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\lefthead{Cole}
\righthead{Passive data processing}
\footer{SEP--61}
\title{Scattering analysis of passive seismic data}
\author{Steve Cole}
 
\ABS{
Blasts set off in a quarry 15 km from the SEP passive experiment
site are easily detected, even if they are quite small, using beam
steering. These blasts have provided a signal with which various
processing techniques can be evaluated before being applied to ambient
noise data.
One such technique is imaging by looking for evidence of diffraction off
near-surface structures. This yields a picture that is fairly consistent
but dominated by plane-wave energy arriving in the same direction
as scattered waves.
One of the most surprising results of the experiment is the observation
of many weak near-vertically incident events during nighttime recording.
While their origin has yet to be explained, these events are not due
to electrical interference.
}
 
\INT
In September of 1988 the SEP conducted a passive seismic experiment on
Stanford land, setting out 4056 geophones in 24-geophone groups,
giving 169 independent recorded channels. The survey area was a square
roughly 500 meters on a side. Our goal was to use industrial recording
techniques to record ambient seismic noise and use it to image the
subsurface.
\par
In SEP--60, the results of some initial processing of the
data were presented. The results were not very encouraging, 
but since then processing
tools have evolved and I have made some significant gains. 
In this report, I will discuss three topics I've been working on.
First, the USGS set off several blasts varying in size in a quarry 
about 15 km
away from our experiment, timed so that we could record
them. Two of the three blasts were so small that they are not observable
on single geophone records at our site.
But beam steering or slant-stacking of the data sees these blasts quite well.
There is evidence in the coda of at least one blast of multipath
effects, which deserve closer study.
\par
Second, we have observed a large number (one every few seconds during
nighttime recording) of weak, near-vertically incident events. While
we cannot explain their origin, it will be shown here that while they are
nearly vertically incident (as electrical interference might be) they have
a distinct, non-vertical incidence angle that rules out the possibility
that they are electrical noise.
\par
Finally, the goal of this work is to use ambient noise recording to image
subsurface structure. One hypothesis is that we can ``see'' ambient
energy diffract off near-surface structure and thereby learn about the
near-surface. I have applied a simple hyperbola-summation method to data
from the quarry blasts as well as ambient noise data in attempt to do this.
At first glance the results are quite consistent. But a closer look shows
that they are dominated by artifacts introduced by plane-wave energy
which stacks in even when hyperbolic paths are used.
 
