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<h1 class="title toc-ignore">Fault Seal Analysis</h1>
<h3 class="author">AmrMoslim</h3>
<h3 class="date">2019-04-24</h3>
</header>
<hr>
<div id="TOC" class="toc">
<ul>
<li><a href="#r-fault-seal-analysis-usong-r-fsar">R Fault Seal Analysis Usong R <em>“FSAR”</em></a><ul>
<li><a href="#data-input">Data Input</a></li>
<li><a href="#data-processing-creating-monte-carlo-model">Data Processing (Creating Monte Carlo Model)</a></li>
<li><a href="#results-and-outputs">Results and Outputs</a><ul>
<li><a href="#shale-gouge-ratio-claculation">Shale Gouge Ratio Claculation</a></li>
<li><a href="#shale-smear-factor-claculation">Shale Smear Factor Claculation</a></li>
</ul></li>
<li><a href="#references">References</a></li>
</ul></li>
</ul>
</div>
<div id="r-fault-seal-analysis-usong-r-fsar" class="section level1">
<h1>R Fault Seal Analysis Usong R <em>“FSAR”</em></h1>
<p>The most two famous and common processes to determine the fault seal analysis are Shale Gouge Ratio <strong>“SGR”</strong> and Shale Smear Factor <strong>“SSF”</strong>.</p>
<div id="data-input" class="section level2">
<h2>Data Input</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(mc2d)
### Inputs
Ftp90 <-<span class="st"> </span><span class="dv">120</span> ### Meters <span class="al">###</span> FAULT THROW MINIMUM VALUE
Ftp10 <-<span class="st"> </span><span class="dv">1000</span> ### Meters <span class="al">###</span> FAULT THROW MAXIMUM VALUE
Ltp90 <-<span class="st"> </span><span class="dv">140</span> ### Meters <span class="al">###</span> LAYER THICKNESS MINIMUM VALUE
Ltp10 <-<span class="st"> </span><span class="dv">500</span> ### Meters <span class="al">###</span> LAYER THICKNESS MAXIMUM VALUE
Ngp90 <-<span class="st"> </span><span class="dv">20</span> ### % <span class="al">###</span> NET OVER GROSS MINIMUM VALUE
Ngp10 <-<span class="st"> </span><span class="dv">60</span> ### % <span class="al">###</span> NET OVER GROSS MAXIMUM VALUE</code></pre></div>
</div>
<div id="data-processing-creating-monte-carlo-model" class="section level2">
<h2>Data Processing (Creating Monte Carlo Model)</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> n =<span class="st"> </span><span class="dv">10000</span> ### NUMBER OF ITERATIONS
seed =<span class="st"> </span><span class="dv">999</span> ### SEED
### Calculate the SD
Ftsd <-<span class="st"> </span><span class="kw">sd</span>(Ftp90<span class="op">:</span>Ftp10)
Ltsd <-<span class="st"> </span><span class="kw">sd</span>(Ltp90<span class="op">:</span>Ltp10)
ngsd <-<span class="st"> </span><span class="kw">sd</span>(Ngp90<span class="op">:</span>Ngp10)
### Calculate the Mean
Ftmean <-<span class="st"> </span><span class="kw">mean</span>(Ftp90<span class="op">:</span>Ftp10)
Ltmean <-<span class="st"> </span><span class="kw">mean</span>(Ltp90<span class="op">:</span>Ltp10)
ngmean <-<span class="st"> </span><span class="kw">mean</span>(Ngp90<span class="op">:</span>Ngp10)
### Fault throw Distribution
Ft =<span class="st"> </span><span class="kw">mcstoc</span>(rnorm, <span class="dt">mean=</span>Ftmean, <span class="dt">sd=</span>Ftsd, <span class="dt">rtrunc=</span><span class="ot">TRUE</span>, <span class="dt">linf=</span>Ftp90, <span class="dt">lsup=</span>Ftp10, <span class="dt">seed =</span> seed, <span class="dt">nsv=</span> n )
### Layer thickness Distribution
Lt =<span class="st"> </span><span class="kw">mcstoc</span>(rnorm, <span class="dt">mean=</span>Ltmean, <span class="dt">sd=</span>Ltsd, <span class="dt">rtrunc=</span><span class="ot">TRUE</span>, <span class="dt">linf=</span>Ltp90, <span class="dt">lsup=</span>Ltp10, <span class="dt">seed =</span> seed, <span class="dt">nsv=</span> n )
### NG Distribution
NG =<span class="st"> </span><span class="kw">mcstoc</span>(rnorm, <span class="dt">mean=</span>ngmean, <span class="dt">sd=</span>ngsd, <span class="dt">rtrunc=</span><span class="ot">TRUE</span>, <span class="dt">linf=</span>Ngp90, <span class="dt">lsup=</span>Ngp10, <span class="dt">seed =</span> seed, <span class="dt">nsv=</span> n)
