mo 49 | *.pot 50 | 51 | # checkpoints 52 | *.checkpoint.ipynb 53 | 54 | # Django stuff: 55 | *.log 56 | 57 | # Sphinx documentation 58 | docs/_build/ 59 | 60 | # PyBuilder 61 | target/ 62 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2014 sgkang 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | 23 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | simpegGPR 2 | ========= 3 | 4 | Forward modeling and inversion of Geo-penetrating Radar (GPR) 5 | -------------------------------------------------------------------------------- /docs/Makefile: -------------------------------------------------------------------------------- 1 | # Makefile for Sphinx documentation 2 | # 3 | 4 | # You can set these variables from the command line. 5 | SPHINXOPTS = 6 | SPHINXBUILD = sphinx-build 7 | PAPER = 8 | BUILDDIR = build 9 | 10 | # User-friendly check for sphinx-build 11 | ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1) 12 | $(error The '$(SPHINXBUILD)' command was not found. 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The XML files are in %BUILDDIR%/xml. 231 | goto end 232 | ) 233 | 234 | if "%1" == "pseudoxml" ( 235 | %SPHINXBUILD% -b pseudoxml %ALLSPHINXOPTS% %BUILDDIR%/pseudoxml 236 | if errorlevel 1 exit /b 1 237 | echo. 238 | echo.Build finished. The pseudo-XML files are in %BUILDDIR%/pseudoxml. 239 | goto end 240 | ) 241 | 242 | :end 243 | -------------------------------------------------------------------------------- /docs/source/api_GPRTD.rst: -------------------------------------------------------------------------------- 1 | .. _api_GPRTD: 2 | 3 | .. math:: 4 | 5 | \renewcommand{\div}{\nabla\cdot\,} 6 | \newcommand{\grad}{\vec \nabla} 7 | \newcommand{\curl}{{\vec \nabla}\times\,} 8 | \newcommand{\Acf}{{\mathbf A_c^f}} 9 | \newcommand{\Ace}{{\mathbf A_c^e}} 10 | \newcommand{\dcurl}{{\mathbf C}} 11 | \newcommand{\dgrad}{{\mathbf G}} 12 | \newcommand{\M}{{\mathbf M}} 13 | \newcommand{\MeMui}{{\M^f_{\mu^{-1}}}} 14 | 15 | Backgrounds 16 | *********** 17 | -------------------------------------------------------------------------------- /docs/source/api_license.rst: -------------------------------------------------------------------------------- 1 | .. _api_license: 2 | 3 | License 4 | ******* 5 | 6 | The MIT License (MIT) 7 | 8 | Copyright (c) 2013-2014 SimPEG Developers 9 | 10 | Permission is hereby granted, free of charge, to any person obtaining a copy of 11 | this software and associated documentation files (the "Software"), to deal in 12 | the Software without restriction, including without limitation the rights to 13 | use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of 14 | the Software, and to permit persons to whom the Software is furnished to do so, 15 | subject to the following conditions: 16 | 17 | The above copyright notice and this permission notice shall be included in all 18 | copies or substantial portions of the Software. 19 | 20 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 21 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS 22 | FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR 23 | COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER 24 | IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 25 | CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 26 | -------------------------------------------------------------------------------- /docs/source/conf.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | # 3 | # SimPEG documentation build configuration file, created by 4 | # sphinx-quickstart on Mon Sep 22 23:11:31 2014. 5 | # 6 | # This file is execfile()d with the current directory set to its 7 | # containing dir. 8 | # 9 | # Note that not all possible configuration values are present in this 10 | # autogenerated file. 11 | # 12 | # All configuration values have a default; values that are commented out 13 | # serve to show the default. 14 | 15 | import sys 16 | import os 17 | 18 | # If extensions (or modules to document with autodoc) are in another directory, 19 | # add these directories to sys.path here. If the directory is relative to the 20 | # documentation root, use os.path.abspath to make it absolute, like shown here. 21 | #sys.path.insert(0, os.path.abspath('.')) 22 | sys.path.append('../') 23 | # -- General configuration ------------------------------------------------ 24 | 25 | # If your documentation needs a minimal Sphinx version, state it here. 26 | #needs_sphinx = '1.0' 27 | 28 | # Add any Sphinx extension module names here, as strings. They can be 29 | # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom 30 | # ones. 31 | extensions = [ 32 | 'sphinx.ext.autodoc', 33 | 'sphinx.ext.doctest', 34 | 'sphinx.ext.intersphinx', 35 | 'sphinx.ext.todo', 36 | 'sphinx.ext.coverage', 37 | 'sphinx.ext.mathjax', 38 | 'sphinx.ext.viewcode', 39 | ] 40 | 41 | # Add any paths that contain templates here, relative to this directory. 42 | templates_path = ['_templates'] 43 | 44 | # The suffix of source filenames. 45 | source_suffix = '.rst' 46 | 47 | # The encoding of source files. 48 | #source_encoding = 'utf-8-sig' 49 | 50 | # The master toctree document. 51 | master_doc = 'index' 52 | 53 | # General information about the project. 54 | project = u'SimPEG' 55 | copyright = u'2014, Seogi Kang' 56 | 57 | # The version info for the project you're documenting, acts as replacement for 58 | # |version| and |release|, also used in various other places throughout the 59 | # built documents. 60 | # 61 | # The short X.Y version. 62 | version = '0.0.1' 63 | # The full version, including alpha/beta/rc tags. 64 | release = '0.0.1' 65 | 66 | # The language for content autogenerated by Sphinx. Refer to documentation 67 | # for a list of supported languages. 68 | #language = None 69 | 70 | # There are two options for replacing |today|: either, you set today to some 71 | # non-false value, then it is used: 72 | #today = '' 73 | # Else, today_fmt is used as the format for a strftime call. 74 | #today_fmt = '%B %d, %Y' 75 | 76 | # List of patterns, relative to source directory, that match files and 77 | # directories to ignore when looking for source files. 78 | exclude_patterns = [] 79 | 80 | # The reST default role (used for this markup: `text`) to use for all 81 | # documents. 82 | #default_role = None 83 | 84 | # If true, '()' will be appended to :func: etc. cross-reference text. 85 | #add_function_parentheses = True 86 | 87 | # If true, the current module name will be prepended to all description 88 | # unit titles (such as .. function::). 89 | #add_module_names = True 90 | 91 | # If true, sectionauthor and moduleauthor directives will be shown in the 92 | # output. They are ignored by default. 