Chapter 19

4D Seismic

Martin Landrø

19.1 Introduction

The term 4D seismic reflects that calendar time rep-resents the fourth dimension. A more precise term isrepeated seismic, because that is actually what is done:a seismic survey over a given area (oil/gas field) isrepeated in order to monitor production changes. Time-lapse seismic is another term used for this. For somereason, the term 4D seismic is most common, and wewill therefore use it here. It is important to note thatif we repeat 2D surveys, it is still denoted 4D seismicaccording to this definition. Recent examples of suchsurveys are repeated 2D lines acquired over the Trollgas province.

Currently there are three major areas where 4Dseismic is applied. Firstly, to monitor changes in aproducing hydrocarbon reservoir. This is now an estab-lished procedure being used worldwide. So far, 4Dseismic has almost exclusively been used for clas-tic reservoirs and only rarely for carbonate reservoirs.This is because carbonate reservoirs (apart from thosein porous chalk) are stiffer, and the effect on the seis-mic parameters of substituting oil with water is farless pronounced. Secondly, 4D seismic is being usedto monitor underground storage of CO2. Presently,there is a global initiative to decrease the atmosphericCO2 content, and one way to achieve this goal is topump huge amounts of CO2 into saline aquifers. Athird application of 4D seismic (with other geophysicalmethods) is the monitoring of geohazards (landslides,volcanoes etc.), however this will not be covered here.

M. Landrø (�)NTNU Trondheim, Trondheim, Norwaye-mail: martin.landro@ntnu.no

The business advantage of using 4D seismic on agiven field is closely correlated with the complexity ofthe field. Figure 19.1 shows a 3D perspective view ofthe top reservoir (top Brent) interface for the GullfaksField. Since the oil is trapped below such a complex 3Dsurface, it is not surprising that oil pockets can remainuntouched even after 10–15 years of production. Since4D seismic can be used to identify such pockets, it iseasy to understand the commercial value of such a tool.However, if the reservoir geometry is simpler, the num-ber of untapped hydrocarbon pockets will be less andthe business benefit correspondingly lower.

The first 4D seismic surveys were probablyacquired in America in the early 1980s. It was soonrealised that heavy oil fields were excellent candidatesfor 4D seismic. Heavy oil is highly viscous, so thermalmethods such as combustion or steam injection wereused to increase its mobility. Combustion describesa burning process, which normally is maintained byinjection of oxygen or air. As the reservoir is heated,the seismic P-wave velocity decreases, and this resultsin amplitude changes between baseline and monitorseismic surveys.

The best known example is maybe the one pub-lished by Greaves and Fulp in 1987, for which theyreceived the award for the best paper in Geophysics.They showed that such thermal recovery methodscould be monitored by repeating conventional 3D landseismic surveys (Fig. 19.2). These early examples ofseismic monitoring of thermal recovery methods didnot immediately lead to a boom in the 4D industry,mainly because they were performed on small and veryshallow onshore fields. The major breakthrough forcommercial 4D seismic surveys in the North Sea wasthe Gullfaks 4D study launched by Statoil in 1995.Together with WesternGeco a pilot study was done

427K. Bjørlykke (ed.), Petroleum Geoscience: From Sedimentary Environments to Rock Physics,DOI 10.1007/978-3-642-02332-3_19, © Springer-Verlag Berlin Heidelberg 2010

428 M. Landrø

341 375 400 425 450 475 500 525 550 575 600 625 650

0 1 km

N

670

Intra-Ness Fm.

Amundsen Fm.

Fault26922596

2348

2100

1852

500

550

600

650

700

750

Fig. 19.1 3D seismic imageof the top reservoir interface(top Brent Group) at theGullfaks Field. Notice thefault pattern and thecomplexity of the reservoirgeometry

S0.3

Holt

PaloPinto

A

B

Tim

e (s

econ

d)

C

0.4

0.4

0.4

20 40 60

CDP

80

0.3

0.3

NW104 W101Fig. 19.2 Shows clear 4D

amplitude brightening (topHolt horizon) as the reservoiris heated. Also note theextended area (marked bywhite arrows) for thisamplitude increase (Greavesand Fulp, Geophysics, 52,1987)

over the major northern part of the field, and the ini-tial interpretation performed shortly after this monitorsurvey demonstrated a promising potential.