<span class="kw">par</span>(<span class="dt">mfrow=</span><span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">3</span>))
<span class="co"># </span>
<span class="co"># hist(Ft, xlab="Fault throw (m)", breaks=100, col="cyan", border = NA)</span>
<span class="co"># hist(Lt, xlab="Layer Thickness (m)", breaks=100, col="red", border = NA)</span>
<span class="co"># hist(NG, xlab="NG (%)", breaks=100, col="yellow", border = NA)</span>
DENFT <-<span class="st"> </span><span class="kw">density</span>(Ft)
DENLT <-<span class="st"> </span><span class="kw">density</span>(Lt)
DENNG <-<span class="st"> </span><span class="kw">density</span>(NG)
<span class="kw">plot</span>(DENFT, <span class="dt">col=</span><span class="st">"#ff606080"</span>, <span class="dt">border=</span><span class="ot">NA</span>,<span class="dt">xlab=</span><span class="st">"Fault throw (m)"</span>,<span class="dt">main =</span> <span class="st">"Fault Throw Distribution"</span>)
<span class="kw">polygon</span>(DENFT, <span class="dt">col=</span><span class="st">"#ff606080"</span>, <span class="dt">border=</span><span class="ot">NA</span>)
<span class="kw">plot</span>(DENLT, <span class="dt">xlab=</span><span class="st">"Layer Thickness (m)"</span>,<span class="dt">main =</span> <span class="st">"Layer Thickness Distribution"</span>)
<span class="kw">polygon</span>(DENLT, <span class="dt">col=</span><span class="st">"#6060ff80"</span>, <span class="dt">border=</span><span class="ot">NA</span>)
<span class="kw">plot</span>(DENNG, <span class="dt">xlab=</span><span class="st">"NG (%)"</span>,<span class="dt">main =</span> <span class="st">"Net/Gross Distribution"</span>)
<span class="kw">polygon</span>(DENNG, <span class="dt">col=</span><span class="st">"#FFDF9F"</span>, <span class="dt">border=</span><span class="ot">NA</span>)</code></pre></div>
<p><img src="FSA_files/figure-html/Processing-1.png" style="display: block; margin: auto;" /></p>
</div>
<div id="results-and-outputs" class="section level2">
<h2>Results and Outputs</h2>
<div id="shale-gouge-ratio-claculation" class="section level3">
<h3>Shale Gouge Ratio Claculation</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> SGR =<span class="st"> </span>(((<span class="dv">100</span><span class="op">-</span>NG)<span class="op">*</span>Lt<span class="op">/</span>Ft))
### Historgam plot for SGR
<span class="kw">hist</span>(SGR, <span class="dt">xlab=</span><span class="st">"SGR (%)"</span>, <span class="dt">breaks=</span><span class="dv">100</span>, <span class="dt">col=</span><span class="st">"seagreen1"</span>)</code></pre></div>
<p><img src="FSA_files/figure-html/SGROutputs-1.png" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> ### density plot for SGR
DENSGR <-<span class="st"> </span><span class="kw">density</span>(SGR)
<span class="kw">plot</span>(DENSGR)
<span class="kw">polygon</span>(DENSGR, <span class="dt">col=</span><span class="st">"#ff606080"</span>, <span class="dt">border=</span><span class="ot">NA</span>)
<span class="kw">rug</span>(SGR, <span class="dt">side =</span> <span class="dv">3</span>)
<span class="kw">abline</span>(<span class="dt">v=</span><span class="kw">c</span>(<span class="dv">18</span>,<span class="dv">22</span>),<span class="dt">lwd =</span> <span class="dv">3</span>,<span class="dt">col =</span> <span class="kw">c</span>(<span class="st">"green"</span>,<span class="st">"red"</span>) , <span class="dt">lty =</span><span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">3</span>))</code></pre></div>
<p><img src="FSA_files/figure-html/SGROutputs-2.png" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> P<-<span class="kw">summary</span>(SGR, <span class="dt">probs =</span> <span class="kw">c</span>(<span class="fl">0.01</span>,<span class="fl">0.1</span>,<span class="fl">0.50</span>,<span class="fl">0.9</span>,<span class="fl">0.99</span>))
Pdata<-<span class="st"> </span><span class="kw">data.frame</span>(<span class="kw">unmc</span>(P))
