seismic inversion: reading between the lines

42 Oilfield Review

Seismic Inversion: Reading Between the Lines

Frazer Barclay Perth, Western Australia, Australia

Anders BruunKlaus Bolding RasmussenCopenhagen, Denmark

Jose Camara AlfaroPemexTampico, Tamaulipas, Mexico

Anthony CookeAberdeen, Scotland

Dennis CookeDarren SalterSantosPerth, Western Australia

Robert GodfreyDominic LowdenSteve McHugoHüseyin ÖzdemirStephen PickeringGatwick, England

Francisco Gonzalez PinedaPemexReynosa, Tamaulipas, Mexico

Jorg HerwangerStefano VolterraniHouston, Texas, USA

Andrea MurinedduAndreas RasmussenStavanger, Norway

Ron RobertsApache CorporationCalgary, Alberta, Canada

For help in preparation of this article, thanks to Trine Alsos,StatoilHydro, Harstad, Norway; Ted Bakamjian, SEG, Tulsa;Richard Bottomley, Mexico City; Jonathan Bown, Henrik JuhlHansen and Kim Gunn Maver, Copenhagen; Tim Bunting,Kuala Lumpur; Karen Sullivan Glaser, Houston; JalalKhazanehdari, Abu Dhabi, UAE; Hasbi Lubis, Gatwick,England; Farid Mohamed, Aberdeen; Richard Patenall, Perth,Western Australia; Pramesh Tyagi, Cairo; and Anke SimoneWendt, Stavanger.ECLIPSE, ISIS and Q-Marine are marks of Schlumberger.

The reflections of seismic waves from subsurface layers illuminate potential

hydrocarbon accumulations. As waves reflect, their amplitudes change to reveal

important information about the underlying materials. Seismic amplitude inversion

uses reflection amplitudes, calibrated with well data, to extract details that can be

correlated with porosity, lithology, fluid saturation and geomechanical parameters.

The undisputed leader among tools foridentifying potential exploration targets is the3D seismic survey. These surveys probe greatvolumes of the subsurface, helping oil and gascompanies map geological structures and selectdrilling locations.

The original use of seismic data, and still themain use today, has been to identify the geometryof reflectors and ascertain their depths. This ispossible because seismic waves reflect atinterfaces between materials of differentacoustic properties.

However, seismic reflection data containinformation beyond reflector location: everyreflection changes the amplitude of the returnedwave. The controlling property in this change atthe interface is the contrast in impedance, whichis the product of density and velocity. Seismicreflection amplitude information can be used toback out, or invert for, the relative impedances ofthe materials on both sides of the interface. Bycorrelating these seismically derived propertieswith values measured in the borehole, inter -preters may be able to extend well informationthroughout the entire seismic volume. Thisprocess, called seismic inversion for reservoir

characterization, can help fill gaps in ourknowledge of formation properties between wells.

This article describes the science and art ofseismic inversion, and how oil and gas companiesare using it to reduce risk in their exploration,development and production operations. After anintroduction to the uses of inversion, we presentits various types, from simple to more complex.Examples from Mexico, Egypt, Australia and theNorth Sea demonstrate applications of inversionto fine-tune drilling locations, characterize hard-to-image reservoirs, map water saturation,improve reservoir simulations and enhanceknowledge of geomechanical properties.

Inversion BasicsMany measurements in the E&P industry rely tosome extent on inversion for their interpretation.The reason is simple. For several measurement-interpretation problems, no equation that directlyrelates the multiple measurements—whichinclude noise, losses and other inaccuracies—canbe solved with a unique answer. We then resort toinversion, which is a mathematical way ofestimating an answer, checking it againstobservations and modifying it until the answer is acceptable.

1. Quirein J, Kimminau S, La Vigne J, Singer J and Wendel F:“A Coherent Framework for Developing and ApplyingMultiple Formation Evaluation Models,” Transactions ofthe SPWLA 27th Annual Logging Symposium, Houston,June 9–13, 1986, paper DD.Jammes L, Faivre O, Legendre E, Rothnemer P, Trouiller J-C, Galli M-T, Gonfalini M and Gossenberg P:“Improved Saturation Determination in Thin-BedEnvironments Using 2D Parametric Inversion,” paperSPE 62907, presented at the SPE Annual TechnicalConference and Exhibition, Dallas, October 1–4, 2000.

Faivre O, Barber T, Jammes L and Vuhoang D: “UsingArray Induction and Array Laterolog Data to CharacterizeResistivity Anisotropy in Vertical Wells,” Transactions ofthe SPWLA 43rd Annual Logging Symposium, Oiso,Japan, June 4–7, 2002, paper M.Marsala AF, Al-Ruwaili S, Ma SM, Modiu SL, Ali Z,Donadille J-M and Wilt M: “Crosswell ElectromagneticTomography in Haradh Field: Modeling to Measurements,”paper SPE 110528, presented at the SPE Annual TechnicalConference and Exhibition, Anaheim, California, USA,November 11–14, 2007.

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Spring 2008 43

Inversion, as the name implies, can beconsidered as the inverse of forward modeling,sometimes simply called modeling. For thepurpose of this article, forward modeling beginswith a model of earth properties, then mathe -mati cally simulates a physical experiment orprocess—for example, electromagnetic, acoustic,nuclear, chemical or optical—on the earthmodel, and finally outputs a modeled response. Ifthe model and the assumptions are accurate, themodeled response looks like real data. Inversiondoes the reverse: it starts with actual measureddata, applies an operation that steps backwardthrough the physical experiment, and delivers anearth model. If the inversion is done properly, theearth model looks like the real earth.

Inversion is used by many E&P disciplinesand can be applied at a wide range of scales andvarying levels of complexity:• calculating borehole-fluid invasion profiles from

induction logging measurements• assessing cement-bond quality from ultrasonic

logs (see “Ensuring Zonal Isolation Beyond theLife of the Well,” page 18).

• extracting layer lithologies and fluid satura-tions from multiple log measurements

• interpreting gas, oil and water volumes fromproduction logs

• inferring reservoir permeability and extentfrom pressure-transient data (see “IntelligentWell Technology in Underground Gas Storage,”page 4).

• mapping fluid fronts from crosswell electro-magnetic measurements

• integrating electromagnetic and seismic measurements for improved delineation ofsubsalt sediments.1

E&P seismic specialists use different types ofinversion—velocity inversion and amplitudeinversion—to solve distinct types of problems.The first type of inversion, velocity inversion,sometimes known as traveltime inversion, is usedfor depth imaging. Using seismic traces at widelyspaced locations, it generates a velocity-depthearth model that fits recorded arrival times ofseismic waves. The result is a relatively coarsevelocity-depth model extending over severalkilometers in depth and perhaps hundreds ofkilometers in length and width. This solution isapplied in data-processing steps such asmigration and stacking, eventually producing the type of seismic image that is familiar to most readers. Seismic interpreters use theseimages to determine the shape and depth of subsurface reflectors.


The second type of inversion, amplitudeinversion, is the focus of this article. Thisapproach uses the arrival time and the amplitudeof reflected seismic waves at every reflectionpoint to solve for the relative impedances offormations bounded by the imaged reflectors.This inversion, called seismic inversion forreservoir characterization, reads between thelines, or between reflecting interfaces, toproduce detailed models of rock properties. Forsimplicity, the following discussion describesonly model-based inversion. Some otheralternatives are space-adaptive and discretespike inversions.2

In principle, the first step in model-basedseismic inversion—forward modeling—beginswith a model of layers with estimated formationdepths, thicknesses, densities and velocitiesderived from well logs. The simplest model,which involves only compressional (P-wave)velocities (Vp) and density (ρ), can be used toinvert for P-wave, or acoustic, impedance.

Models that include shear (S-wave) velocities(Vs) can solve for S-wave, or elastic, impedance.

The simple model is combined with a seismicpulse to create a modeled seismic trace called a synthetic (above). Inversion takes an actualseismic trace, removes the seismic pulse, anddelivers an earth model for that trace location.To arrive at the best-fit model, most inversionroutines iterate between forward modeling andinversion, seeking to minimize the differencebetween the synthetic trace and the data.

In practice, each of these steps may be quiteinvolved and can depend on the type of seismicdata being inverted. For vertical-incidence data,creating the initial model requires bulk densitymeasurements from density logs and compres -sional velocities from sonic logs, both spanningthe interval to be inverted. Unfortunately, thenecessary logs often are acquired only in thereservoir. In the absence of sonic logs, boreholeseismic surveys—vertical seismic profiles(VSPs)—can provide average velocities across

the required interval. If no borehole velocity dataare available, velocities from traveltimeinversion may serve as a substitute. Missingdensity data may be estimated from empiricalrelationships. For nonvertical-incidence data,the model must include both S-wave and P-wave velocities.