However, the first use of 4D seismic in the NorthSea was probably the monitoring of an undergroundflow (Larsen and Lie 1990). In January 1989, when

19 4D Seismic 429

0.6

0.5

0.4

0.6

0.5

0.4

0.6

0.5

0.4100

Reflections from 492 mRKB

150 200Pre-drilling

6 months

4 months after re-entry

250 300

150 200 250 300

150 200 250 300 350

Fig. 19.3 Seismicmonitoring of theunderground flow caused bydrilling a deep Jurassic well in1989 in the North Sea. Thenew seismic event marked bythe red arrow on the middlesection is interpreted as agas-filled sand body. On thelower section (6 months afterthe drilling event) the arealextent of this event hasincreased further. Figureprovided by Dag O. Larsen,from his SEG-presentation in1990

drilling a deep Jurassic well, Saga Petroleum had toshut the well by activating the BOP. The rig was movedoff location, and a relief well was spudded. When therig was reconnected 3 months later, the pressure haddropped, indicating a subsurface fluid transfer. Theflow and the temperature measurements indicated aleak in the casing at 1,334 mSS. A strong amplitudeincrease at the top of a sand layer could be observedon the time-lapse seismic data close to this well(Fig. 19.3) – showing the fluid was gas.

The areal extent of this 4D anomaly increased fromone survey to the next. After 4 months this amplitudeincrease was also observed on shallower interfaces,probably connected to gas migrating upwards to shal-lower sand layers.

19.2 Rock Physics and 4D Seismic

When a hydrocarbon field is produced, there are sev-eral reservoir parameters that might change, mostcrucially:

– fluid saturation changes– pore pressure changes– temperature changes– changes in layer thickness (compaction or

stretching).

A critical part of all 4D studies is to link key reser-voir parameters like pore pressure and fluid saturation

to the seismic parameters. Rock physics provides thislink. Both theoretical rock physics models and lab-oratory experiments are used as important input totime-lapse seismic analysis. A standard way of relatingfor instance P-wave seismic velocity to changes in fluidsaturation is to use the Gassmann model. Figure 19.4shows one example, where a calibrated Gassmannmodel has been used to determine how the P-wavevelocity changes with water saturation (assuming thatthe reservoir fluid is a mixture of oil and water).

In addition, various contact models have beenproposed to estimate the effective modulus of arock. Mavko, Mukerji and Dvorkin present some ofthese models in their rock physics handbook (1998).The Hertz-Mindlin model (Mindlin 1949) can beused to describe the properties of pre-compacted

0,0 0,2 0,4 0,6 0,8 1,0Water saturation

(0,05)

0,00

0,05

0,10

0,15

0,20

0,25

Rel

ativ

e ch

ange

in V

p

Fig. 19.4 Relative change in P-wave velocity versus water satu-ration, estimated from a calibrated Gassmann model. Zero watersaturation corresponds to 100% oil

430 M. Landrø

granular rocks. The effective bulk modulus of dryrandom identical sphere packing is given by:

Keff ={

C2p(1 − ϕ)2G2P

18π2(1 − σ )2

} 13

(19.1)

where Cp is the number of contact points per grain, ϕ

is porosity, G is the shear modulus of the solid grains,σ is the Poisson ratio of the solid grains and P is theeffective pressure (that is P = Peff). The shear modulusis given as:

Geff ={

3C2p(1 − ϕ)2G2P

2π2(1 − σ )2

} 13 5 − 4σ

5(2 − σ )(19.2)

This leads to:

VP =√

Keff + 43 Geff

ρ(19.3)

VS =√

Geff

ρ(19.4)

where Vp and Vs are P- and S-wave velocities, respec-tively, and ρ is the sandstone density. Inserting Eqs.(19.1) and (19.2) into Eqs. (19.3) and (19.4) andcomputing the Vp/Vs ratio, yields (assuming σ = 0):

VP

VS= √

2. (19.5)

This means that according to the simplest granularmodel (Hertz-Mindlin), the Vp/Vs ratio should be con-stant as a function of confining pressure if we assumethe rock is dry. The Hertz-Mindlin model assumes thesand grains are spherical and that there is a certain areaof grain-to-grain contacts. A major shortcoming of themodel is that at the limit of unconsolidated sands,both the P and S-wave velocities will have the samebehaviour with respect to pressure changes, as shownin Eq. (19.5). Combining with the Gassmann (1951)model (i.e. introducing fluids in the pore system of therock), will ensure that the P-wave velocity approachesthe fluid velocity for zero effective stress, and not zeroas in the Hertz-Mindlin model (dry rock assumption).

