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Separation and imaging of seismic diffractions using plane-wave decomposition

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Summary We use the simulated plane wave section method to separate specular reflections and diffraction events. We show that plane wave sections naturally separate specular and diffracted events and allow us to use plane-wave distruction filters to suppress specular events resulting in plane-wave sections of diffractions. A synthetic example demonstrates the effectiveness of our method in imaging faults and small-scale discontinuities.
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Separation and imaging of seismic diffractions using plane-wave decomposition
M. Turhan Taner, Rock Solid Images, Sergey Fomel, University of Texas at Austin, and Evgeny Landa, OPERA
Summary
We use the simulated plane wave section method to
separate specular reflections and diffraction events. We
show that plane wave sections naturally separate specular
and diffracted events and allow us to use plane-wave
distruction filters to suppress specular events resulting in
plane-wave sections of diffractions
. A synthetic example
demonstrates the effectiveness of our method in imaging
faults and small-scale discontinuities.
Introduction
Seismic reflection data contain two types of coherent
events generated from the subsurface discontinuities:
specular reflections and diffractions. Specular reflections
are the ones being used conventionally to interpret
structural and stratigraphic features of the subsurface.
Diffractions have been neglected by most researchers.
Specular reflections are generated by interfaces with
impedance contrasts. Diffractions are generated by local
discontinuities when they act like point sources. These
point sources become active as soon as the direct wave hits
them. Presence of diffractions can indicate faults or
fractures, which is important in carbonate environments,
where locating fractures and their orientation is the
objective of seismic interpretation.
The idea of using diffractions in seismic imaging is not
new. Harlan et al. (1984) used forward modeling and local
slant stacks for extracting velocity information from
diffractions. Landa et al., (1987), Landa and Keydar (1998)
used common-diffraction-point sections for imaging of
diffraction energy and detecting local heterogeneities. In
this paper, we take a different route by attempting to
separate diffraction events before imaging. In a companion
paper (Fomel et al, 2006), we discuss separation and
imaging of diffractions appearing on post-stack sections.
The separation is based on application of plane-wave
destruction filters (Claerbout, 1992 ; Fomel, 2002). An
analogous idea, but with an implementation based on
multidimensional prediction-error filters, was previously
discussed by Claerbout (1994).
In this paper, we use the simulated plane wave section
method (Taner, 1976; Shultz and Claerbout, 1978) to
separate specular reflections and diffraction events. We
show that the plane wave sections naturally separate
specular and diffracted events and allow us to use the
plane-wave distruction filter to suppress specular events
resulting in plane-wave sections of diffractions. We use a
synthetic example to confirm the proposed method.
Method
Let us consider behavior of a plane reflector and a point
diffraction scatterer in case of a point source shot record.
Specular reflection and diffraction from the point scatterer
appear on the seismic record in the form of hyperbolas.
That is both of them behave like a point source, as depicted
schematically in Figure 1. While the
specular interface
acts like a mirror, we will see the point source in its
mirror
position, the diffractor is activated at the moment
when the direct wave arrives and the scatterer point acts as
a source in depth.
(a)
b)
Figure 1. Reflections from a plane reflector and a
diffractor, illuminated by a point source. a) Depth section,
b) Corresponding time section
2401SEG/New Orleans 2006 Annual Meeting
Prestack diffraction separation
If we activate a plane wave source, the reflected event from
a plane specular reflector creates a plane wave, while the
point diffractor behaves the same way as in the previous
case and acts like a point source. (Figure 2)
(a)
(b)
Figure 2. Plane reflector and a diffractor reflections , as
illuminated by a plane source wave: a) Depth section,
b) Corresponding time section.
To generate plane wave sections from a point source
seismic data we invoke two basic laws: superposition and
reciprocity. Reciprocity helps us exchange receiver and
source positions. By the superposition we can combine
different seismic records together to simulate plane-wave
records as if all the sources were exploded simultaneously.
Plane wave decomposition (Taner, 1976) can be
schematically described as follows. Taking one common
shot record and summing the traces horizontally without
any time delay we simulate a trace which we would obtain
if we exploded simultaneously many sources at the receiver
locations and record the reflected data at the source
position. Repeating this procedure for several shot records
we can simulate plane-wave source record. When we deal
with marine case (single end observation geometry) the
cable end creates an edge effect: semi spherical wave field,
we wish to attenuate. To do it, we can use the reciprocity
principle and create an artificial split-spread shot record by
sorting the data to CMP domain, replicating the CMP data
to the opposite sign offsets, and sorting it back to the shot
records.
