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| 1 | +\title{Reproducible experiment: Kirchhoff modeling} |
| 2 | + |
| 3 | +\author{Rodolfo A C Neves (Dirack)} |
| 4 | +\begin{abstract} |
| 5 | +To show how to implement Kirchoff modeling in Madagascar |
| 6 | +package. This paper is part of the current directory |
| 7 | +documentation followed by a SConstruct script |
| 8 | +to run the numerical experiment. |
| 9 | +\end{abstract} |
| 10 | + |
| 11 | +\section{Introduction} |
| 12 | + |
| 13 | +\indent In this directory we build a seismic data cube from a gaussian reflector in a linear velocity model. |
| 14 | +\footnote{This numerical experiment was originaly |
| 15 | +design by Sergey Fomel and Roman Kazinnik in |
| 16 | +the paper Non-hyperbolic common reflection surface |
| 17 | +(2013). |
| 18 | +This paper is avaliable as a reproducible paper in |
| 19 | +the \href{http://www.ahay.org}{Madagascar website}.} |
| 20 | +Velocity increases with depth with a 0.5 |
| 21 | +velocity gradient and near surface velocity |
| 22 | +$v_0=1.5Km/s$. |
| 23 | + |
| 24 | +\indent A seismic data cube means that each sample |
| 25 | +in the data space can be identifyed by it's CMP, |
| 26 | +half-offset and time coordinates. So, the seismic |
| 27 | +data can be represented by an amplitude function |
| 28 | +A(m,h,t), where m is the CMP, h the half-offset |
| 29 | +and t is the time. |
| 30 | + |
| 31 | +Kirchhoff modeling \cite[]{km}: |
| 32 | + |
| 33 | +\begin{quote} |
| 34 | +Kirchhoff modeling can be defined as the |
| 35 | +mathematical transpose of Kirchhoff migration. |
| 36 | +The resulting Kirchhoff modeling algorithm |
| 37 | +has the same low computational cost as |
| 38 | +Kirchhoff migration and, unlike expensive full |
| 39 | +acoustic or elastic wave‐equation methods, |
| 40 | +only models the events that Kirchhoff migration |
| 41 | +can image. |
| 42 | +\end{quote} |
| 43 | + |
| 44 | +\inputdir{scons} |
| 45 | +\plot{gaussianReflectorVelocityModel}{width=\textwidth}{Gaussian reflector model.} |
| 46 | + |
| 47 | +\plot{dataCube}{width=\textwidth}{Seismic data cube.} |
| 48 | + |
| 49 | +\plot{cmpGather}{width=\textwidth}{CMP gather |
| 50 | +extracted from the seismic data cube, |
| 51 | +5Km is the CMP Gather coordinate.} |
| 52 | + |
| 53 | +\bibliographystyle{seg} |
| 54 | +\bibliography{mybib} |
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