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<div class="section" id="module-esys.downunder.forwardmodels.acoustic">
<span id="esys-downunder-forwardmodels-acoustic-package"></span><h1>esys.downunder.forwardmodels.acoustic Package<a class="headerlink" href="#module-esys.downunder.forwardmodels.acoustic" title="Permalink to this headline">¶</a></h1>
<p>Forward model for acoustic wave forms</p>
<div class="section" id="classes">
<h2>Classes<a class="headerlink" href="#classes" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li><a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm" title="esys.downunder.forwardmodels.acoustic.AcousticWaveForm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AcousticWaveForm</span></code></a></li>
<li><a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.ForwardModel" title="esys.downunder.forwardmodels.acoustic.ForwardModel"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ForwardModel</span></code></a></li>
</ul>
<dl class="class">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm">
<em class="property">class </em><code class="descclassname">esys.downunder.forwardmodels.acoustic.</code><code class="descname">AcousticWaveForm</code><span class="sig-paren">(</span><em>domain</em>, <em>omega</em>, <em>w</em>, <em>data</em>, <em>F</em>, <em>coordinates=None</em>, <em>fixAtBottom=False</em>, <em>tol=1e-10</em>, <em>saveMemory=True</em>, <em>scaleF=True</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="esys.downunder.forwardmodels.base.html#esys.downunder.forwardmodels.base.ForwardModel" title="esys.downunder.forwardmodels.base.ForwardModel"><code class="xref py py-class docutils literal notranslate"><span class="pre">esys.downunder.forwardmodels.base.ForwardModel</span></code></a></p>
<p>Forward Model for acoustic waveform inversion in the frequency domain.
It defines a cost function:</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Math:</th><td class="field-body"><code class="xref py py-obj docutils literal notranslate"><span class="pre">defect</span> <span class="pre">=</span> <span class="pre">1/2</span> <span class="pre">integrate(</span> <span class="pre">(</span> <span class="pre">w</span> <span class="pre">*</span> <span class="pre">(</span> <span class="pre">a</span> <span class="pre">*</span> <span class="pre">u</span> <span class="pre">-</span> <span class="pre">data</span> <span class="pre">)</span> <span class="pre">)</span> <span class="pre">**</span> <span class="pre">2</span> <span class="pre">)</span></code></td>
</tr>
</tbody>
</table>
<p>where w are weighting factors, data are the measured data (as a 2-comp
vector of real and imaginary part) for real frequency omega, and u is
the corresponding result produced by the forward model.
u (as a 2-comp vector) is the solution of the complex Helmholtz equation
for frequency omega, source F and complex, inverse, squared p-velocity
sigma:</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Math:</th><td class="field-body"><code class="xref py py-obj docutils literal notranslate"><span class="pre">-u_{ii}</span> <span class="pre">-</span> <span class="pre">omega**2</span> <span class="pre">*</span> <span class="pre">sigma</span> <span class="pre">*</span> <span class="pre">u</span> <span class="pre">=</span> <span class="pre">F</span></code></td>
</tr>
</tbody>
</table>
<p>It is assumed that the exact scale of source F is unknown and the scaling
factor a of F is calculated by minimizing the defect.</p>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>domain</em>, <em>omega</em>, <em>w</em>, <em>data</em>, <em>F</em>, <em>coordinates=None</em>, <em>fixAtBottom=False</em>, <em>tol=1e-10</em>, <em>saveMemory=True</em>, <em>scaleF=True</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>initializes a new forward model with acoustic wave form inversion.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>domain</strong> (<code class="xref py py-obj docutils literal notranslate"><span class="pre">Domain</span></code>) – domain of the model</li>
<li><strong>w</strong> (<code class="docutils literal notranslate"><span class="pre">Scalar</span></code>) – weighting factors</li>
<li><strong>data</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – real and imaginary part of data</li>
<li><strong>F</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – real and imaginary part of source given at Dirac points,
on surface or at volume.</li>
<li><strong>coordinates</strong> (<code class="xref py py-obj docutils literal notranslate"><span class="pre">ReferenceSystem</span></code> or <code class="xref py py-obj docutils literal notranslate"><span class="pre">SpatialCoordinateTransformation</span></code>) – defines coordinate system to be used (not supported yet)</li>
<li><strong>tol</strong> (positive <code class="docutils literal notranslate"><span class="pre">float</span></code>) – tolerance of underlying PDE</li>
<li><strong>saveMemory</strong> (<code class="docutils literal notranslate"><span class="pre">bool</span></code>) – if true stiffness matrix is deleted after solution
of PDE to minimize memory requests. This will
require more compute time as the matrix needs to be
reallocated.</li>
<li><strong>scaleF</strong> (<code class="docutils literal notranslate"><span class="pre">bool</span></code>) – if true source F is scaled to minimize defect.</li>