For conventional inversion of vertical-incidence data, the density-velocity model is thenconverted to a reflectivity model. Reflectivity, theratio of the amplitude of the reflected wave tothat of the incident wave, is the parameter thatgoverns reflection-driven changes in normal-incidence seismic amplitudes. It relates to thedensities and velocities on each side of aninterface through the acoustic impedance con -trast; reflectivity is the ratio of the difference inacoustic impedances to their sum.3 The resultingdepth-based reflectivity model is converted to atime-based model through the velocities.

Combining the time-based model with aseismic pulse creates a synthetic trace. Mathe -matically, this process is known as convolution.4

The seismic pulse, or wavelet, repre sents thepacket of energy arriving from a seismic source. A model wavelet is selected to match theamplitude, phase and frequency characteristicsof the processed seismic data. Convolution of thewavelet with the reflectivity model yields asynthetic seismic trace that repre sents theresponse of the earth as modeled to the inputseismic pulse. Additional steps are required ifnoise, attenuation and multiple reflections are tobe included in the modeled trace.

The inverse operation starts with an actualseismic trace. Because the amplitude and shapeof each swing in the seismic trace affect theoutcome, it is vital that the processing steps up tothis point conserve signal phase and amplitude.

Different types of inversion start withdifferent types of traces. The main distinction isbetween inversion performed before stackingand inversion performed after it—prestack andpoststack. Most seismic surveys provide imagesusing data that have been stacked. Stacking is asignal-enhancement technique that averagesmany seismic traces. The traces representrecordings from a collection of different source-receiver offsets with a common reflectingmidpoint (next page, top left). Each trace isassumed to contain the same signal but differentrandom noise. Stacking produces a single tracewith minimal random noise and with signalamplitude equal to the average of the signal inthe stacked traces. The resulting stacked trace istaken to be the response of a normal-incidencereflection at the common midpoint (CMP).

44 Oilfield Review

2. “Space-Adaptive Inversion,” http://www.slb.com/content/services/seismic/reservoir/inversion/space_adaptive.asp(accessed April 22, 2008).

3. Reflectivity may be positive or negative. Positivereflectivity means the reflected wave has the same

polarity as the incident wave. Negative reflectivitymeans the reflected wave has the opposite polarityrelative to the incident wave.

4. Yilmaz O and Doherty SM: Seismic Data Processing.Tulsa: Society of Exploration Geophysicists, 1987.

>Modeling and inversion. Forward modeling (top) takes a model offormation properties—in this case acoustic impedance developed fromwell logs—combines this with a seismic wavelet, or pulse, and outputs asynthetic seismic trace. Conversely, inversion (bottom) begins with arecorded seismic data trace and removes the effect of an estimatedwavelet, creating values of acoustic impedance at every time sample.

Inversion

Forward Modeling

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Inputwavelet

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trace

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Earth modelof acousticimpedance

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Spring 2008 45

Stacking is a reasonable processing step ifcertain assumptions hold: the velocity of themedium overlying the reflector may vary onlygradually, and the average of the amplitudes inthe stacked traces must be equivalent to theamplitude that would be recorded in a normal-incidence trace. In many cases, these assump tionsare valid, and inversion may be performed on thestacked data—in other words, poststack. Incontrast, when amplitude varies strongly withoffset, these assumptions do not hold, andinversion is applied to unstacked traces—prestack. Before discussing prestack situations indetail, we continue with the simpler case ofpoststack inversion.

A stacked trace is compared with thesynthetic trace computed from the reflectivity

model and wavelet. The differences between thetwo traces are used to modify the reflectivitymodel so that the next iteration of the synthetictrace more closely resembles the stacked trace.This process continues, repeating the generationof a synthetic trace, comparison with thestacked trace, and modification of the modeluntil the fit between the synthetic and stackedtraces is optimized.

There are many ways to construct synthetictraces, and various methods may be used todetermine the best fit. A common approach fordetermining fit is least-squares inversion, whichminimizes the sum of the squares of thedifferences at every time sample. This inversiontechnique operates on a trace-by-trace basis,

while others attempt to globally optimize theinversion of the seismic volume. We discussglobal optimization later.

In the simplest case, inversion produces amodel of relative reflectivity at every timesample, which can be inverted to yield relativeacoustic impedance. To obtain formationproperties such as velocity and density, aconversion to absolute acoustic impedance isnecessary. However, such a conversion requiresfrequencies down to near 0 Hz, lower thancontained in conventional seismic data. Anabsolute acoustic impedance model can beconstructed by combining the relative acousticimpedance model obtained from the seismicfrequency range with a low-frequency modelderived from borehole data (above right).

> Stacking basics. Stacking enhances signal and reduces noise byadding several traces together. The seismic vessel acquires traces atmany offsets from every source (top). S numbers represent sources, Rnumbers represent reflection points, and H numbers representhydrophones. Stacking first gathers traces from all available source-receiver offsets that reflect at a common midpoint (CMP) (middle).Because arrivals from longer offsets have traveled farther, a timecorrection, called normal moveout (NMO) correction, is applied to eachgather to flatten the arrivals (bottom left). The flattened traces areaveraged (bottom right) to produce one stacked trace that represents thenormal-incidence (zero-offset) trace.

CMP

Common midpoint (CMP) gather

H5 H2 H1 S1 S3 S5H4 H3 S2 S4H6 S6

H6 H5 H4 H3 H2 H1

R1 R2 R3 R4 R5 R6

R2 R3 R4 R5 R6 R7

R3 R4 R5 R6 R7 R8

R4 R5 R6 R7 R8 R9

R5 R6 R7 R8 R9 R10

R6 R7 R8 R9 R10 R11

S1 S2 S3 S4 S5 S6

Two-

way

trav

eltim

e

1Trace

2 3 4 5 6

Before NMO correction

Offset

1Trace

2 3 4 5 6

After NMO correction

Offset

1

Stackedtrace

> Relative and absolute acoustic impedance. Inversion of seismicamplitudes yields relative acoustic impedance (AI) (left). However, thetrue absolute acoustic impedance (blue) contains a low-frequencymodel (LFM) (red) that must be obtained from borehole data or modeledby other means (right).

3,600

Tim

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4,400

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3,200Relative Acoustic Impedance Absolute Acoustic Impedance

AILFM

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Relating seismically derived acoustic impe d -ances to formation properties makes use ofcorrelations between logging measurements. Forexample, crossplotting acoustic impedance andporosity measured in nearby wells establishes atransform that allows seismically measuredacoustic impedance to be converted to porosityvalues throughout the seismic volume. Anexample from a carbonate reservoir in Mexicodemonstrates the power of this technique.

Inversion for Porosity in MexicoFollowing the 2003 discovery of the Lobina field offshore Mexico, Pemex contracted withWesternGeco to obtain a seismic survey withbetter resolution than one acquired in 1996.Seismic data with increased frequency contentwould significantly enhance the ability ofinterpreters to map key reservoir layers. Thecompany’s objective was to identify high-porosityzones within two carbonate layers: the primaryJurassic San Andres (Jsa) limestone and theinferior shallower Cretaceous Tamaulipas (Kti)carbonate target.

A Q-Marine high-resolution 3D seismic surveyachieved a maximum frequency of 60 Hz,doubling that of the 1996 survey.5 Inversion of the new data generated porosity maps thathelped rank previously defined drilling locations,determine new potential locations and optimizedevelopment drilling.

Trace-by-trace inversion of the stackedseismic data allowed geophysicists to obtainrelative acoustic impedance at every tracethroughout the seismic volume. Key horizons thathad been interpreted as strong acoustic eventswere converted from time to depth by correlationwith formations seen in well logs. Thiscombination of interpreted horizons and values ofacoustic impedance at these points enabled thecreation of a low-frequency model to convert therelative acoustic impedance to an absolutemeasurement (above left).6

Crossplotting porosity with acoustic impe d -ance from logs and core data in the survey arearevealed a strong correlation between the twoproperties—an increase in porosity causes adecrease in velocity, a decrease in density, andtherefore a corresponding decrease in acousticimpedance (left). Porosity-acoustic impe d ancefunctions were created for the Jsa and Ktiformations separately. Applying these correla tionsto the seismically derived acoustic impedancevolume, geophysicists created fieldwide maps ofporosity. The seismic porosity results were

46 Oilfield Review

> Absolute acoustic impedance from poststack inversion. Inversion ofseismic amplitudes generated the color-coded panel, with low acousticimpedance in pink and red, and high acoustic impedance in blue and green.The acoustic impedance calculated from density and sonic logs, displayedat the well location in the middle of the panel, shows a good correlationwith the seismically derived values.

Two-

way

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Acoustic impedance

Common depth point (CDP)2,700 2,800

> Acoustic impedance and porosity. The strong correlation betweenporosity and acoustic impedance from logs and core data in the Jsaformation indicates a robust transform for application to seismic inversionresults. As in other carbonate rocks, an increase in acoustic impedance isrelated to a decrease in porosity. A separate porosity-acoustic impedancefunction was created for the Kti formation.