93 | #show_authors = False 94 | 95 | # The name of the Pygments (syntax highlighting) style to use. 96 | pygments_style = 'sphinx' 97 | 98 | # A list of ignored prefixes for module index sorting. 99 | #modindex_common_prefix = [] 100 | 101 | # If true, keep warnings as "system message" paragraphs in the built documents. 102 | #keep_warnings = False 103 | 104 | 105 | # -- Options for HTML output ---------------------------------------------- 106 | 107 | # The theme to use for HTML and HTML Help pages. See the documentation for 108 | # a list of builtin themes. 109 | try: 110 | import sphinx_rtd_theme 111 | html_theme = 'sphinx_rtd_theme' 112 | html_theme_path = [sphinx_rtd_theme.get_html_theme_path()] 113 | pass 114 | except Exception, e: 115 | html_theme = 'default' 116 | 117 | # Theme options are theme-specific and customize the look and feel of a theme 118 | # further. For a list of options available for each theme, see the 119 | # documentation. 120 | #html_theme_options = {} 121 | 122 | # Add any paths that contain custom themes here, relative to this directory. 123 | #html_theme_path = [] 124 | 125 | # The name for this set of Sphinx documents. If None, it defaults to 126 | # " v documentation". 127 | #html_title = None 128 | 129 | # A shorter title for the navigation bar. Default is the same as html_title. 130 | #html_short_title = None 131 | 132 | # The name of an image file (relative to this directory) to place at the top 133 | # of the sidebar. 134 | #html_logo = None 135 | 136 | # The name of an image file (within the static path) to use as favicon of the 137 | # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 138 | # pixels large. 139 | #html_favicon = None 140 | 141 | # Add any paths that contain custom static files (such as style sheets) here, 142 | # relative to this directory. They are copied after the builtin static files, 143 | # so a file named "default.css" will overwrite the builtin "default.css". 144 | html_static_path = ['_static'] 145 | 146 | # Add any extra paths that contain custom files (such as robots.txt or 147 | # .htaccess) here, relative to this directory. These files are copied 148 | # directly to the root of the documentation. 149 | #html_extra_path = [] 150 | 151 | # If not '', a 'Last updated on:' timestamp is inserted at every page bottom, 152 | # using the given strftime format. 153 | #html_last_updated_fmt = '%b %d, %Y' 154 | 155 | # If true, SmartyPants will be used to convert quotes and dashes to 156 | # typographically correct entities. 157 | #html_use_smartypants = True 158 | 159 | # Custom sidebar templates, maps document names to template names. 160 | #html_sidebars = {} 161 | 162 | # Additional templates that should be rendered to pages, maps page names to 163 | # template names. 164 | #html_additional_pages = {} 165 | 166 | # If false, no module index is generated. 167 | #html_domain_indices = True 168 | 169 | # If false, no index is generated. 170 | #html_use_index = True 171 | 172 | # If true, the index is split into individual pages for each letter. 173 | #html_split_index = False 174 | 175 | # If true, links to the reST sources are added to the pages. 176 | #html_show_sourcelink = True 177 | 178 | # If true, "Created using Sphinx" is shown in the HTML footer. Default is True. 179 | #html_show_sphinx = True 180 | 181 | # If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. 182 | #html_show_copyright = True 183 | 184 | # If true, an OpenSearch description file will be output, and all pages will 185 | # contain a tag referring to it. The value of this option must be the 186 | # base URL from which the finished HTML is served. 187 | #html_use_opensearch = '' 188 | 189 | # This is the file name suffix for HTML files (e.g. ".xhtml"). 190 | #html_file_suffix = None 191 | 192 | # Output file base name for HTML help builder. 193 | htmlhelp_basename = 'SimPEGdoc' 194 | 195 | 196 | # -- Options for LaTeX output --------------------------------------------- 197 | 198 | latex_elements = { 199 | # The paper size ('letterpaper' or 'a4paper'). 200 | #'papersize': 'letterpaper', 201 | 202 | # The font size ('10pt', '11pt' or '12pt'). 203 | #'pointsize': '10pt', 204 | 205 | # Additional stuff for the LaTeX preamble. 206 | #'preamble': '', 207 | } 208 | 209 | # Grouping the document tree into LaTeX files. List of tuples 210 | # (source start file, target name, title, 211 | # author, documentclass [howto, manual, or own class]). 212 | latex_documents = [ 213 | ('index.rst', 'SimPEG.tex', u'SimPEG Documentation', 214 | u'Seogi Kang', 'manual'), 215 | ] 216 | 217 | # The name of an image file (relative to this directory) to place at the top of 218 | # the title page. 219 | #latex_logo = None 220 | 221 | # For "manual" documents, if this is true, then toplevel headings are parts, 222 | # not chapters. 223 | #latex_use_parts = False 224 | 225 | # If true, show page references after internal links. 226 | #latex_show_pagerefs = False 227 | 228 | # If true, show URL addresses after external links. 229 | #latex_show_urls = False 230 | 231 | # Documents to append as an appendix to all manuals. 232 | #latex_appendices = [] 233 | 234 | # If false, no module index is generated. 235 | #latex_domain_indices = True 236 | 237 | 238 | # -- Options for manual page output --------------------------------------- 239 | 240 | # One entry per manual page. List of tuples 241 | # (source start file, name, description, authors, manual section). 242 | man_pages = [ 243 | ('index.rst', 'simpeg', u'SimPEG Documentation', 244 | [u'Seogi Kang'], 1) 245 | ] 246 | 247 | # If true, show URL addresses after external links. 248 | #man_show_urls = False 249 | 250 | 251 | # -- Options for Texinfo output ------------------------------------------- 252 | 253 | # Grouping the document tree into Texinfo files. List of tuples 254 | # (source start file, target name, title, author, 255 | # dir menu entry, description, category) 256 | texinfo_documents = [ 257 | ('index.rst', 'SimPEG', u'SimPEG Documentation', 258 | u'Seogi Kang', 'SimPEG', 'One line description of project.', 259 | 'Miscellaneous'), 260 | ] 261 | 262 | # Documents to append as an appendix to all manuals. 263 | #texinfo_appendices = [] 264 | 265 | # If false, no module index is generated. 266 | #texinfo_domain_indices = True 267 | 268 | # How to display URL addresses: 'footnote', 'no', or 'inline'. 