If we assume that the in situ (base survey) effectivepressure is P0 we see from Eq. (19.3) that the relativeP-wave velocity versus effective pressure is given as:

VP

VP0

=(

P

P0

) 16

(19.6)

Figure 19.5 shows this relation for an in situ effec-tive pressure of 6 MPa. When such curves are com-pared to ultrasonic core measurements, the slope of themeasured curve is generally smaller than this simpletheoretical curve. The cause for this might be multi-fold: Firstly, the Hertz-Mindlin model assumes thesediment grains are perfect, identical spheres, whichis never found in real samples. Secondly, the ultrasonicmeasurements might suffer from scaling issues, coredamage and so on. Thirdly, cementation effects are

1.1

1

0.9

Rel

ativ

e P

-wav

e ve

loci

ty

0.8

0.7

0.6

0.50 2 4 6

Effective pressure (MPa)

8 10 12

Fig. 19.5 Typical changes in P-wave velocity versus effectivepressure using the Hertz-Mindlin model. In this case the in situeffective pressure (prior to production) is 6 MPa, and we see thata decrease in effective pressure leads to a decrease in P-wave

velocity. The black curve represents the Hertz-Mindlin model(exponent = 1/6, as in Eq. (19.6)), the red curve is a modi-fied version of the Hertz-Mindlin model (exponent = 1/10) thatbetter fits the ultrasonic core measurements

19 4D Seismic 431

not included in the Hertz-Mindlin model. It is there-fore important to note that there are major uncertain-ties regarding the actual dependency between seismicvelocity and pore pressure changes.

19.3 Some 4D Analysis Techniques

The analysis of 4D seismic data can be divided intotwo main categories, one based on the detection ofamplitude changes, the other on detecting travel-timechanges, see Fig. 19.6. Practical experience has shownthat the amplitude method is most robust, and thereforethis has been the most frequently employed method.However, as the accuracy of 4D seismic has improved,the use of accurate measurements of small timeshiftsis increasingly the method of choice. There are sev-eral examples where the timeshift between two seismictraces can be determined with an accuracy of a frac-tion of a millisecond. A very attractive feature of 4Dtimeshift measurement is that it is proportional to thechange in pay thickness, and this method providesa direct quantitative result. The two techniques arecomplementary in that amplitude measurement is alocal feature (measuring changes close to an interface),while the timeshift method measures average changesover a layer, or even a sequence of layers.

In addition to the direct methods mentioned above,4D seismic interpretation is aided by seismic model-ling of various production scenarios, often combined

Two complementary 4D analysis techniques

- Qualitative interpretation

- More noisy

- Quantitative approach

Top reservoir

1985 1995

OWC

- Discriminate between drained and undrained segments

Amplitudechanges

Pullupeffects

Time shift isproportionalto change inpay thickness

Fig. 19.6 Shows the two 4D analysis techniques. Notice thereare no amplitude changes at top reservoir between 1985 and1995, but huge amplitude changes at the oil-water contact(OWC). Also note the change in travel time (marked by theyellow arrow) for the seismic event below the oil-water contact

with reservoir fluid flow simulation and 1D scenariomodelling based on well logs.

19.4 The Gullfaks 4D Seismic Study

One of the first commercially successful 4D examplesfrom the North Sea was the Gullfaks study (Landrøet al. 1999). There are two simple explanations forthis success: the complexity of the reservoir geometry(Fig. 19.1) means that there will be numerous pock-ets of undrained oil, and there is a strong correlationbetween the presence of oil and amplitude brighteningas shown in Fig. 19.7.

In addition to these two observations, a rock physicsfeasibility study was done, and the main results aresummarised in Fig. 19.8. It is important to note that thekey parameter for 4D seismic is not the relative changein the seismic parameters, but the expected change inreflectivity between the base and monitor surveys. Ifwe assume that the top reservoir interface separatesthe cap rock (Layer 1) and the reservoir (Layer 2),it is possible to estimate the relative change in thezero offset reflection coefficient (Landrø et al. 1999)caused be production changes in the reservoir layer.Denoting the acoustic impedances (velocity times den-sity) in Layers 1 and 2 by λ1 and λ2, respectively, andusing B and M to denote base and monitor surveys, wefind that the change in reflectivity is given as (Landrøet al. 1999):

�R

R= λM

2 − λB2

λB2 − λB

1

= �AI(production)

�AI(original). (19.7)

Here we have assumed that the change in acous-tic impedance in Layer 2 is small compared to theactual impedance. Equation (19.7) means that thechange in reflectivity is equal to the change in acous-tic impedance in Layer 2 divided by the original(pre-production) acoustic impedance contrast betweenLayers 1 and 2. For Gullfaks, the expected changein acoustic impedance is 8% (assuming 60% satu-ration change, Fig. 19.8) while the original acousticimpedance contrast for top reservoir was approxi-mately 18%. The estimated relative change in reflec-tivity is therefore 44% (8/18). This is the basic back-ground for the success of using 4D seismic at Gullfaks,

432 M. Landrø

Fig. 19.7 Amplitude map for the top reservoir event at Gullfaks. The purple solid line represents the original oil-water contact.Notice the strong correlation between high amplitudes (red colours) and presence of oil. The size of one square is 1,250 by 1,250 m

Pressure (–4 MPa) Pressure (4 MPa) Saturation (100%) Saturation (60%)–12

–8

–4

0

4

8

12

16

20

Rel

ativ

e ch

ange

(%

)

