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\author{Isaac Newton}%%%%%%%%%%%%%%%%%%%%%%\title{Homework 4}\begin{abstract}In this lab, we will use zero-offset andshot-record migration to create images in complex velocity media.%Every seismic experiment (i.e. shot) can be used to createan image. Every shot can be decomposed in frequency components. How many shots do we need to create a good image?How many frequencies do we need to create a good image?%How do we build a velocity model?What is the impact of the velocity model on the migrated image?%These and other questions are addressed in this lab.\end{abstract}\definecolor{frame}{rgb}{0.905,0.905,1.0}\lstset{language=Python,backgroundcolor=\color{frame},showstringspaces=false}\section{Introduction}Start by running\begin{verbatim}> cd ~/geo391> svn update\end{verbatim}% ------------------------------------------------------------\section{Sigsbee 2A migration}% ------------------------------------------------------------In this exercise, you will modify parameters controlling shot-record wavefield extrapolation migration.Everything is set-up for migration. Your task is toidentify relevant parameters, change them to generate new figures, include them in this document and discussthe importance/effect of your various changes.\inputdir{sigsbee}\plot{slo}{width=6.0in}{Sigsbee 2A velocity}\begin{enumerate}%% \item Change directory \begin{verbatim}> cd ~/geo391/hw4/sigsbee\end{verbatim} \item Run\begin{verbatim}> scons view\end{verbatim}to generate figures and display them on your screen. %%\itemOpen the \texttt{SConstruct} file and find the dictionary named \texttt{par}.Parameters \texttt{ns}, \texttt{js}, and\texttt{fs} control sampling on the shot axis,and parameters \texttt{nw}, \texttt{jw}, and \texttt{fw} control sampling on the frequency axis (``n''=number, ``j''=jump, ``f''=first).%%\itemLocate the loop over migration configuration.A local dictionary named \texttt{loc} allows you to make local changes to some parameters without affectingthe others.Two examples are included in this document(Figures~\ref{fig:img0} and \ref{fig:img1}).You will include and discuss more figures.\plot{img0}{width=6.0in}{Monochromatic image for $1$ shot ($ns=1$, $fs=250$, $nw=1$, $ow=2$).}\plot{img1}{width=6.0in}{ Monochromatic image for $3$ shots ($ns=3$, $fs=50$, $js=150$, $nw=1$, $ow=5$).}%%\itemKeep the number of frequencies fixed (e.g. $nw=1$, $ow=2$),and modify the number of shots used in migration(change $ns$, $js$, $os$).How many shots do you need in order to see the main features of the structure?Can you identify the structure?Include a new figure and discuss your observations.%% % \plot ... %%%%\itemKeep the number of shots fixed (e.g. $ns=1$) and change the migration frequency (change $ow$).The migrated images will change accordingly andthe subsurface illumination will change.Modify the location of the shot (change $fs$)and observe illumination patterns, especially aroundthe salt body.How does illumination change with frequency?Include figures for images at different frequenciesand discuss your observations.%% % \plot ... %%%%\itemKeep the number of shots fixed ($ns=1$) and change the number of frequencies (change $nw$, $jw$, $ow$).How does the image change with increased frequency band?Include figures for shots at different locations in the image and discuss your observations.%% % \plot ... %%%%\itemIncrease the number of shots (change $ns$, $js$, $os$)and frequencies (change $nw$, $jw$, $ow$).until you are satisfied with the quality of the migrated image.How did you decide when to stop?What parameters did you use?Include one or more new figures and discuss your observations and choice of parameters.%% % \plot ... %%%%\itemUsing your optimal choice of parameters for shotsand frequencies from the preceding question, re-migrate the Sigsbee 2A data using a smooth velocity model.Generate new migration rules,experiment with different smoothing parameters and discuss how accurate does the velocity model need to bein order to obtain a good image.Where is the impact of the velocity model accuracy largest?How did you decide how much to smooth? Why?Include one or more new figures and discuss your observations and choice of parameters.%% % \plot ... %%%%\itemThis is a free-form question.Experiment with migration parameters on your own.Include and discuss another migration configurationof your choice. Discuss your new figure and observations.%% % \plot ... %%%% \item After you are done, run\begin{verbatim}> scons lock> scons -c\end{verbatim} \end{enumerate}% ------------------------------------------------------------\section{Blake Outer Ridge migration}% ------------------------------------------------------------In this exercise, you will experiment with zero-offset migration and simple velocity analysis.The \texttt{SConstruct} file is configured with all the rulesused to create a velocity model from semblance scans anddepth-migrate the data.\inputdir{blake}\plot{noff}{width=6.0in}{Blake Outer Ridge near-offset data.}\plot{vscan}{width=6.0in}{Velocity scan.}\plot{picks}{width=6.0in}{Stacking velocity.}\plot{velz}{width=6.0in}{Blake Outer Ridge interval velocity model.}\plot{velz}{width=6.0in}{Blake Outer Ridge interval velocity model.}\plot{img}{width=6.0in}{Blake Outer Ridge migration of near-offset data.}\begin{enumerate}%% \item Change directory \begin{verbatim}> cd ~/geo391/hw4/blake\end{verbatim} \item Run\begin{verbatim}> scons view\end{verbatim}to generate figures and display them on your screen. %%\itemReview all rules in the \texttt{SConstruct} used to generateFigures~\ref{fig:velz} and \ref{fig:img}.\begin{itemize}\item Identify the rules for velocity scans.\item Identify the rules for conversion from stackingto interval velocity.\item Identify the rules for conversion of interval velocityfrom time to depth.\item Identify the rules for datuming and depth migration.\end{itemize}%%\itemAdd rules to perform another migration with constant velocity.Create a new Result and compare it with the imageobtained by migration with a laterally variable velocity.How do the two images compare?Include one or more new figures and discuss your observations.%% % \plot ... %%%%\itemIn the original example, the velocity analysisis performed in the CMP-domain every $10^{th}$ gather.Add rules to recompute velocity scans at every CMP(also adjust the "rect1= rect2=" parameters for optimal smoothing). Create another figure with the image obtained usingyour new velocity model and compare it with the imageproduced by the original \texttt{SConstruct}.How do the two images compare?Include one or more new figures and discuss your observations.%% % \plot ... %%%% \item After you are done, run\begin{verbatim}> scons lock> scons -c\end{verbatim} \end{enumerate}% ------------------------------------------------------------\section{Wrap-up}% ------------------------------------------------------------\begin{enumerate} %%\item Edit the file\verb#~/geo391/hw4/paper.tex# in your favorite editor and change the first line to have your name. Run\begin{verbatim}> scons pdf\end{verbatim}and submit your result (file \texttt{paper.pdf}) on paper or by e-mail.This homework is due in class on November $29^{th}$, $2005$.\end{enumerate}
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