Added teaching activities

TeachingActivities/GeophoneLayout/GeophoneLayoutSeismics.tex

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+\documentclass[11pt]{article}
+
+\usepackage{url}
+\usepackage{hyperref}
+\usepackage{graphicx}
+\setlength{\parskip}{0.5cm plus4mm minus3mm}
+
+\textwidth=6.4in
+\textheight=8.5in
+\hoffset=-0.7in
+\voffset=-0.7in
+
+\setlength{\parindent}{0cm} 
+
+\newcommand{\Yfun}{Y}
+
+\hyphenation{Text-Wrangler}
+
+\title{Choice of geophone layout in a simple near-surface seismics setting}
+\date{\today}
+\author{Alain Plattner}
+
+\begin{document}
+\maketitle
+
+\section{Introduction}
+When running a near-surface seismic survey, the resulting recorded
+wave forms will consist of overlapping arrivals from air waves, direct
+waves, reflected waves, and refracted waves. Correctly identifying
+these waves and picking their onsets, in particular of the direct and
+refracted waves, is crucial for refraction and reflection seismics.
+
+The waveforms recorded by the geophones always contain
+superimpositions of the different types of seismic waves which can
+make their identification difficult.  The only parameter we can
+control is the layout of the geophones. See Fig.~\ref{seismicwaves}
+for a sketch of the geometry.
+
+In many settings we do have a basic idea of the depth of an interface
+and rough estimations for the seismic velocities of the direct
+subsurface and the underlying layer.  In this activity we use this
+information to simulate arrival times and recorded waveforms. We then
+vary the geophone spacing (assuming a fixed number of available
+geophones and the shot at the center) to obtain an ideal setting to
+identify the arrival times of specific waves.
+
+
+\begin{figure}
+  \center
+\includegraphics[width=0.7\textwidth, trim = 3cm 6cm 1.5cm
+  3.5cm,clip]{figures/NSSeismics.pdf}
+\caption{\label{seismicwaves} Air wave, direct wave, reflected wave,
+  and refracted wave in a near-surface seismics setting. The flash
+  represents the seismic source, the triangles are the geophones.}
+\end{figure}
+
+\section{Required \textsc{Matlab}/\textsc{Octave} functions}
+All the \textsc{Matlab}/\textsc{Octave} functions needed for this activity can be
+downloaded from the Seism-O GitHub repository
+
+\url{https://github.com/NSGeophysics/Seism-O}
+
+You can directly download the entire repository using Git
+(\url{https://git-scm.com/}) by running in a command window
+
+\verb#git clone https://github.com/NSGeophysics/Seism-O.git#
+
+\section{Simulation of arrival times}
+Let's assume that in this setting we have a horizontal interface at
+depth \verb#h# = 2 m with shallow seismic velocity \verb#V1# = 600 m/s
+and deeper seismic velocity \verb#V2# = 1000 m/s. Let's start with
+setting the geophone offset (distance between geophones) to
+\verb#offset# = 1 m.
+
+After you start \textsc{Matlab}/\textsc{Octave} , switch to the folder in which you
+installed the Seism-O \textsc{Matlab}/\textsc{Octave}  functions. In \textsc{Matlab}/\textsc{Octave},
+run
+
+\verb#>> [x1,t1]=showReflectedWave(V1,offset,h);#
+
+The resulting figure (Fig.~\ref{arrivalreflect}) shows the arrival
+times of the reflected wave.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.7\textwidth, trim = 1cm 7.5cm 2cm
+    6cm,clip]{figures/ArrivalReflected.pdf}
+  \caption{\label{arrivalreflect} Arrival times of the reflected
+    wave with wave velocity 600 m/s, reflector depth 2 m and geophone
+    spacing 1 m.}
+\end{figure}
+
+\section{Simulation of recorded waveforms}
+
+To show how the corresponding recorded waveforms look like, run
+
+\verb#>> figure#\\
+\verb#>> shotgather(x1,t1);#
+
+The resulting figure should look like Fig.~\ref{reflectwave}.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.7\textwidth, trim = 1cm 7.5cm 2cm
+    6cm,clip]{figures/ReflectedWave.pdf}
+  \caption{\label{reflectwave} Recorded waveforms (shotgather) of the
+    reflected wave with wave velocity 600 m/s, reflector depth 2 m and
+    geophone spacing 1 m.}
+\end{figure}
+
+\section{Superimposed waveforms}
+
+Let's see how a direct wave plotted together with a reflected wave
+would look like. To see how the picked arrival times overlap, run
+
+\verb#>> figure(1)#\\
+\verb#>> [x2,t2]=showDirectWave(V1,offset);#
+
+For geophones away from the source, the arrival times of the direct
+and the reflected wave will be close together. The identification gets
+more difficult when looking at the shot gather:
+
+\verb#>> seis1=shotgather(x1,t1);#\\
+\verb#>> seis2=shotgather(x2,t2);#\\
+\verb#>> seis=addgather(seis1,seis2);#\\
+\verb#>> figure#\\
+\verb#>> plotgather(seis)#
+
+The result should look like Fig.~\ref{directreflect}.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.7\textwidth, trim = 1cm 7.5cm 2cm
+    6cm,clip]{figures/DirectReflected.pdf}
+    \caption{\label{directreflect} Recorded waveforms (shotgather) of
+      the reflected wave and direct wave superimposed. Wave
+      velocity is 600 m/s, reflector depth is 2 m and geophone spacing
+      is 1 m.}
+\end{figure}
+
+Finally, the \textsc{Matlab}/\textsc{Octave} function \verb#showAllWaves.m#
+superimposes the waveforms of the air wave, the direct wave, the
+reflected wave, and a refracted wave:
+
+\verb#>> seis=showAllWaves(V1,offset,h,V2);#\\
+\verb#>> figure#\\
+\verb#>> plotgather(seis);#
+
+The resulting superimposed waveforms (Fig.~\ref{allwaves}) are
+difficult to discern.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.7\textwidth, trim = 1cm 7.5cm 2cm
+    6cm,clip]{figures/AllWaves.pdf}
+  \caption{\label{allwaves} Recorded waveforms (shotgather) of the air
+    wave, direct wave, reflected wave, and refracted wave
+    superimposed. Shallow wave velocity is 600 m/s, deep wave velocity
+    is 1000 m/s, reflector depth is 2 m and geophone spacing is 1
+    m. It is difficult to tell the refracted, reflected, and direct
+    waves apart. The air wave stands out as the slowest wave and can
+    at distances greater than 7 m be identified.}
+\end{figure}
+
+\section{Choosing the right geophone layout}
+
+Remember that the only parameter we can choose in a such a setting is
+the geophone layout (spacing, if we only have a fixed number of
+geophones).
+
+\textbf{Exercise:} Play with the geophone spacing and find a value
+that allows us to easily identify the refracted wave.
+
+\textbf{Exercise:} Choose a different setting, for example \verb#V1# =
+600 m/s, \verb#V2# = 2000 m/s, \verb#h# = 10 m. Find a suited geophone
+spacing value for this situation.
+
+Explore the rest of the Seism-O package. For example, it allows to
+plot common depth point gathers and attempt a (simplified) normal
+move-out correction.
+
+
+\end{document}