\mhead{QUARRY BLAST RECORDINGS}
While most of our recording was done during the night to minimize
interference by cultural noise sources, we also recorded some daytime
records. The USGS was going to set off several blasts in a quarry in
Cupertino, CA (about 15 km away) for a research project of their own,
and they kindly scheduled the blasts so that we could try to record them
with our array. Figure~\ref{map} shows the survey area and indicates
the direction of the quarry.
\plot{map}{4.0in}{}
{Map of survey area showing the nearby Stanford Linear Accelerator, Interstate 280, and the direction of the quarry in which blasts were set off.}
\par
There were three blasts, a large ``quarry blast'', with 1500 pounds of
explosives in a number of different shot holes (this blast is used by
the quarry to dislodge rock) and two smaller single charges of 300 and 100
pounds that were set off for experimental purposes. USGS seismometers
in the vicinity of our array clearly see the quarry blast (indeed, the
quarry blast is visible for hundreds of kilometers) but not the smaller
blasts. 
\par
Figure~\ref{rawblast1} shows portions of the seismograms recorded by 
one of our 169 groups
for the three blast records. The quarry blast appears on the middle
trace at around 10 seconds, but is not very obvious on a 
single-trace display. The smaller blasts arrive around 10.5 seconds on the
other two traces, and are not at all apparent. The signal-to-noise ratio
in our data, at least for daytime recording, is obviously quite small.
\plot{rawblast1}{3.0in}{traces}
{Traces from the same geophone group for three different recording periods, 
parts of the three daytime records where blasts were set off 
in a nearby quarry.  
The largest blast is the event on the middle trace arriving at around
10 seconds. The smaller blasts are not readily distinguishable 
on these single-trace displays.
}
\par
We were lucky to record these blasts at all. Our recording equipment 
consisted of 
169 seismic group recorders (SGRs), each recording data on its own cassette
tape and powered by a battery. This equipment was donated to Stanford by
Amoco. The rechargeable batteries have a lifetime of about a day of normal
operation. They worked fine for our nighttime recording, but had to sit
using power until the middle of the next day for the blast recordings, 
and battery failure began to take its toll. About half the SGRs were still
working for the first blast at 11 AM, and only 38 of the 169 were still
working for the third blast at 12 Noon. 
\par
While the blasts are not readily apparent on individual traces,
beam steering has been a very useful tool for detecting and locating
them. 
Figure~\ref{beamexpl} gives a schematic view of the disc-shaped beam
steering plots which will be used frequently throughout this paper.
Stacking semblance is displayed as function of arrival direction (azimuth) and
apparent slowness in polar coordinates. An apparent slowness of zero,
corresponding to vertically incident events, is plotted at the center.
The highest slowness value, at the edge, corresponds on these plots to
an apparent velocity of 2 km/sec.
These plots could also be described in terms of 
ray parameters $p_x$ and $p_y$
as shown in the figure, illustrating the equivalence of beam steering and slant
stacking.
\par
The orientation of the square in Figure~\ref{beamexpl} is the same
as the orientation of the square indicating our array on the map in
Figure~\ref{map}. Thus it is straightforward to relate azimuth directions
on these beam steering plots to real-world directions.
\plot{beamexpl}{3.5in}{}
{Schematic view of beam steering plots. 
Stacking semblance is plotted as function of arrival direction (azimuth) 
and apparent slowness. 
Vertically incident events would be at the center and those with highest 
apparent slowness 
(corresponding here to an apparent velocity of
2 km/sec) are at the edge. 
For reference, the orientation of the square in these plots 
and in the beam steering plots throughout this paper is the 
same as that in the map in Figure~\protect\ref{map}.
}
Figure~\ref{beamblast1} shows the result of beam steering
the data from the three blasts 
and summing over 100 msec windows centered around the 
first arrivals from the blasts. 
It can be seen that the three blasts arrive from the
same direction, all with an apparent velocity of around 4 km/sec. 
In Figure~\ref{beamblast1}, I gained the
three panels independently so that the three blasts would have the same
relative strength. In fact the blast from the 
middle panel, the quarry blast, is much stronger
than the other two. If we were to perform the same summation over time
as shown in Figure~\ref{beamblast1}, but using the entire 32 second
records instead of a small window, the quarry blast would still dominate
the middle plot, while the two smaller blasts would be lost in the
background noise. Restricting the summation to a small window located
at the right time has enabled us to see all three blasts.
\plot{beamblast1}{2.5in}{3blasts}
{Beam steering result for 100 msec windows centered on the first arrival 
of energy from three blasts in a quarry 15 km distant from the array. 
Refer to figure~\protect\ref{beamexpl} for an explanation of the individual 
plots, and compare to figure~\protect\ref{map} to relate these directions 
to the survey geometry. All three blasts arrive in the same direction with 
apparent velocities around 4 km/sec.}
\par
While the blasts arrive in a consistent direction, 
that direction surprisingly
differs considerably from the direction of the quarry, as can be
seen by comparing these plots and the quarry direction indicated on
the map in Figure~\ref{map}. 
The difference is on the order of 45 degrees.
One possibility is that these first arrivals have traveled
along a path that does not follow a straight line from the quarry
to the array. The local geology gives some support for this theory.
A direct path from the quarry to our survey would pass through
large amounts of sandstone and conglomerate, while a path that
initially turned further to the west and then came back to our
array would remain for the most part in a faster, more well-consolidated
basalt formation that parallels the San Andreas fault, which passes about
5 km to the southwest of our survey area.
Another possibility is that the energy
follows a more direct path and is then rerouted by the near
surface, for instance by a tilted weathered layer beneath the survey.
\par
Another interesting fact to note about the blasts is that there is
strong evidence of energy from the blast following different
paths to reach our array.
Figure~\ref{beamblast3} shows many
100 msec frames from the large quarry blast following the first arrival
shown in Figure~\ref{beamblast1}.
All these frames have been gained identically, so the later arrivals
are truly quite strong. I haven't shown frames from before the blast arrived,
but they are relatively very quiet. Thus we can assume that all
the strong events 
shown in Figure~\ref{beamblast3} are due to the blast. 
Note that this late-arriving
energy comes in a variety of directions, some of it arriving in a direction
much closer to the direction of the quarry. 
One possibility is that the
earliest arrivals traveled through the faster basalts to the west,
and then later energy traveling in the straight-line direction arrived.
\par
Figure~\ref{beamblast4} shows the same sequence of plots following one
of the two smaller blasts, record 44. Although these plots have been
gained so that the first arrivals of the two blasts are similar in
appearance, the smaller blast does not seem to have the same large
amount of energy from the blast arriving at later times.
\plot{beamblast3}{8.0in}{multipath}
{Frames showing the result of beam steering for 100 msec windows following 
the first arrival shown in the middle frame of Figure~\protect\ref{beamblast1}. 
The energy in these frames is much stronger than that in the rest of the 
32 second record, so all this energy must be due to the quarry blast, 
suggesting multiple travel paths or scattering.
}
\plot{beamblast4}{8.0in}{multipath2}
{Same as Figure~\protect\ref{beamblast3} but for one of the smaller blasts, 
the one shown on the left in Figure~\protect\ref{beamblast1}. The coda of
this small blast does not have as much energy as that of the large quarry
blast, even though the data have been gained so that the first arrivals
are similar in appearance.
}