269 | #texinfo_show_urls = 'footnote' 270 | 271 | # If true, do not generate a @detailmenu in the "Top" node's menu. 272 | #texinfo_no_detailmenu = False 273 | 274 | 275 | # -- Options for Epub output ---------------------------------------------- 276 | 277 | # Bibliographic Dublin Core info. 278 | epub_title = u'SimPEG' 279 | epub_author = u'Seogi Kang' 280 | epub_publisher = u'Seogi Kang' 281 | epub_copyright = u'2014, Seogi Kang' 282 | 283 | # The basename for the epub file. It defaults to the project name. 284 | #epub_basename = u'SimPEG' 285 | 286 | # The HTML theme for the epub output. Since the default themes are not optimized 287 | # for small screen space, using the same theme for HTML and epub output is 288 | # usually not wise. This defaults to 'epub', a theme designed to save visual 289 | # space. 290 | #epub_theme = 'epub' 291 | 292 | # The language of the text. It defaults to the language option 293 | # or en if the language is not set. 294 | #epub_language = '' 295 | 296 | # The scheme of the identifier. Typical schemes are ISBN or URL. 297 | #epub_scheme = '' 298 | 299 | # The unique identifier of the text. This can be a ISBN number 300 | # or the project homepage. 301 | #epub_identifier = '' 302 | 303 | # A unique identification for the text. 304 | #epub_uid = '' 305 | 306 | # A tuple containing the cover image and cover page html template filenames. 307 | #epub_cover = () 308 | 309 | # A sequence of (type, uri, title) tuples for the guide element of content.opf. 310 | #epub_guide = () 311 | 312 | # HTML files that should be inserted before the pages created by sphinx. 313 | # The format is a list of tuples containing the path and title. 314 | #epub_pre_files = [] 315 | 316 | # HTML files shat should be inserted after the pages created by sphinx. 317 | # The format is a list of tuples containing the path and title. 318 | #epub_post_files = [] 319 | 320 | # A list of files that should not be packed into the epub file. 321 | epub_exclude_files = ['search.html'] 322 | 323 | # The depth of the table of contents in toc.ncx. 324 | #epub_tocdepth = 3 325 | 326 | # Allow duplicate toc entries. 327 | #epub_tocdup = True 328 | 329 | # Choose between 'default' and 'includehidden'. 330 | #epub_tocscope = 'default' 331 | 332 | # Fix unsupported image types using the PIL. 333 | #epub_fix_images = False 334 | 335 | # Scale large images. 336 | #epub_max_image_width = 0 337 | 338 | # How to display URL addresses: 'footnote', 'no', or 'inline'. 339 | #epub_show_urls = 'inline' 340 | 341 | # If false, no index is generated. 342 | #epub_use_index = True 343 | 344 | 345 | # Example configuration for intersphinx: refer to the Python standard library. 346 | intersphinx_mapping = {'http://docs.python.org/': None} 347 | -------------------------------------------------------------------------------- /docs/source/examples/shotgather.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/simpeg/simpegGPR/fa9f96ddf14dc079e82d8d2dcd330f589a21f9e6/docs/source/examples/shotgather.png -------------------------------------------------------------------------------- /docs/source/index.rst: -------------------------------------------------------------------------------- 1 | .. image:: simpeg-logo.png 2 | :width: 300 px 3 | :alt: SimPEG 4 | :align: center 5 | 6 | SimPEG (Simulation and Parameter Estimation in Geophysics) is a python package for simulation and gradient based parameter estimation in the 7 | context of geoscience applications. simpegGPR uses SimPEG as the framework for the forward modeling and inversion of ground penetrating radar (GPR) geophysical problem. 8 | 9 | Maxwell's equations, which is governing equations of GPR can be solved in both time and frequency domains. We initially discretize those problems to compute forward responses in frequency and time domain. Obvious next step is to apply inverse problems 10 | 11 | We welcome any people who want to contribute this project developing forward modeling and inversion package of GPR data, simpegGPR. 12 | 13 | This package also has educational purposes. For instance, consider the ray paths of GPR: a. air wave, b. ground wave, c. reflected wave and e. refracted wave can be observed in the data: 14 | 15 | .. figure:: examples/shotgather.png 16 | :width: 400 px 17 | :height: 700 px 18 | :align: center 19 | 20 | Figure 1. A shot gather of GPR data. 21 | 22 | In addition, we can clearly identify those phenomenon by simply looking a movie, which shows GPR wave propagation in layer model: 23 | 24 | .. raw:: html 25 | :file: examples/raypaths.html 26 | 27 | Ray paths of EM wave propagation. We identify 28 | 29 | 30 | 31 | Time domain GPR 32 | =============== 33 | 34 | .. toctree:: 35 | :maxdepth: 2 36 | 37 | api_GPRTD 38 | 39 | 40 | License 41 | ======= 42 | 43 | .. toctree:: 44 | :maxdepth: 2 45 | 46 | api_license 47 | 48 | Project Index & Search 49 | ====================== 50 | 51 | * :ref:`genindex` 52 | * :ref:`modindex` 53 | * :ref:`search` 54 | 55 | 56 | -------------------------------------------------------------------------------- /docs/source/simpeg-logo.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/simpeg/simpegGPR/fa9f96ddf14dc079e82d8d2dcd330f589a21f9e6/docs/source/simpeg-logo.png -------------------------------------------------------------------------------- /notebooks/RayPaths.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": { 7 | "collapsed": false 8 | }, 9 | "outputs": [ 10 | { 11 | "name": "stdout", 12 | "output_type": "stream", 13 | "text": [ 14 | "Populating the interactive namespace from numpy and matplotlib\n" 15 | ] 16 | } 17 | ], 18 | "source": [ 19 | "from simpeggpr import *\n", 20 | "%pylab inline" 21 | ] 22 | }, 23 | { 24 | "cell_type": "code", 25 | "execution_count": 2, 26 | "metadata": { 27 | "collapsed": false 28 | }, 29 | "outputs": [], 30 | "source": [ 31 | "# from IPython.display import set_matplotlib_formats\n", 32 | "# set_matplotlib_formats('png')\n", 33 | "# matplotlib.rcParams['savefig.dpi'] = 100 # Change this to adjust figure size" 34 | ] 35 | }, 36 | { 37 | "cell_type": "code", 38 | "execution_count": 3, 39 | "metadata": { 40 | "collapsed": false 41 | }, 42 | "outputs": [], 43 | "source": [ 44 | "cs = 1.5*1e-1\n", 45 | "hx = np.ones(500)*cs\n", 46 | "hy = np.ones(200)*cs\n", 47 | "mesh = Mesh.TensorMesh([hx, hy], 'CC')\n", 48 | "epsilon = epsilon_0*np.ones(mesh.nC)*1.\n", 49 | "epsilon[mesh.gridCC[:,1]<10.] = epsilon_0*8.\n", 50 | "epsilon[mesh.gridCC[:,1]<5.] = epsilon_0*2." 