8

Effe

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10 12 14 16

Edited acoustic impedance (Zp), km/s . g/cm3

0

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30Crossplot Analysis

0.70 0.93Water saturation


Spring 2008 47

checked using “blind wells,” that is, wells thatwere not used in the inversion. The seismicallyderived porosity closely matched the blind-wellporosity logs, adding confidence to the seismicallycalculated results.

The porosity maps had a significant impact ondefining infill drilling locations. In the nearbyArenque field, covered by the same survey,Pemex upgraded four previously identifiedprospects. Increased priority was given to thetwo locations corresponding to higher porosity inthe seismic volume. In one area, the inversioncalculations allowed identification of undrilled,discrete porosity features (right). With theseresults, well placement could be designed tomaximize contact with high-porosity zones in theJsa formation.

In another area where seismic porosityresults were used to guide drilling, a wellproduced oil from the Jsa formation at2,000 bbl/d [318 m3/d]. The seismically derivedresults show excellent correlation with theporosity measured in the well (below right).

Inversion When Offset MattersIn many cases, the stacking process does notadequately preserve amplitude. For example,when traces exhibit amplitude variation withoffset (AVO), the trace that results from stackingdoes not have the same amplitudes as thevertical-incidence, or zero-offset, trace. Underthese conditions, inversion should be performedon data that have not been stacked. Moreover,the parameters that cause the amplitude tochange can be modeled and used to further theinversion process.

Data preparation for inversion of AVO tracesrequires steps similar to those for preparation forstacking. Traces reflecting at a common midpointare gathered and sorted by offset, which isrelated to incidence angle. Then, a velocitymodel is applied to each gather to flatten events

5. Salter R, Shelander D, Beller M, Flack B, Gillespie D,Moldoveanu N, Gonzalez Pineda F and Camara Alfaro J:“Using High-Resolution Seismic for Carbonate ReservoirDescription,” World Oil 227, no. 3 (March 2006): 57–66.

6. Salter R, Shelander D, Beller M, Flack B, Gillespie D,Moldoveanu N, Pineda F and Camara J: “The Impact ofHigh-Resolution Seismic Data on Carbonate ReservoirDescription, Offshore Mexico,” Expanded Abstracts,75th SEG Annual International Meeting and Exposition,Houston (November 6–11, 2005): 1347–1350.

> Identifying undrilled high-porosity targets. Inversion revealed a high-porosity interval (purple and red), helping Pemex delineate zones that couldbe reached with new wells. The black line is a possible well trajectory. Anexisting well is shown in gold.

2,200

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2,6001,100 1,125 1,150 1,175 1,200 1,225 1,250 1,275 1,3001,075

Crossline number

Porosity

> Results of drilling into a zone predicted to have high porosity. A wellpenetrated both the Cretaceous (Kti) and Jurassic (Jsa) reservoirs,encountering porosities that matched values predicted for the twocarbonate zones. The green circle marks the top of the Kti formation, andthe light blue circle marks the top of the Jsa formation. The porosity log,projected on the well path, has the same color-coding as the seismicallypredicted porosities.

Kti

Jp

Jsa

Bas

N

Poro

sity


to a common arrival time over all offsets (above).For a given reflection, amplitudes are trackedand plotted against offset. The flattened gatherand the amplitude variation with offset comprisethe data that will be compared with syntheticsduring the inversion process.

Most AVO inversion algorithms are based onthe relationship between reflection amplitudeand angle of incidence. Therefore, additionalsteps before inversion include converting theoffset values to angles. The traces are initiallylabeled by source-receiver offset. The relation -ship between angle and offset is calculated bytracing a ray from source to receiver in anaccurate velocity model.

To facilitate inversion, an AVO dataset may bedivided into subsets according to angle. Forexample, the near-offset, mid-offset and far-offsettraces may form three separate datasets. Foreach CMP gather, the near-offset traces arestacked and then collected with the near-offsettraces from all the other CMPs, forming a near-offset dataset. Similarly, the mid-offset andfar-offset traces from each CMP gather can begrouped. Each offset group can be invertedseparately. Although some of the AVO infor mationis lost in these partial stacks, sometimes calledoffset or angle stacks, in many cases enoughremains to obtain reasonable inversion results.

Inversion of traces with AVO is morecomplicated than poststack inversion becausethe reflectivity formula is more elaborate, withdependence not only on density and compres -sional velocity, but also on shear velocity andangle of incidence. The general expressions forthe angular dependence of the reflection ofcompressional and shear waves as functions ofdensities, velocities and incident angle areknown as the Zoeppritz equations.7 Because thefull Zoeppritz formulation is cumbersome,approximations are often used to generatesynthetics and facilitate fast inversion.8

Each approximation method attempts to fit asimplified formula to the curve of reflectionamplitude versus angle of incidence (next page,top right). The simplified approaches differ inthe number of terms used in theapproximation—usually two or three—and inthe parameters solved for. Some two-parameterinversions calculate P-wave impedance (Zp,equal to ρVp) and S-wave impedance (Zs, equal toρVs). A three-parameter inversion mightdetermine Zp, Zs and density (ρ), but a three-parameter inversion for Zp, Vp /Vs and ρ wouldcontain the same information. Someapproximations are expressed in terms ofPoisson’s ratio (ν), shear modulus (μ), bulkmodulus (λ) and ρ, which again are related to Vp

and Vs.The number of parameters that can be solved

for depends on the range of offsets—or equiva -lently, angles—available and on data quality. If alarge range of offsets or angles is available andthe signal-to-noise ratio at high offset is good,three parameters may be resolved. If offsets arelimited, then inversion may deliver only twoparameters reliably. Density is the most difficultparameter to invert for; the process requires longoffsets and high-quality data.

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> Amplitude variation with offset (AVO). In steps similar to preparation forstacking, traces reflecting at a common midpoint are gathered and sortedby offset (top), then the arrivals are flattened using a normal moveoutvelocity model while preserving the amplitude information (middle). Clearly,in this case, averaging the four traces would produce a trace that does notresemble the zero-offset trace; in other words, stacking would not preserveamplitudes. The offset versus angle (θ) relationship is determined by raytracing (bottom).

Offset 1

Offset 2

Offset 3

Offset 4

Amplitude increases with offset

Synthetic Traces: CMP Gather

Single-Layer Geometry: Direct Relationship Between and Offset

Offset 4

Offset 3

Offset 2

Offset 1

S4 S3 S2 S1 R1 R2 R3 R4

θ1

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Gas sandCommon midpoint (CMP)

Multilayer Geometry: Complex Relationship Between and Offset

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Spring 2008 49

A case study presents three-parameterinversion on AVO data acquired offshore Egypt.

Inversion in the Nile DeltaApache Egypt Companies, with partners RWEDea and BP Egypt, recorded a 3D seismic surveyin a western Mediterranean deep marineconcession in the Nile Delta.9 The seismic dataexhibited strong amplitudes over a gas-chargedcomplex of channel and levee sands. However,amplitude alone was not a reliable indicator ofgas saturation: distinct accumulations—onewith high gas saturation and the other with lowgas saturation—both displayed high amplitude.Extracting density information from the seismicdata was a key to identifying commercial gas sands.

The main objective of prestack inversion wasto improve the existing reservoir model inpreparation for optimizing the appraisal anddevelopment plan. The survey featured longoffsets, up to 6,000 m [19,690 ft], enabling AVOinversion for three elastic parameters: P-waveimpedance, S-wave impedance and density.Correlation with log data would help Apacheestimate rock and fluid properties throughoutthe 1,500-km2 [580-mi2] study area.

Rock-property correlations using log data fromthe five wells in the concession discrimi natedrock-fluid classes on the basis of Vp / Vs and P-wave impedance (below right). The separationbetween sands with high and low water satura -tions suggested that fluid-content differenceswould be apparent in the inversion results.

7. Zoeppritz K: “Über Erdbebenwellen, VIIB: Über Reflexion und Durchgang seismicher Wellen durchUnstetigkeitsflächen,” Nachrichten der KöniglichenGesellschaft der Wissenschaften zu Göttingen,Mathematisch-physikalische Klasse (1919): 57–84.

8. Aki K and Richards PG: Quantitative Seismology: Theoryand Methods. San Francisco: W.H. Freeman andCompany, 1980.Connolly P: “Elastic Impedance,” The Leading Edge 18,no. 4 (April 1999): 438–452.Pan ND and Gardner GF: “The Basic Equations of PlaneElastic Wave Reflection and Scattering Applied to AVOAnalysis,” Report S-87-7, Seismic Acoustic Laboratory,University of Houston, 1987.Rüger A: “P-Wave Reflection Coefficients forTransversely Isotropic Models with Vertical andHorizontal Axis of Symmetry,” Geophysics 62, no. 3(May–June 1997): 713–722.Shuey RT: “A Simplification of the Zoeppritz Equations,”Geophysics 50, no. 4 (April 1985): 609–614. Smith GC and Gidlow PM: “Weighted Stacking for RockProperty Estimation and Detection of Gas,” GeophysicalProspecting 35, no. 9 (November 1987): 993–1014.