Vp

Vs

Density

Zp

Zs

Vp/Vs

Fig. 19.8 Expected changes (based on rock physics) of key seismic parameters for pore pressure changes (two left columns) andfor two fluid saturation scenario changes (two right columns)

19 4D Seismic 433

1985

1996

Fig. 19.9 Seismic data from 1985 (upper right) and 1996(lower right) and the corresponding 4D interpretation to the left(green representing oil, and blue water)

as shown in Fig. 19.9. The effect of replacing oilwith water is evident on this figure, and is furtherstrengthened by the amplitude difference map takenat the original oil-water contact (Fig. 19.10). SeveralGullfaks wells have been drilled based on 4D inter-pretation, and a rough estimate of the extra incomegenerated by using time-lapse seismic data is morethan 1 billion USD.

19.5 Repeatability Issues

The quality of a 4D seismic dataset is dependenton several issues, such as reservoir complexity andthe complexity of the overburden. However, the mostimportant issue that we are able to influence is therepeatability of the seismic data, i.e. how accuratelywe can repeat the seismic measurements. This acquisi-tion repeatability is dependent on a number of factorssuch as:

• Varying source and receiver positions (x, y and zco-ordinates)

• Changing weather conditions during acquisition• Varying seawater temperature• Tidal effects• Noise from other vessels or other activity in the area

(rig noise)• Varying source signal• Changes in the acquisition system (new vessel,

other cables, sources etc.)• Variation in shot-generated noise (from previous

shot).

Fig. 19.10 Seismic difference section (top) and amplitude difference map at the original oil-water contact (OWC) (bottom). Redcolour indicates areas that have been water-flushed, and white areas may represent bypassed oil

434 M. Landrø

Disregarding the weather conditions (the only wayto “control” weather is to wait), most of the itemslisted are influenced by acquisition planning and per-formance. A common way to quantify repeatability isto use the normalised RMS (root-mean-square)-level,that is:

NRMS = 2RMS(monitor − base)

RMS(monitor) + RMS(base), (19.8)

where the RMS-levels of the monitor and base tracesare measured within a given time window. Normally,NRMS is measured in a time window where no pro-duction changes are expected. Figure 19.11 shows twoseismic traces from a VSP (Vertical Seismic Profile)experiment where the receiver is fixed (in the wellat approximately 2 km depth), and the source co-ordinates are changed by 5 m in the horizontal direc-tion. We notice that the normalised rms-error (NRMS)in this case is low, only 8%.

In 1995 Norsk Hydro acquired a 3D VSP datasetover the Oseberg Field in the North Sea. This datasetconsists of 10,000 shots acquired in a circular shoot-ing pattern and recorded by a 5-level receiver stringin the well. By comparing shot-pairs with differentsource positions (and the same receiver), it is possi-ble to estimate the NRMS-level as a function of thehorizontal distance between the shot locations. Thisis shown in Fig. 19.12, where approximately 70,000

Fig. 19.11 Two VSP-traces measured at exactly the same posi-tion in the well, but with a slight difference in the source location(5 m in the horizontal direction). The distance between twotimelines is 50 ms. The difference trace is shown to the right

0

–500

Shot points

Receiver

Well path

–1000

Dep

th, m

–1500

–2000

–25004.94

4.92

4.9

6.7075

6.707

6.7065

6.706

y-po

sitio

n (m

)

6.7055

6.705

6.7045

6.704

100

90

80

70

60

RM

S er

ror

(%)

50

40

30

20

10

00 10 20 30 40 50

Shot separation distance (m)60 70 80 90 100

4.88 4.885 4.89 4.895 4.9 4.905x-position (m)

4.91 4.915 4.92

4.88 6.708 6.707 6.706 6.705

Y-Coordinate, mX-Coordinate, m

6.704 6.703

N

× 106

× 105

× 105

× 106

Fig. 19.12 Top: The 10,000 shot locations (map view) for the3D VSP experiment over the Oseberg Field. Bottom: NRMS asa function of the source separation distance between approx-imately 70,000 shot pairs for the Oseberg 3D VSP dataset

19 4D Seismic 435

100

Source stability PositioningShot noise Weather related noise....

NR

MS

(%)

01995 2005 2015

Time

Fig. 19.13 Schematic view showing improvement in seismicrepeatability (NRMS) versus calendar time

shot pairs with varying horizontal mis-positioning areshown. The main message from this figure is clear. Itis important to repeat the horizontal positions both forsources and receivers as accurately as possible; even amisalignment of 20–30 m might significantly increasethe NRMS-level.

