Post-convention workshop at the 2005 SEG:
Seismic interferometry, daylight imaging and time-reversal
In passive imaging using interferometric methods waves recorded at two receiver
locations are correlated to find the Green's function between the locations.
Interferometric imaging has been successfully applied to helioseismology (1),
ultrasonics (2) and exploration seismics (3,4).
The subject of time-reversed acoustics was pioneered in physical modelling studies by
the group of Professor Mathias Fink in Paris in the early nineties. In time-reversed
acoustics, invariance of the wave equation for time-reversal is exploited to focus a
wavefield through a highly scattering medium (5). The implications of this work on
the applied geosciences have only started to dawn on our community over the last 2-3
years.
Recently it was shown that there exists a close link between the time-reversed
acoustics and passive imaging disciplines when Derode et al. (6) and Wapenaar (7)
analyzed the emergence of the Green's function from field-field correlations in an
open scattering medium in terms of time-reversal symmetry. The Green's function can
be recovered as long as the sources in the medium are distributed forming a perfect
time-reversal device. Recently, van Manen et al. (8) have shown that these results
have important implications for how one can approach modelling and inversion
problems. On-going work in several research groups promise to deliver results that
may have a significant impact on the exploration seismics community.
In the workshop we will explore the link between the interferometric imaging and
time-reversal concepts, and discuss recent applications in the applied geophysical
sciences.
1. J.E. Rickett and J.F. Claerbout, Sol. Phys. 192, 203 (2000).
2. R.L. Weaver and O.I. Lobkis, Phys. Rev. Lett. 87, 134301 (2001).
3. K. Wapenaar, D. Draganov, J. Thorbecke and J. Fokkema, Geophys. J. Int. 179
(2004).
4. G.T. Schuster, 63rd Mtg. Eur. Assn. Geosci. Eng., Session: A-32 (2001).
5. A. Derode, P. Roux and M. Fink, Phys. Rev. Lett. 75, 4206 (1995).
6. A. Derode, E. Larose, M. Tanter, J. de Rosny, A. Tourin, M. Campillo and M. Fink,
J. Acoust. Soc. Am. 113, 2973 (2003).
7. K. Wapenaar, Phys. Rev. Lett. 93, 254301 (2004).
8. D. J. van Manen, J. O. A. Robertsson, and A. Curtis, Phys. Rev. Lett. 94, 164301
(2005).
Agenda
08:30-08:35 Opening (Organizers)
08:35-09:15 Developments in seismic interferometry (Roel Snieder)
09:15-10:30 Poster session 1: Green’s function construction
 Extracting Greens functions from ocean acoustic and seismic noise (Peter Gerstoft,
Karim Sabra, WA Kuperman, Mike Fehler and Phillipe Roux)
 Making waves by time reversal (Dirk-Jan van Manen, Johan Robertsson and Andrew
Curtis)
 Integral Green function representations of electromagnetic interferometry with
applications for ground penetrating radar (Evert Slob, Deyan Draganov and Kees
Wapenaar)
 Green’s function representations for seismic interferometry (Kees Wapenaar and
Deyan Draganov)
 An introduction to estimating the impulse response between receivers in a controlled
ultrasonic model (Kasper van Wijk)
10:30-10:45 Break
10:45-12:00 Poster session 2: Redatuming
 Seismic imaging and monitoring with Virtual Sources (Andrey Bakulin and Rodney
Calvert)
 Kirchhoff integral and Virtual Source Method (Korneev and Bakulin)
 A novel application of time reversed acoustics: Salt dome flank imaging using
walkaway VSP surveys (Rongrong Lu, Mark Willis, Xander Campman, Nafi Toksöz,
Yang Zhang, and Maarten V. de Hoop)
 Source spacing in virtual source imaging / Analysis of Treasure Island earthquake
data using seismic interferometry (Kurang Mehta, Roel Snieder, Kees Wapenaar and
V. M. Graizer)
 Theoretical Comparison Among Model-Based and Correlation Based Redatuming
Methods (Gerard Schuster and Min Zhou)
12:00-12:30 Panel discussion
12:30-13:30 Lunch
13:30-14:00 From Time reversal to Imaging (Mathias Fink)
14:00-15:30 Poster session 3: Imaging
 Imaging passive seismic data (Brad Artman)
 Adaptive Coherent Interferometric Imaging in Random Media (Liliana Borcea,
George Papanicolaou and Chrysoula Tsogka)
 Bending the wrong way and imaging the right way (Ilana Erez and Luc Ikelle)
 Seismic interferometry, daylaight imaging and time-reversal: application by using
transmitted and reflected wavefields in tunnel seismic while drilling surveys (F.
