\chapter{Depth imaging Valhall passive data}\label{chapter:DepthVal}
\section{Summary}
BP made available 43~hours of passive data from the Valhall Life of Field
Seismic array of 2300 four component receiver stations over the
reservoir in the Norwegian North Sea
from February 2004 and January 2005.  The quality and quantity
of receivers associated with the acquisition, and the extent and
uniqueness of processing algorithms I have applied to the data
represent an industry first in the study of the passive seismic
experiment.  The images in this chapter show that depth migration 
of passive seismic data can image the subsurface structure at the
reservoir scale.  The images are not as high quality as those produced
with active surface seismic experiments, but continuous events are
imaged with the passive data that correspond directly to events in the
active data image.  Using only unidentified ambient seismic energy,
reflectors at 2~km depth are successfully imaged by
direct migration of as little as 100~minutes of passive data.

\section{Introduction}
The main hindrance to the development of passive seismology since
the original conjecture presented in \longcite{GEO33-02-02640269} has
been the availability of quality data sets.  \longcite{Cole.sepphd.86}
presented work with a 13x13 station array in the foothills behind
Stanford University.  This effort did not manage to image subsurface
structure due, I believe, to short time records, too few receiver
stations, and a poor location for the experiment.  Since then, large
dense arrays have not been deployed to test the practicality of the
theory.  \longcite{artman:SI177} showed marginally convincing results
with a 2x2.25~m, 8x9 geophone array on low attenuation beach sand.  Once
again, too few receivers and a small amount of data lead to
questionable results.  That experiment was also marginalized by
imperfect planning.  \longcite{draganov:590} showed positive results
synthesizing shot gathers with 17 traces in a linear array on land.  The 
correlations show two likely reflections in a low signal to noise regime.  
\par
Figure~\ref{fig:areamap} is a map provided by the Norwegian Oil 
Directorate which shows the production infrastructure between the coasts 
of England and Norway with the many developments in the region.  It is 
630 km from the Southern tip of the Norway shown and the city of Teeside 
in England.  The Valhall development is roughly in the center of the line
connecting those two geographic points.  BP, with partners Hess,
Shell, and Total, has donated approximately 43 hours of continuous
passive seismic records from the permanent sensor installation above
the Valhall reservoir, which is located in the Norwegian controlled
water of the North Sea.  
\sideplot{areamap}{width=3.2in,height=3.2in}{English, Norwegian, and
  Danish coasts surrounding the North Sea oil development area.
  The Valhall reservoir is in the South-central area of the map and
  only 20 km from English-controlled waters to the West, and Danish
  waters to the South.}
\par
Passive recordings were made available from 29 hours February 15,
2004, and 14 hours January 19, 2005.  Of the former, some 7 hours was
lost due to a failed disk-drive.  The most likely teleseismic
arrival recordable at the array, as determined by query of the
National Earthquake Information Center event
catalog\footnote{http://earthquake.usgs.gov/regional/neic/}, arrived
approximately 5 hours after the last records donated by BP.  The data
are sampled at 0.004~ms, and written as contiguous files between
12-20~s long.  Chapter~\ref{chapter:TimeShot} presents the analysis of
the raw data and synthesized shot gathers generated by correlating
each trace with every other trace in the array.  
\par
The subsea array of ocean bottom cable (OBC) seismic sensors,
Figure~\ref{fig:maps}, at Valhall was installed in 2003 to 
facilitate time-lapse imaging of the subsurface for production 
monitoring.  There are 13 lines of OBC 4-component (4C) sensors 
in the array.  Of the 2300 4C stations, this work uses the hydrophone
measurement from each location.  This is mostly due to the fact that 
is currently unknown how to separate (with matrix rotations) the 
energy components on the arbitrarily orientated 3C geophones without
any knowledge of the seismic source.  The 9,200 sensors are permanently
installed 1~m below the sea floor, in roughly 70~m of water.  The
array forms a roughly 4x11~km rectangle.  Nominal inline spacing of
receiver stations is 50~m, while the cross-line separation is
300~m. There are five surface structures (roughly over the center of
the reservoir), and two wellhead platforms at the North and South ends
of the NW-SE elongate elliptical reservoir (both roughly 6~km from the
central platforms).  The main fluid export pipeline runs NNW to the
Ekofisk reservoir, about 30~km distant. 