Such a plot can serve as a variogram, since itshows the spread for each separation distance. Detailedstudies have shown that the NRMS-level increases sig-nificantly in areas where the geology along the straightline between the source and receiver is complex. FromFig. 19.12 we see that the NRMS-value for a shotseparation distance of 40 m might vary between 20and 80% and a significant portion of this spread isattributed to variation in geology. This means that it isnot straightforward to compare NRMS-levels betweenvarious fields, since the geological setting might bevery different. Still, NRMS-levels are frequently used,since they provide a simple, quantitative measure.It is also important to note that the NRMS-level is

frequency dependent, so the frequency band used inthe data analysis should be given.

During the last two decades the focus on sourceand receiver positioning accuracy has lead to asignificant improvement in the repeatability of 4Dseismic data. Some of this is also attributed to bet-ter processing of time-lapse seismic data. This trendis sketched in Fig. 19.13. Today the global averageNRMS-level is around 20–30%. It is expected that thistrend will continue, though not at the same rate becausethe non-repeatable factors that need to be tackled to getbeyond 20–30% are more difficult. In particular, roughweather conditions will represent a major hurdle.

19.6 Fixed Receiver Cables

For marine seismic data, there are several ways to con-trol the source and receiver positions. WesternGecodeveloped their Q-marine system, where the stream-ers can also be steered in the horizontal direction (xand y). This means that it is possible to repeat thereceiver positions by steering the streamers into pre-defined positions. The devices are shown attached tothe streamers in Fig. 19.14.

Another way to control the receiver positions is tobury the receiver cables on the seabed. One of the firstcommercial offshore surveys of this kind was launchedat the Valhall Field in the southern part of the NorthSea in 2003. Since then, more than 11 surveys havebeen acquired over this field. The buried cables cover70% of the entire field and the 4D seismic data qual-ity is excellent. The fact that more than 10 surveyshave been recorded into exactly the same receiver posi-tions, opens for alternative and new ways (exploitingthe multiplicity that more than 2 datasets offers) of

Fig. 19.14 Photographs ofthe birds (controlling devices)attached to a marine seismiccable at deployment (left) andin water operation (right).These devices make itpossible to steer the cablewith reasonable accuracy intoa given position (Courtesy ofWesternGeco)

436 M. Landrø

analysing time-lapse seismic data. Other advantagesoffered by permanent receiver systems are:

– cheaper to increase the shot time interval in order toreduce the effect of shot generated noise

– continuous monitoring of background noise– passive seismic– possible to design a dedicated monitoring survey

close to a problem well at short notice.

Despite all these advantages that permanent sys-tems offer, there has not been a marked increase insuch surveys so far, probably because of the relativelyhigh upfront costs and the difficulty in quantifying inadvance the extra value it would bring.

19.7 Geomechanical Effects

Geomechanics has traditionally been an importantdiscipline in both the exploration and production ofhydrocarbons. However, the importance for geome-chanics of time-lapse seismic monitoring was not fullyrealised before the first results from the Chalk fieldsin the southern North Sea (Ekofisk and Valhall) wereinterpreted. Figure 19.15 shows map views of esti-mated travel-time shifts between base and monitorsurveys at Ekofisk (Guilbot and Smith 2002), wherethe seafloor subsidence had been known for manyyears. The physical cause for the severe compactionof the Chalk reservoir is two-fold. Firstly, depletionof the field leads to pore pressure decrease, and hencethe reservoir rock compacts mechanically due to lack

2/4-X-27

1250 m 1250 m

- 0- 2- 4

- 6- 8

- 10

- –10- –8- –6- –4- –2- 0

- 12- 14- 16

- 18- 20

Tim

e (m

s T

WT

)

Tim

e (m

s T

WT

)

NN

2/4-X-09

Fig. 19.15 4D timeshifts for top reservoir interface (left) and for the Ekofisk formation (right). The black area in the middle iscaused by the gas chimney problem at Ekofisk, leading to lack of high quality seismic data in this area (from Guilbot and Smith2002)

19 4D Seismic 437

of pressure support. Secondly, the chemical reactionbetween the chalk matrix and the water replacing theoil leads to a weakening of the rock framework, and acorresponding compaction.

When the reservoir rock compacts, the over- andunder burden will be stretched. This stretch is rel-atively small (of the order of 0.1%). However, thisleads to a small velocity decrease that is observable astimeshifts on time-lapse seismic data. Typical observa-tions of seafloor subsidence show that the subsidenceis less than the measured compaction for the reservoir.The vertical movement of the seafloor is often approx-imately 20% less than that of the top reservoir, thoughis strongly dependent on reservoir geometry and thestiffness of the rocks above and below.

