Despite the success of 3-D seismology, thegeophysical community recognizes that thesesurveys contain more information than sim-ply the structure or identification of isolatedbodies in the subsurface. This conviction hasled to new techniques to exploit the addi-tional information. Amoco’s development ofcoherence cube technology in the 1990s is anexample. At about the same time, based onwork by Roy Lindseth originally done in the1970s, a plethora of 3-D poststack inversionalgorithms arrived that delivered high-reso-lution information about the subsurface fromseismic data.

This paper describes the integration of coherence cubeimaging and seismic inversion and the advantages thataccrue from this combination.

Coherence cube imaging essentially generates a cube ofcoherence coefficients by calculating localized waveformsimilarity in both in-line and cross-line directions. The under-lying assumption is that seismic traces cut by a fault gener-ally have different seismic character than neighboring traces.As a result, there is a sharp discontinuity in local trace-to-trace “coherence.” Similarly, stratigraphic features are asso-ciated with definite seismic waveform expressions. A timeslice from a coherence cube would depict lineaments of lowcoherence along faults and other features like channels, reefs,salt edges, and unconformities.

Traditional seismic time slices are usually used for inter-preting faults that run perpendicular to strike. However, incomplex fault zones, faults running parallel to strike becomemore difficult to see as fault lineaments become superim-posed on bedding lineaments. Because three-dimensional-ity is an essential ingredient of the coherence cube, faults orfractures in any orientation are revealed equally well. Radialand en-echelon faulting also are seen clearly. Furthermore,because features such as beaches and deltas are clearlydefined by coherence cube, a better idea of progression andretreat is possible while trying to reconstruct the sequencestratigraphy of the area. Similarly, the remarkable detail ofmud flows, submarine canyons, and depositional stratigra-phy, that is unidentifiable on seismic reflection data even onclose scrutiny, stands out distinctly.

Figure 1 is offshore Canada’s east coast where NW-SEfaults and fractures, apparently difficult to interpret on con-ventional data, show up clearly on the coherence slice.Overlaying a coherence slice on the seismic slice greatlyhelps interpretation (Figure 1c). Figure 2 illustrates that chan-nel features and reefs show up distinctly on the coherenceslices but not on conventional seismic.

Seismic inversion. Seismic impedance inversion is widelyused today mainly due to the ease and accuracy with whichimpedance data can be interpreted. Also, inversion of seis-mic data to acoustic impedance allows an integratedapproach to geologic interpretation. (This article uses “inver-sion” to mean transformation of poststack seismic reflectiv-ity traces into acoustic impedance data.)

Seismic reflection data represent an interface prop-erty—i.e., reflection events are due to relative changes inacoustic impedance of adjacent rock layers. The observedamplitude changes, however, do not indicate whether theamplitude changes relate to lithology variations above orbelow an interface. Acoustic impedance (the product ofdensity and velocity) is a physical rock property. Well logs

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Integrating coherence cube imaging andseismic inversion

SATINDER CHOPRA, Scott Pickford, Calgary, Alberta, Canada

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Figure 2. Channels (a) and boundaries of reefs (b) aremore distinct on coherence slices than conventionalseismic time slices.

Figure 1. Time slices from seismic and coherence volumes. Notice theclear fault and fracture detail on the coherence data.

a)

b)

Seismic

Seismic Coherence Seismic + Coherence

Coherence

CoherenceSeismic

a) b) c)

measure both these entities directly so, by dividing the den-sity log by the sonic log, the acoustic impedance log isobtained. Thus acoustic impedance is a layer property.Because seismic amplitudes are attributes of layer bound-aries, quantitative interpretation of seismic data in termsof thin stratal interval properties (impedance) should relyon inversion. Acoustic impedance simplifies lithologic andstratigraphic identification (being a layer property) andmay be directly converted to lithologic or reservoir prop-erties such as porosity, fluid fill, and net pay. In such cases,inversion allows direct interpretation of 3-D geobodies.Inversion plays an important role in seismic interpretation,reservoir characterization, time-lapse seismic, pressureprediction, and other geophysical applications.

Because inversion transforms seismic amplitudesdirectly into impedance values, special attention needs tobe paid to their preservation. This ensures that the observedamplitude variations are related to geologic effects. Thus,the seismic data should be free of multiples, acquisitionimprint, have a high S/N ratio, be zero-offset migrated,and without any numerical artifacts. Due to the band-lim-ited nature of seismic data, the lack of low frequencies willprevent the transformed impedance traces from having thebasic impedance or velocity structure (low-frequencytrend) crucial to making a geologic interpretation. Also, theweak high-frequency signal components or their absencefrom the seismic data will find the impedance sectionswanting in terms of resolution of thin layers. Both theseaspects are taken care of during impedance inversion.

