Pore pressure is important for both exploration and drilling.During the exploration phase, a prediction of pore pressurecan be used to develop fluid migration models, to study theeffectiveness of seals, and to rank prospects. In drilling, apredrill pore pressure prediction allows the appropriate mudweight to be selected and allows the casing program to beoptimized, thus enabling safe and economic drilling. Apredrill estimate of pore pressure can be obtained from seis-mic velocities given a suitable velocity to pore pressure trans-form. This paper describes the use of seismic reflectiontomography and 4-C seismic data for pore pressure predic-tion. Reflection tomography gives higher spatial resolutionthan conventional methods based on the Dix equation, whilethe additional information provided by 4-C data may helpto reduce the ambiguity between variations in pore pressureand variations in lithology and fluid content.

Reflection tomography. Seismic velocities used duringprocessing are designed to optimize the stack/migrationresult. Local fluctuations are smoothed out, and the veloc-ity pick interval is usually too coarse for accurate pore-pres-sure prediction. Furthermore, these velocities average thevelocity over the seismic aperture used in the analysis andare not suitable for pore-pressure prediction in the pres-ence of significant lateral variations in the velocity.

Reflection tomography replaces the low resolution,layered medium, and hyperbolic moveout assumptions ofconventional velocity analysis with a completely generalray-trace modeling based approach. While both conven-tional velocity analysis and reflection tomography evalu-ate moveout on gathers of seismic traces, tomographyreplaces the CMP gathers of conventional velocity analy-sis with prestack depth migrated CIP gathers. CIP tomog-raphy is based on a simple observation: With the correctvelocity model, prestack depth migration (PSDM) maps areflector to a common depth for all source-receiver offsetsat which it is illuminated. The method uses ray tracing togenerate a system of residual migration equations thatrelate changes in reflector depth to changes in a velocitymodel of arbitrary spatial complexity. An initial referencemodel is chosen, CIP gathers are generated, depth devia-tions across offset are picked, and the tomographic equa-tions are solved to minimize the residual moveout. Theprocess is iterated to convergence.

As an example, Figure 1 compares prestack depthmigration results for a section from the Gulf of Mexico,using velocities obtained with conventional stacking-veloc-ity analysis on the top, and with reflection tomography onthe bottom (Woodward et al.). Figures 2 and 3 show thecorresponding velocity fields and Figures 4 and 5 the cor-responding pore-pressure predictions. Significant improve-ments in the seismic image are obtained by updating thevelocity field using reflection tomography, but the differ-ence in the pore-pressure prediction is even more dra-matic. An interpretable image might be obtained using arelatively poor but smooth velocity field, but the resolu-tion in pore pressure required for well planning cannot.

Thus, pore-pressure prediction is less robust in the pres-ence of errors in the velocity field than seismic imaging.

Although the initial velocity model predicts the pres-ence of overpressure in this area (Figure 4), the magnitudeand spatial variation shown are not sufficiently accuratefor drilling. By contrast, the tomographically refined veloc-ity model leads to better understanding of the magnitudeand spatial distribution in pore pressure (Figure 5).

To check the accuracy of the velocity field obtained usingreflection tomography, the measured traveltime/depth pairsfrom a check shot that was available for a well in this areawere inverted for velocity as a function of depth. Figure 6compares the initial velocity field obtained from stackingvelocities at the well with the velocity field obtained usingtomography and with the inverted check shot. The tomo-graphically refined velocities accurately predict the depthand magnitude of the velocity reversal occuring at about2.5 km due to overpressure at this depth.

Shear-wave acquisition in the marine environment.Seismic velocities can be influenced by changes in fluidcontent, as well as by changes in pore pressure. Both P-and S-wave velocities can be obtained in the marine envi-ronment using multicomponent receivers at the seafloor.The additional information provided by the S-wave veloc-ity may help reduce ambiguity between variations in porepressure and variations in lithology and fluid content.

The porosity of shales decreases during burial, leading

Seismic pore-pressure prediction usingreflection tomography and 4-C seismic data

COLIN M. SAYERS, Schlumberger, Houston, Texas, U.S.MARTA J. WOODWARD, WesternGeco, Houston, Texas, U.S.ROBERT C. BARTMAN, Devon Energy, Houston, Texas, U.S.

Figure 1. Seismic image in the Gulf of Mexico obtainedby Woodward et al. with prestack depth migration usingvelocities obtained by conventional stacking velocityanalysis (top) and with a velocity field refined by reflec-tion tomography (bottom).

188 THE LEADING EDGE FEBRUARY 2002

to an increase in P- and S-wave velocity. For mudrocks,Castagna et al. found the following empirical, linear relationbetween P- and S-wave sonic logs (the “mudrock line”):

vS = avP - b (1)

where a=0.862 and b=1.172 km/s for mudrocks. A decreasein P-wave velocity due to overpressure would therefore beexpected to be accompanied by a decrease in S-wave veloc-ity. The presence of gas, however, would be expected toreduce P-wave velocity, while leaving the S-wave velocitylargely unaffected. The additional information provided bythe S-wave velocity is therefore useful to check if an observedvelocity decrease may be due to the presence of gas.

