\prefacesection{Abstract}
Passive seismic imaging in a sound theoretic idea that has languished
in the realm of theory for nearly four decades since the original
concept was presented 1968.  Only a small number of experimental tests
have been fielded in that time, and none provided convincing 
results.  The recent surge in interest in the idea has generated a
substantial literature that has proved the validity of the theory
beyond the initial conjecture, as well as experimentally at the lab
scale and the global scale.  This thesis makes a substantive
contribution to the field by extending the processing algorithms
available for passive seismic data and by analyzing a real 3d data
volume from a 2300 station areal array.
\par
The experiments with synthetic transmission wavefields in 
Chapters~\ref{chapter:TimeSynth} and~\ref{chapter:DepthSyn}
show that investigating subsurface structure with body waves can be 
accomplished with a limited distribution of subsurface sources directly 
beneath the sensor array.  Sources at shallow depths near the edges of 
the array are not required.  Without them, however, some artifacts remain 
in synthesized shot gathers.  Chapter~\ref{chapter:DepthSyn} shows that
migration of passive data produces interpretable images of the subsurface
even when the assumptions behind the rigorous theory are violated.  In 
extreme cases, such as capturing only a single subsurface source in passively
recorded data, synthesized gathers look completely incorrect, but migrating
the data produces very good results.  The same conclusion applies
when processing transmission wavefields due to many sources.
\par
Direct migration of transmission wavefields, introduced herein, is a
robust, convenient processing method.  Any conventional shot profile
migration algorithm that maintains separate up-coming and down-going
wavefields can be easily modified to use passive data.  The only
change required is to use the data for the initial condition of the
source wavefield.  Processing passive data by direct migration can
provide substantial computational savings.  This is especially true if
multiple images are produced from the total volume of data collected.  Because we
are relying on the natural rate of seismicity to supply the energy for 
investigating the subsurface, much of the total recording time is likely 
devoid of useful information.  Therefore, it is useful to produce quality 
control images with multiple short windows of data.  However,
synthesized shot gathers may be required for velocity analysis or
addressing common data problems such as noise removal or aliasing.
\par
Over 35~hours of passive data collected at the Valhall development in the 
North Sea was processed to produce synthesized shot gathers and migrated
images.  The synthesized shot gathers did not provide any subsurface
information.  Instead, they were dominated by a direct arrival through the 
water column from the gas flare at a production facility 40~km away from 
the array.  The normal moveout correction applied to the gathers did not 
produce any interpretable subsurface information.  Importantly, the
energy from the gas flare is a coherent noise source that arrives at
the array at such a shallow angle that it is confined to the water
column and does not refract into the subsurface.  As a coherent noise
source, the energy manufactures events in results that are not
subsurface reflectors.  Removing the far-field noise from the
synthesized gathers also removes the interpretable events from the
NMO-stacked result. 
%%  However, some of the 
%%artifacts in those results were reproduced with modeling excersizes that
%%show them to be convolutions of local production noise with the distant
%%production noise.
\par
%%The images are the first 
%%successful large array 3D images of the subsurface using passive seismic 
%%data.  
Images produced with direct migration of the Valhall passive data in
Chapter~\ref{chapter:DepthVal} contain interpretable subsurface events
that seem to correlate with events in active seismic images.  The basic
syncline structure under the array is well represented in the passive
images.  However, data modeled after the coherent noise from the
distant gas flare produces almost identical images to those produced
with field data.  This fact drastically discounts any value in the
images produced with field data even for events that are highly
correlatable between the active and passive images.  Direct migration
and the migration of synthesized shot gathers from modeled data
produces almost identical images.  For the Valhall data, 
however, the two strategies produced markedly different results.  The 
migration of synthesized gathers always produced substantially worse 
results than direct migration.  The reason for this difference is
again due to the far-field production noise.  
\par
The Valhall Life of Field Seismic array is a unique 
installation of seismic sensors.  The geophones can continuously record
data between the active surveys that are performed several times per 
year.  The chief obstacle in continuously processing data from the 
array is the transportation of the large volumes of data from the offshore
installation.  Most, or all, of the tele-communications bandwidth currently 
available at the installation would be used by continuously moving data
to shore for processing.  For a single component, a single day of raw data 
is more than 46~Gbytes.  The correlation volume, in the frequency domain, 
produced from the array is similarly sized.  However, if a modest computer 
cluster were available on-site for processing, a small image volume
can can be transferred easily.  The nature of the
ambient noisefield at Valhall seems to require correlation processing
to remove the far-field energy rather than direct migration, which
would save computation demands.  Unfortunately, my analysis of the
day-long passive records from Valhall do not provide convincing
evidence to justify such an experiment.  
\par
Passive seismic imaging shares many characteristics with addressing
multiples in conventional data.  Imaging with subsurface sources is
kinematically equivalent to imaging primaries with multiples.  These
two imaging techniques rely on the correlation of up-coming and
down-going events in the data.  Predicting multiples for subsequent
removal is often an important processing step for active 
data.  Prediction techniques for surface related multiples rely on
convolution of the traces in a data volume.  I introduce a new,
convenient multiple prediction method that performs the 
convolution during the course of shot profile depth migration of
active seismic data.  This new multiple prediction is defined in the
image domain with space and subsurface-offset dimensions.  Image-space
multiple prediction (IS-SRMP) is velocity independent as is the
data-domain equivalent (SRMP).  The result is the same as that
produced by migrating the SRMP volume.  Because wavefield
extrapolation is such an expensive algorithm, the additional
computational cost of multiple prediction during migration is
small.
