Shallow water flow prediction using prestack waveform .../media/Files/technical_papers/140/1497323.pdf · difficult in a cased-hole environment ... Shallow water flow prediction using

Shallow water flow (SWF) layers are frequently encoun-tered in deepwater areas when drilling into poorly consol-idated geopressured sands (Figure 1). These sands, whenflowing, can cause extensive damage to a borehole. Morethan $200 million has been lost to date for remediation andprevention of SWF problems in the Gulf of Mexico. Lately,this problem has also been a concern in many other deep-water clastic basins in the world.

SWF sands are known to occur in water depths of 450m or more and typically 300-600 m below the mudline. Theyare known to be present in almost all deepwater oceanbasins where the rate of sedimentation is high. Figure 2shows the formation of SWF layers in a deepwater envi-ronment. Loose and unconsolidated sediments with a highrate of sedimentation characterize the overburden and lowpermeability seal is created by compacted shales or mud-stones for which the rate of sedimentation is low. If isolatedsand bodies are in this shale or mudstone, water from suchbodies will not escape easily due to the presence of low-per-meability sediments around them. In addition, the high rateof sedimentation from the overburden exerts an enormouspressure on these sediments, causing these isolated bodiescontaining large amounts of water to be overpressured.These overpressured SWF layers pose a threat to drilling,and their identification prior to drilling is therefore impor-tant in reducing risk. In this paper, we study the feasibilityof detecting SWF layers using prestack waveform inversionof seismic data in conjunction with geologic analysis ofstratigraphic sequences related to SWF zones.

Rock properties of SWF sediments. In-situ measurementsof elastic and other rock properties of SWF sediments arevery limited because SWF layers are associated with verylow sonic velocities. Measurement of such low velocities isdifficult in a cased-hole environment (tool limitations), andopen-hole logging under SWF conditions is hazardous. Wetherefore rely on the elastic property trends of regular sandsand shales to determine the rock properties of SWF sands.In recent articles, Huffman and Castagna (2001) and Zimmeret al. (2002) reviewed the rock properties of SWF sedimentsbased on laboratory measurements. These sediments lie inthe transition zone between suspended materials in fluidand rocks around critical porosity.

These nearly unconsolidated sands exhibit low bulkdensities and anomalously low P- and S-wave velocities(VP and VS). With increasing pressure, they lose cohesion,causing VS to drop faster than VP. This causes VP/VS toincrease and therefore the Poisson’s ratio to increase. VP/VSof the order of 10 or higher (i.e., a Poisson’s ratio of 0.49 orhigher) is typical of these overpressured SWF sediments.Figure 3 summarizes some rock properties of SWF forma-tions. Note that the high VP/VS and Poisson’s ratio is adirect result of poor grain contact in these overpressuredSWF sediments.

Seismic characterization of SWF. Seismic data has longbeen recognized as key to SWF detection prior to drilling.Several seismic methods are available for the detection ofSWF zones. Geohazard or site-survey data provide high-res-

olution images at shallow depths where SWF typicallyoccurs and are good for analyzing stratigraphic sequences.However, because these geohazard data use a very shortcable length, they do not provide reliable velocity informa-tion or sufficient amplitude variation with offset (AVO)information to differentiate rock properties. Huffman andCastagna (2001) suggest using multicomponent data for

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Shallow water flow prediction using prestack waveform inversionof conventional 3D seismic data and rock modelingSUBHASHIS MALLICK and NADER C. DUTTA, WesternGeco, Houston, Texas, U.S.

Figure 1. Shallow water flow problem encountered in deepwater drilling.

Figure 2. Formation mechanism of SWF sands.

Figure 3. Elastic properties of sands and shales. Note that the SWFsands are characterized by low VP, VS, and density.

SWF detection. Although multicomponent seismic data pro-vide an accurate estimate of VP, VS, and density, acquiringsuch data is expensive, especially in deepwater where hard-ware limitations prevent multicomponent technology to beextended to water depths in excess of 5000 ft (1500 m). Fordetection of SWF and quantification of its properties, we aretherefore limited to conventional three-dimensional (3D) P-wave data acquired with a long cable.