\mhead{NEAR-VERTICAL EVENTS}
One of the most interesting features of the dataset, discussed in
SEP--60 (Nichols et al, 1989) was the abundance of near-vertically
incident events in the nighttime records. These events are weak and
not noticeable on individual seismograms. However, Lin Zhang showed
that when the data were stacked along different trajectories (a special case
of beam steering) these events showed up quite well. 
\par
Our first thought was that since the events are almost vertically incident,
they must be due to some electrical interference. More careful beam
steering now suggests that this is not so; these events seem to have a
consistent direction of propagation that is close to vertical but not
quite vertical. If that is so, they cannot be due to electrical noise.
\par
Figure~\ref{vertbeam1} shows the result of beam steering 12 different
nighttime records. The entire 32 second records were used to produce each
of these plots. The dominant feature of most of them, near the center,
is the near-vertically incident events. 
While these events are close to the center, they are consistently
just off-center. Their azimuth and apparent slowness indicate a fairly
consistent arrival direction, from the east, with an apparent velocity of
around 12 km/sec. 
\par
To illustrate why I think the events are not due to electrical interference,
I took the same data and randomly re-ordered the positions of the 169
traces in our array. If the events are real, and not perfectly flat,
then re-ordering the traces in this way
should effectively eliminate them.
Figure~\ref{vertbeam2} shows the result of
beam steering the re-ordered traces. 
There are some strong semblance
values near the center, but they are not as strong as the values in
Figures~\ref{vertbeam1}. More importantly, they are
no longer in the same place, but are mostly clustered around the center.
This is precisely what we would expect to happen; the semblances are not
going to drop to zero because there was strong, near-vertically incident
energy present. After re-ordering it will still stack in to some extent.
But the
directional consistency should be, and is, lost. Thus I think it's clear
that these events are not due to electrical interference.
\par
Figure~\ref{vertbeam3} shows the result of beam steering one of the
12 records, with and without trace re-ordering, at a larger scale.
As is the case in Figures~\ref{vertbeam1} and \ref{vertbeam2}, the two
frames have been gained identically to preserve differences in semblance
values. I think it's clear that re-ordering has reduced the semblance
values considerably, and removed their directional dependence.
\par
What could cause such events? If they were due to a surface source,
the source would have to be very distant in order for the energy to 
arrive so steeply. Yet energy from any surface source that distant
should be attenuated long before it reaches our array.
Another possibility is that they are weak events coming from somewhere
within the earth that typically go undetected but have been noticed by
us because we have so many geophones in a compact area.
\plot{vertbeam1}{8.0in}{vert}
{Result of beam steering for 12 different nighttime records.
The feature consistent from plot to plot represents near-vertically
incident events, arriving from the east with an apparent velocity
of around 12 km/sec.
}
\plot{vertbeam2}{8.0in}{randvert}
{Same as Figure~\protect\ref{vertbeam1} but traces have been re-ordered
before beam steering. The consistent events have been removed by the
re-ordering, suggesting that they are real events and not due to
electrical interference.
}
\plot{vertbeam3}{3.5in}{bothvert}
{One of the records from Figures~\protect\ref{vertbeam1} and 
\protect\ref{vertbeam2} shown without (left) and with (right)
trace re-ordering prior to beam steering.
The re-ordering has removed the high-semblance values seen on
the left, verifying that the high semblance values near the center
of the left plot were due to actual events and not some sort of
interference.
}