Poletto and L. Petronio)
 Linking multiple removal and daylight imaging for regular surface seismic data (Eric
Verschuur and A.J. Berkhout)
 Comparison between interferometric migration and reduced time migration of CDP
Data (Min Zhou and Gerard Schuster)
15:30-15:45 Break
15:45-16:45 Panel discussion
Abstracts
Title: Imaging passive seismic data
Authors: Brad Artman (Stanford)
Correlating transmission wavefields to produce reflection wavefields contains in its
rigorous definition the mandate of processing data due to only a single source. If
more than one source is contained in the wavefield, crosstalk between the sources will
produce a data volume that is not the same as shot gathers with impulsive sources at
each receiver location. When attempting to image the subsurface with the truly
unknown ambient noisefield, parameterizing the field data by individual sources is
impossible.
For truly passive data, the source and time axis are inextricably combined, naturally
and by processing. This changes direct migration to something more akin to plane
wave migration. Since the direct arrival from each source can not be expected to sum
together with a common time-delay, the summation manufactures a source wavefront
with temporal topography rather than a plane wave.
The Fourier transform of field data as a single wavefield provides insight into how
sources are summed during correlation. Also, the transform simultaneously stacks
away useless waiting periods between useful energy bursts and reduces the data
volume. Previously, white, zero-phase source functions were invoked to avoid the
summation problem. However, neither assumption is likely in the real environment of
a long term experiment.
Title: Seismic imaging and monitoring with Virtual Sources
Authors: Andrey Bakulin and Rodney Calvert (Shell International E & P)
Virtual Source method (VSM) has been recently proposed as a way to eliminate
overburden distortions for imaging and monitoring. VSM acknowledges upfront that
our data inversion techniques are unable to unravel the details of the complex
overburdens. Therefore VSM advocates placing permanent downhole geophones
below that most complex overburden while still exciting signals with a surface
sources. By performing data-driven redatuming with measured Green's functions,
these data can be recast into complete downhole dataset with buried Virtual Sources
located at each downhole geophone. This step can be effectively thought of as a time
reversal and it's remarkable feature is that velocity model between sources and
receivers is not required to perform it.
We will show various applications of the VSM method to several synthetic and real
time-lapse datasets to illustrate the following advantages:
1) ability of VSM to eliminate overburden distortions without knowing velocity
model,
2) greater quality of Virtual Sources under complex scattering overburdens,
3) beneficial downward only radiation pattern,
4) ability to correct non-repeatability in acquisition geometry and temporal changes
in the near surface,
5) ability to create P-wave Virtual Sources without shear radiation and S-sources
without P-waves.
Title: Adaptive Coherent Interferometric Imaging in Random Media
Authors: Liliana Borcea (Rice), George Papanicolaou (Stanford) and
Chrysoula Tsogka (U. Chicago)
I will discuss a robust, coherent interferometric approach for array imaging in
cluttered media, in regimes with significant multipathing of the waves by the
inhomogeneities in clutter. In such scattering regimes, the recorded traces of the
scattered echoes at the array are noisy and exhibit a lot of delay spread (coda).
Classic imaging methods give for such data unreliable, statistically unstable results.
Coherent interferometry is essentially a statistically smoothed migration technique
that exploits systematically the spatial and temporal coherence in the data to obtain
stable images.
I will describe in some detail the resolution of this method and explain the delicate
balance between having enough smoothing and yet sharp images. The optimal
smoothing is clutter dependent and this is usually unknown in practice. However, I
will show how one can determine the optimal smoothing adaptively, during the image
formation process.