Popular techniques for estimating rock properties fromsuch conventional data are the AVO-based methodsdescribed by Ostrander (1984), Rutherford and Williams(1989), and Connolly (1999) among others. These attemptto fit an approximate form of P-wave reflection coefficientas a function of angle-of-incidence to the P-wave reflection

amplitudes. AVO theory, however, assumes that reflectionevents on prestack P-wave data are primary reflections onlyand not contaminated by interference effects. Using syntheticdata, Mallick (2001, 2002) has demonstrated that such anassumption is valid for relatively small (usually less than25° to 30°) incidence angles. At higher angles, other wave-modes such as mode-converted reflections and interbedmultiple reflections interfere severely with P-wave primaryreflections. As a result, application of AVO has so far onlybeen successful at small angles of incidence, generally lessthan 25-30°. But, for accurate estimation of VP/VS andPoisson’s ratio from P-wave seismic data, AVO informationto angles higher than 25-30° is necessary. Because success-ful detection of SWF requires quantitative evaluation ofVP/VS and Poisson’s ratio, conventional AVO—limited tosmall angles of incidence—is not very useful.

Prestack waveform inversion (Sen and Stoffa, 1991, 1992;Stoffa and Sen, 1991; Mallick, 1995, 1999) offers a bettersolution because it uses an accurate forward modelingmethodology for inverting prestack seismic data thataccounts for interference of P-wave reflections with otherwave modes. Consequently, these techniques can handledata to large angles-of-incidence and provide reliable esti-mates of VP and VS (and, in turn, VP/VS and Poisson’s ratio).In this paper, we suggest an approach based on this prestackwaveform inversion that allows us to quantify the rockproperties of SWF formations using the entire offset rangeof conventional 3D seismic data. Further, the methodologyuses geologic model building aimed at understanding thestratigraphic and structural control on SWF formations.Some of this material was previously discussed by de Koket al. (2001).

Integrated approach for SWF detection. Figure 4 shows afive-step approach to SWF identification. The first steprequires best quality 3D seismic data with offsets largeenough to provide incidence angles up to 40° or higher. Forincreased resolution, reprocessing the data at a 2-ms sam-pling interval with particular emphasis to the shallow tar-get areas is desirable. Special care should be exercised withdynamic correction, amplitude preservation, and large off-set handling. The mute function should be omitted or be asmild as possible.

The second step involves stratigraphic interpretation ofthe reprocessed and stacked data to outline potentially haz-ardous sand bodies. The third step, which confirms thepotential for SWF identification prior to prestack inversion,is AVO analysis of the prestack data. The data volume is thenvisualized using conventional visualization platforms.

After AVO analysis and identification of potentially haz-ardous zones, prestack waveform inversion is carried outat selected locations. This is the fourth and most importantstep. For prestack inversion, we use the genetic algorithm(GA) based methodology developed by Mallick (1995, 1999)which allows accurate estimates of VP, VS, and bulk densityas functions of time and depth at the selected locations. TheGA prestack inversion is an optimization algorithm thatfinds a suitable earth model by minimizing the misfitbetween observed and synthetic data traces. It should benoted that the GA uses an exact wave equation based for-ward modeling, which allows one to calculate all primary,multiple, and mode-converted reflections. Consequently,all interference or tuning effects due to thin layers, andtransmission effects due to velocity gradients, are accuratelymodeled in the inversion process. Because GA uses a sta-tistical optimization process in searching for the best-fit elas-tic model, it also generates a measure of the error bounds

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Figure 4. The five-step process of SWF detection.

Figure 5. Synthetic seismogram, computed using elastic properties of aSWF environment. The reflection from the SWF layer is marked by anarrow.