\mhead{IMAGING}
The ultimate goal of this work is to use ambient seismic energy to
image the subsurface. In SEP--60, two approaches to this problem
were proposed. Lin Zhang (Zhang, 1989) proposed that a reflection
coefficient series could be recovered from autocorrelations of passive
recordings. I proposed (Cole, 1989) looking for evidence of ambient
energy scattering off near surface structure. Scatterers near the array
should act as secondary sources. While we can't image these sources
with conventional migration since we don't know the time at which they
``explode'', we should be able to see in the data the moveout patterns
that identify the source location.
\par
In SEP--60, the technique I used was to downward continue the wavefields,
then sum power in the images at each depth, looking for the large power
values that would result when energy is focused to a point in space,
the source location. While that method is reasonable, I decided to
backtrack and try to do the same imaging with a conceptually simpler
scheme, used by Nikolaev (1987) to image scatterers using teleseismic
data {\it and} ambient noise data with the NORSAR array.
\par
In Nikolaev's scheme, we create a 3-D grid of possible scatterer
locations in the subsurface. For each location, we find the moveout
trajectory for energy coming from that point, and compute semblance
over time along this trajectory in our data. 
We can then look at the average semblance over time, or the
maximum semblance observed over all times, to get an idea of
the scatterers that may lie in the subsurface.
\par
An important first question is, given the size of our array, how
far away can scatterers be identified as such? 
The limited size of the array will make it impossible
to see any moveout for events coming from scatterers beyond a 
certain distance. Beyond this distance, scattered energy will be
indistinguishable from plane waves. Nikolaev was using the NORSAR
array, 110 km across, and was therefore theoretically able to image
very deep structures. Our array is only 500 meters across, so our
scattering analysis will be more localized. Figure~\ref{tdifarray}
shows the moveout across the array for a scattered event versus
distance of the scatterer from the array. This figure assumes a 
constant velocity of 2000 meters/sec, a very favorable choice. For
higher velocities the dropoff will be sharper. The time difference
drops to less than four milliseconds at around 5 kilometers from the
array, so our scattering analysis definitely cannot go beyond that
point. I have chosen one kilometer as an upper bound in the analysis
that follows, to avoid coming too close to the limit.
\plot{tdifarray}{3.0in}{tdif}
{Moveout observable across our array for a scattering event as a function 
of scatterer distance from the array. Beyond about 5 kilometers the 
observable moveout drops to less than the time sampling interval, 
so scattered events will be indistinguishable from plane waves.
}
\par
Figure~\ref{image0} shows the image that is obtained for the $z=0$ depth
level when this scattering algorithm is applied to 
portions of several different
nighttime and daytime records.
The x and y dimensions of the grid of scattering locations shown are
three times the size of the survey. Thus points up to 750 meters
from the array center are shown in this plot. The dominant features
in this plot are the radial streaks. These are due to the fact that as
we get further from the array center, our summation path becomes flatter
and flatter. Eventually we reach the point where we are summing along
a plane wave path, and from there out we would just get a radial streak.
\par
Figures~\ref{image500} and \ref{image1000}
show the results for depths of 500 and 1000 meters.
A feature worth noting in all of these is the general agreement among the
daytime blast records, and among the nighttime records, but
not between the two groups.
The reason for
this is that what we are seeing when we sum along these hyperbolic paths
is, predominantly, plane wave energy, which was quite different
during day and night recording periods.
In Figure~\ref{image1000p}, I've
performed the same computation as for Figure~\ref{image1000}, but I've
summed along plane wave paths rather than hyperbolic paths. The fact
that these two plots are quite similar is disappointing; it means that
the algorithm is seeing mainly plane wave energy imperfectly stacked
along hyperbolic paths, rather than scattered energy.
\par
If we are to see scattered energy, probably it is necessary to filter
out the strong plane waves present throughout our dataset.
\plot{image0}{8.0in}{depth0}
{Semblance measure of scatterer strength as a function of position
for a depth of 0 meters. The different frames correspond to different
recording periods. The top four panels are nighttime records; the bottom
four are daytime records. Of these, all but record 45 contain blasts.
These plots cover a 1500 meter square
area centered around the array.
}
\plot{image500}{8.0in}{depth500}
{Same as Figure~\protect\ref{image0} but for a depth of 500 meters.
}
\plot{image1000}{8.0in}{depth1000}
{Same as Figure~\protect\ref{image0} but for a depth of 1000 meters.
}
\plot{image1000p}{8.0in}{depthplane1000}
{Same as Figure~\protect\ref{image1000} but summing along plane wave
fronts rather than the hyperbolic paths due to scattering. The similarity
of this figure to Figure~\protect\ref{image1000} suggests that most of 
the energy seen by this analysis is plane wave energy, which is apparently
much stronger than any scattered energy present.
}
 
\CON
Our passive dataset contains some interesting plane wave energy.
The weak but abundant near-vertically incident events are 
surprising, but their origin remains a mystery. The quarry blasts
show evidence of multiple propagation paths or scattering in their
coda which merits more careful investigation. 
\par
Looking for scattered energy in the dataset is hampered by the fact
that plane wave energy seems so strong that it overwhelms any
scattered energy present. Some sort of filtering in velocity space
can hopefully remove the plane wave energy and make scattered energy
more apparent.
 
\REF
\reference{Claerbout, J., Cole, S., Nichols, D. and Zhang, L., 1988, Why a
	   big 2-D array to record microseisms?: SEP--{\bf 59}, 1-10.}
\reference{Cole, S., 1989, Downward continuation analysis of passive
	   seismic data: SEP--{\bf 60}, 97-108.}
\reference{Nichols, D., Cole, S. and Zhang, L., 1989, An introduction to 
 	   the SEP passive dataset: SEP--{\bf 60}, 67-76.}  
\reference{Nikolaev, A., and Troitskiy, P., 1987, Lithospheric studies based
	   on array analysis of P-coda and microseisms: Tectonophysics,
	   {\bf 140}, 103-113.}