Gulf of Mexico example. Figures 7 and 8 show the PP andPS images obtained using an isotropic prestack depthmigration for a 4-C line in the Gulf of Mexico. A sonic log,check shot, and mud weights used during drilling wereavailable for a vertical and a deviated well on this line.

Figure 9 compares the P-wave velocity obtained bytomography at the deviated well with the interval veloc-ities obtained by inverting the check shot and by upscal-ing the sonic log. Figure 10 compares the P-wave velocityobtained by tomography at the vertical well with the inter-val velocity obtained by upscaling the sonic log (no checkshot being available for this well). Good agreement is

Figure 3. Final velocity field (m/s) obtained using reflec-tion tomography.

Figure 4. Pore-pressure prediction (ppg) obtained usingthe initial velocity field derived using conventional,premigration stacking velocity analysis.

Figure 5. Pore-pressure prediction (ppg) obtained usingthe final velocity field derived using reflection tomogra-phy.

Figure 6. Comparison of the initial velocity field obtainedusing conventional stacking velocity analysis, the finalvelocity field obtained using reflection tomography, andthe velocity field obtained by inverting a check shot.

Figure 2. Initial velocity field (m/s) obtained using con-ventional stacking velocity analysis.

FEBRUARY 2002 THE LEADING EDGE 189

observed with a noticeable velocity reversal at about 2km. Also shown is the S-wave velocity at the well, com-pared with the S-wave velocity predicted from the tomo-graphic P-wave velocity using the mudrock line. TheS-wave velocity obtained by tomography is greater thanthat predicted by the mudrock line using the Castagna coef-ficients. One possible reason for this disagreement is thatisotropy was assumed in the tomographic inversion.Seismic anisotropy, if present, increases the ratio of themoveout velocities for S- and P-waves and might explainwhy the S-wave velocities obtained using reflection tomog-raphy are greater than those predicted using the mudrockline. Anisotropy was therefore included in the inversion,assuming that Thomsen’s δ parameter is zero and by per-forming reflection tomography and prestack depth migra-

tion for various values of Thomsen’s parameter ε. It wasfound that, for ε = 0, the reflectors on the PS section appeartoo deep when compared with the corresponding reflec-tors on the PP section (compare Figures 7 and 8) and, forε = 0.025, the PS reflectors appear too shallow (Figure 11).Best PS image quality and best PS/PP depth alignment (asmeasured visually and by cross-correlation) were achievedwith ε = 0.015 (Figure 12). Although small, a value of ε =0.015 has a significant effect on the small-offset moveoutvelocity for mode-converted S-waves, since it enters theexpression for the moveout velocity in the combination

Figure 9. Comparison (left) of the P-wave velocityobtained using isotropic tomography at the deviatedwell with the interval velocity obtained by inverting thecheck shot and by upscaling the sonic log using Backusaveraging. The isotropic tomographic S-wave velocity(right) at the well compared with prediction of themudrock line using tomographic P-wave velocities.

Figure 10. Comparison (left) of the P-wave velocityobtained by isotropic tomography at the vertical wellwith the interval velocity obtained by upscaling thesonic log using Backus averaging. The isotropic tomo-graphic S-wave velocity (right) at the well comparedwith prediction of the mudrock line using thetomographic P-wave velocities.

Figure 7. PP image for a 4-C line over an overpressuredarea in the Gulf of Mexico obtained using isotropicprestack depth migration.

Figure 8. PS image for a 4-C line over an overpressuredarea in the Gulf of Mexico obtained using isotropicprestack depth migration.

190 THE LEADING EDGE FEBRUARY 2002

and can be large for undercompacted sediments. Here V0P

and V0S are the vertical velocities for P- and S-waves, respec-

tively.A dipole sonic log was also available for a well in this

region. Figure 13 compares a plot of VS versus VP for thiswell with a locally calibrated fit of equation (1) and themudrock line of Castagna et al. Figure 14 compares the ver-tical S-wave velocity obtained by reflection tomographyfor δ=0 and ε = 0.015 with the prediction of the locally-cal-ibrated mudrock line for the deviated and vertical well.The agreement is much improved. Although not as pro-nounced as that predicted from the P-wave velocity usingthe locally calibrated mudrock line, the S-wave velocityshows a clear velocity reversal. This suggests that thereversal in the P-wave velocity cannot be explained by thepresence of a different pore fluid (e.g., gas) because the S-wave velocity is expected to be affected much less by a

change in pore fluid than is the P-wave velocity.Apore-pressure prediction was made using the P-wave

velocities, obtained by tomography, using Eaton’s method(Eaton, 1975) with an exponent n=4 and a normal trendline given by v(z) = v0 + kz.