Figure 6. Result of prestack inversion of the synthetic data of Figure 5.The true model is shown in black while the inverted model is shown inred.

or uncertainties in the estimation of the earth model.The fifth and final step deals with pore-pressure esti-

mation using VP values derived from the GA inversion. Thehigh-resolution VP field, obtained from the prestack GAinversion, provides more accurate pore pressure than thatpredicted from a conventional velocity analysis.

Figure 5 illustrates a synthetic seismic data set createdusing a reflectivity-modeling algorithm developed by Mallickand Frazer (1987, 1990). Figure 6 shows prestack GA inver-sion; the true model is black and the inverted model is red.We have used the VP, VS, and density trends for SWF sandsfrom Figure 3 to represent the SWF layers in this syntheticexample. Figure 5 shows that the SWF reflection is a strongnegative reflection at zero offset. Reflection amplitudesincrease with offset, change polarity at some intermediate off-set, and finally become a strong positive reflection at largeoffsets. Such AVO behavior of SWF sands is exactly oppositeto that of a class 1 gas sand reflection (Rutherford andWilliams, 1989). Also notice from Figure 6 that the prestackinversion estimated the input model to a reasonable accuracy.

Examples from real data. For tests on real data, we selecteda 3D seismic data volume from the Gulf of Mexico(Mississippi Canyon area, offshore Louisiana) where SWFconditions are known to occur. The seismic volume encom-passed the Ursa development site (blocks 809, 810, 853 and854) around well MC-854 2. We reprocessed the seismic dataat a 2-ms sampling interval for high-resolution trace inver-sion. A stacked section, reprocessed at 2 ms, is shown inFigure 7. Well MC 854 2 is indicated with markers at thethree known SWF levels. Notice that the reflection strengthof the SWF sands is weak, often making them less visiblethan other sands. This is because the SWF reflections on theprestack data have a polarity reversal around 30°, and sum-ming the negative and positive reflections tends to weakenthe reflection strength on the stacked data. Figures 8 and 9show the results of prestack inversion. Figure 8 comparesobserved prestack data with synthetic data computed usingthe inverted elastic earth model. Figure 9 shows the P-to-S-wave velocity ratio, VP/VS, estimated from inversion. Notethat the high values of VP/VS obtained from the prestackinversion matched closely with the zones where SWF lay-ers were experienced during drilling.

Figures 10-12 show another example from the same area.Figure 10 shows the stacked section along with the well loca-tion and identified SWF zones. Figure 11 compares observedand synthetic data. Figure 12 is VP/VS obtained from inver-sion. Once again, the anomalously high VP/VS values cor-related quite well with known SWF formations.

Discussion and conclusion. Prestack waveform inversionof conventional 3D seismic data with long offsets can yieldquantitative information about the rock parameters associ-ated with SWF formations prior to drilling. These forma-tions have an anomalously high VP/VS, often causing

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Figure 7. Stacked section from the Ursa site. Well MC-854 2 is shownon the section with three known SWF layers marked.

Figure 8. Comparison of observed prestack data with synthetic data com-puted using the prestack inverted elastic model at the MC-854 2 welllocation. Reflections from the known SWF layers are marked with arrows.

Figure 9. VP/VS obtained from prestack waveform inversion at the MC-854 2 location. The SWF zones correspond to high VP/VS values.

Figure 10. Stacked section from another area around the Ursa site. Thewell located on this section is indicated with its known SWF problems.

polarity reversals at large offsets. Of course, the success notonly depends on data quality and the choice of the dis-criminator, but also, and possibly more importantly, on theinversion method being used. In contrast to traditional inver-sion algorithms, a full waveform prestack inversion isdesigned to obtain both low and high frequency velocityvariations through the simultaneous modeling of moveoutand elastic reflection amplitudes. In addition, such an inver-sion correctly handles the interference of primary reflectionswith other wave-modes, leading to an accurate elastic earthmodel to a resolution of 1/6th to 1/4th wavelength of thedominant seismic frequency (Mallick et al., 2000).Application of prestack waveform inversion is therefore thekey to success of SWF detection at the Ursa well sites.