\sideplot{maps}{width=3.2in}{Valhall receiver array in
  North-East UTM coordinates and rotated field coordinates.  Coordinates
  $x,y$ are inline and crossline coordinates used in the images
  below.}
\par
Approximately half-way down the North axis of Figure~\ref{fig:maps},
the cables on the Western side of the array are truncated.  This is
where the production facilities are located to which the instruments
are telemetered.  Also noticeable is the deviation of the ends of
cables on the North side of lines 5-7 (E=1000~m) to the NNW.  This is
the corridor for the export lines to Ekofisk.  Production facilities are 
continuously manned and operated, to include: Over 150 total well-bores
into the reservoir section, current production of approximately
80,000~b/d oil and gas from 43 wells, water injection through (at
least) 3 wells, generation of almost 80 MW of electric power with gas
turbines, flow through the export lines, and the continual presence of
multiple modes of transportation\footnote{www.npd.no/engelsk/}.  Valhall 
is located in a heavily developed area, within kilometers of
developments in the English and Norwegian controlled waters and is
about half-way between the two countries.  Also important to the chalk
oil trend of this part of the North Sea is the rate of subsidence
associated with pressure withdrawal during production.  In its first 15
years of production (to 1997), the sea-floor subsided 3.5~m at the
crest of the reservoir structure \cite{subside}. 
\par
To date, there have been numerous towed marine surveys,
multi-component OBC surveys, and extensive well log analysis of the
reservoir.  That
extensive body of work has generated 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 active surface seismic data using 
the same velocity model.  BP's image was generated with a shot profile 
depth migration algorithm that is very similar
to my own implementation.  
\par
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 correlation.  Therefore the virtual source axis and the
receiver axis are identically sampled.  The active surveys performed
to target fine-scale reservoir changes over time use more than an
order of magnitude more shot locations than the 2300 receivers in the
array.  To more accurately represent the best possible results I can
achieve with purely passive data, the data from an active survey were
subsampled before migration along the shot axis to provide a volume
analogous to synthesized shot gathers from passive data.  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.  Note the migration diffraction noise on the
crossline panel due to the large source and receiver spacing in that
direction.  The oil-filled chalk reservoir is below 2300~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.  
\plot{Vactive}{width=\textwidth}{Control image produced with active
  seismic data using only shots locations directly above a receiver
  location.}
\par
Figure~\ref{fig:random} shows two control images produced to
test the validity of images produced with the passive data.  Both
images were produced with the direct migration strategy.  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.  The appearance of coherent 
structure in either image would indicate that the convolution of
randomness with the velocity model during migration could lead to
believable events.  Neither image indicates that the migration
algorithm itself produces artifacts that mimic Earth 
structure.  Therefore, I assume that the events in the various images
presented below using volumes of real passive data are not simply
artifacts of the processing algorithm (depth migration).  However, 
the details in the shallow section of Figure~\ref{fig:random}\pan{a} 
require more analysis.  
\plot{random}{width=\textwidth}{Control images produced with: a) random
  noise as data, b) 100~minutes of passive field data with random receiver
  locations.}
\par
Figure~\ref{fig:rz} 
is a zoomed image of the result created with random noise 
traces showing roughly flat, jittery events.  The events are present
at shallow depths before energy from the individual traces has
propagated across the null traces between OBC lines.  Below 550~m
these artifacts disappear.  The events on the crossline section are
expanding wavefronts beneath the receiver locations.  The moveout in
the crossline direction is the result of the sparse crossline sampling
leading to insufficient interference to form coherent layers or cancel
completely.  The image produced with active data, Figure~\ref{fig:Vactive},
has similar character in the crossline direction for the flat
shallow events.  What differentiates the flat events in the shallow
section of the active data image is the depth alignment of the bottom
of the bowl-shapes on the crossline panel.  If more traces had been
recorded between the lines, the bowl shapes would sum to flat events
through destructive interference.  The image generated with the random
noise traces does not share this character across the $y-$axis.  Therefore,
shallow events in the images presented below must be
analyzed carefully for depth alignment across the cross-line dimension
of the image to avoid over interpreting the results produced with
passive data. 