The commonest way to interpret 4D seismic datafrom a compacting reservoir is to use geomechanicalmodelling as a complementary tool. One such exam-ple (Hatchell and Bourne 2005) is shown in Fig. 19.16.Note that the negative timeshifts (corresponding toa slowdown caused by overburden stretching) con-tinue into the reservoir section. This is due to thefact that the reservoir section is fairly thin in thiscase and even a compaction of several metres is notenough to shorten the travel time enough to counteractthe cumulative effect. Similar effects have also beenobserved for sandstone reservoirs, such as the Elgin

and Franklin fields. Normally, sandstone reservoirscompact less that chalk reservoirs and the correspond-ing 4D timeshifts are therefore less, although stilldetectable. Most of the North Sea sandstone reser-voirs show negligible compaction, and therefore theseeffects are normally neglected in 4D studies. However,as the accuracy of 4D seismic is increasing, it isexpected that compaction will be observed for severalof these fields as well. For instance, the anticipatedcompaction of the Troll East field is around 0.5–1 mafter 20 years of production, and this will probably bedetectable by 4D seismic.

A major challenge when the thickness of subsurfacelayers is changed during production, is to distinguishbetween thickness changes and velocity changes. Oneway to resolve this ambiguity is to use geomechan-ical modelling as a constraining tool. Another wayis to combine near and far offset travel time analy-sis (Landrø and Stammeijer 2004) to estimate velocityand thickness changes simultaneously. Hatchell et al.and Røste et al. suggested in 2005 using a factor(R) relating the relative velocity change (dv/v) to therelative thickness change (dz/z; displacement)

R = −dv/v

dz/z. (19.9)

TWTT [ms]

1500Top porosity

2000

2500

3000

1500

2000

2500

3000Speed-up

–10 10

Time-lapse timeshift [ms]

Slow-down

Fig. 19.16 Comparison ofmeasured timeshifts from 4Dseismic data (top) andgeomechanical modelling.The black solid line representsthe top reservoir. Notice thatthe slowdown (blue colours)continues into the reservoir(from Hatchell and Bourne2005)

438 M. Landrø

Hatchell et al. found that this factor varies between1 and 5, and is normally less for the reservoir rock thanthe overburden rocks. For sandstones and clays it iscommon to establish empirical relationships betweenseismic P-wave velocity (v) and porosity (ϕ). Theserelations are often of the simple linear form:

v = aϕ + b, (19.10)

where a and b are empirical parameters. If a rock isstretched (or compressed), a corresponding change inporosity will occur. Assuming that the lateral extentof a reservoir is large compared to the thickness, it isreasonable to assume a uniaxial change as sketched inFig. 19.17. From simple geometrical considerations wesee that the relation between the thickness change andthe corresponding porosity change is:

dz

z= dϕ

1 − ϕ, (19.11)

In the isotropic case (assuming that the rock isstretched in all three directions), we obtain:

dz

z= dϕ

3(1 − ϕ). (19.12)

Inserting Eqs. (19.10) and (19.11) into (19.9) weobtain an explicit expression for the dilation factor R:

R = 1 − a + b

v, (19.13)

Uniaxial stretching of a rockx

x

h

h(x + x – h) (h + dx)x + (x – h)hx(x + dx)x2

dφ

φ 1 φ 2

1 – φ=

dx

x

h+dx x+dx

x

= =

Fig. 19.17 Cartoon showing the effect of increased porositydue to stretching of a rock sample

which is valid for the uniaxial case. Using Eq. (19.12)instead of (19.11) gives a similar equation for theisotropic case.

19.8 Discrimination Between PorePressure and Saturation Effects

Although the main focus in most 4D seismic studiesis to study fluid flow and detect bypassed oil pockets,the challenge of discriminating between pore pressurechanges and fluid saturation changes occurs frequently.From rock physics we know that both effects influencethe 4D seismic data. However, as can be seen fromFig. 19.8, the fluid pressure effects are not linked tothe seismic parameters in the same way as the fluidsaturation effects. This provides an opportunity to dis-criminate them, since we have different rock physicsrelations for the two cases. Some of the early attemptsto perform this discrimination between pressure andsaturation were presented by Tura and Lumley (1999)and Landrø (1999). In Landrø’s method (2001) therock physics relations (based on Gassmann and ultra-sonic core measurements) are combined with simpleAVO (amplitude versus offset) equations to obtaindirect expressions for saturation changes and pressurechanges. Necessary input to this algorithm is near andfar offset amplitude changes estimated from the baseand monitor 3D seismic cubes. This method was testedon a compartment from the Cook Formation at theGullfaks Field. Figure 19.18 shows a seismic profile(west–east) through this compartment.

A significant amplitude change is observed for thetop Cook interface (red solid line in the figure), bothbelow and above the oil-water contact. The fact thatthis amplitude change extends beyond the oil-watercontact is a strong indication that it cannot be solelyrelated to fluid saturation changes, and a reasonablecandidate is therefore pore pressure changes. Indeed,it was confirmed that the pore pressure had increasedby 50–60 bars in this segment, meaning that the reser-voir pressure is approaching fracture pressure. We alsoobserve from this figure that the base reservoir event(blue solid line) is shifted slightly downwards, by 2–3 ms. This slowdown is interpreted as a velocity dropcaused by the pore pressure increase in the segment.