51 | ] 52 | }, 53 | { 54 | "cell_type": "code", 55 | "execution_count": 4, 56 | "metadata": { 57 | "collapsed": false 58 | }, 59 | "outputs": [ 60 | { 61 | "data": { 62 | "text/plain": [ 63 | "(,)" 64 | ] 65 | }, 66 | "execution_count": 4, 67 | "metadata": {}, 68 | "output_type": "execute_result" 69 | }, 70 | { 71 | "data": { 72 | "image/png": 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73 | "text/plain": [ 74 | "" 75 | ] 76 | }, 77 | "metadata": {}, 78 | "output_type": "display_data" 79 | } 80 | ], 81 | "source": [ 82 | "mesh.plotImage(epsilon)" 83 | ] 84 | }, 85 | { 86 | "cell_type": "code", 87 | "execution_count": 5, 88 | "metadata": { 89 | "collapsed": false 90 | }, 91 | "outputs": [ 92 | { 93 | "name": "stdout", 94 | "output_type": "stream", 95 | "text": [ 96 | "You are good to go:)\n", 97 | ">> Stability information\n", 98 | " dt: 2.00e-10 s\n", 99 | " Optimal dt: 2.50e-10 s\n", 100 | " Cell per wavelength (G): 7.07e+00\n", 101 | " Optimal G: 1.20e+00\n", 102 | ">> sm: 3.00e+00, lamda: 1.06e+00, sigm: 6.67e-02\n" 103 | ] 104 | } 105 | ], 106 | "source": [ 107 | "dt = 2.0e-10\n", 108 | "fmain = 1e8\n", 109 | "time = np.arange(1500)*dt\n", 110 | "options={'tlag':2./fmain, 'fmain':fmain}\n", 111 | "x_rx = np.arange(101)*0.3+0.3\n", 112 | "rx = GPRTEzRx(np.c_[x_rx, 10.*np.ones(x_rx.size)], 'Ex')\n", 113 | "tx = GPRTEzSrc(np.r_[0, 10.], time, [rx], srcType='Mz', **options)\n", 114 | "survey = SurveyGPRTime([tx])\n", 115 | "wave = tx.RickerWavelet()\n", 116 | "prob = GPR2DTEzProblemPML(mesh)\n", 117 | "prob.pair(survey)\n", 118 | "mu = mu_0*np.ones(mesh.nC)\n", 119 | "sighalf = 0.\n", 120 | "sig0 = sighalf*np.ones(mesh.nC)\n", 121 | "prob.setPMLBC(15, dt)\n", 122 | "prob.sm = 3.\n", 123 | "prob.stabilitycheck(epsilon, mu, sig0, time, fmain, sigs=0.)\n", 124 | "storefield = True" 125 | ] 126 | }, 127 | { 128 | "cell_type": "code", 129 | "execution_count": 6, 130 | "metadata": { 131 | "collapsed": false 132 | }, 133 | "outputs": [ 134 | { 135 | "data": { 136 | "image/png": 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clMuJLcbWNpRZGOUWnzILo9zyQct/x9TdDb/9LWzaNHz7k0/CMcfAt74FF+XiFmsiIiLj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\nzAWWm9nFlUv5ql4EPFbvIERy4Czgh0T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137 | "text/plain": [ 138 | "" 139 | ] 140 | }, 141 | "metadata": {}, 142 | "output_type": "display_data" 143 | } 144 | ], 145 | "source": [ 146 | "plt.plot(time, tx.wave)\n", 147 | "plt.xlabel('Time (s)')\n", 148 | "plt.grid(True)" 149 | ] 150 | }, 151 | { 152 | "cell_type": "code", 153 | "execution_count": 7, 154 | "metadata": { 155 | "collapsed": false 156 | }, 157 | "outputs": [ 158 | { 159 | "name": "stdout", 160 | "output_type": "stream", 161 | "text": [ 162 | "\n", 163 | "***** Start Computing Electromagnetic Wave *****\n", 164 | "\n", 165 | ">> dt: 2.00e-10 s\n", 166 | ">> Optimal dt: 2.50e-10 s\n", 167 | ">> Main frequency, fmain: 1.00e+08 Hz\n", 168 | ">> Cell per wavelength (G): 7.07e+00\n", 169 | " Src at ( 0.00, 0.00): 1/ 1\n", 170 | ">>Elapsed time: 5.38e+01 s\n" 171 | ] 172 | } 173 | ], 174 | "source": [ 175 | "Fields = prob.fields(epsilon, mu, sig0)" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": 30, 181 | "metadata": { 182 | "collapsed": false 183 | }, 184 | "outputs": [ 185 | { 186 | "data": { 187 | "image/png": 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xGUlRxrrr+PazV/nCl75G6mKuLa1yz5kzHDlyBDOjOb/IyRedhrjBgUNHuXb1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\nQggxNhIQQgghhBgbCQghhBB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188 | "text/plain": [ 189 | "" 190 | ] 191 | }, 192 | "metadata": {}, 193 | "output_type": "display_data" 194 | } 195 | ], 196 | "source": [ 197 | "icount = 400\n", 198 | "extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()]\n", 199 | "plt.imshow(np.flipud(Fields['H', tx][:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'gray', extent=extent)\n", 200 | "dat = plt.imshow(np.flipud(epsilon.reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'jet', alpha = 0.1, extent=extent )\n", 201 | "plt.plot(rx.locs[:,0], rx.locs[:,1], 'r.', ms = 5)\n", 202 | "# plt.colorbar(dat)\n", 203 | "plt.show()" 204 | ] 205 | }, 206 | { 207 | "cell_type": "code", 208 | "execution_count": 9, 209 | "metadata": { 210 | "collapsed": false 211 | }, 212 | "outputs": [], 213 | "source": [ 214 | "# from simpegseis import UtilsSeis" 215 | ] 216 | }, 217 | { 218 | "cell_type": "code", 219 | "execution_count": 10, 220 | "metadata": { 221 | "collapsed": false 222 | }, 223 | "outputs": [], 224 | "source": [ 225 | "data = survey.projectFields(Fields)" 226 | ] 227 | }, 228 | { 229 | "cell_type": "code", 230 | "execution_count": 11, 231 | "metadata": { 232 | "collapsed": false 233 | }, 234 | "outputs": [], 235 | "source": [ 236 | "def PrimaryWave(tintercept, time, velocity):\n", 237 | " return velocity*time + tintercept" 238 | ] 239 | }, 240 | { 241 | "cell_type": "code", 242 | "execution_count": 12, 243 | "metadata": { 244 | "collapsed": false 245 | }, 246 | "outputs": [], 247 | "source": [ 248 | "from SimPEG.Utils import sdiag\n", 249 | "noise = np.random.randn(data[tx, rx].shape[0],data[tx, rx].shape[1])*0.1\n", 250 | "data_temp = sdiag(x_rx**0.5)*data[tx, rx] *sdiag(time**0.)\n", 251 | "# data_temp = data_temp/data_temp.max()+noise\n", 252 | "data_temp = data_temp/data_temp.max()" 253 | ] 254 | }, 255 | { 256 | "cell_type": "code", 257 | "execution_count": 13, 258 | "metadata": { 259 | "collapsed": false 260 | }, 261 | "outputs": [], 262 | "source": [ 263 | "np.save('shot_raypaths', data_temp)\n", 264 | "np.save('time', time)" 265 | ] 266 | }, 267 | { 268 | "cell_type": "code", 269 | "execution_count": 24, 270 | "metadata": { 271 | "collapsed": false 272 | }, 273 | "outputs": [], 274 | "source": [ 275 | "# fig = plt.figure()\n", 276 | "# kwargs = {\n", 277 | "# 'skipt':1,\n", 278 | "# 'scale': 0.5,\n", 279 | "# 'lwidth': 0.1,\n", 280 | "# 'sampr': dt*1e9,\n", 281 | "# 'dx': 0.4\n", 282 | "# }\n", 283 | "# extent = [-1, 40, 300, 0]\n", 284 | "# fig, ax1 = plt.subplots(1,1, figsize = (8,5))\n", 285 | "# ax1.invert_yaxis()\n", 286 | "# ax1.axis(extent)\n", 287 | "# UtilsSeis.wiggle(data_temp, **kwargs)\n", 288 | "# # ax1.plot(PrimaryWave(0., time, 1/np.sqrt(epsilon_0*mu_0)), time, 'r--', lw=2)\n", 289 | "\n", 290 | "# ax1.set_xlabel('Channel')\n", 291 | "# ax1.set_ylabel('Time (ns)')\n", 292 | "# ax1.set_title('Shot Gather')\n", 293 | "# fig.tight_layout()\n", 294 | "# fig.savefig('shotgather.png', dpi = 200)" 295 | ] 296 | }, 297 | { 298 | "cell_type": "code", 299 | "execution_count": 26, 300 | "metadata": { 301 | "collapsed": false 302 | }, 303 | "outputs": [], 304 | "source": [ 305 | "# from JSAnimation import IPython_display\n", 306 | "# from matplotlib import animation\n", 307 | "# extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min()-10., mesh.vectorCCy.max()-10.]