The success at Ursa does not automatically imply thatit is always possible to use prestack waveform inversion indetecting the SWF sands. Note that the SWF reflectionsexhibit a characteristic AVO behavior (Figure 5). The suc-cess of SWF detection therefore depends on how well sucha characteristic AVO behavior is present on real data. In thecase of Ursa, reflections from SWF sands exhibited this AVOcharacteristic quite well and, consequently, were successfully

detected by prestack inversion. Note that such typical reflec-tion behavior depends on the elastic properties of the SWFlayers and on those of the shale/mudstone formations thatsurround the SWF sands (Figure 2). Although the SWF sandsare believed to have VP of 1500-1800 m/s and low VS suchthat VP/VS is between 3.5 and 10, elastic properties of theshale/mudstone formations can vary quite widely from oneocean basin to another. Depending on the elastic propertiesof these formations, the reflection characteristics from SWFlayers are also likely to vary.

In addition, although identification of SWF is sensitiveto VP/VS, reflection amplitudes on seismic data as functionsof offset/angle-of-incidence are more sensitive to Poisson’sratio rather than the VP/VS (Koefoed, 1955, 1962; Bortfeld,1961; Shuey, 1985). Poisson’s ratio and VP/VS are related toone another, and one can be derived from the other (Figure13). For a typical shale/gas sand reflection, the Poisson’s ratioof shale is of the order of 0.35 while that of gas sand is ofthe order of 0.1 (Mavko et al, 1998). This corresponds to aVP/VS of shale of about 2 and that for gas sand of 1.5. Onthe other hand, SWF sands can have Poisson’s ratio between0.46 and 0.49. This corresponds to a VP/VS between 3.5 and10. The Poisson’s ratio of the shale/mudstone, surroundingthe SWF sand can have Poisson’s ratio between 0.35 and 0.44,corresponding to VP/VS values between 2 and 3 (de Kok etal, 2001). Notice that SWF reflections are characterized bya high contrast in VP/VS and relatively low contrast inPoisson’s ratio. Gas-sand reflections are characterized by lowcontrast in VP/VS and high contrast in Poisson’s ratio.

Figure 14 shows the P-wave reflection coefficient as afunction of angle of incidence for a typical gas sand and twoSWF reflections (SWF 1 and SWF 2). All these reflections coef-ficients were computed using the exact reflection coefficientformula, given in Aki and Richards (1980). For the gas sandreflection, the P-wave velocity, density, and Poisson’s ratiofor the overlying shale were assumed to be 2300 m/s, 2.1g/cm3, and 0.35 and those for gas sand were assumed to be2250 m/s, 2.05 g/cm3, and 0.10, respectively. For the SWFreflection, a P-wave velocity of 1550 m/s, density of 1.85g/cm3, and Poisson’s ratio of 0.48 were used for the SWFlayer. In SWF 1, the surrounding shale/mudstone wasassumed to have a P-wave velocity of 1600 m/s, density 1.9g/cm3 and Poisson’s ratio of 0.44. In SWF 2, in contrast, P-wave velocity and density were kept the same while thePoisson’s ratio was changed to 0.38.

For the gas sand reflection, the Poisson’s ratio contrastis 0.25 while the contrast in VP/VS is 0.5. For the SWF 1 reflec-tion, the Poisson’s ratio contrast is 0.04 and the VP/VS con-trast is 4. Finally, for the SWF 2 reflection, the Poisson’s ratioand VP/VS contrasts are 0.1 and 4.5, respectively. Reflection

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Figure 11. Comparison of observed prestack data with synthetic datacomputed using the prestack inverted elastic model at the second Ursalocation. Reflections from the known SWF layers are marked witharrows.

Figure 12. VP/VS obtained from prestack waveform inversion at thesecond Ursa location. The SWF zones once again correspond to highVP/VS values.