When we sum a split spread shot record horizontally, we
simulate a plane wave propagating vertically downward at
the inception. If we shift the traces linearly before
summation, we generate a
dipping plane wave. By
repeating summations with various dips, we actually
generate a τ-p section corresponding to our shot record, or
the Radon transform estimate. There
are many procedures
to compute the Radon transform (Gardner and Lu, 1991),
and we do not discuss them here.
More details about plane-wave decomposition are
described by Yilmaz and Taner (1994). A section of a
constant plane-wave slope p illuminates the subsurface
with a specific angle at the surface. On these constant p
sections we will have specular reflections appear as quasi-
linear continuous events and diffracted waves will appear
in the quasi-hyperbolic shaped traveltimes (Green’s
functions). We can now use the plane-wave destruction
filter (Fomel, 2002) to suppress the specular events and to
obtain a section containing mainly diffracted events and
residual specular reflection energy. Since the resulting
traces are Radon transformed traces, their S/N ratio should
be better than the original traces in the time domain. The
scattering objects (faults, fractures etc.) will be imaged on
the migrated (time or depth) common p sections.
In summary, our flow for wavefield separation is:
1) Generate split spread common source records;
2) Plane-wave decompose each common source
record;
3) Sort into constant p sections;
4) Plane-wave destruction filter on constant p
sections;
5) Velocity analysis for migration;
6) Migrate individual p sections and then sum to
produce a prestack migration image.
Example
Figure 3a shows a synthetic single end shot gather for a
model containing numerous sharp structural discontinuities
producing numerous diffraction events. To perform plane-
wave decomposition for shot records we constructed a split
spread observation geometry using the reciprocity as it is
described above (Figure 3b). Figure 4a shows plane-wave
decomposed shot gather and Figure 4b illustrates the same
shot gather reconstructed by an inverse Radon transform.
2402SEG/New Orleans 2006 Annual Meeting
Prestack diffraction separation
Repeating plane-wave decomposition for all shot records
we obtain common p section for entire line. Figure 5 and 6
show two common p sections for different p parameter: 0,
0.5. Applying the plane-wave distruction filter to each of
the total wavefield sections (left) we obtain the
corresponding sections containing mostly diffraction
energy (right). It is interesting to observe that some of the
separated events in the deeper part of the sections are
actually not diffractions but triplications of the propagating
plane wave caused by lateral velocity variations.
Figure 3. Single ended (left) and split-spread (right) shot
gather.
Figure 4. Radon transformed (left) and reconstructed by
inverse Radon transform shot gather
Figure 5. Common p (p=0) section of the total wavefield
(left) and after wavefield separation (right).
Figure 6. Common p (p=0.5) section of the total wavefield
(left) and after wavefield separation (right)
Sorting back to shot domain and applying inverse Radon
transform we obtain seismic records containing diffraction
events and residual specular reflection energy. These
records now can be used for velocity model estimating,
time or depth imaging and should emphasize sharp
discontinuities of the subsurface. Figure 7 shows prestack
depth migrated image of the total wavefield (a) and
“diffractions only” components (b). Most of the scattering
objects which are masked on the conventional section (a)
can be observed on the “diffractions only” section (b).
2403SEG/New Orleans 2006 Annual Meeting
Prestack diffraction separation
(a)
(b)
Figure 7. Prestack depth migration of the full wave-field (a)
and the separated diffractions (b).
Conclusions
The objective of this paper is to show that plane-wave
constant p sections contain diffraction patterns that directly
obey the wave equation together with specular reflectors. In
contrast to point source sections, plane-wave sections
contain specular events that appear as simply shaped
laterally continuous events. Diffracted events appear in the
form of focusing operators with a delay equal to the travel
time from the source wave origin to the point scatterer.
This observation allowed us to develop a method for
diffraction separation and imaging based on applying
plane-wave destruction filtering on plane-wave sections.
Separated and imaged diffractions can provide valuable
information about small-scale subsurface features such as
faults, fractures, rough salt boundaries, channels, etc.
Although we show only a 2-D example in this paper, our
method is applicable to 3-D plane-wave decompositions
such as those recently described by Zhang et al (2005).
References
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Fomel, S., 2002, Applications of plane-wave destruction
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2404SEG/New Orleans 2006 Annual Meeting
EDITED REFERENCES
Note: This reference list is a copy-edited version of the reference list submitted by the
author. Reference lists for the 2006 SEG Technical Program Expanded Abstracts have
been copy edited so that references provided with the online metadata for each paper will
achieve a high degree of linking to cited sources that appear on the Web.
REFERENCES
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Scientific Publications, Inc.
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3D depth migration: Geophysics,
70, E21–E28.
2405SEG/New Orleans 2006 Annual Meeting
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