\sideplot{rz}{width=3in}{Shallow section of image produced with random
noise traces (Figure~\ref{fig:random}\pan{a}).  Flat events on inline
sections are produced by the processing algorithm.  Coherent events 
are absent below 500~m.}
\section{Depth imaging results}
Following the theory from \longcite{kees04}, the principal assumption behind
processing passively recorded seismic records to produce results equivalent
to those produced with the conventional active seismic experiment
is that individual transmission wavefields should be processed before summing 
the results.  Because windowing individual arrivals from the +36 hours
of passive data is impractical (because of the large volume and the
lack of identifiable events) it is impossible to identify and process
individual transmission wavefields when only a single event is active.  I 
make the assumption that processing data in 12~s sections is a
reasonable approximation to the requirement, which corresponds
to the approach adopted to synthesize shot gathers presented
in Chapter~\ref{chapter:TimeShot}.  Thus images, $i$, were produced by 
the migration strategy
\begin{equation}\label{image}
i_z({\bf x})= \sum_\xi E^+ T_{z-1}({\bf x},\omega,\xi) \;
                       [E^- T_{z-1}({\bf x},\omega,\xi)]^*
\end{equation}
where $\xi$ is the set of sequential 12~s windows of data and
$E^\pm$ are the mixed domain SSF-PI extrapolators used in the
migration code.  The development of direct migration and examples with
synthetic data are presented in Chapter~\ref{chapter:DepthSyn}. I
also migrated the synthesized shot gathers presented in
Chapter~\ref{chapter:TimeShot} with the conventional shot 
profile migration algorithm.  Two preprocessing steps
were applied to all data before migration.  Spectral whitening
was performed to balance the frequency content of the traces by
\begin{equation}\label{white}
\tilde{T}({\bf x},\omega,\xi)=\frac{T({\bf x},\omega,\xi)}
{T({\bf x},\omega,\xi)\;T^*({\bf x},\omega,\xi)}\;.
\end{equation}
Frequencies between 8-30~Hz were used for migration, with a cosine
taper applied at the cutoff frequencies.  In the frequency-wavenumber
domain, I applied a tapered mute to remove energy slower than
1500~m/s.
\par
Amplitude differences between images produced with passive data and
active data should be disregarded as this work is concerned only with
structural imaging.  Amplitude differences can be attributed to two
causes.  First, subsurface sources are weak and variable compared to
controlled active sources. Second, energy from active experiments need
only make two-way travel-paths from the surface to reflectors whereas
energy from subsurface sources needs to make three trips: first to the
surface then a two-way path.  The extra travel length for the subsurface
sources within an attenuating medium will, at best, diminish the
amplitudes of events, and worse, result in energy not returning to the
geophone array to be recorded again after investigating the subsurface. 
\par
Figure~\ref{fig:first200} is a comparison between the active data image
(\pan{a},\pan{c}) and the best image produced by direct migration.  Only 
100 minutes of passive data was used to generate panels \pan{b}, and
\pan{d}.  The two rows show different sections from the 
3D image volumes.  500 consecutive 12~s windows of data were independently 
migrated and summed.  The direct migration compares favorably with the
active image.  The general character of the passive result represents
well the general features within the active image: Flat layers at
shallow depths, and an anticline structure after $z=1175$~m.  In 
panels \pan{a} and \pan{b} there is a general correspondence in the
representation of the anticline on the depth slice.  The
inline-crossline location selected for panels \pan{c},\pan{d} is away
from the anticline in panels \pan{a},\pan{b}.  Again, the passive
result conforms to the structure imaged with active surface seismic
data.  Several key features are indicated by the ovals superimposed on
the panels.  The images and ovals in the left and right columns are
identically sized and placed.
\plot{first200}{width=\textwidth}{a,c) Image produced with decimated
  (along the shot axis) active data provided by BP.  b,d) Image produced
  by direct migration of 100~minutes of passive data.} 
\par
The ovals in Figures~\ref{fig:first200}\pan{a},\pan{b} are centered
around a reflector on the cross-line axis around $z=1750$~m.  The
event dips down and to the right across the $y$-axis with continuity in
the passive image, \pan{b}, similar to panel \pan{a}.  The event in the passive
image is a little lower frequency, but this image represents the first
successful imaging of subsurface structure with passive seismic data.  The
flat events across the $x$-axis of the passive images are obvious and
continuous.  However, without continuity across the $y$-axis, they can
not be positively interpreted as real subsurface structure.  The ovals
in panels \pan{c} and \pan{d} highlight continuity of flat events at
$z=525$~m and $z=1600$~m.  A third well imaged event is also visible
just above the upper ovals in panels \pan{c} and \pan{d}.  