<span class="kw">colnames</span>(Pdata)<-<span class="st"> </span><span class="kw">c</span>(<span class="st">"Mean"</span>,<span class="st">"SD"</span>,<span class="st">"1%"</span>,<span class="st">"10%"</span>,<span class="st">"50%"</span>,<span class="st">"90%"</span>,<span class="st">"99%"</span>)
<span class="kw">rownames</span>(Pdata)[<span class="dv">1</span>] <-<span class="st"> "SGR"</span>
SGRdata <-<span class="st"> </span><span class="kw">as.data.frame</span>(Pdata[<span class="dv">3</span><span class="op">:</span><span class="dv">7</span>])
knitr<span class="op">::</span><span class="kw">kable</span>(Pdata[,<span class="dv">1</span><span class="op">:</span><span class="dv">7</span>], <span class="dt">digits =</span> <span class="dv">0</span>, <span class="dt">caption =</span> <span class="st">"SGR MC Distribution "</span>,<span class="dt">booktabs =</span> <span class="ot">TRUE</span>)</code></pre></div>
<table>
<caption>SGR MC Distribution</caption>
<thead>
<tr class="header">
<th></th>
<th align="right">Mean</th>
<th align="right">SD</th>
<th align="right">1%</th>
<th align="right">10%</th>
<th align="right">50%</th>
<th align="right">90%</th>
<th align="right">99%</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>SGR</td>
<td align="right">37</td>
<td align="right">13</td>
<td align="right">21</td>
<td align="right">24</td>
<td align="right">34</td>
<td align="right">54</td>
<td align="right">82</td>
</tr>
</tbody>
</table>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">plot</span>(<span class="dt">x=</span><span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">10</span>,<span class="dv">50</span>,<span class="dv">90</span>,<span class="dv">99</span>), <span class="dt">y=</span>Pdata[<span class="dv">3</span><span class="op">:</span><span class="dv">7</span>], <span class="dt">type=</span><span class="st">"o"</span>,<span class="dt">lwd =</span> <span class="dv">3</span>,
<span class="dt">col=</span><span class="st">"blue"</span>, <span class="dt">main =</span> <span class="st">"SGR Probability Density Distribution"</span>,
<span class="dt">xlab =</span> <span class="st">"Distribution Percentages %"</span>,
<span class="dt">ylab =</span> <span class="st">"SGR Distribution"</span>)
<span class="kw">abline</span>(<span class="dt">v=</span><span class="kw">c</span>(<span class="dv">10</span>,<span class="dv">50</span>,<span class="dv">90</span>),<span class="dt">lwd =</span> <span class="dv">3</span>,<span class="dt">col =</span> <span class="kw">c</span>(<span class="st">"green"</span>,<span class="st">"blue"</span>,<span class="st">"red"</span>) , <span class="dt">lty =</span><span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>))</code></pre></div>
<p><img src="FSA_files/figure-html/SGROutputs-3.png" style="display: block; margin: auto;" /></p>
</div>
<div id="shale-smear-factor-claculation" class="section level3">
<h3>Shale Smear Factor Claculation</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> SSF =<span class="st"> </span>(Ft<span class="op">/</span>((<span class="dv">100</span><span class="op">-</span>NG)<span class="op">*</span>Lt))<span class="op">*</span><span class="dv">100</span>
### Histogram plot for SSF
<span class="kw">hist</span>(SSF, <span class="dt">xlab=</span><span class="st">"SSF (%)"</span>, <span class="dt">breaks=</span><span class="dv">100</span>, <span class="dt">col=</span><span class="st">"orange"</span>)</code></pre></div>
<p><img src="FSA_files/figure-html/SSFOutputs-1.png" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> ### density plot for SSF
DENSSF <-<span class="st"> </span><span class="kw">density</span>(SSF)
<span class="kw">plot</span>(DENSSF)
<span class="kw">polygon</span>(DENSSF, <span class="dt">col=</span><span class="st">"#ff606080"</span>, <span class="dt">border=</span><span class="ot">NA</span>)
<span class="kw">rug</span>(SSF, <span class="dt">side =</span> <span class="dv">3</span>)</code></pre></div>
