CRS seismic processing: a quick tutorial

V. Grosfeld, R. Biloti and R. Portugal

State University of Campinas, Brazil

Abstract

The aim of this work is to present an alternativeway that could be introduced in the conventionalseismic processing, using a macro model indepen-dent method. We will show how to take advantageof the results of this process to incorporate them inthe normal flowchart of processing. We also presenta didactic synthetic example to ilustrate how theflowchart works.

Introduction

In the last few years a new method to obtain azero-offset (ZO) stack section was introduced in theliterature: common reflection surface (CRS) stack(Mann et al., 1999). It is macro-velocity model in-dependent method and has the advantage of usingmore traces than the conventional process. More-over, the CRS stack method also provides severalkinematic parameters, which can be used to inverta velocity model. Consequently, the introduction ofthe CRS method into the conventional seismic pro-cessing can be advantageous. This work presentsan alternative flowchart seismic process based onCRS and totally model independent.

CRS method

The CRS method is based on a multi-parametertraveltime apprroximation, called the hyperbolictraveltime formula(Tygel et al., 1997) which relatesthe traveltime of two rays. One of them is taken asreference ray, and is called central ray.In the CRSmethod, the central ray is chosen as a ZO ray andits reflection point is called Normal Incidence Point(NIP). The formula read

T 2(xm, h) =(

t0 +2xm sin β0

v0

)2

+

2t0 cos2 β0

v0(KN x2

m + KNIP h2) ,

where xm = (xG+xS)/2−x0 and h = (xG−xS)/2,x0 is the coordinate of the central point, xG andxS are the horizontal coordinates of the receiverand source, respectively,, t0 the zero-offset two waytraveltime, β0 the emergence angle measured with

respect to the normal surface,, KNIP and KN andtwo wavefront curvatures associated to two hypo-thetical eigenwaves N-wave and NIP-wave,Tygel etal. (1997), see Figure 1.

Σ

S GX0

NIPR

β0

NIP-wavefront

N-wavefront

Figure 1: CRS Parameters for a normal central rayX0 NIP X0: the emergence angle β0 and the NIP-and N-wavefront curvatures. Σ is the reflector, X0

is the central point coordinate, and S and G arethe source and receiver positions for a paraxial ray,reflecting at R.

Processing sequence

The process is the same as the conventional pro-cess up to NMO stack, which is automatically per-formed during the CRS stack. At the end, theCRS stack method came up with three parame-ter sections, one coherency section and, in general,a more accurate ZO simulated section. The mostrelevant aspect is that the whole procedure is com-pletely velocity-model independent and a largernumber of traces is stacked than in the conven-tional NMO/DMO process, increasing the redun-dancy and the signal-to-noise ratio.

Once a ZO section is available, the methodalso provides a Post Stack Time Migration, withoutthe requirement of having a velocity model in timedomain. This can be achieved using only the CRSparameters.

As we have just pointed out, the CRS pa-rameters carry to much information about the me-dia and then we should use this parameters asmuch as possible. Following this idea, the classi-cal layer-stripping velocity inversion algorithm ofHubral and Krey (1980) can be recast by using

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Grosfeld et al.

of the CRS (Biloti et al., 2001). It inverts itera-tively on the depth homogeneous layers and inter-face positions. The interfaces are constructed ascubic splines, which are suitable for further blockray tracing algorithms. This process involves lowcomputational costs since the CRS parameter arealready available.

Once we have the inverted velocity model, itis possible to perform a complete PreStack DepthMigration (PreSDM), using weights to compen-sate amplitudes for geometrical spreading. Also,an unweighted PreSDM can be realized followedby a a posteriori amplitude correction for somecommon-reflection points (CRP) gathers (Portugalet al., 2001). This correction is performed in threesteps: (i) for the selected depth point computethe traveltime, incidence angles and geometrical-spreading factors by modeling, using the invertedmodel; (ii) pick the amplitude from the originaldata, using the traveltime information and, (iii)multiply them by corresponding the geometrical-spreading. This CRP points are chosen in a un-weigth PreSDM, which has the characteristic toshow a good kinematic image of the subsurface.After the AVO/AVA curves are constructed.

Synthetic example

To illustrate the just described procedure, we showstep-by-step how it works on synthetic data. Fig-ure 2 shows the compressional velocity field of syn-thetic model. The shear-velocity at each pointis set to the compressional velocity dived by

√3.