<li><strong>fixAtBottom</strong> (<code class="docutils literal notranslate"><span class="pre">bool</span></code>) – if true pressure is fixed to zero at the bottom of
the domain</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getArguments">
<code class="descname">getArguments</code><span class="sig-paren">(</span><em>sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getArguments" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns precomputed values shared by <a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getDefect" title="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getDefect"><code class="xref py py-obj docutils literal notranslate"><span class="pre">getDefect()</span></code></a> and <a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getGradient" title="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getGradient"><code class="xref py py-obj docutils literal notranslate"><span class="pre">getGradient()</span></code></a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>sigma</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – a suggestion for complex 1/V**2</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">solution, uTar, uTai, uTu</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,), 3 x <code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getCoordinateTransformation">
<code class="descname">getCoordinateTransformation</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getCoordinateTransformation" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the coordinate transformation being used</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">CoordinateTransformation</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getDefect">
<code class="descname">getDefect</code><span class="sig-paren">(</span><em>sigma</em>, <em>u</em>, <em>uTar</em>, <em>uTai</em>, <em>uTu</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getDefect" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the defect value.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>sigma</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – a suggestion for complex 1/V**2</li>
<li><strong>u</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – a u vector</li>
<li><strong>uTar</strong> (<code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>) – equals <code class="xref py py-obj docutils literal notranslate"><span class="pre">integrate(</span> <span class="pre">w</span>  <span class="pre">*</span> <span class="pre">(data[0]*u[0]+data[1]*u[1]))</span></code></li>
<li><strong>uTai</strong> – equals <code class="xref py py-obj docutils literal notranslate"><span class="pre">integrate(</span> <span class="pre">w</span>  <span class="pre">*</span> <span class="pre">(data[1]*u[0]-data[0]*u[1]))</span></code></li>
<li><strong>uTu</strong> (<code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>) – equals <code class="xref py py-obj docutils literal notranslate"><span class="pre">integrate(</span> <span class="pre">w</span>  <span class="pre">*</span> <span class="pre">(u,u))</span></code></li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><code class="docutils literal notranslate"><span class="pre">float</span></code></p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getDomain">
<code class="descname">getDomain</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getDomain" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the domain of the forward model.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Domain</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getGradient">
<code class="descname">getGradient</code><span class="sig-paren">(</span><em>sigma</em>, <em>u</em>, <em>uTar</em>, <em>uTai</em>, <em>uTu</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getGradient" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the gradient of the defect with respect to density.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>sigma</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – a suggestion for complex 1/V**2</li>
<li><strong>u</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – a u vector</li>
<li><strong>uTar</strong> (<code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>) – equals <code class="xref py py-obj docutils literal notranslate"><span class="pre">integrate(</span> <span class="pre">w</span>  <span class="pre">*</span> <span class="pre">(data[0]*u[0]+data[1]*u[1]))</span></code></li>
<li><strong>uTai</strong> – equals <code class="xref py py-obj docutils literal notranslate"><span class="pre">integrate(</span> <span class="pre">w</span>  <span class="pre">*</span> <span class="pre">(data[1]*u[0]-data[0]*u[1]))</span></code></li>
<li><strong>uTu</strong> (<code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>) – equals <code class="xref py py-obj docutils literal notranslate"><span class="pre">integrate(</span> <span class="pre">w</span>  <span class="pre">*</span> <span class="pre">(u,u))</span></code></li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getSourceScaling">
<code class="descname">getSourceScaling</code><span class="sig-paren">(</span><em>u</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getSourceScaling" title="Permalink to this definition">¶</a></dt>