9. Roberts R, Bedingfield J, Phelps D, Lau A, Godfrey B,Volterrani S, Engelmark F and Hughes K: “HybridInversion Techniques Used to Derive Key ElasticParameters: A Case Study from the Nile Delta,” The Leading Edge 24, no. 1 (January 2005): 86–92.

> Amplitude variation with offset data and reflection coefficient versus angle of incidence. Severalreflections in the CMP gather (left) exhibit amplitude variation with offset. These data come from theNorth Sea example described on page 51. The nearly vertical black lines delimit angle rangescomputed by ray tracing. The reflection of interest is at 1.26 s (yellow). At zero offset (normalincidence), the reflection has slightly positive amplitude—a swing to the right—then turns negative,with a swing to the left. Several methods can be used to model the reflection coefficient versus angle(right). The properties of the two-layer model are shown (top). R0 stands for reflection coefficient atzero offset. The exact solution by the Zoeppritz equations is shown by the black curve. The othercurves are approximations taken from the work described in reference 8.

Refle

ctio

n co

effic

ient

Average angle, deg

ZoeppritzAki and RichardsPan-GardnerGidlow 3-Term

Shuey 2-TermGidlow 2-TermConnollyAnisotropic

0 20 40 60 80

0

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Vp Vs Vp / Vsρ Ro

Poisson’sRatio

Layer 1

Layer 2

> Correlating acoustic properties with water saturation (Sw). Logmeasurements of P-wave impedance, water saturation and Vp / Vs arecrossplotted to show relationships that can be applied to seismic inversionresults. Clean gas sands are plotted in red, laminated sands in green, andwater-filled sands in blue. (Adapted from Roberts et al, reference 9.)

V p/V

s

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3.0

12,500 15,000 17,500 20,000 22,500

P-wave impedance, ft/s.g/cm3

Water-filledsands

Gas sands

0.1 0.9Sw

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The inversion workflow combined full-waveform prestack inversion with three-termAVO inversion. The prestack inversion, per -formed at sparsely sampled locations, providedbackground Vp / Vs trends, which, with the welldata, were used to build low-frequency models tomerge with the results of the AVO inversion.Agreement between synthetic predictions andactual results was generally good (left).

The three-parameter AVO inversion resultswere converted into relative impedances andmerged with the low-frequency backgroundmodels to generate 3D volumes of P-waveimpedance, S-wave impedance and density.With transforms derived from rock-physicsanalysis, these elastic attributes were thenconverted to volumes of net-to-gross sand andbulk water saturation.

The density volume was found to be a reliableindicator of fluid saturation. For example, theAbu Sir 2X well, drilled at a location of highseismic amplitudes, encountered one zone withhigh gas saturation and two deeper zones withlow gas saturation (below left). A seismicallyderived density profile through the well predictslow gas saturation in the deeper layers. Thedensity results from seismic inversion delineatea single high-saturation interval and also show itslimited lateral extent.

The inversion results can be examined from avariety of perspectives. For instance, trackingone of the layers that was uneconomic in the AbuSir 2X well throughout the seismic volumereveals a region where that layer might containhigh gas saturation (next page, bottom).Although this accumulation is downdip from thereservoir encountered in other wells in the area,the density and water-saturation maps supportthe interpretation that the downdip area hashigh gas saturation and is not water-filled. As aconsequence of this study, a new well, Abu Sir 3X,is planned for this area.

50 Oilfield Review

10. For more on drilling injectite targets: Chou L, Li Q,Darquin A, Denichou J-M, Griffiths R, Hart N, McInally A,Templeton G, Omeragic D, Tribe I, Watson K andWiig M: “Steering Toward Enhanced Production,”Oilfield Review 17, no. 3 (Autumn 2005): 54–63.

11. Pickering S and McHugo S: “Reservoirs Come in AllShapes and Sizes, and Some Are More Difficult ThanOthers,” GEO ExPro no. 1 (June 2004): 34–36.McHugo S, Cooke A and Pickering S: “Description of aHighly Complex Reservoir Using Single Sensor SeismicAcquisition,” paper SPE 83965, presented at SPEOffshore Europe, Aberdeen, September 2–5, 2003.

> Comparison between observed and synthetic AVO gathers. The observedAVO gather (right) was inverted for Vp , Poisson’s ratio and density. Theresults (left three panels) are plotted with associated uncertainty range(yellow). A synthetic gather generated from the Vp , Poisson’s ratio anddensity models appears in the fourth panel. The close match between theobserved and synthetic AVO gathers indicates that the property models aregood representations of actual earth properties. (Adapted from Roberts etal, reference 9.)

Poisson’sRatio

Densityg/cm3

1.5 2.5Vp Synthetic Gather Observed Gather

2.0

2.5Two-

way

tim

e, s

> Inversion for density. Inversion of AVO data over gas fields in the Nile Delta predicts low density(red) in the upper part of the reservoir (Zone 1) and higher densities (green and yellow) deeper in thereservoir (Zones 2 and 3). The density measured at the well location is inserted in the center of thepanel and plotted on the same color scale as the seismic-inversion density. The well logs (inset right)show where sands were logged (yellow shaded gamma ray) and where high resistivity (red curve)indicates hydrocarbon. The seismic amplitude section, not shown, exhibited high amplitudes in allzones of the reservoir, and so was unable to distinguish the low gas saturation in Zones 2 and 3 fromthe high gas saturation of Zone 1. (Adapted from Roberts et al, reference 9.)

GammaRay Resistivity

Abu Sir 2X

Density, g/cm31.95 2.48

Low-saturation gas

Gas/water contact

Zone 1

Zone 2

Zone 3


Spring 2008 51

Inversion to Enhance VisibilityIn some cases, the acoustic impedance contrastbetween two lithologies may be so small that theinterface between them generates almost nonormal-incidence reflection. For example, an oil-filled sandstone with high density and lowP-wave velocity might have nearly the sameacoustic impedance as a shale with lower densityand higher P-wave velocity. Without an acousticimpedance contrast, such oil reservoirs areextremely difficult to detect using traditionalsurface seismic acquisition and processing.

An example of a low-contrast reservoir is theAlba field in the North Sea. Alba and reservoirslike it are interpreted to be injectites, formed bythe injection, or remobilization, of unconsoli -dated sand into overlying shale layers duringperiods of differential stress (above right). Thesecomplex reservoirs are characterized byirregular morphology and chaotically distributedhigh-porosity sands. Often, such accumulations

are not discovered by seismic imaging, but areencountered inadvertently while drilling todeeper targets.10

In one area of the central North Sea, anoperating company wanted to improve the

seismic characterization of injected reservoirsands in the Balder interval that wereparticularly difficult to image.11 Modeling studiesusing rock properties from well data establishedthat prestack inversion of seismic data could

> Tracking inversion results through the reservoir. Parameters extracted from the seismic data and itsinversion are displayed for Zone 2—one of the zones that had uneconomic gas saturations in the AbuSir 2X well. The amplitudes of the original seismic data (top left) show anomalies near the Abu Sir 2Xwell, but the density plot (bottom left) does not. Low amplitudes are plotted in blue and green, andhigh amplitudes are plotted in red and purple. Low densities are plotted in red and high densities areplotted in blue and green. Amplitude, density and P-wave impedance (top right) all exhibit exceptionalvalues in the southeast corner, where a well is planned. Low P-wave impedances are plotted in redand purple, and high impedances are plotted in blue and green. Conversion of the inversion results towater saturation (bottom right) indicates that the planned well should encounter low water saturation.(Adapted from Roberts et al, reference 9.)

Conventional Amplitude

Abu Sir 2X

Abu Sir 1X

Planned well

P-Wave Impedance

Abu Sir 2X

Abu Sir 1X

Planned well

Density

Abu Sir 2X

Abu Sir 1X

Planned well

Water Saturation

Water saturation0 1

Planned well

Abu Sir 1X

Abu Sir 2X

> Sand-injection features, or injectites. The remobilization of unconsolidatedsand (gold) into overlying shale layers (gray) can result in injectites. Thesesandstone features have irregular shapes and are difficult to image seismically.

Sand Injectite


potentially distinguish the clean sands from thesurrounding shales, but the existing surfaceseismic data were of insufficient resolution forthis purpose.

A new survey was designed to map the distri -bution and thickness of reservoir pay, delineate thegeometry of individual sand wings and assessreservoir connectivity. Acquisition with the Q-Marine system would allow accurate cablepositioning, fine spatial sampling and calibrationof sources and receivers. Together, these capabili -ties facilitate precision imaging, improved noiseattenuation, increased band width and preser -vation of amplitude and phase information—allimportant for successful inversion.

