\chapter{Time sections from Valhall}\label{chapter:TimeCMP}
\section{Summary}

I performed NMO-stack, using a velocity model generated with active seismic
surveys, on synthesized shot gathers produced from 
the Valhall passive seismic array.  Inline sections show strong events 
with minor deviation from horizontal.  The events are completely discontinuous
across the crossline direction and uninterpretable on time slices.  While
some events can be tracked between crossline sections, others
appear/disappear completely.  While aliasing could be the cause, the 
apparent dips of these events are geologically unreasonable.
\par
I performed various muting and modeling tests using the kinematics
of the energy from the production facility 40~km away from the array.  Shot
gathers were muted, windowed, and modeled before NMO-stack processing to 
compare to results produced with the synthesized gathers.  These tests show 
that the direct arrival and ringing correlation side-lobes are a coherent 
noise source that gives rise to the events that are immediately apparent 
with this simple processing sequence.  The most interpretable volumes of 
stacked data are produced by muting to the time of the direct 
arrival.  However, such volumes do not yield obvious and convincing subsurface 
information.

\section{Introduction}
After synthesizing shot gathers from the passive data collected by the
Valhall subsea array, I applied normal moveout (NMO) and stacked the 
volume across offset.  A similar processing flow with the same data
was described by \longcite{hohl:1560} using a single 2D section of 
raw data.  Several coherent, roughly flat (in inline sections) events 
are revealed in the resulting data volumes produced with all the various 
time windows over which the raw data were subdivided for processing.  
\par
Of paramount concern with this
workflow is the presence of the strong direct arrival from 40~km away
from the array investigated in Chapter~\ref{chapter:TimeShot}.  With
a single strong source dominating the data, so far away from the
array, the synthesized gathers did not reveal obvious subsurface
information that conform to the kinematics of surface data.  The coherent 
noise event violates the kinematic assumptions inherent in both the CMP
coordinate system and NMO.  I employed two main methodologies to 
investigate whether the events in the stacked sections are actual subsurface 
reflections or the coherent stack of the distant production noise:  
Constant water velocity NMO, and various modeling and muting experiments 
using the inversion results described in the previous chapter.  I generated
comparative volumes of NMO-stacked results with these strategies to 
investigate the effects of the distant noise source in the stacked domain.

