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\chapter{Depth imaging: Valhall passive seismic}\label{chapter:DepthVal}
\section{Summary}
Need one.
\section{Introduction}
The subsea array of OBC deployed geophones at the Valhall reservoir in
the North Sea was installed in 2004 to produce a time series of subsurface
images for production monitoring.  To date, there have been numerous
towed marine surveys, multi-component OBC surveys, and extensive well
log analysis.  This body of work results in an accurate subsurface
velocity model that was donated by BP along with the passive seismic
data.  To evaluate the results of my work with the passive data, BP
also provided an image produced with the same velocity model.  The
imaging was accomplished using a Split-step Fourier Plus Interpolation
(SSF-PI) shot profile depth migration algorithm that is very similar
to my own implimentation.  The active surveys performed to target
fine-scale reservoir changes over time use more than an order of
magnitude more shot locations than the 2500 receivers in the 
array.  To more accurately represent the best possible results I can
achieve with purely passive data, the data from the active survey was
subsampled along the shot axis to provide an analogous volume before
migration.  Synthesizing shot gathers from transmission wavefields
produces a volume of data with the assumption that an impulsive
virtual source for each gather is located at the receiver location
used as a master trace for corrleation.  Therefore the virstual source
axis and the receiver axis are sampled identically.  The active data
used to generate the control image for my experiments only used shot
gathers collected from source locations directly over a receiver
location. 
\par
Figure~\ref{fig:Vactive} shows two cuts through the image provided by
BP produced with the active data.  The near surface reflectors have
very little structure.  The oil-filled chalk reservoir is below 2500~m
and spans much of the image domain.  The oil has a high gas-oil ratio
which has lead to the accumulation of low-saturation gas in the 
central sedimentary column above the reservoir.  This low-velocity
zone above the reservoir leads to imaging problems that can be
partially addressed with converted-wave seismic experiments, which was
part of the justification for installing the OBC array.  I have used
only the hydrophone component of the array of sensors on the sea
bottom for this thesis.  This is mostly due to the fact that the
matrix rotations required to seperate the energy components are very
difficult without any knowledge of the seismic source. 
\activeplot{Vactive}{width=\textwidth}{NR}{Control image produced with active
  seismic data using only shots locations directly above a receiver
  location.}
\par
Figure~\ref{fig:random} shows two further control images produced to
test the validity of images produced with the passive data.  The left
image was produced by migrating data replaced entirely with random
noise traces.  Notice the receiver pattern visible on the depth slices
in the figure.  The right image was produced by migrating real passive 
data with random noise (scaled between $\pm 1$~km) added to the header
coordinates of the receiver locations.  Neither image shows any
structure.  Therefore, I assume that the events in the various images
presented below using volumes of real passive data are not simple
artifacts of the processing algorithm (depth migration).  
\activeplot{random}{width=\textwidth}{NR}{Control images produced with random
  noise as data (left) and real passive data with random receiver
  locations (right).}

\section{Images}
\section{Conclusion}

\clearpage

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