\n", 308 | "# fig, ax = plt.subplots(1,1, figsize = (12, 8))\n", 309 | "# ax.set_xlabel('x (m)', fontsize = 16)\n", 310 | "# ax.set_ylabel('y (m)', fontsize = 16)\n", 311 | "# ax.set_xlim(extent[:2])\n", 312 | "# ax.set_ylim(extent[2:])\n", 313 | "# ax.text(0., 1, 'Tx', fontsize=20)\n", 314 | "# ax.text(30., 1., 'Rx', color='r', fontsize=20)\n", 315 | "# ax.text(-30., 1., 'Air layer, $\\epsilon_r$=1', color='k', fontsize=20)\n", 316 | "# ax.text(-30., -3.2, 'Layer 1, $\\epsilon_r$=?', color='k', fontsize=20)\n", 317 | "# ax.text(-30., -10, 'Layer 2, $\\epsilon_r$=?', color='k', fontsize=20)\n", 318 | "\n", 319 | "\n", 320 | "# nskip = 60\n", 321 | "# def animate(i_id):\n", 322 | "# icount = i_id*nskip\n", 323 | "# frame = ax.imshow(np.flipud(Fields['H', tx][:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'gray', extent=extent)\n", 324 | " \n", 325 | "# ax.imshow(np.flipud(epsilon.reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'jet', alpha = 0.1, extent=extent )\n", 326 | "# rxframe = ax.plot(rx.locs[:,0], rx.locs[:,1]-10., 'r.', ms = 10)\n", 327 | "# ax.set_title(('Time = %10.1f ns')%(time[i_id*nskip]*1e9), fontsize = 16)\n", 328 | "# ax.get_xaxis().set_visible(False)\n", 329 | "# ax.get_yaxis().set_visible(False)\n", 330 | "# return frame, rxframe\n", 331 | "# animation.FuncAnimation(fig, animate, frames=20, interval=40, blit=True)" 332 | ] 333 | }, 334 | { 335 | "cell_type": "code", 336 | "execution_count": null, 337 | "metadata": { 338 | "collapsed": false 339 | }, 340 | "outputs": [], 341 | "source": [] 342 | } 343 | ], 344 | "metadata": { 345 | "anaconda-cloud": {}, 346 | "kernelspec": { 347 | "display_name": "Python [default]", 348 | "language": "python", 349 | "name": "python2" 350 | }, 351 | "language_info": { 352 | "codemirror_mode": { 353 | "name": "ipython", 354 | "version": 2 355 | }, 356 | "file_extension": ".py", 357 | "mimetype": "text/x-python", 358 | "name": "python", 359 | "nbconvert_exporter": "python", 360 | "pygments_lexer": "ipython2", 361 | "version": "2.7.12" 362 | } 363 | }, 364 | "nbformat": 4, 365 | "nbformat_minor": 0 366 | } 367 | -------------------------------------------------------------------------------- /notebooks/shot_raypaths.npy: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/simpeg/simpegGPR/fa9f96ddf14dc079e82d8d2dcd330f589a21f9e6/notebooks/shot_raypaths.npy -------------------------------------------------------------------------------- /notebooks/time.npy: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/simpeg/simpegGPR/fa9f96ddf14dc079e82d8d2dcd330f589a21f9e6/notebooks/time.npy -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | numpy 2 | scipy 3 | ipython 4 | matplotlib 5 | -------------------------------------------------------------------------------- /simpeggpr/GPRTimeSurvey.py: -------------------------------------------------------------------------------- 1 | from SimPEG import * 2 | from SimPEG.Utils import sdiag, mkvc, sdInv, speye 3 | 4 | class SurveyGPRTime(Survey.BaseSurvey): 5 | """ 6 | **SurveyAcousitc** 7 | 8 | Geophysical Acoustic Wave data. 9 | 10 | """ 11 | 12 | def __init__(self, srcList,**kwargs): 13 | self.srcList = srcList 14 | Survey.BaseSurvey.__init__(self, **kwargs) 15 | 16 | def projectFields(self, u): 17 | data = {} 18 | 19 | for i, src in enumerate(self.srcList): 20 | for rx in src.rxList: 21 | 22 | Proj = rx.getP(self.prob.mesh) 23 | if rx.rxtype.find('E') >= 0: 24 | flag = 'E' 25 | elif rx.rxtype.find('H') >= 0: 26 | flag = 'H' 27 | data[src, rx] = (Proj*u[flag, src]) 28 | 29 | return data 30 | -------------------------------------------------------------------------------- /simpeggpr/GPRTimeTEz.py: -------------------------------------------------------------------------------- 1 | from SimPEG import * 2 | from SimPEG.Utils import sdiag, mkvc, sdInv, speye 3 | import matplotlib.pyplot as plt 4 | from time import clock 5 | from scipy.constants import mu_0, epsilon_0 6 | from GPRTimeSurvey import SurveyGPRTime 7 | 8 | class GPRTEzSrc(Survey.BaseSrc): 9 | 10 | tlag = None 11 | fmain = None 12 | 13 | def __init__(self, loc, time, rxList, srcType='Mz', **kwargs): 14 | 15 | Survey.BaseSrc.__init__(self, rxList, **kwargs) 16 | 17 | self.dt = time[1]-time[0] 18 | self.time = time 19 | self.loc = loc 20 | self.rxList = rxList 21 | self.srcType = srcType 22 | # self.kwargs = kwargs 23 | 24 | 25 | def RickerWavelet(self): 26 | 27 | """ 28 | Generating Ricker Wavelet 29 | 30 | .. math :: 31 | 32 | """ 33 | tlag = self.tlag 34 | fmain = self.fmain 35 | t = self.time 36 | self.wave = np.exp(-2*fmain**2*(t-tlag)**2)*np.cos(np.pi*fmain*(t-tlag)) 37 | return self.wave 38 | 39 | def Wave(self, tInd): 40 | 41 | """ 42 | Generating Ricker Wavelet 43 | 44 | .. math :: 45 | 46 | """ 47 | tlag = self.tlag 48 | fmain = self.fmain 49 | t = self.time[tInd] 50 | self.wave = np.exp(-2*fmain**2*(t-tlag)**2)*np.cos(np.pi*fmain*(t-tlag)) 51 | return self.wave 52 | 53 | def getq(self, mesh): 54 | 55 | if self.srcType=='Mz': 56 | 57 | srcind = Utils.closestPoints(mesh, self.loc, gridLoc='CC') 58 | jm = np.zeros(mesh.nC) 59 | jm[srcind] = 1./mesh.vol[srcind] 60 | return np.r_[jm, jm]*0.5, np.zeros(mesh.nE) 61 | 62 | elif self.srcType=='Jx': 63 | srcind = Utils.closestPoints(mesh, self.loc, gridLoc='Ex') 64 | je = np.zeros(mesh.nE) 65 | je[srcind] = 1./mesh.edge[srcind] 66 | 67 | return np.zeros(2*mesh.nC), je 68 | 69 | elif self.srcType=='Jy': 70 | srcind = Utils.closestPoints(mesh, self.loc, gridLoc='Ey') 71 | je = np.zeros(mesh.nE) 72 | je[srcind] = 1./mesh.edge[srcind] 73 | return np.zeros(2*mesh.nC), je 74 | 75 | else: 76 | Exception("Not implemented!!") 77 | 78 | class GPRTEzRx(Survey.BaseRx): 79 | 80 | def __init__(self, locs, rxtype, **kwargs): 81 | self.locs = locs 82 | self.rxtype = rxtype 83 | self._Ps = {} 84 | @property 85 | def nD(self): 86 | """ The number of data in the receiver.""" 87 | return self.locs.shape[0] 88 | 89 | def getP(self, mesh): 90 | # TODO: need to be changed: do not generate every time 91 | if self.rxtype == 'Ex': 92 | P = mesh.getInterpolationMat(self.locs, 'Ex') 93 | elif self.rxtype == 'Ey': 94 | P = mesh.getInterpolationMat(self.locs, 'Ey') 95 | elif self.rxtype == 'Hz': 96 | P = mesh.getInterpolationMat(self.locs, 'CC') 97 | return P 98 | 99 | class GPR2DTEzProblemPML(Problem.BaseProblem): 100 | """ 101 | 102 | """ 103 | surveyPair = SurveyGPRTime 104 | Solver = Solver 105 | storefield = True 106 | verbose = False 107 | stability = False 108 | sigx = False 109 | 110 | def __init__(self, mesh, **kwargs): 111 | Problem.BaseProblem.