\section{{NMO-S}tack time sections}
Figure~\ref{fig:events} shows strong coherent events in inline
sections after NMO-stack using a velocity model provided by BP.  The
shot gathers were synthesized with the spectral whitening correlation
strategy explained in the previous chapter.  The top images were
generated using 9 hours of raw data from February 14, 2004.  The
bottom images used 5 hours of data 25 hours later.  The two volumes
were processed identically.  The left columns are sections extracted
from the 3D cube at the central CMP in the crossline direction and
bandpassed from 10 to 25~Hz. The sections on the right column were
extracted from the next crossline CMP, +150~m.  The dissimilarity
between the results produced with data differentiated only by when
they were recorded leads immediately to the conclusion that the events
seen in the sections are artifacts rather than subsurface reflections.
\par
The shallow geology under the array consists of very flat, continuous 
layers (active seismic image is presented in Figure~\ref{fig:Vactive}).  These NMO-stack results have no
continuity on time-slice panels, and the events change radically in
character and timing between adjacent crossline CMP locations.  Some
events (dis)appear with no continuity between crossline locations.  Other
events are correlatable between the two sections, though move approximately
0.2~s.  Assuming that the events are aliased in the crossline direction,
this is an apparent velocity of 725~m/s.  The definition of
the CMP coordinate system requires CMP spacings half of the receiver
spacing (for this acquisition geometry).  However, a direct arrival
through the water column violates the two-way travel path assumed in
the CMP coordinate transform.  The appropriate source receiver
distance for a direct arrival is not 1/2 the receiver spacing, but
still the full distance.  Therefore, 300~m/0.2~s=1450~m/s is
an appropriate water-velocity arrival consistent with the distant
noise event identified in the previous chapter.  Because this event is
not a subsurface reflection, the CMP coordinate transform does not map
the event correctly into the CMP domain.  The strength of the events
is also suspicious as the shot-gathers shown in the previous chapter
do not contain obvious reflections from geologic events at these times.
\par
\plot{events}{width=\textwidth}{NMO-stacked inline sections from
  the center (left) of the Valhall array, and (right) the neighboring
  crossline CMP (+150~m).  Top and bottom rows were processed
  identically using data collected 25 hours apart in February,
  2004.} 
Figure~\ref{fig:water} used the same data used to produce top row of 
Figure~\ref{fig:events} and a constant water velocity for the NMO 
correction.  The two panels are the same crossline sections from the 
center of the array in Figure~\ref{fig:events}.  Coherent 
events are present, but have
troubling characteristics again.  There is now some consistency of
events in the crossline direction. Figure~\ref{fig:waterslice} is a
time slice through the same data cube at 0.4~s.  The panel shows some
uniformity of polarity,  which is indicative of flat events.  The
parallel events at early time in Figure~\ref{fig:water} are all at
integer multiples of 0.048~s, which is the time through the 70~m water
column.  Since NMO was performed with water velocity, multiples are
flattened in this volume.  It is impossible to determine if these
events are multiples or correlation side-lobes in this 
case.  Figure~\ref{fig:water} does show that NMO with water velocity 
drastically changes the events that coherently stack compared to
Figure~\ref{fig:events}.  The sections are obviously
different.  Despite the fact that the synthesized shot gathers did not
capture the apex of the hyperbola due to the distant noise source, the
water velocity NMO was close enough to destroy almost all of the odd events
in Figure~\ref{fig:events}.
\plot{water}{width=\textwidth}{Inline sections corresponding to the
  data on the left of Figure~\ref{fig:events} using constant water
  velocity for NMO.}
\sideplot{waterslice}{width=2in}{Time slice, 0.4~s, through the
  NMO-stacked cube using water velocity.  Some continuity exists across
  the panel, while individual lines in the CMP-X direction show strong
  coherence.} 
\par
The inversion described in the previous chapter provides very accurate
prediction of the kinematics of the strong event in the correlated
gathers.  Figure~\ref{fig:modldat} shows three correlated shot
gathers from the Valhall array.  Panel \pan{a} is a modeled gather
produced by convolving a wavelet with the forward modeled time picks
for the distant production noise described in
Chapter~\ref{chapter:TimeShot}.  The first trace is the zero-offset
trace.  Panel \pan{b} was synthesized from passive data and muted
to 0.128~s after the arrival time of the event in the top 
panel.  Notice that there are significant correlation 
side-lobes remaining in the section.  Panel \pan{c} was produced by
keeping only a short time window around the arrival of the noise
event in the synthesized gather.
\par
\plot{modldat}{width=\textwidth}{Shot gathers used to test the
  origin of the events in Figure~\ref{fig:events}.  Panel \pan{a} is
  a modeled shot gather using the inversion results presented in 
  Chapter~\ref{chapter:TimeShot}.  Panel \pan{b} is muted
  to the kinematics of the distant noise source.  Panel \pan{c} is a
  short window of data around the modeled event.}
Figure~\ref{fig:evnttest} shows inline time sections exploring the
relationship of the direct arrival from the distant production
facilities to the events observed in Figure~\ref{fig:events}.  Panel
\pan{a} is the same as Figure~\ref{fig:events}\pan{a}.  Panel
\pan{b} was produced with the muted data from 
Figure~\ref{fig:modldat}\pan{b}.  Panel \pan{c} used the data in
Figure~\ref{fig:modldat}\pan{c}.   The final section, \pan{d}, is the 
result of processing the forward modeled shot gathers,
Figure~\ref{fig:modldat}\pan{a}.  Differences between 
Figure~\ref{fig:evnttest}\pan{a}
and \pan{b} are nearly impossible to find.  Inspecting panels \pan{c} 
and \pan{d} from the bottom up, there are many similar features,
that share characteristics: location, length, dip, and curvature.  The
steeply dipping events in panel \pan{c} are not present in \pan{d},
but almost all other main features are identifiable.  The inclusion of
a small amount of data around the direct arrival, and the instability of
the wavelet associated with the distant source energy differentiates the 
results in panels \pan{c} and \pan{d}.  Correlation side lobes in 
the real data add repeated events and more noise to the section at 
$t=0.6$~s.
\plot{evnttest}{width=\textwidth}{Inline NMO-stacked 
sections from the center of the array.  \pan{a}) Section produced with used all
data available after correlation.  \pan{b}) Section produced with 
correlations after application of a mute to the modeled direct 
arrival.  \pan{c}) Section produced with data windowed around the direct
arrival.  \pan{d}) Section produced with a modeled data volume containing
only the direct arrival.}
\par
Figure~\ref{fig:modldat2} compares 
the muted shot gather generated with the first 9 hours of passive data
(Figure~\ref{fig:modldat}\pan{b}) with one, bottom panel, from data
collected 25 hours later.  In contrast to the top panel, the data from a
day later do not suffer as much from the ringing correlation 
side-lobes.  The mute leaves a small amount of co-parallel energy, but
this time does a much better job at removing most of 
it.  Figure~\ref{fig:evnttest2} compares the NMO-stacked sections
created with this second volume of data with and without the mute to
the direct arrival.  Panel \pan{a} is the same as 
Figure~\ref{fig:events}\pan{c} and panel \pan{b} was produced with the muted
volume of synthesized gathers.  Most of the strong flat events have been
eliminated in panel \pan{b}.