Title: Bending the wrong way and imaging the right way
Authors: Ilana Erez and Luc T. Ikelle (Texas A&M)
An analysis of scattering diagrams (i.e., Feynmann-like diagrams for wave scattering)
of the correlation-type representation theorem has recently revealed a new type of
scattering in inhomogeneous media. Unlike common scattering events, the new events
are inconsistent with the current interpretation of some of the basic physical laws,
such as Snell's law, just like the so-called ``negative refraction'' in optics. Yet we find
them very useful, for instance, in suppressing some undesired events from scattering
data, in separating reflected and refracted waves, even in imaging seismic data. We
will describe the results of these applications of this new type of scattering.
Title: Extracting Greens functions from ocean acoustic and seismic noise
Authors: Peter Gerstoft and Karim Sabra, Bill Kuperman (Scripps Institution
of Oceanography, University of San Diego), Mike Fehler (Los Alamos National
Laboratory), and Phillippe Roux (University of Paris)
Using ocean acoustic data and seismic data, we will demonstrate experimentally and
theoretically that an estimate of the Green's tensor between two sensors can be
obtained from long term averaging of the cross correlation at the two stations. This
result provides a means to generate high quality images Earth structure using the
ambient noise field only, without the use of active seismic sources or earthquakes.
Seismic noise data from 148 broadband seismic stations in Southern California were
used to extract the surface wave arrival-times between all station pairs in the network
in the frequency band 0.05-0.4 Hz. In this frequency band, ambient noise (originating
from ocean microseisms) propagating over long distances is typically dominated by
surface waves. A record section of the waveforms as a function of increasing receiver
separation shows clearly that the recovered signals are propagating wavetrains. The
seismic data were then used in a simple, but densely sampled tomographic procedure
to estimate the surface wave velocity structure for a region in Southern California.
The result compares favorably with previous estimates obtained using more
conventional and elaborate inversion procedures. This demonstrates that coherent
ambient noise between station pairs can be used for seismic imaging purposes.
Further, we demonstrate the use of the method to extract P-waves from noise in the
Parkfield area, Influence of noise from hurricane Katrina on the Greens function
extraction, monitoring volcanoes and interferometric processing in ocean acoustics.
Map of the 150 online
stations in the Southern
California Seismic
network.
Shot record generated
from one month
averaging of the
noise.
Surface group velocity map for the Southern
California. The maximum a posteriori solution
for the tomographic inversion scheme using
noise. (A: San Joaquin valley, B: Ventura, C: Los
Angeles, D: Salton Sea Trough)
Title: Kirchhoff integral and Virtual Source Method
Authors: Valeri Korneev (LBNL) and Andrey Bakulin (Shell)
The Virtual Source method (VSM) has recently been proposed as a new practical
approach to reduce distortions of seismic images caused by shallow heterogeneous
overburden. VSM is demanding at the acquisition stage because it requires placing
downhole geophones below the most complex part of the heterogeneous overburden.
Where such acquisition is possible, however, it pays off later at the processing stage
because it does not require knowledge of the velocity model above the downhole
receivers. This study demonstrates that VSM may be viewed as an application of the
Kirchhoff-Helmholtz integral (KHI) with an experimentally measured Green’s
function. Direct measurement of the Green’s function ensures the effectiveness of the
method in highly heterogeneous subsurface conditions.
Numerous conditions needed to apply the KHI are not satisfied in practice, and it is
very unlikely that VSM can reconstruct true amplitudes of Green’s functions between
subsurface points. We provide considerations suggesting reasonable assurance that
VSM can accurately recover phase responses needed for high-fidelity imaging. The
actual performance of VSM in realistic situations is the subject of future
investigations.
Title: A Novel Application of Time-Reversed Acoustics: Salt Dome Flank
Imaging Using Walk Away VSP Surveys
Authors: Rongrong Lu, Mark E. Willis, Xander Campman, M. Nafi Toksöz,
Yang Zhang (MIT), and Maarten V. de Hoop (CSM)
We present initial results of applying Time-Reversed Acoustics (TRA) technology to
seismic imaging of a salt dome flank. We create a set of synthetic acoustic traces
representing a multi-level, walk away VSP for a model composed of a simplified Gulf
of Mexico vertical velocity gradient and an embedded salt dome. To process these
data, we first apply the concepts of TRA to the synthetic traces. This creates a set of
redatummed traces without having to perform any velocity analysis, moveout
corrections or complicated processing. Each of these redatummed traces approximates
the output of a zero offset, down hole source and receiver pair. We then apply
conventional post stack depth migration to this zero offset section to produce the final
image of the salt dome flank. Our results show a very good image of the salt when
compared to an image derived using data from down hole, zero offset source and
receiver pairs. We explore the effects of aperture on the TRA redatummed traces.
