Lavrans Field lies offshore Norway on the western extremeof Halten Terrace, 15 km south of Smørbukk Field (Figure1). Exploration in this area has been extremely active, yield-ing two large gas and condensate discoveries withinPetroleum License 199—Lavrans Field to the east andKristin Field to the west. Combined reserves are approxi-mately 1200 million barrels oil equivalent of gas and con-densate. Unique conditions have come together to providehydrocarbons and preserved porosity at depths greaterthan 5 km.

Hydrocarbon-bearing sandstones at Lavrans have athickness of 600 m. These reservoirs consist of shallow-marine deposits of Jurassic age. Although the facies can belaterally extensive, the overprint of diagenesis makes pre-diction of reservoir quality difficult. Seismic inversion pro-vides insight to porosity variations away from limited wellcontrol. Thus, seismic inversion can be a valuable tool forreservoir characterization prior to field development. Thisstudy developed out of a need to better understand the sig-nificance of seismic amplitude variations over the crest ofLavrans Field (Figure 2). Hypotheses examined to explainamplitude variations were fluid effects, porosity, pressurechanges, or processing and illumination artifacts.

Seismic inversion. One method chosen to better under-stand the amplitude variations was 3-D seismic inversion.This was carried out using CGG’s 3-D inversion packageTDROV (Gluck et al., 1997), which combines seismic infor-mation with an a priori model. Acoustic impedances areproduced in thin microlayers. For the inversion to be asaccurate as possible the 3-D seismic volume ideally wouldbe multiple free, zero-offset, migrated, and (preferably)zero-phased. The seismic wavelet is extracted from the datavia a matching filter between the synthetic trace derivedfrom the impedance log and the seismic trace at the welllocation. The a priori model is then constructed from well-log information combined with interpreted horizons. Thea priori model attaches time and impedance values to theprimary interpreted horizons. The output seismic inversionis brought back into the workstation, where consistencywith input horizons and well-derived acoustic impedancesserves as quality control. Figure 3 shows the invertedacoustic impedance along the same conventional seismicline as in Figure 2. Note that the amplitude anomaly iden-tified below the Top Ile reflector in Figure 2 corresponds toa low-acoustic impedance anomaly in Figure 3. Figure 4illustrates both input and inverted acoustic impedanceresponses for the two well locations. Due to drilling restric-tions, the lower part of well 6406/2-1 was left open for sev-eral months. This led to extensive cave-ins and poor logmeasurements. Well 6406/2-2 had the best log data qual-ity and was therefore used for wavelet estimation. The bestmatch between input and modeled results lies in the inter-val between the Top Ile and Top Tilje markers. This inter-val includes two of the most important reservoir units atLavrans, Ile, and Tofte formations. The third importantreservoir unit is the heterolithic Tilje Formation. However,

small acoustic impedance separation between poor andgood reservoir in this formation limited the potential of seis-mic inversion here.

Rock physics. To understand the effect of porosity, pres-sure, and fluid type on seismic velocity, 3 core plugs weretaken from well 6406/2-1 and 11 from well 6406/2-2.Measurements of porosity, permeability, grain volume,grain density, and ultrasonic VP and VS were made in thelaboratory. Interpretation of P- and S-wave sonic logs, andlog estimates of porosity, shale velocity, density, and satu-ration were also done. Acoustic impedance is a function ofboth density and velocity. Density variations have someimpact on acoustic impedance, but velocity variations aremuch more significant. Lab data indicate that at depthsgreater than 4000 m, velocities are most sensitive to changesin porosity. Velocity changes resulting from changes in fluidtype or pressure are small in comparison. Figure 5 showsultrasonic VP and VS versus porosity at 20 megapascals(MPa). This graph illustrates that a VP reduction resulting

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Porosity prediction from seismic inversion,Lavrans Field, Halten Terrace, Norway

DAVID M. DOLBERG, Mobil Exploration Norway, Stavanger, NorwayJAN HELGESEN, TORE HÅKON HANSSEN, INGRID MAGNUS, GIRISH SAIGAL, and BENGT K. PEDERSEN, SagaPetroleum ASA, Sandvika, Norway

Figure 1. Lavrans and Kristin fields relative to Smør-bukk. Field outlines (rose) are drawn on the map of theBase Cretaceous Unconformity. View is to the north.