The velocity to pore pressure transform was calibratedusing the mud weights at the vertical well. This gave para-meters v0 = 1.571 km/s and k=0.783 s-1. The tomographicvelocity, normal trend, pore-pressure prediction, and mudweights used in drilling the vertical well are shown in Figure15. Keeping the parameters fixed, the pore pressure wasthen predicted at the deviated well. The tomographic veloc-ity, normal trend, pore-pressure prediction, and mud weightsused in drilling the deviated well are shown in Figure 16.

Conclusion. A predrill estimate of formation pore pressureis a key for safe and economic drilling of deepwater wells.

FEBRUARY 2002 THE LEADING EDGE 191

Figure 11. PS image for a 4-D line over an overpressuredarea in the Gulf of Mexico obtained using anisotropicprestack depth migration and tomography with δ = 0and ε = 0.025.

Figure 12. PS image for a 4-C line over an overpressuredarea in the Gulf of Mexico obtained using anisotropicprestack depth migration and tomography with δ = 0 andε = 0.015.

Figure 13. VS plotted against VP for a well in the regionwith a fit of equation 1 and the mudrock line ofCastagna et al.

Figure 14. The tomographic S-wave velocity for δ = 0 andε = 0.015 at the vertical well (left) and deviated well(right) compared with prediction of the locally calibratedmudrock line using the tomographic P-wave velocities.

Although the use of seismic velocities for pore pressure pre-diction is well known, the interval velocities need to bederived using a method capable of giving a spatial resolu-tion sufficient for well design. Moveout velocities averagethe velocity over the seismic aperture. These velocities aretherefore not suitable for pore-pressure prediction in thepresence of lateral variations as may arise from the presenceof dipping structures, lithology variations, salt layers of vari-able thickness, fault blocks, or variations in compaction andpore pressure. Reflection tomography gives improved spa-tial resolution of the seismic velocity field and thus allowsa more reliable predrill pore pressure cube to be obtained.However, seismic velocities can be influenced by changes inlithology and fluid content, as well as by changes in porepressure. Both P- and S-wave data can be acquired in themarine environment using multicomponent receivers at theseafloor. The additional information provided by the S-wavevelocity may help to reduce the ambiguity between varia-tions in pore pressure and variations in lithology and fluidcontent. However, anisotropy, if present, needs to be

accounted for in comparing predictions made using P- andS-wave velocities. Finally, note that any predrill pore pres-sure prediction will contain inaccuracies due to errors in thevelocity and due to errors in the velocity to pore pressuretransform. Measurements acquired while drilling can beused to update the velocity to pore pressure transform whiledrilling, so that the best possible pore pressure predictioncan be made ahead of the bit.

Suggested reading. “Estimation of formation pressures fromlog-derived shale properties” by Hottman and Johnson (JPT,1965). “Seismic data indicate depth, magnitude of abnormal pres-sure” by Pennebaker (World Oil, 1970). “The equation for geo-pressure prediction from well logs” by Eaton (SPE 5544, 1975).“Pore-pressure estimation from velocity data: Accounting forpore pressure mechanisms besides undercompaction” byBowers (SPE Drilling and Completion, 1995). “Pressure predic-tion from seismic data: Implication for seal distribution andhydrocarbon exploration and exploitation in deepwater Gulf ofMexico” by Dutta (NPF Special Publication No. 7, Elsevier, 1997).“Illuminating the shadows: Tomography, attenuation, and pore-pressure processing in the South Caspian Sea” by Lee et al. (TLE,1998). “3-D geopressure analysis in the deepwater Gulf ofMexico” by Kan et al. (TLE, 1999). “Predrill pore-pressure esti-mation from velocity data” by Sayers et al. (paper IADC/SPE59122 at the 2000 IADC/SPE Drilling Conference). “Reflectiontomography in the postmigrated domain” by Stork (GEOPHYSICS,1992). “Macro velocity model estimation through model-basedglobally optimized residual-curvature analysis” by Wang et al.(SEG 1995 Expanded Abstracts). “Automated 3-D tomographicvelocity analysis of residual moveout in prestack depth migratedcommon image point gathers” by Woodward et al. (SEG 1998Expanded Abstracts). “Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks” byCastagna et al. (GEOPHYSICS, 1985). “Weak elastic anisotropy” byThomsen (GEOPHYSICS, 1986). “Anisotropic velocity analysisusing mode-converted S-waves” by Sayers (Journal of SeismicExploration, 1999). LE

Acknowledgments: Thanks to Uwe Albertin and Clement Kostov forhelpful discussions.

Corresponding author: cmsayers@slb.com

192 THE LEADING EDGE FEBRUARY 2002

Figure 15. P-wave velocity at the vertical well (left)obtained using tomography compared with the normaltrend. Pore-pressure prediction (right) using Eaton’smethod.

Figure 16. P-wave velocity (left) at the deviated wellobtained using tomography compared with the normaltrend. Pore-pressure prediction (right) using Eaton’smethod.