\par
Figure~\ref{fig:shal200} is a zoomed in view of the shallow section of
Figure~\ref{fig:first200}\pan{b} compared to the image produced with
random noise traces shown in Figure~\ref{fig:random}\pan{a}.  After
approximately $z=250$~m, the shallow events in \pan{a} are
sufficiently different from the repeated flat events produced by
migrating random noise, \pan{b}, that I believe they are real
subsurface reflections rather than artifacts associated with the
processing algorithm.  The first clear reflector in panel \pan{a}
is at $z=260$~m.   Clear continuous events in panel \pan{a} are seen
across both depth sections, with particularly good continuity across
the $y$-axis at depths $z=260,360,550$~m.  These events are not seen in
panel \pan{b}.  The random noise traces in panel \pan{b} were filtered
to match the frequency content of the passive data.  The control image
shows mono-frequency repetitions of the flat artifacts.  These
repeating events are mostly destroyed after depth $z=500$~m, with a last
faint event at about $z=660$~m.

\plot{shal200}{width=\textwidth}{a) Shallow section of image
  produced with random noise for data.  b) Shallow section of image
  produced with 100~minutes of passive data,
  Figure~\ref{fig:first200}\pan{b}.}
\par
Figure~\ref{fig:zoom1} shows two more comparisons between the images
produced with active seismic data, \pan{a}, and transmission
wavefields, \pan{b}.  The sections shown in \pan{b} are from the same
image volume used in the previous figures.  The highest two ovals
highlight events on the $y$-axis that dip down and 
to the right.  The two ovals on the front frames of the panels,
$x$-axis, highlight the inflection points on either side of the
anticlynal structure imaged by both data sets.  The lowest ovals on
the $y$-axis of the images show events dipping down and to the left
with both data inputs, though at this depth the crossline section of
the passive image does not show very good continuity.
\plot{zoom1}{width=\textwidth}{a) Image produced with decimated
  (along the shot axis) active data provided by BP.  b) Image produced
  by direct migration of 100~minutes of passive data.}
\par
Figure~\ref{fig:shortlong} is a comparison of images produced with
9~hours of passive data (processed 12~s at a time), to the
previous results, produced with 100~minutes of passive data.  The 100
minutes of data are contained within the 9~hour data volume.  Panels
\pan{a}, and \pan{c}, are from the image volume produced with less 
data.  The low frequency noise on the left of the left column of
images is diminished in panels \pan{b} and \pan{d}, and the shallow
events look better imaged.  The inline sections in the left column are
less pleasing than the results produced with 9~hours of data to the
right.  The events within and above the shallow oval in \pan{a} are
comparable to those in panel \pan{b}.  However, processing more data
has not improved the quality of the results everywhere. The event
within the lowest oval in panel \pan{b} looks more continuous and
interpretable than its counterpart in panel \pan{c}.  
\plot{shortlong}{width=\textwidth}{a,c) Images produced by direct
  migration of 100~minutes of passive data.  b,d) Images produced by
  direct migration of 9~hours of passive data.}
\par
Figure~\ref{fig:longact} compares the results with active surface seismic
data (left) with images produced with 9~hours of passive recordings
(right).  The overall character of the images produced with the
two data sets is again comparable.  The upper ovals in panels \pan{b}, and 
\pan{d} contain events very comparable to the those in the images immediately
to their left (panels \pan{a}, and \pan{c}).  The lowest ovals in
panels \pan{a} and \pan{b} also show events that are most likely
imaging the same subsurface structure.  The central sections of
the $yz$-frame of the passive images are not very coherent.  The
sections and oval overlays in panels \pan{e} and \pan{f} are the same
as those in Figures~\ref{fig:first200}\pan{a},\pan{b}
and~\ref{fig:shortlong}\pan{c},\pan{d}.  The event in the oval in
panel \pan{e} is not well imaged by processing this 9~hours of data.
\plot{longact}{height=\textheight}{a,c,e) Active seismic data 
  images.  b,d,f)  Direct migration images using 9~hours of 
  passive data.}
\par
Figure~\ref{fig:migdmig} shows comparisons of images produced by the
migration of synthesized shot gathers to images produced by the sum of 
direct migrations of the same transmission wavefields.  In both cases
transmission wavefields were defined as 12~s of passive data and were 
processed independently.  Both images used the same 9~hours of passive
recordings.  Panels \pan{a},\pan{c} are migrations of synthesized
gathers.  Panels \pan{b},\pan{d} are sums of direct migrations.  The
migration of synthesized gathers is not as good as the sum of direct
migrations.  The migration of synthesized gathers is lower frequency
and looks less believable than the direct migration.  Panel \pan{a}
does not capture the peak of the syncline in the center of the
$x$-axis, though the left flank of the structure is well imaged.  The
shallow events in panel \pan{c} appear fairly continuous, but the deep
structure looks almost random.