Log data from three wells intersecting thereservoir were analyzed for correlationsbetween P- and S-wave velocities, ρ, μ, λ,lithology and fluid saturation. For example,crossplotting Vp / Vs with the product μρ, andcolor-coding by lithology, showed that high sandcontent correlated with low Vp / Vs and high μρvalues (left). These relationships were thenapplied to Vp / Vs calculated from seismicinversion to map high sand content throughoutthe seismic volume.

The prestack seismic data were divided into seven angle stacks, each containingreflections in a 7° range of incidence angles outto 49° (next page, bottom). Three-parameter AVOinver sion generated estimates of P- and S-wavereflectivities and density contrast. These volumeswere inverted for P- and S-wave impedances anddensity, from which volumes of μρ, Vp / Vs and λ /μwere generated.

Crossplots of seismically derived Vp / Vs andμρ through the interval containing the injectedsands were color-coded by sand probability(left). Applying the color-coding to the rock-constant volumes obtained from seismicinversion yielded interpretable 3D cubes of sandprobability. A close-up of a section through thesand-probability volume highlights a steeplydipping sand-injection feature (next page, top).

The sand-probability volume can beilluminated by rendering the surroundingshales—lithologies with low probability of

52 Oilfield Review

> Correlating acoustic properties with lithology. A crossplot of Vp / Vs withthe product of shear modulus (�) and density (ρ) shows a trend related tosand volume: high sand content correlates with low Vp / Vs and high �ρvalues. Applying this relation to Vp / Vs and �ρ values obtained frominversion yields lithology maps of the subsurface.

V p/V

s

2.5

2.0

3.0

2 4 6 8 10 12 14

Log Data

0.05 0.95Volume of sand

Shear modulus . density ( ), GPa . g/cm3μρ

> Sand probability. The correlation between inversion outputs Vp / Vs and�ρ with sand probability shows a direct relationship: increasing �ρ anddecreasing Vp / Vs point to higher probability of sand. This relationship wasapplied to the seismic inversion results to obtain maps of sand probability.

V p/V

s

2.5

2.0

3.0

2 4 6 8 10 12 14

Seismic Values

Shear modulus . density ( ), GPa . g/cm3μρ

0 100Sand probability, %


Spring 2008 53

> AVO inversion workflow. The input data consisted of prestack AVO gathers in 7° offset ranges, along with sonic and density well logs (left). The first step,three-parameter AVO inversion, produced estimates of P-wave and S-wave reflectivities and density contrast. These volumes were inverted for P-waveand S-wave impedances and density. The final step extracted rock properties, in the form of �ρ, Vp / Vs and λ/�.

Input Data AVO Analysis Acoustic Properties Rock Constants

P-wave impedance

S-wave impedance

Density

P-wave reflectivity

S-wave reflectivity

Density contrast

Synthetics Density Sonic

Seven angle gathers(0 to 49°)

Conditioned well data

μρ

Vp /Vs

λ/μ

> Comparing seismic reflection amplitudes with sand probability. A steeply dipping feature seen in thecenter of the seismic reflection image (left) has a high probability of being sand (right). This structure,which is 80 m [260 ft] high, has the shape and aspect expected of a sand injectite.

Distance, m Distance, m0 750 0 750

Seismic Amplitude Sand Probability

80 m

0 100Sand probability, %


sand—transparent using 3D visualizationtechnology (above). This characterization of theextent and quality of the injected sand bodies can help optimize development of thesecomplex features.

Simultaneous InversionThe examples presented so far have shown theresults of techniques that invert tracesseparately and then combine the results in adisplay of reflectivity. Geophysicists at theDanish company Ødegaard, now part ofSchlumberger, have developed a simultaneousinversion technique that examines all traces atonce to invert for a globally optimized model ofrock properties.12

Global optimization is a term describingseveral methods designed to find the best overallsolution of a problem that has multiple localsolutions. An inversion problem may be cast asfinding the absolute minimum of a multi -dimensional, nonlinear function (right). This canbe likened to placing a ball on a hilly surface andletting it roll to the lowest level. Depending onwhich hill the ball starts on and which directionit rolls, it may get stuck in a nearby low spot—alocal minimum—or land in the lowest area in thespace—the global minimum.

Analogously, some inversion techniquesdepend heavily on the starting model—which hillthey start on—and so may find a local minimum

rather than the absolute minimum. Global optimi -zation attempts to find the absolute minimum byadopting new ways of searching for solutioncandidates. Various strategies may be utilized toreach a solution. The approach taken by the ISISsuite of reservoir characterization technologydeveloped by Ødegaard is simulated annealing.

Simulated annealing is based on a physicalanalogy. In metallurgy, annealing is the processof controlled heating and subsequent cooling of ametal. Heating increases the internal energy ofthe metal atoms, causing them to abandon theirplaces in the crystal structure. Gradual coolingallows the atoms to reach lower energy states.Under properly controlled heating and cooling,the system becomes more ordered; crystal sizeincreases, and the resulting material hasminimal defects.

Instead of minimizing the thermodynamicenergy of a system, inversion by simulatedannealing aims to minimize an objective function,also called a cost function. The algorithm replacesthe starting solution with another attempt byselecting a random solution not far from the first.If the new solution reduces the cost function, it iskept, and the process is repeated. If the newsolution is not much better than the previous one,another random solution is tested. However,simulated annealing improves over some othermethods by allowing a “worse” solution if it helpsinvestigate more of the solution space.

The ISIS simultaneous inversion costfunction is made up of four penalty terms thatare collectively minimized to deliver the bestsolution. The first term contains a penalty fordifferences between the seismic data and thesynthetic. The second term includes the low-frequency acoustic impedance trend in theinversion through a penalty for deviation of theestimated acoustic impedance model from thelow-frequency model. The third term attenuateshorizontally uncorrelated noise by introducing apenalty for horizontal variations in the estimatedacoustic impedance model. The fourth termintroduces a sparsely parameterized backgroundmodel of layer boundaries. These terms can bemodified to include requirements of morecomplex data types, such as time-lapse surveysand shear waves.

Compared with trace-by-trace reflectivitymethods, simultaneous inversion has severalbenefits. Honoring the full bandwidth of theseismic signal—low and high frequenciestogether—enhances resolution and accuracy.

The ISIS inversion algorithm can be used onmany types of seismic data (next page, top right).The remainder of the article focuses on threedistinct applications: a 3D AVO study fromAustralia, a time-lapse example from the NorthSea and a multicomponent case using seabottomsensors also from the North Sea.

Revealing a Reservoir in AustraliaMany seismic surveys are acquired andprocessed purely for reflector-imaging purposes,without inversion in mind. However, inversion

54 Oilfield Review

> Seeing the sand. Volumes with high sand probability are colored yellow, gold and red, and the portionswith low probability of sand have been made transparent. The top surface of the underlying sandformation from which the injectite was ejected is blue. (Adapted from Pickering and McHugo,reference 11.)

Sand-Intrusion Visualization

> Finding the minimum. Many inversion schemesattempt to minimize a multidimensional,nonlinear cost function with multiple minima. Inthis case, the minima are shown as low points inthis 3D surface. Depending on the inversionalgorithm and starting point, the process mightend in a local minimum—the point that is thelowest in a neighborhood—instead of the globalminimum—the lowest point of all.

Z

Y

X


Spring 2008 55

can deliver even better results when surveydesign, acquisition and processing are tailored tothe requirements of the inversion scheme.

Operating offshore Western Australia, SantosLtd. and partners wanted to enhance recoveryfrom their reservoir, and accurate mapping would help achieve this.13 However, even afterreprocessing, the seismic data acquired in 1998were not of sufficient quality to allow inter pre -tation of the top and base of the primary reservoir.14

Rock-physics analysis of well logs revealedthat the contrast in P-wave impedance betweenthe reservoir and the overlying shale was subtle.This explained some of the difficulty inidentifying the reservoir in vertical-incidencereflection data. However, a large contrast inPoisson’s ratio should be observable if AVO datain the appropriate offset range were acquired.

In addition to the low-reflectivity problem,the 1998 survey data were noisy. The continentalshelf offshore northwest Australia has a layer ofhigh acoustic impedance contrast near theseafloor. This layer traps seismic energy,generating reverberations called multiples thatcontaminate the seismic record.

WesternGeco survey evaluation and design(SED) specialists investigated ways to eliminatenoise and improve overall recording in a newsurvey. Removing the noise from multiplesrequired an accurate image of the seafloor, whichcould be acquired if extremely short offsets wererecorded. The 3.125-m [10.25-ft] spacing of Q-Marine hydrophones would adequately sampleboth the desired signal and the noise, facilitatingeffective removal of the latter. Modeling showedthat a streamer length exceeding 5,000 m[16,400 ft] would be needed to capture AVOeffects at the reservoir level. This length wouldprovide data over an incidence-angle range of10 to 50°.