Figure 2. Cross-line 3185 is a dip line through well6406/2-2. Seismic anomalies are seen below the Top IleFormation. Understanding the meaning of theseamplitudes was a primary motivation for this study.

from a change in porosity from 0 to 35% would be morethan 1500 m/s. Figure 6 illustrates that VP values takenfrom logs are similar to VP values from cores in well 6406/2-2. The data are also plotted against trend lines from previ-ous work (Han, 1986; Nur et al.,1991). Han’s trend line wasderived from many formations at various depths and loca-tions in the Gulf Coast. The mechanism of porosity reduc-tion seen in Han’s data is believed to be due to compactionand diagenesis. This plot illustrates that the Lavrans’ logand core data are consistent with observations from otherformations in other locations. This plot further supports thehypothesis that the VP-porosity relationship at Lavrans iscontrolled by diagenesis. VP-porosity slopes tend to be steepwhen porosity is controlled by diagenesis and flat in areaswhen porosity is controlled by grain size (Mavko, 1998).

Figure 7 plots VP against effective pressure for various

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Figure 3. Cross-line 3185 through well 6406/2-2 show-ing acoustic impedance. The high amplitudes inFigure 2 are in yellow and represent low acousticimpedances. The rock physics study showed that thisindicated higher porosities.

Figure 4. Final inversion results for wells 6406/2-1 (left)and 6406/2-2. Black curves within the yellow band rep-resent log-measured acoustic impedance. Red, blockycurves represent the modeled acoustic impedanceresponse. The double line dark yellow curve is themodeled low frequency at each well. The yellow banddefines an area where no penalty is applied in theerror function for the inversion. Outside the yellowcorridor, soft constraints are applied. The seismicresponse at each well is on the right. The red curve onthe right is the synthetic modeled trace.

Figure 6. VP versus porosity from Lavrans core and logdata plotted with trends found in other studies.

Figure 5. Velocity changes resulting from a porosityincrease of 0 to 35% are greater than 1500 m/s.

Figure 7. Velocity is plotted against effective pressurefor various fluid states for one sample. Results aresimilar for other samples. There is increasing separa-tion between water-saturated and gas-saturated sam-ples as pressure decreases. At 10 MPa, the maximumvelocity change is 100-150 m/s. At Lavrans Field theeffective pressure is at 50 MPa. Thus, porosity’s effecton velocity is at least 10 times more significant thanvelocity change related to fluid and pressure.

fluid states. At Lavrans Field, initial effective reservoir pres-sures are more than 50 MPa (500 bars). As effective pres-sure decreases, there is a slight increase in velocityseparation between water-wet samples and gas-filled sam-ples. This increase in separation can be as large as 100-150m/s at 10 MPa. As production starts, effective pressures atLavrans will increase, further decreasing the velocity effect.With these conditions, it is unlikely that initial pressureanomalies or changes in pressure due to production couldbe monitored with seismic. These rock physics results sug-gest that neither pressure nor fluid effects have significantimpact on seismic response. Differences in acoustic imped-ance are essentially correlated to variations in porosity.

Satistical analysis and implementation. From the rockphysics results, it is clear that a relationship betweenacoustic impedance and porosity should also exist withinthe well information. Log porosity data was tied to over-burden-corrected core data. These porosity results, density,sonic, gamma ray, Vshale and other log-derived data wereimported into SigmaView for bivariate analyses. Cross-plotting shows that acoustic impedance is strongly corre-lated to porosity. Figure 8 shows the relationship of acousticimpedance to porosity for Ile Formation using the twowells from Lavrans Field. Sensitivity analysis shows thatmaximum correlation between well and seismically derivedacoustic impedance occurs at a vertical scale of 15-30 m. At this scale, seismic data predicts porosity witha maximum correlation (R) of .70. The uncertainty in thisrelationship increases when sampling seismic below thisvertical resolution. Therefore, it is important to understandat which scale the seismic can be measured with the leastuncertainty (smallest residual). The effectiveness of poros-ity mapping using acoustic impedances is maximized insand-prone intervals. Because acoustic impedance valuesfrom shales can be similar to those of sands, an under-standing of how the stratigraphy correlates to a typicaldiagnostic vertical acoustic impedance profile is requiredbefore acoustic impedance values can be exported frombetween two horizons. At Lavrans Field, the Ile sandstonereservoir is overlain by the Not Shale, which always exhibitsvery low acoustic impedance values. The underlying UpperRor Shale exhibits high acoustic impedances. The acousticimpedance derived from the seismic is plotted against theacoustic impedance encountered within the 6406/2-2 well