Title: Making waves by time reversal
Authors: Dirk-Jan van Manen (WesternGeco, University of Edinburgh), Johan
Robertsson (WesternGeco) and Andrew Curtis (University of Edinburgh)
We present a methodology that provides a new perspective on modeling and inversion
of wave propagation satisfying time-reversal invariance and reciprocity in generally
inhomogeneous media. The approach relies on a representation theorem of the wave
equation to express the Green's function between points in the interior as an integral
over the response in those points due to sources on a surface surrounding the medium.
Following a predictable initial computational effort, Green's functions between
arbitrary points in the medium can be computed as needed using a simple cross
correlation algorithm. The method is both flexible and efficient because it is no longer
necessary to define source and receiver locations upfront and all intermediate (finitedifference) calculations can be re-used. We illustrate the approach on a 4 x 4 km
region of the elastic Pluto model and show that full waveforms are reconstructed
accurately. There are no instabilities using this approach and tests show that the
source distribution on the surrounding surface can be severely decimated and still
yield useful results.
Title: Source spacing in virtual source imaging / Analysis of Treasure Island
earthquake data using seismic interferometry
Authors: K. J. Mehta, R. K. Snieder (Colorado School of Mines), K.
Wapenaar (Delft University), and V. M. Graizer (California Geological Survey)
Virtual source imaging (interferometric imaging) is a technique applied by Andrey
Bakulin and Rodney Calvert at Shell to the Peace River data for imaging below the
very complex near surface overburden without any knowledge of the overburden
velocity or near surface changes. An important consideration in a virtual source
imaging experiment is the spacing of the source locations. As in any other seismic
experiment, the sources should be placed at fine enough intervals to prevent spatial
aliasing. Stationary phase analysis is one approach to understand the optimum source
spacing in order to prevent spatial aliasing. We carried out this analysis for a
homogeneous isotropic medium and found that location of the receivers, depth of
reflector and velocity determine the maximum source spacing.
Seismic interferometry is a powerful tool in extracting the response of ground motion.
We show the use of seismic interferometry for analysis of an earthquake recorded by
Treasure Island Geotechnical Array near San Francisco, California on 06/26/94. It
was a magnitude 4.0 earthquake located at a depth of 6.6 km and distance of 12.6 km
from the sensors in borehole. There were six 3-component sensors located at different
depths. This problem is similar to the analysis by Snieder and Safak for the Robert A.
Millikan Library in Pasadena, California where they deconvolve the recorded
wavefield at each of the library floors with the top floor to see the upgoing and the
downgoing waves and using that, estimate a shear velocity and a quality factor. They
have also shown that for such applications of seismic interferometry, deconvolution of
waveforms is superior to correlation. For the Treasure Island data, deconvolving the
vertical component of the wavefield for each sensors with the sensor at the surface
gives a similar superposition of an upgoing and a downgoing wave. The velocity of
these waves agrees well with the compressional wave velocity. We compute the radial
and the transverse components. When we window the shear wave arrivals in
transverse components at each depth and deconvolve with the one on the surface, the
resultant up and down going waves travel with the shear wave velocity. Similar
windowing and deconvolution for the radial component also agrees with the shear
wave velocity. However, when the radial component is windowed around the
compressional waves and deconvolved, the up and the down going waves travel with
the shear wave velocity suggesting that there is a conversion at a depth below the
deepest sensor. Receiver functions, defined as the spectral ratio of the radial
component with vertical component, can be used to characterize the converted waves.
For the Treasure Island data, this spectral ratio shows an arrival at time close to t=0
for the deepest sensor located at 104 m depth indicating a P to S conversion very close
to this sensor. The travel time of this propagating wave in the receiver function is in
agreement with the calculated travel time of converted waves using the compressional
and shear wave velocities. Hence, we show that simple deconvolution can be used to
understand the velocity structure of the subsurface using earthquake data.
