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质量反演方法 - Road to Geophysics
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<h1 class="title" itemprop="name">质量反演方法</h1>
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<h1 id="toc_0">通用公式</h1>
<h2 id="toc_1">一般球谐展开式</h2>
<pre><code>\\[f\left( {\theta ,\varphi } \right) = \sum\limits_{l = 0}^\infty {\sum\limits_{m = 0}^l {{{\tilde P}_{lm}}\left( {\cos \theta } \right)\left\{ {{C_{lm}}\cos m\varphi + {S_{lm}}\sin m\varphi } \right\}} } \\]
\\[\left\{ {\begin{array}{*{20}{c}}
{{C_{lm}}}\\
{{S_{lm}}}
\end{array}} \right\}\\]
</code></pre>
<h1 id="toc_2">SADI</h1>
<h2 id="toc_3">Matlab代码</h2>
<ul>
<li><code>[mass, LLZ_mass_trend, LLZ_d_F] =
ctl_SADI( SH_G, SH_d, LLZ_ind_obs, LLZ_ind_mass, m2matrix, N_lonlat, smooth, alpha )</code><br/>
空间域反演控制文件。其中：
<ul>
<li>SH_G:</li>
<li>SH_d:</li>
<li>LLZ_ind_obs</li>
<li>LLZ_ind_mass</li>
<li>m2matrix</li>
<li>N_lonlat, smooth</li>
<li>当alpha为矩阵的时候（如：<code>alpha=10^(-10:1:0)</code>），会调用这个函数内部的<code>[std_m,std_fit] = plot_l_curve(G,d,alpha)</code>画L曲线</li>
<li>当alpha为一个确定的值时，会反演并返回结果<br/></li>
</ul></li>
</ul>
<h3 id="toc_4">辅助代码</h3>
<ul>
<li><code>plot_inversion_map(LLZ_mass_trend, LLZ_d_F, cran, N_lonlat, N_lonlat_G, smooth)</code><br/>
画出反演结果的平面图。</li>
</ul>
<h1 id="toc_5">ITER</h1>
<h2 id="toc_6">Matlab代码</h2>
<ul>
<li><code>[rg_mass, SH_residue, totalmass]= ctrl_ITER_batch(SHs, LLZ_mask, smooth, Nstep, icheck, imethod)</code><br/>
调用<code>ctl_ITER_yi</code>或者<code>ctl_ITER_chen</code>，imethod设定</li>
<li><code>[rg_mass, s_list, varargout]= ctl_ITER_chen(SH_model0, LLZ_mask, smooth, Nstep)</code><br/>
chen的反演方法，海洋覆盖一层负质量</li>
<li><p><code>[rg_mass, s_list, sh_residue]= ctl_ITER_yi(SH_model0, LLZ_mask, smooth, Nstep)</code><br/>
我的反演方法，只有陆地有质量。rg_mass是格网值，只有mask为1的地方才有值；LLZ_mask只包含0和1；sh_residue为拟合残余系数，无量纲化。</p>
<p>s_list, 包含Nstep每一步的结果: <br/>
rg_F（rg_mass的展开结果）, <br/>
rg_rsd（原始观测值减去rg_F）, <br/>
rg_mass（反演出来的质量，第Nstep步就是最终返回值）, <br/>
totalmass（rg_mass的总质量), <br/>
ratio（在mask为1的位置拟合残差比例）</p></li>
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