__init__(self, mesh) 112 | Utils.setKwargs(self, **kwargs) 113 | 114 | def setPMLBC(self, npad, dt, sm=3., Rth=1e-8): 115 | ax = self.mesh.vectorCCx[-npad] 116 | ay = self.mesh.vectorCCy[-npad] 117 | 118 | indy = np.logical_or(self.mesh.gridCC[:,1]<=-ay, self.mesh.gridCC[:,1]>=ay) 119 | indx = np.logical_or(self.mesh.gridCC[:,0]<=-ax, self.mesh.gridCC[:,0]>=ax) 120 | 121 | tempx = np.zeros_like(self.mesh.gridCC[:,0]) 122 | tempx[indx] = (abs(self.mesh.gridCC[:,0][indx])-ax)**2 123 | tempx[indx] = tempx[indx]-tempx[indx].min() 124 | tempx[indx] = tempx[indx]/tempx[indx].max() 125 | tempy = np.zeros_like(self.mesh.gridCC[:,1]) 126 | tempy[indy] = (abs(self.mesh.gridCC[:,1][indy])-ay)**2 127 | tempy[indy] = tempy[indy]-tempy[indy].min() 128 | tempy[indy] = tempy[indy]/tempy[indy].max() 129 | 130 | self.tempx = tempx 131 | self.tempy = tempy 132 | 133 | self.Lx = self.mesh.hx[-npad:].sum() 134 | self.Ly = self.mesh.hy[-npad:].sum() 135 | self.sm = sm 136 | self.Rth= Rth 137 | 138 | 139 | def stabilitycheck(self, epsilon, mu, sig0, time, fmain, sigs=0.): 140 | 141 | self.epsilon = epsilon 142 | self.mu = mu 143 | self.sig0 = sig0 144 | self.dxmin = min(self.mesh.hx.min(), self.mesh.hy.min()) 145 | self.c = 1./np.sqrt(self.epsilon*self.mu) 146 | self.topt = self.dxmin/self.c.max()*0.5 147 | self.dt = time[1]-time[0] 148 | self.fmain = fmain 149 | self.wavelen = self.c.min()/self.fmain 150 | self.G = self.wavelen/self.dxmin 151 | self.sigm = -(self.epsilon.max()*self.c.max()/(0.5*(self.Lx+self.Ly)))/(1.+self.sm*(1./3+2./(np.pi**2)))*np.log(self.Rth) 152 | self.sm_ref = self.wavelen/(2*self.mesh.hx.min())-1. 153 | self.sigx = self.sigm*np.sin(0.5*np.pi*np.sqrt(self.tempx))**2 154 | self.sigy = self.sigm*np.sin(0.5*np.pi*np.sqrt(self.tempy))**2 155 | self.sx0 = 1.+self.sm*self.tempx 156 | self.sy0 = 1.+self.sm*self.tempy 157 | self.sigs = np.ones_like(self.sigx)*sigs 158 | 159 | 160 | if self.dt > self.topt: 161 | print "Warning: dt is greater than topt" 162 | self.stability = False 163 | elif self.G < 0.1: 164 | print "Warning: Wavelength per cell (G) should be greater than 0.5" 165 | self.stability = False 166 | elif self.sm < self.sm_ref: 167 | self.stability = False 168 | print ("sm should be smaller than %5.2e") % (self.sm_ref) 169 | else: 170 | print "You are good to go:)" 171 | self.stability = True 172 | 173 | print ">> Stability information" 174 | print (" dt: %5.2e s")%(self.dt) 175 | print (" Optimal dt: %5.2e s")%(self.topt) 176 | print (" Cell per wavelength (G): %5.2e")%(self.G) 177 | print (" Optimal G: %5.2e")%(1.2) 178 | print ('>> sm: %5.2e, lamda: %5.2e, sigm: %5.2e') % (self.sm, self.wavelen, self.sigm) 179 | 180 | def fields(self, epsilon, mu, sig0): 181 | 182 | Smu = sp.block_diag([sdiag(mu*self.sy0), sdiag(mu*self.sx0)]) 183 | SmuI = sp.block_diag([sdiag(1./(mu*self.sy0)), sdiag(1./(mu*self.sx0))]) 184 | Smuisig = sp.block_diag([sdiag(self.sigs*self.sigy*(1./epsilon)*self.sy0), sdiag(self.sigs*self.sigx*(1./epsilon)*self.sx0)]) 185 | Ssig = sp.block_diag([sdiag((self.sigy*mu/epsilon+self.sigs)*self.sy0), sdiag((self.sigx*mu/epsilon+self.sigs)*self.sx0)]) 186 | Mesepsisig = sdiag(self.mesh.aveE2CCV.T*np.r_[1./epsilon*sig0*self.sigy*self.sy0, 1./epsilon*sig0*self.sigx*self.sx0]) 187 | Messig = sdiag(self.mesh.aveE2CCV.T*np.r_[(sig0+self.sigy)*self.sy0, (sig0+self.sigx)*self.sx0]) 188 | Meseps = sdiag(self.mesh.aveE2CCV.T*np.r_[epsilon*self.sy0, epsilon*self.sx0]) 189 | MesepsI = sdInv(Meseps) 190 | Icc = sp.hstack((speye(self.mesh.nC), speye(self.mesh.nC))) 191 | curl = self.mesh.edgeCurl 192 | curlvec = sp.block_diag((curl[:,:self.mesh.nEx], curl[:,self.mesh.nEx:])) 193 | 194 | if self.stability==False: 195 | raise Exception("Stability condition is not satisfied!!") 196 | elif self.sigx is False: 197 | print "Warning: Absorbing boundary condition was not set yet!!" 198 | start = clock() 199 | print "" 200 | print "***** Start Computing Electromagnetic Wave *****" 201 | print "" 202 | print (">> dt: %5.2e s")%(self.dt) 203 | print (">> Optimal dt: %5.2e s")%(self.topt) 204 | print (">> Main frequency, fmain: %5.2e Hz")%(self.fmain) 205 | print (">> Cell per wavelength (G): %5.2e")%(self.G) 206 | 207 | 208 | if self.storefield==True: 209 | self._Fields ={} 210 | #TODO: parallize in terms of sources 211 | nsrc = len(self.survey.srcList) 212 | for isrc, src in enumerate(self.survey.srcList): 213 | print (" Src at (%7.2f, %7.2f): %4i/%4i")%(src.loc[0], src.loc[0], isrc+1, nsrc) 214 | hd0 = np.zeros(2*self.mesh.nC) 215 | hd1 = np.zeros(2*self.mesh.nC) 216 | hId0 = np.zeros(2*self.mesh.nC) 217 | hId1 = np.zeros(2*self.mesh.nC) 218 | e0 = np.zeros(self.mesh.nE) 219 | e1 = np.zeros(self.mesh.nE) 220 | eI0 = np.zeros(self.mesh.nE) 221 | eI1 = np.zeros(self.mesh.nE) 222 | time = src.time 223 | dt = src.dt 224 | jm, je = src.getq(self.mesh) 225 | h = np.zeros((self.mesh.nC, time.size)) 226 | e = np.zeros((self.mesh.nE, time.size)) 227 | 228 | for i in range(time.size-1): 229 | eI0 = eI1.copy() 230 | eI1 = eI0 + dt*e0 231 | e1 = e0 + MesepsI*dt*(curl.T*(Icc*hd1)-Messig*e0-Mesepsisig*eI1-je*src.wave[i]) 232 | e0 = e1.copy() 233 | e[:,i] = e1 234 | hId0 = hId1.copy() 235 | hId1 = hId0 + dt*hd0 236 | hd1 = hd0 - SmuI*dt*(curlvec*e0+Ssig*hd0+Smuisig*hId1+jm*src.wave[i]*0.5) 237 | hd0 = hd1.copy() 238 | h[:,i] = Icc*hd1 239 | 240 | self._Fields['E', src]= e 241 | self._Fields['H', src]= h 242 | elapsed = clock()-start 243 | print (">>Elapsed time: %5.2e s")%(elapsed) 244 | 245 | return self._Fields 246 | 247 | 248 | elif self.storefield==False: 249 | Data = {} 250 | nsrc = len(self.survey.srcList) 251 | for isrc, src in enumerate(self.survey.srcList): 252 | print (" Src at (%7.2f, %7.2f): %4i/%4i")%(src.loc[0], src.loc[0], isrc+1, nsrc) 253 | hd0 = np.zeros(2*mesh.nC) 254 | hd1 = np.zeros(2*mesh.nC) 255 | hId0 = np.zeros(2*mesh.nC) 256 | hId1 = np.zeros(2*mesh.nC) 257 | e0 = np.zeros(mesh.nE) 258 | e1 = np.zeros(mesh.nE) 259 | eI0 = np.zeros(mesh.nE) 260 | eI1 = np.zeros(mesh.nE) 261 | time = src.time 262 | dt = src.dt 263 | jm, je = src.getq(self.mesh) 264 | h = np.zeros((mesh.nC, time.size)) 265 | e = np.zeros((mesh.nE, time.size)) 266 | 267 | for i in range(time.size-1): 268 | eI0 = eI1.copy() 269 | eI1 = eI0 + dt*e0 270 | e1 = e0 + MesepsI*dt*(curl.T*(Icc*hd1)-Messig*e0-Mesepsisig*eI1-je*src.wave[i]) 271 | e0 = e1.copy() 272 | e[:,i] = e1 273 | hId0 = hId1.copy() 274 | hId1 = hId0 + dt*hd0 275 | hd1 = hd0 - SmuI*dt*(curlvec*e0+Ssig*hd0+Smuisig*hId1+jm*src.wave[i]) 276 | hd0 = hd1.copy() 277 | h[:,i] = Icc*hd1 278 | 279 | for rx in src.rxList: 280 | Proj = rx.getP(self.mesh) 281 | if rx.rxtype.find('E') >= 0: 282 | flag = 'E' 283 | Data[src, rx] = (Proj*e) 284 | elif rx.rxtype.find('H') >= 0: 285 | flag = 'H' 286 | Data[src, rx] = (Proj*h) 287 | 288 | elapsed = clock()-start 289 | print (">>Elapsed time: %5.2e s")%(elapsed) 290 | 291 | return Data 292 | 293 | 294 | if __name__ == '__main__': 295 | 296 | 297 | dt = 1e-11 298 | fmain = 3e9 299 | time = np.arange(650)*dt 300 | options={'tlag':50*dt, 'fmain':fmain} 301 | rx = GPRTEzRx(np.r_[0, 0.], 'Ex') 302 | src = GPRTEzSrc(np.r_[0, 0.], time, [rx], srcType='Mz', **options) 303 | survey = SurveyGPRTime([src]) 304 | wave = src.RickerWavelet() 305 | cs = 1.0*1e-2 306 | hx = np.ones(200)*cs 307 | hy = np.ones(200)*cs 308 | mesh = Mesh.TensorMesh([hx, hy], 'CC') 309 | prob = GPR2DTEzProblemPML(mesh) 310 | prob.pair(survey) 311 | epsilon = epsilon_0*np.ones(mesh.nC)*1. 