\plot{modldat2}{width=\textwidth}{Top:Muted shot gather corresponding
  to the first 9 hours of data (Figure~\ref{fig:modldat} top).
  Bottom:  Muted shot gather generated with 5 hours of data 25 hours
  after those used to create the top panel.}
\plot{evnttest2}{width=\textwidth}{NMO-stacked sections from center
  crossline location generated from data a day after those used for
  Figures~\ref{fig:modldat} and~\ref{fig:evnttest}.  Muting down to
  the direct arrival (Figure~\ref{fig:modldat2}) successfully
  eliminates all coherent events.}
\par
Figure~\ref{fig:evnttest2}\pan{b} shows a stacked section
of data from which the bulk of coherent noise has been removed before
NMO-stack processing.  This volume then represents the best candidate
for finding subsurface structure.  Notice a roughly sinusoidal series
of identifiable events across the section between 0.0-0.2~s including the
bowl-shaped events in the center of the section.  Similar events are 
present in Figure~\ref{fig:evnttest}.

\par
Figure~\ref{fig:Fourth.mute} shows two neighboring slices through the
3D volume of the stacked data produced with the muted shot gathers.  The  
volume has been bandpassed from 8-15~Hz.  The bottom panels show the same
sections as those above, but produced with a gain function to enhance the 
events at in the middle of the time axis. The time slices in panels 
\pan{b} and \pan{d} were extracted through the curving events near time zero
within the ovals in panels \pan{a} and \pan{c}.  Within the circle on the time
slices, there is a roughly circular feature identifiable as a mostly white ring
with a dark center. In movies progressing down the time axis, these
events are shrinking, circular rings centered around the location of
the surface production facilities.  This location suggests that the events
are associated with production noise at the production facilities.
\par
\plot{Fourth.mute}{width=\textwidth}{Best 3D time sections processed
  from 5 hours of passive data in February, 2004.  Processing flow:
  Correlation, deconvolution, mute, NMO, and stack.}
There is little continuity in the crossline direction throughout the 
bulk of the stacked volume.  The events that approach the edge of the
array are suspicious since these CMP locations do not have the
complete coverage needed to build reflection gathers as discussed in
Chapter~\ref{chapter:TimeSynth}.  However, there are a few events that
could be real subsurface structure.  There is a fairly continuous event 
that can be interpreted across the front frames of all panels at
just less than 2~s (lower ovals).  The event is interpretable between
the adjacent inline sections (left and right columns) and corresponds 
to a black-white-black event on the crossline panels
(circled) where the section line cuts through 2~s.  This seems like the most
likely event in the volume to be a genuine reflector.  
\par
A second coherent reflection in Figure~\ref{fig:Fourth.mute} is between 
6000-8000~m just beneath the time line on the front 
frames of panels \pan{b} and \pan{d}.   The event is broken and somewhat 
discontinuous on the crossline axis, but could be interpreted with 
marginal confidence.  At approximately the same time on the right edge of the 
sections, this event is again present.  This event could be associated with  
production noise (bowl shape described above), or a real subsurface reflection 
that is interrupted in the middle of the array.  
\par
Because the distant production noise is localized in space, the
direction of its arrival can be used to avoid correlating traces along
the azimuth of the arrival.  In so doing, it might be possible to
avoid the overpowering influence of the production noise when
synthesizing shot gathers.  Figure~\ref{fig:oneside} is an NMO-stack
image produced by selecting from the total correlation trace pairs
toward the location of the source energy.  In this way, the strong
event is in the acausal part of the correlations (and discarded), and
geologic reflectors might be imaged away from its influence.  However,
even though the arrival is not kept in the correlation output, its
effects are still in the calculation.  Figure~\ref{fig:oneside} does
not show any coherent reflections.  The swooping down to the left
character in the inline panel mimics the effects of distant production
noise in other results.  The crossline panel shows no consistency.  
\sideplot{oneside}{width=3in}{NMO-stack image created with only
  source-receiver trace combinations resulting in negative offset
  values.  By correlating toward the source location, the strong
  arrival in the synthesized shot gathers is discarded with the acausal
  correlation lags.}
\par
Figure~\ref{fig:synNMO} uses the synthetic transmission functions from
Chapter~\ref{chapter:TimeSynth} to analyze the effects of the distant 
production noise on passive data.  The first panel is a transmission 
wavefield due to a source below the center of the model domain with the 
addition of an event (0.75-0.9~s across the wavefield) modeled from the 
analysis of the far-field noise in  Chapter~\ref{chapter:TimeShot}.  The 
second and third panels present NMO-stacked sections produced from the
correlations of single transmission wavefields.  The result in panel \pan{b} 
was produced with a transmission wavefield due to a subsurface source below 
$x=1800$~m and the modeled direct arrival.  The result in panel \pan{c}
was produced with the wavefield in panel \pan{a}.

