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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

Claerbout, J. F., 1992, Earth sounding analysis: Processing

versus inversion: Blackwell.

Claerbout, J. F., 1994, Applications of two- and three-

dimensional filtering: 64th Ann. Internat. Mtg, Soc. of

Expl. Geophys., 1572–1575.

Fomel, S., 2002, Applications of plane-wave destruction

filters: Geophysics, 67, 1946–1960.

Fomel, S., E. Landa, and M. T. Taner, 2006, Post-stack

velocity analysis by separation and imaging of seismic

diffractions: 76th Ann. Internat. Mtg, Soc. of Expl.

Geophys., submitted.

Gardner, G. F. and L. Lu, eds., 1991, Slant-stack

processing: Soc. Of Expl. Geophys.

Harlan, W. S., J. F. Claerbout, and F. Rocca, 1984,

Signal/noise separation and velocity estimation:

Geophysics, 49, 1869-1880.

Landa, E., V. Shtivelman, and B. Gelchinsky, 1987, A

method for detection of diffracted waves on common-offset

sections: Geophysical Prospecting, 35, 359-373.

Landa, E. and S. Keydar, 1998, Seismic monitoring of

diffracted images for detection of local heterogeneities:

Geophysics, 63, pp 1093

Schultz, P. S. and J.F. Claerbout, J. F., 1978, Velocity

estimation and downward continuation by wavefront

synthesis: Geophysics, 43, 691-714.

Taner, M. T., 1976, Simplan: similated plane-wave

exploration, 46th Ann. Internat. Mtg., Soc. Expl.

Geophys., 186-187.

Yilmaz, O. and M. T. Taner, 1994, Discrete plane-wave

decomposition by least-mean-square-error method:

Geophysics, 59, 973-982.

Zhang, Y., J. Sun, C. Notfors, S. H. Gray, L. Chernis, and

J. Young, 2005, Delayed-shot 3D depth migration:

Geophysics, 70, E21-E28.

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

Claerbout, J. F., 1992, Earth sounding analysis: Processing versus inversion: Blackwell

Scientific Publications, Inc.

———, 1994, Applications of two- and three-dimensional filtering: 64th Annual

International Meeting, SEG, Expanded Abstracts, 1572–1575.

Fomel, S., 2002, Applications of plane-wave destruction filters: Geophysics,

67, 1946–

1960.

Fomel, S., E. Landa, and M. T. Taner, 2006, Post-stack velocity analysis by separation

and imaging of seismic diffractions: Presented at the 76th Annual International

Meeting, SEG.

Gardner, G. F., and L. Lu, eds., 1991, Slant-stack processing: SEG.

Harlan, W. S., J. F. Claerbout, and F. Rocca, 1984, Signal/noise separation and velocity

estimation: Geophysics,

49, 1869–1880.

Landa, E., and S. Keydar, 1998, Seismic monitoring of diffracted images for detection of

local heterogeneities: Geophysics,

63, 1093.

Landa, E., V. Shtivelman, and B. Gelchinsky, 1987, A method for detection of diffracted

waves on common-offset sections: Geophysical Prospecting,

35, 359-373.

Schultz, P. S., and J. F. Claerbout, 1978, Velocity estimation and downward continuation

by wavefront synthesis: Geophysics,

43, 691–714.

Taner, M. T., 1976, Simplan: Similated plane-wave exploration: 46th Annual

International Meeting, SEG, Expanded Abstracts, 186–187.

Yilmaz, O., and M. T. Taner, 1994, Discrete plane-wave decomposition by least-mean-

square-error method: Geophysics,

59, 973–982.

Zhang, Y., J. Sun, C. Notfors, S. H. Gray, L. Chernis, and J. Young, 2005, Delayed-shot

3D depth migration: Geophysics,

70, E21–E28.

2405SEG/New Orleans 2006 Annual Meeting