<dd><p>returns the scaling factor s required to rescale source F to minimize defect <code class="docutils literal notranslate"><span class="pre">|s</span> <span class="pre">*</span> <span class="pre">u-</span> <span class="pre">data|^2</span></code></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>u</strong> (<code class="docutils literal notranslate"><span class="pre">escript.Data</span></code> of shape (2,)) – value of pressure solution (real and imaginary part)</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getSurvey">
<code class="descname">getSurvey</code><span class="sig-paren">(</span><em>index=None</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.getSurvey" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the pair (data, weight)</p>
<p>If argument index is ignored.</p>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.rescaleWeights">
<code class="descname">rescaleWeights</code><span class="sig-paren">(</span><em>scale=1.0</em>, <em>sigma_scale=1.0</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.rescaleWeights" title="Permalink to this definition">¶</a></dt>
<dd><p>rescales the weights such that</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Math:</th><td class="field-body"><p class="first">integrate( ( w omega**2 * sigma_scale * data * ((1/L_j)**2)**-1) +1 )/(data*omega**2 * ((1/L_j)**2)**-1) * sigma_scale )=scale</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>scale</strong> (positive <code class="docutils literal notranslate"><span class="pre">float</span></code>) – scale of data weighting factors</li>
<li><strong>sigma_scale</strong> (<code class="docutils literal notranslate"><span class="pre">Scalar</span></code>) – scale of 1/vp**2 velocity.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.AcousticWaveForm.setUpPDE">
<code class="descname">setUpPDE</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.AcousticWaveForm.setUpPDE" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates and returns the underlying PDE.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="xref py py-obj docutils literal notranslate"><span class="pre">lpde.LinearPDE</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="esys.downunder.forwardmodels.acoustic.ForwardModel">
<em class="property">class </em><code class="descclassname">esys.downunder.forwardmodels.acoustic.</code><code class="descname">ForwardModel</code><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.ForwardModel" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>An abstract forward model that can be plugged into a cost function.
Subclasses need to implement <a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getDefect" title="esys.downunder.forwardmodels.acoustic.ForwardModel.getDefect"><code class="xref py py-obj docutils literal notranslate"><span class="pre">getDefect()</span></code></a>, <a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getGradient" title="esys.downunder.forwardmodels.acoustic.ForwardModel.getGradient"><code class="xref py py-obj docutils literal notranslate"><span class="pre">getGradient()</span></code></a>, and possibly
<a class="reference internal" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getArguments" title="esys.downunder.forwardmodels.acoustic.ForwardModel.getArguments"><code class="xref py py-obj docutils literal notranslate"><span class="pre">getArguments()</span></code></a> and ‘getCoordinateTransformation’.</p>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.ForwardModel.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialize self. See help(type(self)) for accurate signature.</p>
</dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.ForwardModel.getArguments">
<code class="descname">getArguments</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getArguments" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.ForwardModel.getCoordinateTransformation">
<code class="descname">getCoordinateTransformation</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getCoordinateTransformation" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.ForwardModel.getDefect">
<code class="descname">getDefect</code><span class="sig-paren">(</span><em>x</em>, <em>*args</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getDefect" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.downunder.forwardmodels.acoustic.ForwardModel.getGradient">
<code class="descname">getGradient</code><span class="sig-paren">(</span><em>x</em>, <em>*args</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.downunder.forwardmodels.acoustic.ForwardModel.getGradient" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
</div>
<div class="section" id="functions">
<h2>Functions<a class="headerlink" href="#functions" title="Permalink to this headline">¶</a></h2>
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<div class="section" id="others">
<h2>Others<a class="headerlink" href="#others" title="Permalink to this headline">¶</a></h2>
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<li>HAVE_DIRECT</li>
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<div class="section" id="packages">
<h2>Packages<a class="headerlink" href="#packages" title="Permalink to this headline">¶</a></h2>
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