312 | epsilon[mesh.gridCC[:,1]<0.5] = epsilon_0*2. 313 | mu = mu_0*np.ones(mesh.nC) 314 | sighalf = 1e-3 315 | sig0 = sighalf*np.ones(mesh.nC) 316 | prob.setPMLBC(30, dt) 317 | prob.stabilitycheck(epsilon, mu, sig0, time, fmain, sigs=0.) 318 | storefield = True 319 | if storefield == False: 320 | prob.storefield = False 321 | Data = prob.fields(epsilon, mu, sig0) 322 | plt.plot(time, Utils.mkvc(Data[src,rx])) 323 | 324 | elif storefield == True: 325 | Fields = prob.fields(epsilon, mu, sig0) 326 | icount = 600 327 | extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()] 328 | 329 | plt.imshow(np.flipud(Fields['H', src][:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent) 330 | plt.show() 331 | 332 | data = survey.projectFields(Fields) 333 | plt.plot(time, Utils.mkvc(data[src, rx])) 334 | 335 | plt.show() 336 | -------------------------------------------------------------------------------- /simpeggpr/GPRTimeTMz.py: -------------------------------------------------------------------------------- 1 | from SimPEG import * 2 | from SimPEG.Utils import sdiag, mkvc, sdInv, speye 3 | import matplotlib.pyplot as plt 4 | from time import clock 5 | from scipy.constants import mu_0, epsilon_0 6 | from GPRTimeSurvey import SurveyGPRTime 7 | 8 | class GPRTMzSrc(Survey.BaseSrc): 9 | 10 | 11 | def __init__(self, loc, time, rxList, srcType='Mz', **kwargs): 12 | 13 | Survey.BaseSrc.__init__(self, rxList, **kwargs) 14 | 15 | self.dt = time[1]-time[0] 16 | self.time = time 17 | self.loc = loc 18 | self.rxList = rxList 19 | self.srcType = srcType 20 | self.kwargs = kwargs 21 | 22 | 23 | def RickerWavelet(self): 24 | 25 | """ 26 | Generating Ricker Wavelet 27 | 28 | .. math :: 29 | 30 | """ 31 | tlag = self.kwargs['tlag'] 32 | fmain = self.kwargs['fmain'] 33 | t = self.time 34 | self.wave = np.exp(-2*fmain**2*(t-tlag)**2)*np.cos(np.pi*fmain*(t-tlag)) 35 | return self.wave 36 | 37 | def Wave(self, tInd): 38 | 39 | """ 40 | Generating Ricker Wavelet 41 | 42 | .. math :: 43 | 44 | """ 45 | tlag = self.kwargs['tlag'] 46 | fmain = self.kwargs['fmain'] 47 | t = self.time[tInd] 48 | self.wave = np.exp(-2*fmain**2*(t-tlag)**2)*np.cos(np.pi*fmain*(t-tlag)) 49 | return self.wave 50 | 51 | def getq(self, mesh): 52 | 53 | if self.srcType=='Jz': 54 | 55 | srcind = Utils.closestPoints(mesh, self.loc, gridLoc='CC') 56 | je = np.zeros(mesh.nC) 57 | je[srcind] = 1./mesh.vol[srcind] 58 | return np.r_[je, je]*0.5, np.zeros(mesh.nE) 59 | 60 | elif self.srcType=='Mx': 61 | srcind = Utils.closestPoints(mesh, self.loc, gridLoc='Ex') 62 | jm = np.zeros(mesh.nE) 63 | jm[srcind] = 1./mesh.edge[srcind] 64 | 65 | return np.zeros(2*mesh.nC), jm 66 | 67 | elif self.srcType=='My': 68 | srcind = Utils.closestPoints(mesh, self.loc, gridLoc='Ey') 69 | jm = np.zeros(mesh.nE) 70 | jm[srcind] = 1./mesh.edge[srcind] 71 | return np.zeros(2*mesh.nC), jm 72 | 73 | else: 74 | Exception("Not implemented!!") 75 | 76 | class GPRTMzRx(Survey.BaseRx): 77 | 78 | def __init__(self, locs, rxtype, **kwargs): 79 | self.locs = locs 80 | self.rxtype = rxtype 81 | self._Ps = {} 82 | @property 83 | def nD(self): 84 | """ The number of data in the receiver.""" 85 | return self.locs.shape[0] 86 | 87 | def getP(self, mesh): 88 | # TODO: need to be changed: do not generate every time 89 | if self.rxtype == 'Hx': 90 | P = mesh.getInterpolationMat(self.locs, 'Ex') 91 | elif self.rxtype == 'Hy': 92 | P = mesh.getInterpolationMat(self.locs, 'Ey') 93 | elif self.rxtype == 'Ez': 94 | P = mesh.getInterpolationMat(self.locs, 'CC') 95 | return P 96 | 97 | class GPR2DTMzProblemPML(Problem.BaseProblem): 98 | """ 99 | 100 | """ 101 | surveyPair = SurveyGPRTime 102 | Solver = Solver 103 | storefield = True 104 | verbose = False 105 | stability = False 106 | sigx = False 107 | 108 | def __init__(self, mesh, **kwargs): 109 | Problem.BaseProblem.__init__(self, mesh) 110 | Utils.setKwargs(self, **kwargs) 111 | 112 | def setPMLBC(self, npad, dt, sm=3., Rth=1e-8): 113 | ax = self.mesh.vectorCCx[-npad] 114 | ay = self.mesh.vectorCCy[-npad] 115 | 116 | indy = np.logical_or(self.mesh.gridCC[:,1]<=-ay, self.mesh.gridCC[:,1]>=ay) 117 | indx = np.logical_or(self.mesh.gridCC[:,0]<=-ax, self.mesh.gridCC[:,0]>=ax) 118 | 119 | tempx = np.zeros_like(self.mesh.gridCC[:,0]) 120 | tempx[indx] = (abs(self.mesh.gridCC[:,0][indx])-ax)**2 121 | tempx[indx] = tempx[indx]-tempx[indx].min() 122 | tempx[indx] = tempx[indx]/tempx[indx].max() 123 | tempy = np.zeros_like(self.mesh.gridCC[:,1]) 124 | tempy[indy] = (abs(self.mesh.gridCC[:,1][indy])-ay)**2 125 | tempy[indy] = tempy[indy]-tempy[indy].min() 126 | tempy[indy] = tempy[indy]/tempy[indy].max() 127 | 128 | self.tempx = tempx 129 | self.tempy = tempy 130 | 131 | self.Lx = self.mesh.hx[-npad:].sum() 132 | self.Ly = self.mesh.hy[-npad:].sum() 133 | self.sm = sm 134 | self.Rth= Rth 135 | 136 | 137 | def stabilitycheck(self, epsilon, mu, sig0, time, fmain, sigs=0.): 138 | 139 | self.epsilon = epsilon 140 | self.mu = mu 141 | self.sig0 = sig0 142 | self.dxmin = min(self.mesh.hx.min(), self.mesh.hy.min()) 143 | self.c = 1./np.sqrt(self.epsilon*self.mu) 144 | self.topt = self.dxmin/self.c.max()*0.5 145 | self.dt = time[1]-time[0] 146 | self.fmain = fmain 147 | self.wavelen = self.c.min()/self.fmain 148 | self.G = self.wavelen/self.dxmin 149 | self.sigm = -(self.epsilon.max()*self.c.max()/(0.5*(self.Lx+self.Ly)))/(1.+self.sm*(1./3+2./(np.pi**2)))*np.log(self.Rth) 150 | self.sm_ref = self.wavelen/(2*self.mesh.hx.min())-1. 151 | self.sigx = self.sigm*np.sin(0.5*np.pi*np.sqrt(self.tempx))**2 152 | self.sigy = self.sigm*np.sin(0.5*np.pi*np.sqrt(self.tempy))**2 153 | self.sx0 = 1.+self.sm*self.tempx 154 | self.sy0 = 1.