\lefthead{Guerra and Biondi}
\righthead{  }
\footer{SEP--13 }
\title{   }
\author{Claudio Guerra and Biondo Biondi}

\maketitle

\begin{abstract}
Analyze the asymptotic behavior of the rotation integrals
\end{abstract}

\section{Analysis}

This section describes the rotation applied to the prestack image, $H(z,h,x)$, computed 
by means of a wave-equation migration algorithm, prior to modeling areal data using the 
prestack exploding reflector method. This rotation necessary to obtain kinematically correct 
areal shot migration results using the modeled areal data.
\par 
We start by analyzing the behavior of the Radon integral which 
decomposes the prestack image, $H(z,h,x)$, into a prestack image, $A(z,\gamma,\alpha,x)$, where
 $\gamma$ and $\alpha$ are the apparent aperture angle and the apparent geological dip 
angle, respectively. We call those angles apparent because no assumption of the correctness 
of the velocity model is considered to produce the initial prestack image.
\par
\begin{equation}
A(z,\gamma,\alpha,x) = \int_{\Gamma} \int_{\Alpha} H(z,h,x)] dh dx' \arrowvert_{z = \zeta(\gamma,\alpha,h,x') } ,
\end{equation}
where, $z$ is depth, $h$ is the subsurface offset, and $\zeta(\gamma,\alpha,h,x')$ is the summation path given by 
\begin{equation}
\zeta(\gamma,\alpha,h,x') = z + h \tan \gamma + (x - x') \tan \beta.
\label{eq:slant}

\section{Acknowledgements}

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