Comparison of a reflection-amplitude imagefrom the 2006 Q-Marine survey with one from thereprocessed 1998 dataset shows improvedstructural imaging and reduced noise (right).Testing during processing identified the stepsthat would optimize inversion.

12. Rasmussen KB, Brunn A and Pedersen JM: “SimultaneousSeismic Inversion,” presented at the 66th EAGEConference and Exhibition, Paris, June 7–10, 2004.

13. Partners were Kuwait Foreign Petroleum ExplorationCompany (KUFPEC), Nippon Oil Exploration andWoodside Energy.

14. Barclay F, Patenall R and Bunting T: “Revealing theReservoir: Integrating Seismic Survey Design,Acquisition, Processing and Inversion to OptimizeReservoir Characterization,” presented at the 19th ASEGInternational Geophysical Conference and Exhibition,Perth, Western Australia, November 18–22, 2007.

> Applications of ISIS simultaneous inversion.

Partial-stack AVO data

Intercept and gradient AVO data

Multicomponent partial-stackAVO data

Borehole seismic (VSP) data

Time-lapse full-stack data (whichmay include multicomponentfull-stack data)

Time-lapse partial-stack AVO data(which may include multicomponentpartial-stack AVO data)

Full-stack data

Multicomponent full-stack data(P-to-P and P-to-S conversions)

Data Type

P-wave impedance

P-wave impedance and S-wave impedance

Physical Properties

Acoustic impedance from the intercept data;shear impedance from shear seismic datacalculated from the intercept and gradient data

P-wave impedance, Vp/Vs (or S-wave impedance)and density

Acoustic impedance from the PP data; shearimpedance from the PS data

Simultaneous time-lapse inversion for baselineproperties and the changes: for example, fo rpartial-stack data, inversion can determinebaseline P-wave impedance, Vp/Vs (or S-waveimpedance) and density and the changes inthese properties over the time interval.

Simultaneous time-lapse inversion for baselineP-wave impedance and the changes in P-waveimpedance for each time interval: formulticomponent data, inversion will also outputbaseline S-wave impedance and changes inS-wave impedance over the time interval.

P-wave impedance, Vp/Vs (or S-wave impedance)and density, from which Poisson’s ratio, andcan be estimated.

λ μ

> Seismic images in an Australian field. Multiples generated by a high acoustic impedance layer nearthe seafloor make it difficult to image the low-impedance-contrast reservoir, which is within theshaded interval, at approximately 2,100 to 2,200 ms. The Q-Marine image (right) exhibits less noise andbetter resolution of structural features than the 1998 dataset (left). (Adapted from Barclay et al,reference 14.)

1998 Survey with 2006 Reprocessing 2006 Q-Marine Survey1,700

1,800

1,900

2,000

2,100

2,200

2,300

2,400

2,500

2,600

2,700

2,800

2,900

3,000

3,100

3,200

3,300

Tim

e, m

s

5,6254,2005,700 3,135

Crossline number Crossline number


The inversion for P-wave impedance gavehigh-quality results that correlated strongly withvalues measured in four of the field’s wells (left).The subtle rise in acoustic impe d ance at the topof the reservoir, although significantly smallerthan those in the overlying layers, is accuratelydetected by the simul taneous inversion.

The P-wave impedance contrast at the top ofthe reservoir is small, but the contrast in Poisson’sratio is significant, and so is a potentially moreuseful indicator of reservoir quality. Poisson’s ratiois more accurately estimated by including largeincidence angles in the inversion. A comparison ofPoisson’s ratio obtained by incorporating differentranges of incidence angles showed greaterresolution and less noise when wider angles wereincluded (below).

Time-Lapse InversionSimultaneous inversion can incorporate datafrom various vintages to highlight time-lapsechanges in rock and fluid properties. Thisapproach has recently been tested on the Nornefield, where operator StatoilHydro is trying toincrease oil recovery from 40% to more than 50%.

The Norne field has had multiple time-lapse,or 4D, seismic surveys.15 The high-qualitysandstone reservoirs, with porosities of 25 to 32%

56 Oilfield Review

> Simultaneous inversion for P-wave impedance. Impedance sections from inversion show excellentcorrelation with values in four wells. In each panel, the impedances measured in the well are color-coded at the same scale as the inversion results and inserted in the middle of the panel. The top ofthe reservoir is marked with a nearly horizontal black line. The white curves are unscaled watersaturation logs, with water saturation decreasing to the left. To the right of each panel is a display ofthe log acoustic impedance (red) and the seismically estimated acoustic impedance at the welllocation (blue). (Adapted from Barclay et al, reference 14.)

Two-

way

tim

e, s

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

Acoustic impedance, km/s . g/cm35.7 8.2

> Inversion for Poisson’s ratio. In this field, Poisson’s ratio provides a better measure than acoustic impedance for assessing reservoir quality. LowPoisson’s ratio (green) is generally indicative of higher quality sand. Reflection amplitudes are more affected by Poisson’s ratio at larger angles ofincidence. When a larger range of angles (5 to 42°) is included in the inversion (right), the estimation of Poisson’s ratio shows less noise, and the regions ofsimilar Poisson’s ratio appear more continuous than when inversion uses a smaller range (5 to 35°) of angles (left). White circles are well locations.(Adapted from Barclay et al, reference 14.)

450 460 470 450 460 470

Poisson’s ratio0.34 0.43CrosslineCrossline

Inline

Inline


Spring 2008 57

and permeabilities ranging from 200 to 2,000 mD,are conducive to successful time-lapse moni -toring; changes in fluid saturation and pressuregive rise to noticeable differences in seismicamplitudes and elastic impedances.

The first 3D surface seismic survey over thefield was acquired in 1992. This large explorationsurvey was acquired before production and waterand gas injection, but was not considered abaseline for time-lapse monitoring. In 2001,Norne’s first Q-Marine survey was acquired, withrepeatable acquisition, forming the baseline forthe 2003, 2004 and 2006 monitor surveys—allacquired with Q-Marine technology.

From the start, time-lapse monitoringdelivered crucial information for optimizing fielddevelopment. Differences in the AVO inversionsof the 2001 and 2003 surveys revealed changes inacoustic impedance that could be interpreted asincreases in water saturation.16 In one area, thetrajectory of a planned well was modified to avoida zone inferred to have high water saturation.17

Recently, the evaluation of changes in effec -tive stress has become important for optimiz ingreservoir depletion and injection strategies. Tounderstand the continuing effects of productionon the field, StatoilHydro and Schlumbergerundertook a simultaneous inversion project thatincorporated all available seismic data, log datafrom seven wells and production data from theECLIPSE reservoir model.18

The ISIS simultaneous inversion estimatedbaseline values and changes in acousticimpedance and Poisson’s ratio from the time-lapse seismic data (right). To compensate for thelack of low-frequency information in the seismicbandwidth—needed to determine absoluteelastic properties—background models wereconstructed. For the baseline survey, thebackground model was derived by propagatingborehole values of elastic properties throughoutthe zone of interest, constrained by keyinterpreted horizons and the seismic velocitiesin each interval.

15. Osdal B, Husby O, Aronsen HA, Chen N and Alsos T:“Mapping the Fluid Front and Pressure Buildup Using 4DData on Norne Field,” The Leading Edge 25, no. 9(September 2006): 1134–1141.

16. Khazanehdari J, Curtis A and Goto R: “Quantitative Time-Lapse Seismic Analysis Through Prestack Inversion andRock Physics,” Expanded Abstracts, 75th SEG AnnualInternational Meeting and Exposition, Houston,November 6–11, 2005: 2476–2479.

17. Aronsen HA, Osdal B, Dahl T, Eiken O, Goto R,Khazanehdari J, Pickering S and Smith P: “Time Will Tell:New Insights from Time-Lapse Seismic Data,” OilfieldReview 16, no. 2 (Summer 2004): 6–15.

18. Murineddu A, Bertrand-Biran V, Hope T, Westeng K andOsdal B: “Reservoir Monitoring Using Time-LapseSeismic over the Norne Field: An Ongoing Story,”presented at the Norsk Petroleumsforening BiennialGeophysical Seminar, Kristiansand, Norway, March 10–12, 2008.

> Time-lapse inversion. Results for acoustic impedance (top) and Poisson’s ratio (bottom) use a low-frequency model based on simulation results. In the 3D volume (top right), the back and side panelsshow acoustic impedance values from the 2003 survey. The horizontal surface is a time-slice of theratio of acoustic impedance in 2006 to that in 2001. The increase (red) has been interpreted asreplacement of oil by water. Absolute acoustic impedance comparisons at two wells (top left) showgood correlation between well measurements and the 2003 acoustic impedance values. The redarrows in each log track point to the top of the horizon of interest. The log tracks display well data(red), seismically derived values (blue) and the low-frequency model (green). Results for Poisson’sratio (bottom) are plotted similarly. Well C is outside the 3D volume.