The low-frequency trend of acoustic impedance is usu-ally derived from well logs or stacking velocities and usedas a priori information during inversion. This helpsenhance the lateral consistency of the resulting impedancedata. The weak high-frequency signal components indi-cate notches or roll-offs on the higher end of amplitudespectra of seismic traces. Processing steps that tendto broaden the spectral band are usually adoptedso that data input to inversion has an enhancedeffective frequency bandwidth. Time-variant spec-tral whitening is one such process that flattens theamplitude spectra of the traces without alteringthe phase. Wavelet processing is another attractiveoption. A wavelet-processed section is one whereinthe embedded wavelet is zero phase. The wavelet-processed section has better resolution and pro-vides a more accurate indication of reflector time.Also, it makes the comparison of the seismic sec-tion with a well log simpler. These reasons suggest,and rightly so, that a wavelet-processed sectionshould be input for seismic inversion.

Several different techniques/methodologies are com-monly used to perform acoustic impedance inversion.

Recursive inversion is the most basic type of inversion andalso the earliest methodology. It essentially assumes thatseismic amplitudes are proportional to reflection coeffi-cients and transforms input seismic traces to acousticimpedance traces. Input data are usually wavelet-processed. This does not fully satisfy the basic assumption,as the wavelet is not removed. Consequently, tuning andwavelet sidelobe effects are not reduced. Also, the resultsare produced within the seismic bandwidth, so that themethod does not offer a significant advantage relative toconventional interpretation.

A broadband reflectivity series can be obtained byremoving the embedded wavelet from the seismic trace.However, the removal of the wavelet from the trace toarrive at a suitable reflection coefficient series is not unique(i.e., more than one solution exists). To overcome this math-ematical limitation, some inversion methods adopt con-straints for the possible solution and get a correct inversionvolume within the seismic bandwidth.

Blocky inversion models the subsurface as layers or blocksin terms of acoustic impedance and time. The startingmodel is defined by a few 3-D main time horizons. Welllogs tie the main time horizons to the seismic data anddefine the impedance bounds for each model layer. Theimpedance within each layer may vary laterally and ver-tically. The impedance bounds are set to keep the optimizedmodel laterally smooth and within given limits. Thenonuniqueness is taken care of by restricting the numberof layers relative to the number of seismic samples. Thestarting model is compared to the seismic data and itera-tively updated to better match the seismic data.

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Figure 4. Time slices from different kinds of data volumes.

Figure 3. Mechanism of composite displays.

a) b) c)

Sparse spike inversion estimates the reflectivityseries that would approximate the seismicdata with a minimum number (sparse) ofspikes. Nonuniqueness is taken care of byapplying the sparse reflectivity criterion.Maximum likelihood deconvolution (Chi etal., 1984) and L1 norm (Oldenburg et al., 1983)algorithms are commonly used.

As sparse-spike inversion tends to removethe embedded wavelet from the data, theinversion results are broadband for the higherfrequencies, maximizing vertical resolutionand minimizing the tuning effects.

Stratigraphic inversion attempts to construct astratigraphic model from seismic data. Thesemethods often introduce complex spatialstratigraphic relationships (e.g., conformity,angular unconformity, baselap) between lay-ers.

Geostatistical inversion combines geostatisticaldata analysis and modeling with seismicinversion. Geostatistical analysis generatesspatial statistics; vertical variograms are gen-erated from well bore measurements, and hor-izontal variograms are estimated from theacoustic impedance values afforded by start-ing impedance model generated from seismicdata, e.g. recursive inversion. Starting from thewell log control points, geostatistical model-ing simulates data at grid points. While car-rying out the inversion, the simulated pointsare modified so as to agree with both well andseismic data.

All the model-based inversion methodsbelong to a category called local optimizationmethods. A common characteristic is that theyiteratively adjust the subsurface model in such a way thatthe misfit function (between synthetic and actual data)decreases monotonically. In the case of good well control,the starting model is good, and local optimization methodsproduce satisfactory results. For sparse well control or wherethe correlation between seismic events and nearby well con-trol is made difficult by fault zones, thinning of beds, localdisappearance of impedance contrast, or the presence ofnoise, these methods do not work satisfactorily. In such cases,global optimization methods (e.g., simulated annealing) areneeded. Global optimization methods employ statisticaltechniques and give reasonably accurate results.

But no matter what inversion approach is adopted, theacoustic impedance volumes so generated have significantadvantages. These include increased frequency bandwidth,enhanced resolution, and reliability of amplitude interpre-tation through detuning of seismic data and obtaining alayer property that affords convenience in understanding andinterpretation.