Figure 13. VP/VS plotted as a function of Poisson’s ratio.

coefficient plots of Figure 14 clearly show that Poisson’s ratio,not VP/VS, controls the behavior of the P-wave reflectionamplitudes as functions of angle of incidence. For the gas-sand reflection, although VP/VS contrast is low, the Poisson’sratio contrast is high. This high contrast in Poisson’s ratiocauses the difference in P-wave reflection coefficient betweensmall and large angles of incidence to be so big that it isclearly visible on real seismic data. This is the primary rea-son for the success of AVO and other prestack methods suchas prestack waveform inversion in detecting gas sands fromseismic data. For the SWF reflections, VP/VS contrast is largebut Poisson’s ratio contrast is not so large. If the range ofangles available in prestack data are 0-40°, gas-sand reflec-tion amplitudes change from -0.03 to -0.16, SWF 1 ampli-tudes change from -0.03 to 0.04, and SWF 2 amplitudeschange from -0.03 to 0.13. A reflection behavior such as SWF1 is likely to be hidden below the noise level, and thereforebe quite difficult to detect from prestack seismic data. Inorder to detect SWF reflections, AVO behavior must at leastbe similar to the SWF 2 reflection. By computing reflectioncoefficients for a variety of SWF models, we found that toachieve an AVO behavior close to a SWF 2 reflection, aPoisson’s ratio contrast of 0.07 or more is required.

Poisson’s ratio of the SWF layer itself is expected to beclose to, but less than, that of water (0.5). Therefore, ifPoisson’s ratio of the SWF layer is 0.45-0.49, detecting anSWF layer from seismic reflection measurements wouldrequire that Poisson’s ratio of the surrounding shale/mud-stone formation must lie between 0.38 and 0.42, or below.If the Poisson’s ratio of the shale/mudstone formation isabove this range, the AVO behavior of SWF will be too weakto be detected.

Now coming back to the real data example at Ursa:Figure 15 shows the VP/VS plot of Figure 9 and the corre-sponding Poisson’s ratio, computed from this VP/VS. Theuncertainties or the error bounds in the estimates of thesequantities that were obtained from prestack inversion arealso shown. Notice that in this example, three identified SWFlayers are surrounded by layers with Poisson’s ratio valuesbetween 0.35 and 0.41. As discussed previously, for SWF lay-ers where the Poisson’s ratios of the surroundingshale/mudstone lie between 0.38 and 0.42 or below, it is pos-sible to detect SWF layers successfully from prestack seis-mic data. Consequently, the SWF layers were successfullyidentified from prestack inversion. In addition, notice thatthe error bounds in the estimates of the Poisson’s ratio orthe VP/VS for the SWF layers lie outside the range of theerror bounds in the estimates of these quantities for sur-rounding formations. This further indicates that VP/VS in

this example are estimated with reasonable accuracy.Figure 16 shows Poisson’s ratio and VP/VS from prestack

inversion of another data example. This example shows amultitude of spikes with high VP/VS values. Also notice thatthe background Poisson’s ratio for the formations sur-rounding these high VP/VS formations lie between 0.45 and0.46. According to the discussions above, the AVO behav-ior of prestack seismic data may not be strong enough todetect SWF layers in this case. Therefore, although Figure16 shows layers with VP/VS values higher than the ones inFigure 15, they may not necessarily be associated with SWFlayers. In addition, note that the error bounds in the highVP/VS zones in this example overlap those for the sur-rounding formations, indicating that the estimates of VP/VSvalues are questionable and they should be treated with cau-tion.

In conclusion, success in the identification of SWF lay-ers from prestack inversion depends largely on the elasticproperties of the formations that surround these SWF lay-ers. When these formations are consolidated with Poisson’s

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Figure 14. P-wave reflection coefficient as a function of angle-of-inci-dence for a typical gas sand reflection and two SWF reflections, SWF1and SWF2.

