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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.55\textwidth]{figures/finite-wells.png} | ||
\end{center} | ||
\caption{ | ||
Currents in a DC resistivity experiment with the positive electrode connected to the top of the casing. | ||
(a) Downward-going currents in the casing for different lengths of well. The x-axis is depth normalized by the length of the casing. | ||
Annotations are the short and long well approximations from \cite{Kaufman1993}. For the long-well approximation, we use $L_c = 8000m$, the length of the longest well included in the simulation. | ||
(b) Leak-off currents from the well (left axis) and charges on the outer casing wall (right axis). | ||
Figure follows \cite{Heagy2019a}. | ||
} | ||
\label{fig:finite-wells} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.8\textwidth]{figures/impact-of-wells-data.png} | ||
\end{center} | ||
\caption{ | ||
Simulated electric field measurements for the DC resistivity experiment shown in Figure \ref{fig:impact-of-wells}. | ||
The plots show the data with (solid blue) and without (dashed blue) the target. The orange line is the difference between the two; this is the signal due to the target. | ||
Without the casing, the response due to the target is below a $10^{-7}$ V/m noise floor, whereas with the casing, the signal is detectable. | ||
} | ||
\label{fig:impact-of-wells-data} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.9\textwidth]{figures/impact-of-wells-em-data-resistive.png} | ||
\end{center} | ||
\caption{ | ||
Amplitude of the radial electric field data using the same model and survey geometry as Figure \ref{fig:impact-of-wells-em-data} but with a resistive target (1000 $\Omega$ m). | ||
} | ||
\label{fig:impact-of-wells-em-data-resistive} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.9\textwidth]{figures/impact-of-wells-em-data.png} | ||
\end{center} | ||
\caption{ | ||
Amplitude of radial electric field data in a time-domain EM experiment with a conductive target (10 $\Omega$ m) as shown in Figure \ref{fig:impact-of-wells}. | ||
The data are collected along a line perpendicular to the transmitter wire, and the color of each line indicates the distance from the well where the timeseries is collected. | ||
The panels on the left show (a) the simulation for a conductive well which has a magnetic permeability equal to that of free space ($\mu_0$) and on the right, (b) we consider a well that has a permeability of $100 \mu_0$. | ||
The top plots show the simulated data for the scenario with (solid) and without (dashed) the conductive target. The thin plots on the left zoom in to the earliest times to show the DC response. | ||
The center plots show the difference between with and without the target. For the earliest times, a circle is used to denote where the amplitude difference is positive (the amplitude with the target is larger than without), and squares are used to show when the difference is negative. The bottom show that difference as a percentage of the results without the target. | ||
} | ||
\label{fig:impact-of-wells-em-data} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=1\textwidth]{figures/impact-of-wells.png} | ||
\end{center} | ||
\caption{ | ||
Example to illustrate the impact of wells on the ability to detect targets at depth. The image on the left shows the model of a target in a half-space with a steel-cased well. The image in the center shows current density if no casing were present and the image on the right shows the currents with the conductive casing present. The arrows indicate the direction of current flow and the color is the amplitude of the current density. | ||
} | ||
\label{fig:impact-of-wells} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.9\textwidth]{figures/kaufman-dc.png} | ||
\end{center} | ||
\caption{ | ||
DC resistivity experiment where a point source is positioned inside of a long steel-cased well $5\times10^6$ S/m in a $100$ $\Omega$m wholespace. (a) Conductivity model with positive electrode location (red plus); (b) current density; (c) charge density, note that the colorbar has been saturated; (d) electric fields. Figure follows \cite{Heagy2019a} | ||
} | ||
\label{fig:kaufman-dc} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=1\textwidth]{figures/tdem-currents-cross-section-target.png} | ||
\end{center} | ||
\caption{ | ||
(a) Current density for a conductive target (10 $\Omega$m) in a $100 \Omega$m half-space with a purely conductive casing. | ||
(b) Anomalous current density due to the conductive target (simulation with casing and target minus the simulation of casing in a halfspace). | ||
(c) Current density for a resistive target (1000 $\Omega$m). | ||
(d) Anomalous current density due to the resistive target. | ||
} | ||
\label{fig:tdem-currents-cross-section-target} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.8\textwidth]{figures/tdem-currents-cross-section.png} | ||
\end{center} | ||
\caption{ | ||
Current density for a grounded-source time-domain EM experiment over a $100 \Omega$m half-space (left) and a half-space that includes a 1km steel-cased well (right). The positive electrode is at x=0 and the return electrode is in this cross-section at x=1000m. A step-off waveform is used. | ||
} | ||
\label{fig:tdem-currents-cross-section} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=1\textwidth]{figures/tdem-currents-depth-slice-target.png} | ||
\end{center} | ||
\caption{ | ||
Depth slices of the current density immediately below the surface ($z=-2.5$m) corresponding to the scenarios shown in Figure \ref{fig:tdem-currents-cross-section}: (a) current density for a conductive target in a halfspace with a conductive casing, (b) anomalous current density due to the conductive target, (c) current density for a resistive target with casing, and (d) anomalous current density due to the resistive target. The white dashed line indicates the survey line corresponsing to the electric field data shown in Figures \ref{fig:impact-of-wells-em-data} and \ref{fig:impact-of-wells-em-data-resistive}. | ||
} | ||
\label{fig:tdem-currents-depth-slice-target} | ||
\end{figure} |
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\begin{figure}[!htb] | ||
\begin{center} | ||
\includegraphics[width=0.8\textwidth]{figures/tdem-currents-depth-slice.png} | ||
\end{center} | ||
\caption{ | ||
Depth slice at z=-10m showing the currents at t=0.1ms for the half-space (left), casing (center) and difference due to the casing (right). | ||
} | ||
\label{fig:tdem-currents-depth-slice} | ||
\end{figure} |
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