\def\figdir{Fig}
\lefthead{Guerra}
\righthead{Term paper -- Fall 2008}
\footer{Fall 2008}
\title{Image-space wave-equation tomography with image-space phase-encoded wavefields: Field data example}
\author{Claudio Guerra}

\maketitle

\begin{abstract}
In SEP, the 3D Elf-North Sea dataset has been used in projects involving the definition of depth-migration velocity. Here, I show the first 2D results of field data using image-space phase-encoded wavefields as input to the wave-equation tomography in the image space. In addition, the common-azimuth 3D migration with the initial velocity model has been started on CEES computers (cees-opteron). 
\end{abstract}

\section{Introduction}
I present field data results of using image-space phase-encoded wavefields (ISPEW) in the image-space wave-equation tomography (ISWET). The field dataset is taken from the in-line 2500 of the 3D-Elf North-Sea, which has been submitted to azimuth-moveout correction (AMO).
\par
The goal is to evaluate the issues of using ISPEW on field data to define the velocity model to support the oncoming application to the entire 3D data.
\par
The final velocity model is accurate.
\section{2{D}-Processing flow}
The 3D Elf-North Sea dataset was submitted to AMO to be subsequently migrated with common-azimuth migration. Therefore, its dimensions are given in number of in-lines, cross-lines, source-receiver offsets and frequency. It is composed of 216 in-lines, 672 cross-lines, 72 offsets with interval of 50 m and 360 frequencies. The in-line and cross-line intervals are 20 m. I selected in-line 2500 from the 3D dataset; the seismic data was sorted back to the shot domain and it had its offsets and shot interval interpolated to 25 m. A split-spread geometry was generated using on reciprocity. Eight-one plane-wave areal shots were computed. They are used in the initial and intermediate migrations, on which results horizons were interpreted. The top of the chalk layer was interpreted on a 2D section migrated with the original velocity model. This interface is the upper-limit of the region where the original velocity model was edited to generate the initial velocity model. Above it, the original velocity is unchanged. The initial velocity model(\ref~{fig:vinit}) was obtained by smoothing and scaling the vertical slice at in-line 2500 of the original 3D velocity model computed with ray-tracing tomography. The interval slowness ratio between the original and initial velocity models ranges form 0.1 to 0.3 (Figure \ref~{ref:vratio}).
\activeplot{vinit}{width=3.0in}{ER}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}
\activeplot{vratio}{width=3.0in}{ER}{Edited BP benchmark velocity model -- the shallow low-velocity anomalies occur were substituted by the background velocity.}
\subsection {Velocity update}
Initially, a quasi-Newton optimization scheme with the L-BFGS algorithm \cite[]{nocedal} was used to perform the non-linear update of the velocity model. Differently from the example with synthetic data in which it performed satisfactorily \cite[]{guerra139}, the algorithm was not able to provide a useful velocity update. Even though the objective function decreased during the initial iterations, it gradually moved back to the value computed with the initial model during the subsequent iterations. This behavior is not completely understood and deserves further analysis. Therefore, a simple bounded steepest-descent algorithm with parabolic line-search was coded for the velocity optimization.
\par
The entire velocity update can be summarized according to the flowchart of Figure \ref{fig:flow}. The gray box corresponds to iterations of modeling image-space phase-encoded wavefields and velocity model update. Three iterations were performed, corresponding to the velocity update of the chalk layer and two additional layers below. With a satisfactory velocity model for the sediment portion, the right flank of the salt body and its top were interpreted and used as reference to generate a new velocity model with salt flooding. After plane-wave migration with this new velocity model, salt overhang on the left and its base were picked and used to finally delineate the salt body (Figure \ref{fig:vfinal}). This is considered the final velocity model because due to poor angular coverage in the deeper levels velocity updates are not reliable.
\activeplot{flow}{width=3.0in}{NR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}
For the velocity update of the chalk layer, a reflector close to its base was interpreted on an initial prestack image computed with the initial velocity model (Figure~\ref{fig:binit}). The choice of this reflector was motivated by its stronger signal-to-noise ratio and better continuity than the base of chalk itself. The updated velocity was subsequently extrapolated down to the base of chalk. 
\activeplot{binit}{width=3.0in}{CR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}

\section{Results}
Here, I will compare the prestack images obtained with the initial and final velocity models. Also, I compare the final image with the image computed with the vertical slice taken from the velocity cube estimated with 3D horizon-based ray-tracing tomography. This last comparison may not be completely fair, but can give a sense of how close the final velocity computed with wave-equation tomography in the image space using ISPEW is to industry standards.
\par
\activeplot{borig}{width=3.0in}{CR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}
\activeplot{bfinal}{width=3.0in}{CR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}
\activeplot{fanginit}{width=3.0in}{CR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}
\activeplot{fangorig}{width=3.0in}{CR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}
\activeplot{fangfinal}{width=3.0in}{CR}{BP benchmark velocity model -- Selected portion where shallow low-velocity anomalies occur.}

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