The model is composed by four layers bounded by

2

2.2

2.4

2.6

Dep

th (

km)

Distance (km)0 4 8

0

1

2

3

4

Figure 2: Synthetic model.

smooth interfaces. The top and bottom layers arehomogeneous and the two intermediated layers areinhomogeneous both in x-direction and z-direction.The multicoverage data is formed by a collectionof 150 common-offset section, with offset varyingfrom 20 m up to 3000 m, with around 500 source-receiver pairs each. In Figure 3 we can see a typi-

cal common-offset section with offset 1500 m. Thesignal-noise ratio added to the data was 7:1.

0

1

2

3

4

Tim

e (s

)

0 2 4 6 8 10Midpoint coordinate (km)

Figure 3: Example of a common-offset section.

After performing the CRS stack method, theobtained simulated ZO section is shown in Figure 4.Note the great improvement in the signal-to-noiseratio. As an example, Figure 5 presents one of the

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Zer

o-of

fset

trav

eltim

e (s

)

200 400 600 800CDP number

Figure 4: CRS simulated ZO section.

parameters section the emergence angle section. Itis important to note that the parameter value foreach point of the section make sense only if thepoint is indeed a reflection event. After the con-clusion of the first step of the CRS, we directlyproceed to the invertion step. In Figure 6 we showthe inverted model where it is possible to observethat the recovered model fits very well the synthetic

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CRS seismic processing: a quick tutorial

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Zer

o-of

fset

trav

eltim

e (s

)

200 400 600 800CDP number

-20

-10

0

10

20

Figure 5: Emergence angle section

model, even in the inhomogeneous layers.

2

2.2

2.4

2.6

Dep

th (

km)

Distance (km)0 4 8

0

1

2

3

4

Figure 6: Inverted velocities model.

The velocity model is now smoothed in orderto apply PreSDM, which is performed using thetraveltime tables generated on the fly by wavefrontconstruction method (Vinje et al., 1993 ). Eachcommon-offset section is migrated separately (seeFigure 7), and then stacked migrated section, seeFigure 8.

The stacked migration section does not haveinformation about correct amplitudes, but it servesas an image to chose points (the CRP points) toperform the AVO/AVA curves. This is done as wasdiscussed in the Processing Sequence section. Theresult for one ponint is show in Figure 9

Conclusion

The CRS method provides a powerful tool to pro-cess multi-coverage data. It allow us not only toobtain a good simulated ZO section, but also geta tool for the next steps in the conventional pro-

1000

1500

2000

2500

3000

3500

Dep

th (

m)

3000 4000 5000 6000 7000Distance (m)

Figure 7: typical migrated section.

1000

1500

2000

2500

3000

3500

Dep

th (

m)

3000 4000 5000 6000 7000Distance (m)

Figure 8: Stacked migrated section.

cesses. One more interesting application, that weare working on is to incorporate the acquisition to-pography in the method. We hope to obtain goodresults in cases with strong variations in the acqui-sition surface.

Acknowledgements

This work was partially supported by FAPESP(Grants 97/12125-8 and 97/12318-0), CAPES andby the sponsors of the WIT Consortium.

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Grosfeld et al.

0 10 20

Reflection angle (degree)

0

0.5

1.0

1.5

Nor

mal

ized

R(θ

)

AVA Curve

0 1000 2000

Offset (m)

0

0.5

1.0

1.5

Nor

mal

ized

R(h

)AVO Curve

Figure 9: AVO/AVA for a point in the second in-terface.

References

Biloti, R., Santos, L., and Tygel, M., 2001, Layeredvelocity model from kinematic attributes:, in 7thInternational Congress Brazilian Geophysical So-ciety.

Hubral, P., and Krey, X., 1980, Interval velocitiesfrom seismic reflection time measurements: Soc.of Expl. Geophys.

Mann, J., Hubral, P., Hocht, G., Jaeger, R., andMueller, T., 1999, Applications of the common-reflection-surface stack:, in 69th Ann. Internat.Mtg Soc. of Expl. Geophys., 1829–1832.

Portugal, R. S., Biloti, R., Santos, L. T., andTygel, M., 2001, CRS as tool for true amplitudeimaging:, in 7th International Congress BrazilianGeophysical Society.

Tygel, M., Muller, T., Hubral, P., and Schleicher,J., 1997, Eigenwave based multiparameter trav-eltime expansions:, in 67th Ann. Internat. MtgSoc. Of Expl. Geophys., 1770–1773.

Vinje, V., Iversen, E., and Gjøystdal, H., 1993,Traveltime and amplitude estimation usingwavefront construction: Geophysics, 58, no. 08,1157–1166.

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