to verify that the correct interval is being extracted (Figure9). Thus, with this understanding, Ile Formation intervalcan be identified and sculpted out (Figure 10). VoxelGeooutputs average acoustic impedance values for specificsculpted seismic intervals. At Lavrans, the approximatethickness of extracted acoustic impedance zones were onthe order of 60 m. 2-D average acoustic-impedance hori-zons were combined with porosity transforms from the sta-tistical analyses (Figure 8) to yield 2-D pseudoporositymaps. Figure 11 shows how grouping specific acousticimpedance ranges can identify areas with a particular reser-voir quality. In this example, only lower acoustic imped-ances (higher porosities) were selected. Seismic trend data(pseudoporosity) yielded important information for thereservoir engineer, with respect to lateral reservoir quality,and helped the geologist to validate and modify geologicmodels. Additionally, seismic inversion and pseudoporos-

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Figure 10. By understanding the acoustic impedancevertical profile, Ile Formation can be partitionedthrough detailed mapping of acoustic impedance inter-faces. These horizons are used to sculpt intervals ofinterest for determining average acoustic impedance.Additionally, binning or grouping of specific acousticimpedances can isolate reservoir of a specific quality.

Figure 8. Relationship of acoustic impedance to log-estimated porosity for Ile Formation in wells 6406/2-1and 6406/2-2. Samples with water saturation greaterthan 65% have been filtered out.

Figure 9. Seismically derived acoustic impedances areplotted beside those derived from well information.The figure indicates that, at Lavrans, acoustic imped-ance is not a good indicator of lithology. Ile sands areoverlain by low-impedance shales and underlain byhigh-impedance shales. At Lavrans, partitioning reser-voir units assures that acoustic impedance values canbe correlated to calibrated porosities. Within the Ilepackage, low impedances mark sands with goodporosity.

ity maps provided a methodology for estimating porositybetween wells, and helped to identify areas for future wellplacement.

Quality control. It is evident from Figure 2 that seismicamplitudes tend to decrease on the eastern flank of LavransField. Using the relationships derived from the rock physicsand well data, the decrease in reflector strength would bemodeled as an acoustic impedance increase or a decreasein porosity. Results from this area became suspect becausethis increase in acoustic impedance seemed to lie furtherwestward with each successively deeper horizon, was notlocated at a known hydrocarbon contact, and seemed toexist along a change in dip (Figures 2 and 3). Seismic mod-eling was designed to test whether some decrease in ampli-tude may be a result of processing artifacts. Map horizonsand velocity layers were used to construct a velocity model.Synthetic seismic was generated, processed, and migrated(Figure 12). Reflector amplitude diminishes as dip increases.Thus, some amplitude decrease on the eastern flank ofLavrans Field may be related to illumination and process-ing. Another effect, often overlooked, is data degradationbecause of geometry. Due to the large burial depths (morethan 4 s TWT), curvature also affects amplitude strength(Figure 13). Geometry irregularities may cause amplitudesto weaken or strengthen, depending on whether thereflected waves add constructively or destructively. In thisexample, concave reflectors focus and convex reflectorsdefocus seismic energy. Thus, modeling indicates thatgeometry may contribute to the uneven capture of 3-Damplitude data.

Making corrections to the seismic energy in these high-dip areas is possible, but devising a reliable methodology

was considered difficult and costly. Thus, lateral variationsnoted in these suspect areas were used only for qualitativepurposes and not included in trend extrapolations or quan-titative reservoir description.