Figure 15. Poisson’s ratio and VP/VS from prestack inversion at theUrsa well site MC-854 2. Error bounds, or the uncertainties in esti-mating these quantities, are also shown in the figure. Note that theerror bounds in VP/VS and Poisson’s ratio for SWF zones do not over-lap with those for the surrounding formations. Detection of SWF for-mations using prestack inversion under these circumstances is feasible.

Figure 16. Poisson’s ratio and VP/VS from prestack inversion at anotherlocation where the sediments are poorly consolidated. Note that the errorbounds at the zones having high VP/VS and Poisson’s ratio overlap withthose having relatively lower VP/VS and Poisson’s ratio. Detection ofSWF layers from prestack inversion is difficult in such a case.

ratio of 0.42 or lower, it is feasible to identify SWF layersusing a prestack waveform inversion. On the other hand,when they are poorly consolidated, with Poisson’s ratiohigher than 0.42, it is difficult to identify SWF layers fromprestack seismic data.

Suggested reading. Quantitative Seismology by Aki and Richards(W. H. Freeman, 1980). “Approximation to the reflection andtransmission coefficients of plane longitudinal and transversewaves” by Bortfeld (Geophysical Prospecting, 1961). “Elasticimpedance” by Connolly (TLE, 1999). “Deepwater geohazardanalysis using prestack inversion” by de Kok et al. (SEG 2001Expanded Abstracts). “Peroophysical basis for shallow-waterflow prediction using multicomponent seismic data” byHuffman and Castagna (TLE, 2001). “Deepwater geohazardprediction using prestack inversion of large offset P-wave dataand rock model” by Dutta (TLE, 2002). “On the effect ofPoisson’s ratios of rock strata on the reflection coefficients ofplane waves” by Koefoed (Geophysical Prospecting, 1955).“Reflection and transmission coefficients for plane waves in elas-tic media” by Koefoed (Geophysical Prospecting, 1962). “Model-based inversion of amplitude-variations-with-offset data usinga genetic algorithm” by Mallick (GEOPHYSICS, 1995). “Some prac-tical aspects on implementation of prestack waveform inver-sion using a genetic algorithm: An example from east TexasWoodbine gas sand” by Mallick (GEOPHYSICS, 1999). “Waveforminversion of multicomponent seismic data” by Mallick (SEG2000 Expanded Abstracts). “AVO and Elastic Impedance” byMallick (TLE, 2001). “AVO inversion, two term or three term”

by Mallick (TLE, 2002, submitted). “Practical aspects of reflec-tivity modeling” by Mallick and Frazer (GEOPHYSICS, 1987).“Computation of synthetic seismograms for stratifiedazimuthally anisotropic media” by Mallick and Frazer (Journalof Geophysical Research, 1990). “Hybrid seismic inversion: Areconnaissance tool for deepwater exploration” by Mallick etal. (TLE, 2000). The Rock Physics Handbook by Mavko et al.(Cambridge, 1998). “Plane-wave reflection coefficients for gassands at nonnormal angles of incidence” by Ostrander(GEOPHYSICS, 1984). “Amplitude-versus-offset variations in gassands” by Rutherford and Williams (GEOPHYSICS, 1989).“Nonlinear one-dimensional seismic waveform inversion usingsimulated annealing” by Sen and Stoffa (GEOPHYSICS,1991).”Rapid sampling of model space using genetic algorithms:Examples from seismic waveform inversion” by Sen and Stoffa(Geophysical Journal International, 1992). “A simplification of theZoeppritz equations” by Shuey (GEOPHYSICS, 1985). “Nonlinearmultiparameter optimization using genetic algorithms:Inversion of plane-wave seismograms” by Stoffa and Sen(GEOPHYSICS, 1991). “Pressure and porosity influences on VP/VSratios in unconsolidated sands” by Zimmer et al. (TLE, 2002).TLE

Acknowledgments: We thank WesternGeco for permission to publish thispaper. We also thank Laurent Meister, Alfonso Gonzalez, and SteveSwarts for reviewing the manuscript and suggesting improvements.

Corresponding author: [email protected]

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