<p><img src="FSA_files/figure-html/SSFOutputs-2.png" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> SSFP<-<span class="kw">summary</span>(SSF, <span class="dt">probs =</span> <span class="kw">c</span>(<span class="fl">0.01</span>,<span class="fl">0.1</span>,<span class="fl">0.50</span>,<span class="fl">0.9</span>,<span class="fl">0.99</span>))
PSSFdata<-<span class="st"> </span><span class="kw">data.frame</span>(<span class="kw">unmc</span>(SSFP), <span class="dt">drop=</span> <span class="ot">TRUE</span>)
<span class="kw">colnames</span>(PSSFdata)<-<span class="st"> </span><span class="kw">c</span>(<span class="st">"Mean"</span>,<span class="st">"SD"</span>,<span class="st">"1%"</span>,<span class="st">"10%"</span>,<span class="st">"50%"</span>,<span class="st">"90%"</span>,<span class="st">"99%"</span>)
<span class="kw">rownames</span>(PSSFdata)[<span class="dv">1</span>] <-<span class="st"> "SSF"</span>
SSFy5 =<span class="st"> </span><span class="kw">list</span>(PSSFdata[<span class="dv">3</span><span class="op">:</span><span class="dv">7</span>])
knitr<span class="op">::</span><span class="kw">kable</span>(PSSFdata[,<span class="dv">1</span><span class="op">:</span><span class="dv">7</span>], <span class="dt">digits =</span> <span class="dv">0</span>, <span class="dt">caption =</span> <span class="st">"SSF MC Distribution "</span>,<span class="dt">booktabs =</span> <span class="ot">TRUE</span>)</code></pre></div>
<table>
<caption>SSF MC Distribution</caption>
<thead>
<tr class="header">
<th></th>
<th align="right">Mean</th>
<th align="right">SD</th>
<th align="right">1%</th>
<th align="right">10%</th>
<th align="right">50%</th>
<th align="right">90%</th>
<th align="right">99%</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>SSF</td>
<td align="right">3</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">2</td>
<td align="right">3</td>
<td align="right">4</td>
<td align="right">5</td>
</tr>
</tbody>
</table>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"> <span class="kw">plot</span>(<span class="dt">x=</span><span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">10</span>,<span class="dv">50</span>,<span class="dv">90</span>,<span class="dv">99</span>), <span class="dt">y=</span>PSSFdata[<span class="dv">3</span><span class="op">:</span><span class="dv">7</span>], <span class="dt">type =</span> <span class="st">"o"</span>,<span class="dt">col=</span><span class="st">"red"</span>,<span class="dt">lwd =</span> <span class="dv">3</span>, <span class="dt">main =</span> <span class="st">"SSF Probability Density Distribution"</span>,
<span class="dt">xlab =</span> <span class="st">"Distribution Percentages %"</span>,
<span class="dt">ylab =</span> <span class="st">"SSF Distribution"</span>)
<span class="kw">abline</span>(<span class="dt">v=</span><span class="kw">c</span>(<span class="dv">10</span>,<span class="dv">50</span>,<span class="dv">90</span>),<span class="dt">lwd =</span> <span class="dv">3</span>,<span class="dt">col =</span> <span class="kw">c</span>(<span class="st">"green"</span>,<span class="st">"blue"</span>,<span class="st">"red"</span>) , <span class="dt">lty =</span><span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>))</code></pre></div>
<p><img src="FSA_files/figure-html/SSFOutputs-3.png" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="references" class="section level2">
<h2>References</h2>
<ul>
<li><a href="https://wiki.aapg.org/Shale_smear_factor" class="uri">https://wiki.aapg.org/Shale_smear_factor</a><br />
</li>
<li><a href="https://wiki.aapg.org/Quantitative_fault_seal_analysis" class="uri">https://wiki.aapg.org/Quantitative_fault_seal_analysis</a></li>
</ul>
<div id="section" class="section level44">
<p></p>
<p>Shinyapp has been created to calculate FSA Parameters automatically without the hassel of changing the code. You can just play with the essential parameters and you get all the results instantaneously.</p>
<p>Please dont hesitate to contact me over <a href="mailto:a_moslim@live.com">a_moslim@live.com</a> to share your comments.</p>
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