Conclusions. Seismic porosity prediction can improvereservoir characterization by providing information on thespatial variation of the reservoir away from existing wellcontrol. Seismically generated maps and volumes have ver-tical resolution in tens of meters. Thus, seismically derivedporosity maps have the effect of averaging vertically, reduc-ing variations in porosity that may be significant at reser-voir characterization scale. Therefore, seismic porositiesare more appropriately used as a steering component toderive trends, for larger-scale volumetric estimations, andto identify reservoir “sweet-spots.” Finer vertical detail,which may be required for reservoir simulation, is perhapsbetter handled through simulation or stochastic techniquesbased upon residual distribution (see the following paperon Kristin Field). When applying seismic inversion for

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Figure 11. Grouping acoustic impedances into specificbin ranges allows an areal assessment of reservoirquality. In this example from Lavrans, both the 2-Dmap view (top) and 3-D perspective show impedancesof 5500-8800.

Figure 12. Simple processing of synthetic data from acommon-shot survey shows that migration could beaffecting amplitude strength.

Figure 13. The top and middle figures illustrate howamplitude varies with geometry and distance from thereflector. Differences in amplitude between (A) and(B) are related to distance from the receiver, (C) is amodeling artifact due to irregularities in the geometryof the crest/shoulder, (D) decrease in amplitude due tosteep dip (large distance from shot/receiver to reflec-tor), and between (E) and (F) there is a spread ofamplitudes related to the concave syncline. The bot-tom figure shows how migration changes the ampli-tudes and how the result varies with input velocities.The amplitude decrease seen from the slope is causedby illumination and processing deficiencies.

porosity prediction, the following procedures are vital toensure robust and reliable conclusions:

1) Rock physics studies must be conducted to provide thephysical basis for understanding how changes in rockand fluid properties will affect seismic response.

2) Statistical analysis of well and core information mustshow relationships consistent with rock physics stud-ies. In this case, a relationship between porosity andacoustic impedance is documented.

3) Once a trend is established from well data, well infor-mation must be upscaled to seismic resolution. Anassessment of how accurately seismic predicts well infor-mation is required before results can be accuratelyweighted and their impact understood.

4) Data quality must be assessed. Even though 3-D seis-mic should maintain absolute amplitude information,assessment of data quality is required to ensure thatacquisition or processing problems have not alteredamplitude response.

5) Identification of the implementation scale is necessary.Estimation is valid only when features can be resolvedby the seismic.

When these procedures have been followed and the nec-essary conditions met, seismic inversion can add value:

• by providing information on reservoir quality away fromthe wellbore

• by providing input to geologic modeling• by ensuring that lateral reservoir heterogeneities are

included in reservoir simulations• as a tool to high-grade well locations and reduce risk• as a trend tool for porosity mapping

Despite vertical resolution limitations, seismic inversionprovides powerful information for predicting lateral vari-ations in reservoir quality, not accessible through well data.

Suggestions for further reading. Effects of Porosity and ClayContent on Acoustic Properties of Sandstones and UnconsolidatedSediments by Han (doctoral dissertation, Stanford University,1986). “Wave velocities in sediments” by Nur et al. (in ShearWaves in Marine Sediments, Kluwer Academic Publishers, 1991).“High-resolution impedance layering through 3-D strati-graphic inversion of the post-stack seismic data,” by Gluck etal. (TLE, 1997). The Rock Physics Handbook by Mavko et al.(1998). LE

Acknowledgments: The authors thank the Haltenbanken Sør partner-ship for permission to publish this paper. Thanks are also extended toCGG in Oslo, Norway, and Gary Mavko from Stanford University fortheir comments and suggestions.

Corresponding author: david_dolberg@email.mobil.com. Several authorshave changed employment since this paper was written. Those authorsand their new locations are: David Dolberg, Mobil Oil Canada, Calgary,Alberta, Canada; Jan Helgesen, CGG Norge, Høvik, Norway; Tore HåkonHanssen, Fortum Petroleum, Oslo, Norway; Ingrid Magnus, NorskHydro ASA, Bergen, Norway; Girish Saigal, Norsk Hydro ASA, Oslo,Norway; and Bengt K. Pedersen, Norwegian University of Science andTechnology, Trondheim, Norway.

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