Integrating coherence cube and inversion. The coherencecube offers a high resolution unbiased image of the varia-tions within the volume, wherein geologic features and faultsare enhanced. As stated earlier, the inverted seismic volumeexhibits an improved image of the impedance variations,which can be used for lithologic and stratigraphic interpre-tations. By integrating the coherence and impedance vol-umes, acoustic impedance changes can be readily identifiedwithin sedimentary systems, resulting in unparalleled detail

of subtle sedimentary depositional features. Acoustic imped-ance results may be numerically combined with the coher-ence results to produce a volume that would allowinterpreters to display the stratigraphic images from the 3-D seismic data and examine the acoustic impedance contrastacross them. For example, sand deposition within a channelthat is gas charged would exhibit low impedance. So, a rangeof low impedances representing the gas sands may beselected and merged with the coherence cube. The com-posite merged volume may again be sliced through to seelow impedance (in color) displayed within the boundariesof the channel.

Figure 3 illustrates how the low end of the impedancerange of values is cut off from the impedance volume andmerged with the coherence volume.

Channel sand reservoirs are difficult to develop effi-ciently, but often they have excellent production character-istics. The depositional mechanisms involved in channels cancreate sand bodies whose thickness and quality can varyrapidly over short distances. Such rapid variations make itdifficult to use conventional seismic data successfully formapping. Impedance inversion helps in such cases.

Figure 4a shows a coherence slice depicting two chan-nels that stand out clearly in a high coherence background.The impedance slice (Figure 4b) indicates low impedancewithin the channels implying the presence of hydrocarbonbearing sands. A composite volume may be generatedwherein the low end of the impedance amplitudes is mergedwith the coherence coefficients. When stretched over a suit-

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a)

b)

c)

Figure 5. (a) Time slice from coherence cube on seismic data and (b)from impedance volume. (c) The same time slice from coherence cuberun on impedance volume.

able color scale (Figure 4c), the variation within the low endof the range of the impedance values chosen is clearly seenwithin the boundaries of the channel.

Such composite plots can define precise reservoir andnonreservoir facies boundaries and reservoir compartments.

Coherence cube and inverted volumes.Applying the coher-ence cube technique to seismic data gives the spatial wave-form coherence measurement in place of the amplitudemeasurement. However, it is possible to apply this tech-nique to the inverted volume—i.e., run coherence cube pro-cessing on the acoustic impedance volume. In such a case,rather than measuring local waveform similarity, the searchis focused on acoustic impedance matching. The output vol-ume is still coherence but of acoustic impedance rather thanof seismic data. Because the inversion volume has a highervertical resolution than the input seismic data and enhancedS/N ratio, the coherence resolution from acoustic impedancedata is significantly superior to the coherence process appliedto seismic data. Figure 5 compares time slices (at 1044 ms)from coherence cubes run on seismic (Figure 5a) and the cor-responding inverted volume (Figure 5c). Constrained inver-sion (blocky) was carried out on the input seismic volume,and the time slice at 1044 ms is shown in Figure 5b. Noticein Figure 5c how the distinct boundaries of another channelemerged in addition to the low coherence features in 5a.

As mentioned earlier, reflection is an interface property,and impedance is a layer property; so there is an inherentphase difference between the two attributes. It could beargued therefore that the coherence slice in Figure 5c, thoughat the same time, may not be comparable to the coherenceslice in Figure 5a. However, the fact that coherence on inver-sion affords a better image could still be verified by com-paring a coherence slice with a succession of slices from thecoherence volume of Figure 5c.

Figure 6 shows such a succession. Each slice confirmsthe conclusion stated above.

Suggested reading. “Coherency calculations in the presence ofstructural dip” by Marfurt et al. (GEOPHYSICS, 1999). “Fault inter-pretation—The coherence cube and beyond” by Chopra andSudhakar (Oil and Gas Journal, 2000). “Azimuth based coherencefor detecting faults and fractures” by Chopra et al. (World Oil,2000). “An interpreter’s guide to understanding and workingwith seismic-derived acoustic impedance data” by Latimer etal. (TLE, 2000). “Geostatistical inversion—A sequential methodof stochastic reservoir modeling constrained by seismic data”by Haas and Dubrule (First Break, 1994.) “Acomputationally fastapproach to maximum likelihood deconvolution” by Chi et al.(GEOPHYSICS, 1984). “Recovery of the acoustic impedance fromreflection seismograms” by Oldenburg et al. (GEOPHYSICS, 1983).Introduction to Seismic Inversion Methods by Russell (SEG, 1988).Reservoir Geophysics edited by Sheriff (SEG, 1992). LE

Acknowledgments: Thanks to Scott Pickford for permission to publish thispaper. The term Coherence Cube is a trademark of Core Laboratories.

Corresponding author: S. Chopra, schopra@scop-ica.com

Satinder Chopra obtained his master’s degree inphysics (1978) from Himachal Pradesh University.He joined India’s Oil and Natural Gas Corporationin 1984. His experience is in the fields of seismicprocessing and interpretation, specializing in depthimaging, inversion, and AVO analysis. He is amember of SEG, CSEG, and EAGE.

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Figure 6. Horizon slices from coherence cubes run onseismic data (a) and impedance data (b-g).

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g) +6 ms

+4 ms

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-4 ms