S11E-0334
Passive Seismic Imaging
Noise to data via cross-correlation
r1
r1
r2
r2
r1*r1
Shot-gather from cross-correlation
The importance of velocity
r1*r2
Brad Artman,
Stanford University
brad@sep.stanford.edu
Application to the shallow subsurface
hollow pipe
lag
equivalent shot-gather
after correlations
ambient energy and
recording geometry
t
raw data
Because every trace records both the incident wave-field,
which is the source, and the energy returning from
subsurface reflectors, all traces have ‘source’ energy as
well as ‘data’ information. This is similar to the case of
surface related multiples. The correlation of every trace
with every other builds hyperbolas from subsurface
reflectors as well as removes the unknown time offset and
phase characteristics of the probing energy.
equivalent reflection data
passive transmission data
Correlating every trace with every other squares the number of
traces from the experiment. However, only the correlation lags
corresponding to the depth of the deepest reflector of interest
need be kept. This decimates the time axis by several orders of
magnitude.
hollow pipe
water table?
Wave-equation migration
day 2
x
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x
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7000
0
Application fo CASC-like synthetic
7000
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Cross-correlation of 72 channel acquisition on the beach of Monterey,
California lead to too few channels in any direction to find hyperbolas.
The wave-front healing capacity of wave-field propagation allows infill with
zero-traces that will interpolate the data during migration. This leads to
garbage at shallow depth, but produces an interpretable result at greater
depth. Deconvolution prior to migration as well as simple band-pass
versions of data were used from several different times of the day.
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400
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Thankfully, all these operators commute which allows
the correlation in migration to satisfy the correlation
required to produce the reflection response of the
subsurface from the transmission records. This is the
case if the transmission records are used as both the
source and receiver wave-fields.
0
day 1
100
Wave-equation migration of reflection seismic data to
produce images of the subsurface entails four basic
operations:
•Summation of all shots
•Wave-field extrapolation (phase shift operator)
•Cross-correlation of source (U) with data (D)
•Zero lag extraction by S
R(x,z,w)
w
Direct migration of raw transmission data
Application to the coda
Standard Migration
R0= U0D0*
R1= R0 e+i Kz Dz
+i Kz Dz
*
R1= U0D0 e
R1= U0D0* e+i Kz(U) Dz + i Kz(D) Dz
= U0 e+i Kz(U) Dz (D0 e-i Kz(D) Dz )*
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x
3500
7000
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hidden primary
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I thank Deyan Dragonov of Delft University for modeling
transmission panels, and Jeff Shragge and Biondo
Biondi for many discussions.
x
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Direct migration of passive data uses the transmission
wave-field, T, for both upgoing, U, and downgoing, D,
wave-fields in the same structure.
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* = T T*
R0= UD
0 0
0 0
300
The reciprocity theory tells us that another factorization
of R, besides UD is the cross-correlation of T, or:
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Passive Migration
0
100
This shows the commutability of the correlation and
extrapolation operators (and coincidentally the
equivalence of shot-profile and source-receiver
migration) due to the seperability of the exponential
operator.
Extracting the zero time of the wavefield R at any depth
level gives the image at that depth.
Theory dictates that a truly identical data set, including amplitude
accuracy, is generated by correlating the transmission records. This
holds true only if the distribution of source energy is spatially even.
Irregularity of the strength and distribution of subsurface energy leads
to variations of the illumination of the model space.
multiple
Migration with a true velocity model (rather than 1D) images yeilds crisp
images even of the steeply dipping flanks of the syncline. However, if
the location is subject to difficulties such as inter-bed multiples,
inappropriate energy can mask the true reflectors just like conventional
reflection.
The case presented next door explains the use of a modified shotprofile migration algorithm to image the subsurface with telesiesmic
coda energy. However, the theory of passive seismic imaging
extends directly to allow us to migrate the raw data without
imposing (incorrect) assumptions during pre-processing steps such
as deconvolution or rotation.
Using a wave-equation based migration algorithm, and performing
the correlations after the extrapolation step, the physics of wave
propagation is honored for all, however complicated, energy
available within the data set. This extends the imaging process to
higher frequency local noise, as well as removing ambiguities
associated with human interpretation of data before migration.
The use of depth migration requires a velocity model. To image
converted modes, both shear and compresional models are
needed. Images produced with this technique however show
remarkable tolerance to produce reasonable images despite gross
errors in velocity, as well as provide a tool to update the velocity
model to accommodate errors in the output model space.