+self.sm*self.tempy 155 | self.sigs = np.ones_like(self.sigx)*sigs 156 | 157 | 158 | if self.dt > self.topt: 159 | print "Warning: dt is greater than topt" 160 | self.stability = False 161 | elif self.G < 0.1: 162 | print "Warning: Wavelength per cell (G) should be greater than 0.5" 163 | self.stability = False 164 | elif self.sm < self.sm_ref: 165 | self.stability = False 166 | print ("sm should be smaller than %5.2e") % (self.sm_ref) 167 | else: 168 | print "You are good to go:)" 169 | self.stability = True 170 | 171 | print ">> Stability information" 172 | print (" dt: %5.2e s")%(self.dt) 173 | print (" Optimal dt: %5.2e s")%(self.topt) 174 | print (" Cell per wavelength (G): %5.2e")%(self.G) 175 | print (" Optimal G: %5.2e")%(1.2) 176 | print ('>> sm: %5.2e, lamda: %5.2e, sigm: %5.2e') % (self.sm, self.wavelen, self.sigm) 177 | 178 | def fields(self, epsilon, mu, sig0): 179 | 180 | Seps = sp.block_diag([sdiag(epsilon*self.sy0), sdiag(epsilon*self.sx0)]) 181 | SepsI = sp.block_diag([sdiag(1./(epsilon*self.sy0)), sdiag(1./(epsilon*self.sx0))]) 182 | Sepsisig = sp.block_diag([sdiag(sig0*self.sigy*(1./epsilon)*self.sy0), sdiag(sig0*self.sigx*(1./epsilon)*self.sx0)]) 183 | Ssig = sp.block_diag([sdiag((self.sigy+sig0)*self.sy0), sdiag((self.sigx+sig0)*self.sx0)]) 184 | Mesmuisigs = sdiag(self.mesh.aveE2CCV.T*np.r_[self.sigs*self.sigy/epsilon*self.sy0, self.sigs*self.sigx/epsilon*self.sx0]) 185 | Messigs = sdiag(self.mesh.aveE2CCV.T*np.r_[(self.sigs+self.sigy*mu/epsilon)*self.sy0, (self.sigs+self.sigx*mu/epsilon)*self.sx0]) 186 | Mesmu = sdiag(self.mesh.aveE2CCV.T*np.r_[mu*self.sy0, mu*self.sx0]) 187 | MesmuI = sdInv(Mesmu) 188 | Icc = sp.hstack((speye(self.mesh.nC), speye(self.mesh.nC))) 189 | curl = self.mesh.edgeCurl 190 | curlvec = sp.block_diag((curl[:,:self.mesh.nEx], curl[:,self.mesh.nEx:])) 191 | 192 | if self.stability==False: 193 | raise Exception("Stability condition is not satisfied!!") 194 | elif self.sigx is False: 195 | print "Warning: Absorbing boundary condition was not set yet!!" 196 | start = clock() 197 | print "" 198 | print "***** Start Computing Electromagnetic Wave *****" 199 | print "" 200 | print (">> dt: %5.2e s")%(self.dt) 201 | print (">> Optimal dt: %5.2e s")%(self.topt) 202 | print (">> Main frequency, fmain: %5.2e Hz")%(self.fmain) 203 | print (">> Cell per wavelength (G): %5.2e")%(self.G) 204 | 205 | 206 | if self.storefield==True: 207 | self._Fields ={} 208 | #TODO: parallize in terms of sources 209 | nsrc = len(self.survey.srcList) 210 | for isrc, src in enumerate(self.survey.srcList): 211 | print (" Src at (%7.2f, %7.2f): %4i/%4i")%(src.loc[0], src.loc[0], isrc+1, nsrc) 212 | h0 = np.zeros(self.mesh.nE) 213 | h1 = np.zeros(self.mesh.nE) 214 | hI0 = np.zeros(self.mesh.nE) 215 | hI1 = np.zeros(self.mesh.nE) 216 | 217 | ed0 = np.zeros(2*self.mesh.nC) 218 | ed1 = np.zeros(2*self.mesh.nC) 219 | eId0 = np.zeros(2*self.mesh.nC) 220 | eId1 = np.zeros(2*self.mesh.nC) 221 | 222 | time = src.time 223 | dt = src.dt 224 | je, jm = src.getq(self.mesh) 225 | h = np.zeros((self.mesh.nE, time.size)) 226 | e = np.zeros((self.mesh.nC, time.size)) 227 | 228 | for i in range(time.size-1): 229 | 230 | eId0 = eId1.copy() 231 | eId1 = eId0 + dt*ed0 232 | 233 | ed1 = ed0 + SepsI*dt*(curlvec*(h1) - Ssig*ed0 - Sepsisig*eId1-je*src.wave[i]) 234 | ed0 = ed1.copy() 235 | e[:,i] = Icc*ed1 236 | 237 | hI0 = hI1.copy() 238 | hI1 = hI0 + dt*h0 239 | h1 = h0 - MesmuI*dt*(curl.T*(Icc*ed0)+Messigs*h0+Mesmuisigs*hI1+jm*src.wave[i]) 240 | h0 = h1.copy() 241 | h[:,i] = h1 242 | 243 | self._Fields['E', src]= e 244 | self._Fields['H', src]= h 245 | 246 | elapsed = clock()-start 247 | print (">>Elapsed time: %5.2e s")%(elapsed) 248 | 249 | return self._Fields 250 | 251 | 252 | elif self.storefield==False: 253 | Data = {} 254 | nsrc = len(self.survey.srcList) 255 | for isrc, src in enumerate(self.survey.srcList): 256 | print (" Src at (%7.2f, %7.2f): %4i/%4i")%(src.loc[0], src.loc[0], isrc+1, nsrc) 257 | h0 = np.zeros(mesh.nE) 258 | h1 = np.zeros(mesh.nE) 259 | hI0 = np.zeros(mesh.nE) 260 | hI1 = np.zeros(mesh.nE) 261 | 262 | ed0 = np.zeros(2*mesh.nC) 263 | ed1 = np.zeros(2*mesh.nC) 264 | eId0 = np.zeros(2*mesh.nC) 265 | eId1 = np.zeros(2*mesh.nC) 266 | 267 | time = src.time 268 | dt = src.dt 269 | je, jm = src.getq(self.mesh) 270 | h = np.zeros((mesh.nE, time.size)) 271 | e = np.zeros((mesh.nC, time.size)) 272 | 273 | for i in range(time.size-1): 274 | eId0 = eId1.copy() 275 | eId1 = eId0 + dt*ed0 276 | 277 | ed1 = ed0 + SepsI*dt*(curlvec*(h1) - Ssig*ed0 - Sepsisig*eId1-je*wave[i]) 278 | ed0 = ed1.copy() 279 | e[:,i] = Icc*ed1 280 | 281 | hI0 = hI1.copy() 282 | hI1 = hI0 + dt*h0 283 | h1 = h0 - MesmuI*dt*(curl.T*(Icc*ed0)+Messigs*h0+Mesmuisigs*hI1+jm*wave[i]) 284 | h0 = h1.copy() 285 | h[:,i] = h1 286 | 287 | for rx in src.rxList: 288 | Proj = rx.getP(self.mesh) 289 | if rx.rxtype.find('E') >= 0: 290 | flag = 'E' 291 | Data[src, rx] = (Proj*e) 292 | elif rx.rxtype.find('H') >= 0: 293 | flag = 'H' 294 | Data[src, rx] = (Proj*h) 295 | 296 | elapsed = clock()-start 297 | print (">>Elapsed time: %5.2e s")%(elapsed) 298 | 299 | return Data 300 | 301 | if __name__ == '__main__': 302 | 303 | 304 | dt = 1e-11 305 | fmain = 3e9 306 | time = np.arange(650)*dt 307 | options={'tlag':50*dt, 'fmain':fmain} 308 | rx = GPRTMzRx(np.r_[0, 0.], 'Hx') 309 | src = GPRTMzSrc(np.r_[0, 0.], time, [rx], srcType='Jz', **options) 310 | survey = SurveyGPRTime([src]) 311 | wave = src.RickerWavelet() 312 | cs = 1.0*1e-2 313 | hx = np.ones(200)*cs 314 | hy = np.ones(200)*cs 315 | mesh = Mesh.TensorMesh([hx, hy], 'CC') 316 | prob = GPR2DTMzProblemPML(mesh) 317 | prob.pair(survey) 318 | epsilon = epsilon_0*np.ones(mesh.nC)*1. 319 | epsilon[mesh.gridCC[:,1]<0.5] = epsilon_0*2. 320 | mu = mu_0*np.ones(mesh.nC) 321 | sighalf = 1e-3 322 | sig0 = sighalf*np.ones(mesh.nC) 323 | prob.setPMLBC(30, dt) 324 | prob.stabilitycheck(epsilon, mu, sig0, time, fmain, sigs=0.) 325 | 326 | storefield = True 327 | if storefield == False: 328 | prob.storefield = False 329 | Data = prob.fields(epsilon, mu, sig0) 330 | plt.plot(time, Utils.mkvc(Data[src,rx])) 331 | 332 | elif storefield == True: 333 | Fields = prob.fields(epsilon, mu, sig0) 334 | icount = 600 335 | extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()] 336 | 337 | plt.imshow(np.flipud(Fields['E', src][:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent) 338 | plt.show() 339 | 340 | data = survey.projectFields(Fields) 341 | plt.plot(time, Utils.mkvc(data[src, rx])) 342 | 343 | plt.show() 344 | -------------------------------------------------------------------------------- /simpeggpr/__init__.py: -------------------------------------------------------------------------------- 1 | from GPRTimeSurvey import * 2 | from GPRTimeTEz import * 3 | from GPRTimeTMz import * 4 | 5 | --------------------------------------------------------------------------------