Title: Seismic interferometry, daylaight imaging and time-reversal: application
by using transmitted and reflected wavefields in tunnel seismic while drilling
surveys
Authors: F. Poletto and L. Petronio (OGS, Trieste, Italy)
We discuss the use of autocorrelogram interferometric techniques in seismic-whiledrilling applied to tunnel (TSWD) by using the tunnel-boring machine drilling noise.
The tunnel geometry, unlike reverse drill-bit VSP, makes it possible to record both the
backward reflected waves and those transmitted ahead of the tunnel face. Backward
waves are processed as a sort of RVSP dataset obtained by conventional pilotcorrelation techniques. Waves transmitted ahead are processed by autocorrelogram
techniques. The joint use of these wavefields offers advantages over conventional
borehole drill-bit VSPs. The most important of these are:
1) the advantage of getting reflected from transmitted wavefields by utilizing Kunetzs
equation and time-reversed traces;
2) the improvement in the analysis of the transmitted amplitudes;
3) the improvement in the deconvolution of the reflected waves by using the
transmitted wavefields, i.e., by using the operator derived by interferometric analysis.
These results are obtained by assuming the one-dimensional model approximation
with sub-vertical interfaces. TSWD data acquired during the excavation of 950 m
tunnel are presented. The results obtained by processing the front time-reversed and
back reflection fields are compared with those obtained by the amplitude analysis and
estimation of reflection coefficients. The results agree with the geological setting
along the tunnel.
Title: A Theoretical Overview Among Model-Based and Correlation-Based
Redatuming Methods
Authors: Gerard Schuster and Min Zhou (U. of Utah)
We overview the equations for correlation-based redatuming methods in this paper. A
correlation-based redatuming method uses natural phase information in the data to
time shift the weighted traces so that they appear to be generated by sources (or
recorded by geophones) shifted in location. This compares to model-based
redatuming which effectively time shifts the traces using traveltimes computed from
an a priori velocity model. For wavefield redatuming, the daylight imaging,
interferometric imaging, reverse-time acoustics (RTA) and virtual source methods all
require weighted correlation of the traces with one another, followed by summation
over all sources (and sometimes receivers). These methods differ from one another by
their choice of weights. The least squares interferometry and virtual source imaging
methods are potentially the most powerful because they account for a wide diversity
of arrivals in the data, leading to the possibility of superresolution. Interferometry, on
the other hand, has the flexibility of selecting imaging conditions that target almost
any type of event. Stationary phase principles lead to a Fermat-based redatuming
method known as redatuming by a semi-natural Green's function. No crosscorrelation
is needed, and so it is far less expensive than the other methods. Finally, we show
how the principles of interferometry and Fermat can be used to redatum traveltimes.
Title: Integral Green function representations of electromagnetic
interferometry with applications for ground penetrating radar
Authors: Evert Slob, Deyan Draganov and Kees Wapenaar (Delft University,
The Netherlands)
We present electromagnetic Green function representations for radar wave
interferometry in open systems. First we use the known configuration with two
passive recording stations inside a volume with equivalent boundary sources present
on the closed boundary surface. For this configuration we derive representations for
the real part of the electric field Green’s function due to a source of the electric
current type.
We introduce a new configuration where one passive recording station is inside the
domain, while the other is outside this domain. For this configuration we derive
representations for the Green’s function itself. For this new configuration we extend
the notion of interferometry to include correlation of a signal with a time-reversed
signal, which is expressed by a time convolution. For this time convolution type of
interferometry we derive representations for the Green’s function itself. The major
advantage of convolution over correlation type interferometry is that it is exact for
media with relaxation and/or loss mechanisms. Consequentially, it is also valid and
exact for fields where the wave energy is assumed to be zero, like difussive fields,
potential fields and stationary flow fields.
For these three basic exact representations we investigate their practical applicability
in ground penetrating radar explorations. We investigate the effects of the necessary
simplifications introduced and the effects of electric conduction losses on the
correlation type of interferometry.
Title: Linking multiple removal and daylight imaging for active surface seismic
data
Authors: Eric Verschuur and A.J. Berkhout (Delft University, The
Netherlands)
In most seismic processing flows multiples have been considered as noise and,
therefore, are discarded after the removal process. In this paper it is argued that
multiple reflections contain a wealth of information that should be used in seismic
processing to improve the resolution of reservoir images beyond current capability.