Poisson’s ratio 0.450.20

Log curveInversion resultLow-frequency model

Two-

way

tim

e, s

1.9

2.8

Two-

way

tim

e, s

1.9

2.8

Well A

Well C

Poisson’s ratio change,2006/2001, %

10–10

Poisson’s Ratio

Pois

son’s

ratio

, 200

30.36

0.18

AB

Acoustic impedance

125

Log curveInversion resultLow-frequency model

Two-

way

tim

e, s

1.9

2.8

Two-

way

tim

e, s

1.9

2.8

Well A

Well B

Acoustic impedancechange, 2006/2001, %

5–5

9

5

Acou

stic

impe

danc

e, 2

003

Acoustic Impedance

AB

MPa . s/m


For the time-lapse low-frequency models,estimates of elastic properties were obtainedfrom the ECLIPSE reservoir simulator in threesteps: reservoir properties were converted fromdepth to time using the velocity model, thenconverted to elastic-property changes using rock-physics models. Finally, the spatial and temporaldistributions of the property changes wereconstrained by seismic-velocity changesobserved in time-lapse traveltime differences.

This unique combination of time-convertedreservoir properties with seismic-derivedtraveltime changes delivered accurate changesin elastic properties consistent with the reservoirsimulation. Significant differences were foundbetween inversion results that did and did notuse updated background models (above).

The StatoilHydro reservoir management teamplans to use these results to track the movementof the waterflood front, evaluate the progress ofwater and gas injection, estimate the pressuredistribution and update the reservoir model.

Multicomponent InversionThe previous examples dealt with inversion of P-wave data. Towed-streamer seismic surveys aredesigned to generate and record only P-waves; S-waves do not propagate in fluids. Compressionalwaves generated by the source may convert toshear waves at the seafloor or below and thentravel as such through the solid formations of thesubsurface, but they must convert again to P-waves to travel through the water and berecorded by the receivers. Information about S-wave velocity and shear modulus, μ, may be

58 Oilfield Review

> Effect of background models on inversion. Time-lapse inversion for acoustic impedance (top) andPoisson’s ratio (bottom) shows different results using different background models. These panelsfocus on a region where the reservoir simulation model contains a transmissible fault that allows gasmigration. The acoustic impedance section calculated with a background model that incorporatedtime-lapse effects (top left) indicates a decrease in acoustic impedance (red) across the fault. In theacoustic impedance section calculated without a time-lapse background model (top right), thedecrease in acoustic impedance is constrained to the area above the fault, suggesting the fault is nottransmissible. The inversion for Poisson’s ratio also suggests a transmissible fault, but only when abackground model is used that honors simulator data (bottom left). The black curve on each panel isthe top of the formation indicated by red arrows in the previous figure. The amplitudes are the ratio ofthe 2004 values to the 2001 values.

Two-

way

tim

e, s

2.2

2.3

2.4

2.5

2.61,545

Crossline number1,645 1,745 1,845 1,945 2,1452,045

Background Model withTime-Lapse Information

Acoustic impedance change

Permeable fault?

1,545


Background Model withNo Time-Lapse Information

Acoustic impedance change

Impermeable fault?

Two-

way

tim

e, s

1,545


2.2

2.3

2.4

2.5

2.6

Poisson’s ratio change

Amplitude 1.060.94

1,545


Poisson’s ratio change

>Multicomponent seismic data. Commonmidpoint (CMP) gathers of PZ (top) and PS (bottom)reflection data show traces at increasing offsetfrom left to right. Color bands delineate angleranges. Several reflections exhibit AVO effects,which may differ in their expressions on PZ andPS gathers. For example, in the PZ gather, thereflection at the dotted red line is slightly positiveat zero offset, and decreases to nearly zeroamplitude with increasing offset. Arrivals fromthe same reflector in the PS gather are stronglypositive at zero offset and decrease graduallywith increasing offset.

PZ CMP Gather

PZ ti

me

PS CMP Gather

PS ti

me


Spring 2008 59

gleaned through AVO analysis, but S-wavesthemselves are not recorded.

However, it is possible to acquire S-wave dataif the receivers are coupled to the seafloor.Ocean-bottom cables (OBCs) are designed forthis purpose. Typically, these cables contain fourmulticomponent sensors—three geophones anda hydrophone—spaced at intervals determinedby the survey requirements.19 The geophonesdetect the multiple components of S-wavemotion, and the hydrophone—like towed-streamer hydrophones—detects P-wave signals,designated as PP arrivals. The P-wave is alsodetected by the geophones, mainly on thevertical component, giving rise to PZ signals.

The sources used in these surveys are thesame as those in towed-streamer surveys,generating P-waves that convert to S-waves atthe seafloor or deeper. The resulting signals arecalled PS data. Although multicomponentsurveys are more complex to acquire and processthan single-component surveys, they providedata that single-component surveys cannot.

Schlumberger has inverted multicomponentseismic data from a gas and condensate field inthe North Sea. The main objective of theinversion study was to generate elasticproperties—P-wave impedance, Vp / Vs anddensity—from the seismic datasets as input forcalculating large-scale geomechanical properties.The geomechanical properties would be used forbuilding a 3D mechanical earth model (MEM).20

Processing of PZ and PS data is far morecomplex than conventional single-componentdataset processing. The two data types camefrom the same survey, but showed manydifferences. For example, amplitudes, velocitiesand AVO behavior were markedly differentbetween the two datasets (previous page, right).

To assess the value of the PS data, simul -taneous inversion of the PZ data was comparedwith simultaneous inversion of the combined PZand PS datasets (right).21 The acousticimpedance and density derived from the PZ andPS reflection amplitudes were much betterresolved and matched the well values better thanthose calculated from PZ arrivals alone.

19. Surveys that acquire such multicomponent data are alsocalled 4C surveys. For more on 4C surveys: Barkved O,Bartman B, Compani B, Gaiser J, Van Dok R, Johns T,Kristiansen P, Probert T and Thompson M: “The ManyFacets of Multicomponent Seismic Data,” OilfieldReview 16, no. 2 (Summer 2004): 42–56.

20. Mohamed FR, Rasmussen A, Wendt AS, Murineddu Aand Nickel M: “High Resolution 3D Mechanical EarthModel Using Seismic Neural Netmodeling: Integrating

Geological, Petrophysical and Geophysical Data,” paperA043, prepared for presentation at the 70th EAGEConference and Exhibition, Rome, June 9–12, 2008.

21. Rasmussen A, Mohamed FR, Murineddu A andWendt AS: “Event Matching and SimultaneousInversion—A Critical Input to 3D Mechanical EarthModeling,” paper P348, prepared for presentation at the 70th EAGE Conference and Exhibition, Rome, June 9–12, 2008.

> Simultaneous inversion of multicomponent data. Acoustic impedance (left) and density (right) frominversion using only PZ data (top) lack the resolution and continuity of the results of inversion usingPZ and PS data (bottom). In particular, compared with PZ inversion, the densities predicted byinversion of PZ and PS data showed much better correlation with log values. In the panels showinginversion results, the nearly horizontal black lines are interpreted horizons. (Adapted from Rasmussenet al, reference 21.)

PZ and PS InversionAcoustic impedance Density

PZ Inversion

Log curveInversion resultLow-frequencymodel

Log curveInversion resultLow-frequencymodel

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km/s . g/cm3 105

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kg/m3 3,0002,000


The acoustic impedances from seismic inver -sion improved the accuracy of the mechanicalearth model. In a blind-well test, acoustic impe d -ances predicted by inversion were comparedwith those measured in a well that had not beenused for inversion calibration (left). In the 10layers of the MEM, the well log acousticimpedances showed an extremely close matchwith impedances from the seismic inversion.Correlations with models built using conven -tional methods of generating geomechanicalproperties—methods that do not incorporateseismically calculated properties—did notmatch as well and exhibited large errors inseveral layers.

Looking Forward with InversionSeismic inversion is a powerful tool for extractingreservoir rock and fluid information from seismicdata. Although most seismic surveys are designedfor imaging alone, companies are increasinglyapplying inversion to get more out of theirinvestments in seismic data. Some companiesnow perform inversion on every seismic datasetand won’t drill without it.

Inversion for reservoir characterization is amultistep process that requires, in addition tothe inversion algorithm itself, careful datapreparation, seismic data processing, log editingand calibration, rock-property correlation andvisualization. Workflows are being developed tocombine these steps for optimal results.

The addition of new measurements from otherdisciplines, such as from deep electro magneticsensing, promises to bring enhance ments toseismic inversion results. Work on magneto -tellurics and controlled-source electromagneticsfor the marine environment is generatingconsiderable interest among geophysicists, andthese techniques may hold the key to detectingproperties that elude seismic surveys.