Figure 19.19 shows an attempt to discriminatebetween fluid saturation changes and pressure changes

19 4D Seismic 439

1985OWC

C-3Top Cook

1996

Fig. 19.18 Seismic sectionthrough the Cook Formationat Gullfaks. The cyan solidline indicates the originaloil-water contact (markedOWC). Notice the significantamplitude change at top Cookbetween 1985 and 1996, andthat the amplitude changeextends beyond theOWC-level, a strongindication that the downflankamplitude change is caused bypore pressure changes

Fig. 19.19 Estimated fluid saturation changes (left) and porepressure changes (right) based on 4D AVO analysis for the topCook interface at Gullfaks. The blue solid line represents the

original oil-water contact. Notice that the estimated pressurechanges extend beyond this blue line to the west, and terminateat a fault to the east. Yellow colours indicate significant changes

for this compartment using the method described inLandrø (2001). In 1996, 27% of the estimated recov-erable reserves in this segment had been produced, sowe know that some fluid saturation changes should beobservable on the 4D seismic data.

From this figure we see that in the western partof the segment most of the estimated fluid saturationchanges occur close to the oil-water contact. However,some scattered anomalies can be observed beyond theoil-water contact in the northern part of the segment.These anomalies are probably caused by inaccuraciesin the algorithm or by limited repeatability of the time-lapse AVO data. The estimated pressure changes aremore consistent with the fault pattern in the region,and it is likely that the pressure increase is confinedbetween faults in almost all directions. Later time-lapse surveys show that the eastern fault in the figurewas “opened” some years later.

19.9 Other Geophysical MonitoringMethods

Parts of this section are taken from “Future challengesand unexplored methods for 4D seismics”, by Landrø,Recorder (2005).

Up to now, 4D seismic has proved to be themost effective way to monitor a producing reser-voir. However, as discussed above, there are severalsevere limitations associated with time lapse seis-mic. One of them is that seismic reflection data issensitive to acoustic impedance (velocity times den-sity). Although 4D time shift can reveal changes inaverage velocity between two interfaces, an indepen-dent measurement of density changes would be a use-ful complement to conventional 4D seismic. The ideaof actually measuring the mass change in a reservoir

440 M. Landrø

caused by hydrocarbon production has been aroundfor quite some time. The limiting factor for gravi-metric reservoir monitoring has been the repeatability(or accuracy) of the gravimeters. However, Sasagawaet al. (2003) demonstrated that improved accuracy canbe achieved by using 3 coupled gravimeters placedon the seabed. This technical success led to a fullfield programme at the Troll Field, North Sea. Anothersuccessful field example was time-lapse gravitymonitoring of an aquifer storage recovery project inLeyden, Colorado (Davis et al. 2005), essentially map-ping water influx. Obviously, this technique is bestsuited for reservoirs where significant mass changesare likely to occur, such as water replacing gas.Shallow reservoirs are better suited than deep. The sizeof the reservoir is a crucial parameter, and a given min-imum size is required in order to obtain observableeffects. In quite another field, gravimetric measure-ments might help in monitoring volcanic activity bydistinguishing between fluid movements and tectonicactivity within an active volcano.

Around 2000 the hydrocarbon industry startedto use electromagnetic methods for exploration.Statoil performed a large scale research project thatshowed that it is possible to discriminate betweenhydrocarbon-filled and water-filled reservoirs fromcontrolled source electromagnetic (CSEM) measure-ments. Since this breakthrough of CSEM surveys someyears ago (Ellingsrud et al. 2002) this technique hasmainly been used as an exploration tool, in orderto discriminate between hydrocarbon-filled rocks andwater-filled rocks. Field tests have shown that suchdata are indeed repeatable, so there should definitelybe a potential for using repeated EM surveys to moni-tor a producing reservoir. So far, frequencies as low as0.25 Hz (and even lower) are being used, and then thespatial resolution will be limited. However, as a com-plementary tool to conventional 4D seismic, 4D EMmight be very useful. In many 4D projects it is hard toquantify the amount of saturation changes taking placewithin the reservoir, and time-lapse EM studies mightbe used to constrain such quantitative estimates of thesaturation changes. Furthermore, unlike conventional4D seismic which is both pressure and saturation sensi-tive, the EM technique is not very sensitive to pressurechanges, so it may be a nice tool for separating betweensaturation and pressure changes.