The proposed method, multi-channel weighted cross-correlation (WCC), in
combination with surface-related multiple elimination (SRME) allows the
transformation of multiples into primaries for surface seismic data. The latter means
that nonlinear seismic imaging can be implemented by a number of linear steps.
Within the field of daylight imaging, the use of multiples for extracting information
about primary reflections has already been an accepted phenomenon. However, this
requires seismic measurements from a random distribution of seismic source from
within the earth. It has been theoretically proven that by a multidimensional crosscorrelation of the seismic measurements Green's functions between two surface
locations can be extracted.
However, this approach cannot be applied without modification to active surface
seismic measurements, as the source distributions is no longer random, but is very
well organized (i.e. located at the surface). Therefore, a straightforward application of
cross-correlation will generate unwanted artifacts.
The developed weighted cross-correlation technique resolves this issue by two
modifications: 1) an estimate of the primary reflection data is used as the correlation
operator and is applied to the surface data with multiples and 2) the cross-correlation
process is replaced by a multi-dimensional inversion procedure, which is
implemented as a weighted cross-correlation.
The proposed method is illustrated with synthetic and field data examples.
Title: Green’s function representations for seismic interferometry
Authors: Kees Wapenaar and Deyan Draganov (Delft University, The
Netherlands)
Seismic interferometry is the process of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of
this principle was derived in 1968 by Claerbout, who showed that the reflection
response of a horizontally layered medium can be synthesized from the
autocorrelation of its transmission response. From Rayleigh's reciprocity theorem and
the principle of time-reversal invariance it follows that the acoustic Green's function
between two points in a lossless arbitrary three-dimensional inhomogeneous medium
can be represented by an integral of cross-correlations of wave field observations
at those two points. The integral is along sources on an arbitrarily shaped closed
surface; no assumptions are made with respect to the diffusivity of the wave field.
The Rayleigh-Betti reciprocity theorem leads to a similar representation of the
elastodynamic Green's function. When a part of the closed surface is the Earth's free
surface, the integral need only be evaluated over the remaining part of the closed
surface. In practice not all sources are equally important: the main contributions to the
reconstructed Green's function come from sources at stationary points on this surface.
When the sources emit transient signals, a shaping filter can be applied to correct for
the differences in source wavelets. When the sources are uncorrelated noise sources,
the representation simplifies to a direct cross-correlation of wave field observations at
two points, similar as in methods that retrieve Green's functions from diffuse wave
fields in disordered media or in finite media with an irregular bounding surface.
Title: An introduction to estimating the impulse response between receivers in
a controlled ultrasonic model
Authors: K. van Wijk (Physical Acoustics Laboratory and Department of
Geophysics, Colorado School of Mines, Golden, Colorado, 80401 USA)
A controlled ultrasonic laboratory model provides the backdrop for a detailed analysis
of retrieving an estimate of the Green's function between receivers in an elastic
medium. Instead of producing a formal derivation, this work appeals to a series of
intuitive operations common practice in geophysical data processing, to understand
these basic principles of Seismic Interferometry. Whereas the retrieval of the full
Green's function is based on the crosscorrelation of receivers in the presence of
equipartitioned signal, part of the causal Green's function is successfully recovered
with 40~sources in a line covering six wavelengths at the surface.
Title: Comparison between interferometric migration and reduced time
migration of CDP Data
Authors: Min Zhou and Gerard Schuster (University of Utah)
One of the difficulties in seeing beneath salt is that the migration velocity in the salt
and above is often not well known. This can lead to defocusing of migration images
beneath the salt. To mitigate this problem reduced-time migration (RTM) and
interferometric migration (IM) are proposed. The RTM method shifts the data with a
time difference between the calculated and natural arrival times of a reference
reflection. This correction can be shown to greatly reduce the defocusing problems
due to an incorrect velocity model of the overburden. The IM method on the other
hands requires: 1) extrapolation of the surface data below salt using the natural arrival
times of the subsalt reference reflector, and 2) migration of the extrapolated data
below the salt. Our synthetic and field CDP data tests indicate that both RTM and IM
can mostly remove the kinematic effects of the overburden without a good knowledge
of the overburden velocity.