\plot{synNMO}{width=\textwidth}{a) Transmission wavefield from the modeled
  data presented in Chapter~\ref{chapter:TimeSynth} due to a source
  below the center of the domain.  b) NMO-stack image produced from a
  transmission wavefield due to a source below the left edge of the
  domain.  c) Stacked time image produced from the transmission wavefield
  in panel \pan{a}.}
\par
The steeply dipping events in the NMO-stacked sections in Figure~\ref{fig:synNMO}
are readily identified in the sections produced with real data 
above (e.g. Figures~\ref{fig:evnttest2} and~\ref{fig:Fourth.mute}).  Also 
note the concave-up features that connect to the steep 
events at the surface.  These noise events are large hyperbolas, centered 
over the location of the subsurface source, that have been folded down 
at the free surface.  These events are not present in sections produced 
without the addition of the far-field noise event.  Sections produced with only 
the far-field noise event contain only a
strong event at $t=0$~s.  The steep events are caused by the convolution
of the far-field noise event with events in the transmission 
wavefield.  Therefore, the bowl-shaped structures in Figure~\ref{fig:Fourth.mute}
are due to the presence of the distant noise source and a local energy 
source in the transmission wavefield.  The energy is centered 
at the production facilities.  Obvious water velocity events sourced at the 
Valhall production facilities were presented and analyzed in 
Chapter~\ref{chapter:TimeShot}.  I interpret these events as the convolution
of the far-field energy with local cultural noise produced during the 
synthesis of shot gathers by correlation of multiple direct arrivals.
\section{Discussion and conclusions}
NMO-stack of the whitened, correlated passive data from the Valhall
OBC array produces strong events on inline sections.  Other authors
have interpreted these as geologic information after processing only
2D subsets of the data \cite{hohl:1560} spanning a limited acquisition
duration.  Very good imaging from many active surveys has been carried
out at the location that shows the shallow geology to be flat and
uniform in both map directions.  The time sections shown above
however have several unbelievable characteristics that lead me to
conclude that these are coherent noise rather than genuine subsurface
information.  Of paramount importance, the same section produced with
the same processing flow using different windows of the available data
(separated by 25 hours) have dramatically different events.  
\par
Because the kinematics of the direct arrival in the shot gathers are
well constrained, it was possible to mute, model, and window around
the event before NMO-stack.  Using the gathers generated with the
first section of data, the muted volume was barely distinguishable
from the result produced with the full data.  However, the section
produced with a short time window around the event was very comparable
to that produced by forward modeling the event.  I performed similar
experiments with data from 25 hours later.  The NMO-stacked section
produced with the muted gathers from that data had no evidence of the events seen 
previously.  Comparing the muted shot gathers produced from the two
data subsets showed that there is significant ringing (correlation side lobes)
present in the gathers produced with the data from early in the
recording effort.  
\par
Using a constant (water) velocity for NMO processing completely eliminates 
the strong events present when using the correct velocity model.  Instead,
several orders of flat multiples are present in this volume related to the 
70~m of water above the geophone array.  The OBC
cables are buried approximately 1~m beneath the sea floor.  Thus,
within the first 2 samples (10~m depth), the interval velocity model
has values in excess of 1600~m/s which is much too fast to correctly
NMO the direct arrival that arrives at 1450~m/s.  This experiment again
confirms that the strong events produced by NMO processing the correlated
gathers are due to coherent noise arriving through the water column 
rather than reflections from the subsurface.
\par
These experiments lead me to conclude that the strong events revealed
by sorting the gathers to CMP coordinates, NMO, and stack are
artifices of the coherent noise event generated by a production
facility 40~km away from the Valhall array.  While there may be
subsurface information in the time domain gathers, it is weak and
distributed amongst the volume making it very hard to interpret in
both the shot domain and the CMP domain.  Muting the synthesized shot
gathers before NMO-stack to remove the distant production noise
source, produced a much simplified data volume.  A second noise source
was then identified in the volume as expanding rings emanating from
the production facilities contained within the array.  These features
correspond to the local water-velocity events picked on the raw and
correlated data sections in the previous chapter.  These experiments do
not provide convincing results that the
passive data recordings can illuminate the subsurface at Valhall.

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