Another area of potential improvement lies inenhancing the data content in seismicrecordings. Low frequencies not contained inmost seismic data have to be obtained ormodeled from log data for inversion to absoluterock properties. However, in areas far from wells,this step may introduce unwanted bias into theresults. For example, when lithologies thin,thicken, disappear or appear between wells, datafrom wells might not form an accurate basis forseismic models.

A new seismic data-acquisition technique isbeing evaluated as a means of supplyingnecessary low-frequency information in theabsence of log data. Known as over/under

60 Oilfield Review

22. Camara Alfaro J, Corcoran C, Davies K, GonzalezPineda F, Hampson G, Hill D, Howard M, Kapoor J,Moldoveanu N and Kragh E: “Reducing ExplorationRisk,” Oilfield Review 19, no. 1 (Spring 2007): 26–43.Moldoveanu N, Combee L, Egan M, Hampson G,Sydora L and Abriel W: “Over/Under Towed-StreamerAcquisition: A Method to Extend Seismic Bandwidth toBoth Higher and Lower Frequencies,” The LeadingEdge 26, no. 1 (January 2007): 41–58.

23. Özdemir H: “Unbiased Seismic Inversion: Less Model,More Seismic,” presented at the Petroleum ExplorationSociety of Great Britain, Geophysical Seminar, London,January 30–31, 2008.

24. Özdemir H, Leathard M and Sansom J: “Lost FrequenciesFound—Almost: Inversion of Over/Under Data,” paperD028, presented at the 69th EAGE Conference andExhibition, London, June 11–14, 2007.

> Acoustic properties in a 3D mechanical earth model (MEM). Seismically derived acousticimpedances helped populate a 3D MEM with mechanical properties. The inset (right) shows one of 10layers in the model. Acoustic impedance (AI) values extracted along a wellbore (Well X) that had notbeen used in building the model (Track 1) are compared with values predicted by three methods:seismic inversion (Track 2), sequential Gaussian simulation (SGS) (Track 3) and kriging (Track 4). SGSand kriging do not use seismic data as input. Error bars (red) in each track display percentage error.The match with seismically derived acoustic impedance is significantly better than with results fromthe other two methods. (Adapted from Mohamed et al, reference 20.)

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AI AI AI AI

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MPa.s/mMPa.s/m MPa.s/m MPa.s/m

>Wedge model of acoustic impedance. Layers thicken from left to right.Synthetic wells are shown as black curves at selected CDP numbers. Thecurves represent water saturations. This model was used to generatesynthetic seismic sections. The acoustic impedance at CDP 5 was the basisof the background model used to invert the synthetic sections.

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Spring 2008 61

acquisition, the technology effectively eliminatesthe gaps in seismic bandwidth that plague mostsurveys.22 The additional low frequenciescontained in over/under data have been shown toimprove imaging of deep reflectors (above). Thelow frequencies, often below 6 Hz, are also usefulfor enhancing inversion.23

Modeling has been used to study the impactof these additional low frequencies on seismicinversion.24 The starting point is a wedge-shaped acoustic impedance model withreservoir intervals of varying thickness(previous page, bottom left). Two syntheticseismic sections are constructed: one with awavelet extracted from a conventional surveyand the other with a wavelet extracted from anover/under survey (right). In essence, the first

> Seismic sections from a conventional survey with deep source and receivers (left) and an over/under survey (right). The over/under survey showssignificant signal strength from deep reflectors below the basalt. In the conventional survey, the basalt blocks the penetration of seismic energy.

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> Spectra of conventional and over/under wavelets. The over/under wavelet(green) is richer in low frequencies, especially from 3 to 6 Hz, than theconventional wavelet (dark blue). The frequency content of the syntheticacoustic impedance log at CDP 5 of the wedge model is shown in brown. A low-pass filtered version of this log (gold) formed the background model forinversion of the synthetic seismic sections.

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synthetic section has the frequency content ofa conventional survey, and the second syntheticsection has the enhanced frequency content ofan over/under survey.

These synthetic seismic sections were invertedusing a single low-frequency background model.The background model was created by low-passfiltering (between 0 and 3 to 4 Hz) the acousticimpedance from one well. This simulates anexploration setting in which data from only one well are available for constraining theinversion model.

Comparing inversion results of the conven -tional and the over/under sections shows that theacoustic impedances from the over/under sectioncorrelated much better with acoustic imped -ances “measured” at wells, and thereforematched the actual model better than did theresults using the conventional data as input(above). The addition of data in the range from 3to 6 Hz, supplied by the over/under technique,made a significant difference in the inversion,returning reliable rock-property informationalthough log data were sparse.

Seismic data with a large bandwidth and highpositioning accuracy also allow detection andmeasurement of minute stress effects in 3D and4D seismic data.25 For example, the effects ofsubsidence-induced stress have been seen in theproperties of S-wave velocities measured by amulticomponent survey in the North Sea (nextpage). Seismic inversion can potentially be usedto infer spatial and temporal stress changes inthe subsurface from seismic data.26

Schlumberger geophysicists envision the use ofseismic inversion for determining the triaxial

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25. Olofsson B, Probert T, Kommedal JH and Barkved OI:“Azimuthal Anisotropy from the Valhall 4C 3D Survey,”The Leading Edge 22, no.12 (December 2003): 1228–1235.Hatchell P and Bourne S: “Rocks Under Strain: Strain-Induced Time-Lapse Time Shifts Are Observed forDepleting Reservoirs,” The Leading Edge 24, no. 12(December 2005): 1222–1225. Herwanger J and Horne S: “Predicting Time-LapseStress Effects in Seismic Data,” The Leading Edge 24,no. 12 (December 2005): 1234–1242.

Herwanger J, Palmer E and Schiøtt CR: “AnisotropicVelocity Changes in Seismic Time-Lapse Data,” presentedat the 75th SEG Annual International Meeting andExposition, San Antonio, Texas, September 23–28, 2007.

26. Sarkar D, Bakulin A and Kranz RL: “Anisotropic Inversionof Seismic Data for Stressed Media: Theory and aPhysical Modeling Study on Berea Sandstone,”Geophysics 68, no. 2 (March–April 2003): 690–704.

Sayers CM: “Monitoring Production-Induced StressChanges Using Seismic Waves,” presented at the 74thSEG Annual International Meeting and Exposition,Denver, October 10–15, 2004.

> Inversion of synthetic conventional and over/under data. Both datasets were inverted using abackground model comprising a filtered version of the acoustic impedance log at CDP 5. Theover/under acoustic impedance section (right) delivers a wedge-shaped result that more closelymatches the well information than does the conventional acoustic impedance section (left). Theover/under version maps the low acoustic impedances (green) of the reservoir, which thickens to theright, and also produces a better match with the high acoustic impedance zones (yellow and red)below the reservoir, which also thicken to the right.

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Spring 2008 63

stress state of the reservoir and overburden as afunction of time. This knowledge can be used toplan well trajectories and anticipate wellborefailure and rock damage. Characterizingmechanical properties of the overburden andmonitoring stress changes over time open a newfield of application for seismic inversion.

Seismically derived rock and fluid propertiesare playing an increasing role in characterizationof geological models, and therefore extendnaturally into the domain of the reservoirproduction simulator. This characterization ofrock properties can be extended into theoverburden. The next steps in the progression of

seismic inversion will include increasing use ofreservoir and geomechanical simulation resultsto generate starting models for inversion, andvice versa. Closing this loop and operating in realtime on time-lapse data will take seismicinversion far beyond reading between the lines toreading between wells. —LS

>Modeled and observed subsidence-induced shear-wave splitting in the shallow subsurface. A 3D geomechanical model (A)was constructed to investigate the effects of subsidence of a shallow layer (Layer 1, dark blue) caused by compaction of adeeper reservoir (green intervals in Wells W1, W2, W3 and W4) under production. The resulting ground displacement in theshallow subsurface causes a nearly circular subsidence bowl (B). Changes in effective stress associated with the modeleddeformation (C) are greatest in the center of the bowl. These stress changes give rise to elastic anisotropy, which in turncauses shear-wave splitting, a phenomenon in which two orthogonally polarized shear waves propagate at different speeds.The largest shear-wave splitting occurs at the flanks of the subsidence bowl (D), where the difference between the horizontalstresses is largest. At the center of the subsidence bowl, where horizontal stress changes are large but isotropic, shear-wavesplitting is minimal. The azimuth of the bars shows the polarization direction of the fast shear wave, and the length of eachbar is proportional to the time lag between fast and slow shear waves. Observed shear-wave splitting in a subsidence bowlover a compacting North Sea reservoir (E) follows a pattern similar to the modeled phenomenon.

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seismic inversion: reading between the lines

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