\plot{migdmig}{width=\textwidth}{a,c) Images produced by migrating 
 synthesized gathers produced with 9~hours of passive data.  b,d) 
 Images produced by the sum of direct migrations of the same volume 
 of passive data.}

\section{Conclusion}
The images presented above show that correct processing of passive 
seismic recordings can produce images of subsurface structure at the
reservoir scale.  Subsurface reflectors were imaged consistently in
the shallow, flat geology that correspond well with reflectors in the
control image provided by BP using active surface seismic data.  A
strong dipping reflector was imaged at roughly 1750~m below the sea
floor which corresponds exactly to an event in the active 
image.  Although the best passive images show continuous events on
inline sections below 2000~m, the images loose coherence in the crossline
direction.  This could be due to the limited aperture of the array in
that direction, but without continuity in both perpendicular planes,
my confidence of these events representing real structure is
diminished.
\par
The quality of the image is predicated on the 
presence, number, and strength of the subsurface sources within the
transmission wavefields.  The energy must be strong enough to be
recorded by the sensors in the array and travel back into the
subsurface to be reflected by reflectors before being recorded again.  The 
images produced with passive data shown above are not as high quality 
as those produced with active seismic data.  Shallow reflectors are 
consistently imaged fairly well compared to deep reflectors.  This is
undoubtedly due to the shorter travel paths along which the energy must 
remain above the noise level while suffering the deleterious effects 
of attenuation.  
\par
The best images presented above were produced with a small amount of
the data available.  Investigating the images produced with the various time windows 
and sums of time windows from the passive data donated by BP
draws similar conclusions to those drawn within the body of this 
chapter.  Relatively short time windows image reflectors well that are
diminished in images produced with more transmission wavefields.  At
the limit of an infinite recording period, the stationary reflections
should be imaged above the noise level, but in the short term good
information can be subsumed below the noise level by processing too
much random noise between useful, episodic noise events.  This shows
that quality control of the results produced with subsets of passively
recorded data is an important step in utilizing such data.  If the
bulk of the passive records contain background/instrument noise, the
small number of time windows that produce meaningful images are
important to separate so that the subsurface information is not
needlessly damped with random energy.  Unfortunately, this requires
generating and viewing interpretable volumes of data from the passive
records often enough such that the good information can be saved,
and the useless time windows rejected. 
\par
The fact that small time windows of passive data recorded during episodic
noise events produces better images than longer spans of passive data
is a good case for creating images with direct migration as data is
acquired.  Using the cost relations from the Discussion section in
Chapter~\ref{chapter:DepthSyn}, creating and migrating synthesized
gathers is over 6 times more expensive than the direct migration of
100~minutes of data.  Empirically, using a 30~node cluster of dual
processor 64-bit machines, the cost of migration alone is 6~days
(for the gathers) compared to 1~day (for direct migrations).  To
save cost, such intermediate migrations of correlated gathers are not
likely to be performed when attempting to utilize continuously
produced passive records from large permanent arrays.
\par
It is not clear exactly why the images produced by migration of
correlations with the Valhall passive data are of 
consistently worse quality compared to images produced by summing direct
migration results.  The experiments with synthetic data in 
Chapter~\ref{chapter:DepthSyn} produced results with negligible differences
between the two approaches.  If small errors propagate through the processing
of the data, the size of the data and the image domains may lead to more 
marked differences between the results produced with the different 
strategies.  Another source of error could be in the modeling of an 
appropriate source wavelet to use in the down-going wavefield for 
migration of the correlated gathers.  The spectrum of the synthesized 
gathers was whitened during the correlation processing.  I used a 
Ricker wavelet with center frequency 22~Hz for the wavelet.  While this
does correspond to the bandwidth of the far-field arrival identified in
Chapter~\ref{chapter:TimeShot}, it may not be appropriate for the energy
that is actually investigating the subsurface and providing the information
in the direct migrations presented above.  Avoiding this potential mismatch
is a strong case for processing the passive data with direct migration 
where no such decisions need be made since the upcoming and downgoing
wavefields are the same recorded data.