In a recent paper, Johansen et al. (2005) show thatthe EM response over the Troll West gas province

is significantly above the background noise level, seeFig. 19.20. If we use the deviation from a smoothresponse as a measure of the repeatability level, arelative amplitude variation of approximately 0.1–0.2 (measured in normalised EM amplitude units) isobserved. Compared to the maximum signal observedat the crest of the field (2.75) this corresponds to arepeatability level of 4–7%, which is very good com-pared to conventional time-lapse seismic. This meansit is realistic to assume that time-lapse EM data canprovide very accurate low-resolution (in x-y plane)constraints on the saturation changes observed on 4Dseismic data. Recently, Mittet et al. (2005) showedthat depth migration of low frequency EM data maybe used to enhance the vertical resolution. In a fielddata example, the vertical resolution achieved by thistype of migration is maybe of the order of a few hun-dred metres. The EM sensitivity is determined by thereservoir thickness times the resistivity, underlining thefact that both reservoir thickness and reservoir resistiv-ity are crucial parameters for 4D CSEM. This meansthat the resolution issue with the active EM methodis steadily improving, and such improvements will ofcourse increase the value of repeated CSEM data as acomplement to conventional 4D seismic.

By using the so-called interferometric syntheticaperture radar principle obtained from orbiting satel-lites, an impressive accuracy can be attained in mea-suring the distance to a specific location on the earth’ssurface. By measuring the phase differences for asignal received from the same location for differentcalendar times, it is possible to measure the relativechanges with even higher accuracy. By exploiting asequence of satellite images, height changes can bemonitored versus time. The satellites used for thispurpose orbit at approximately 800 km.

Several examples of monitoring movements of thesurface above a producing hydrocarbon reservoir havebeen reported, though there are of course limitationsto the detail of information such images can providefor reservoir management. The obvious link to thereservoir is to use geomechanical modelling to tie themovements at the surface to subsurface movements.For seismic purposes, such a geomechanical approachcan be used to obtain improved velocity models ina more sophisticated way. If you need to adjustyour geomechanical model to obtain correspondencebetween observed surface subsidence and reservoircompaction, then this adjusted geomechanical model

19 4D Seismic 441

0 5000 10000

Horizontal distance (m)

Offset (m)

Water 1 5 10 15

TWGP

20 24

Sediments

Dep

th b

elow

sea

leve

l (m

)

Nor

mal

ised

mag

nitu

deat

6.5

km

off

set

Nor

mal

ized

mag

nitu

des

15000 20000 250001800

1600

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.010000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1400

1200

1000

800

600

400

200

0

Fig. 19.20 Modelled (opencircles) and measured (redcircles) relative electrical fieldstrength as a function of offset(top). The values arenormalised to the responseoutside the reservoir (bluecircels). Bottom figure showsrelative values for a constantoffset of 6.5 km along aprofile, where the backgroundshows the reservoir model.Notice that the relative signalincreases by a factor of 3above the thickest part of thereservoir (figure taken fromJohansen et al. 2005)

can be used to distinguish between overburden rockswith high and low stiffness for instance, which againcan be translated into macro-variations of the over-burden velocities. The deeper the reservoir, the lowerthe frequency (less vertical resolution) of the surfaceimprint of the reservoir changes, thus this methodcan not be used directly to identify small pockets ofundrained hydrocarbons. However, it can be used asa complementary tool for time-lapse seismic since itcan provide valuable information on the low frequencyspatial signal (slowly varying in both horizontal andvertical directions) of reservoir compaction.

19.10 CO2 Monitoring

This text is taken from the paper “Quantitative SeismicMonitoring Methods” by Landrø (2008), in ERCIMNews 74, pp. 16–17:

Interest in CO2 injection, both for storage and asa tertiary recovery method for increased hydrocar-bon production, has grown significantly over the lastdecade. Statoil has stored approximately 10 milliontons of CO2 in the Utsira Formation at the SleipnerField, and several similar projects are now beinglaunched worldwide. At NTNU our focus has beento develop geophysical methods to monitor the CO2-injection process, and particularly to try to quantify thevolume injected directly from geophysical data.

One way to improve our understanding of howthe CO2 flows in a porous rock is to perform small-scale flooding experiments on long core samples. Suchexperiments involve injecting various fluids in the endof a 30–40 cm long core (Fig. 19.21). An exampleof such a flooding experiment and corresponding X-ray images for various flooding patterns is shown inFig. 19.21. By measuring acoustic velocities as theflooding experiment is conducted, these experiments

442 M. Landrø

7 ml 22 ml 27 ml

37 mlIn

Out

Slice

Bulk density g/cm3

52 ml 72 ml

Fig. 19.21 Long core (left) showing the location for theX-ray cross-section (red arrow). Water injection is 50 g/l. Tothe right: X-ray density maps of a core slice: 6 time steps during

the injection process (from Marsala and Landrø, EAGE extendedabstracts 2005)

can be used to establish a link between pore scale CO2-injection and time-lapse seismic on the field scale.

Figure 19.22 shows an example of how CO2 influ-enced the seismic data over time. By combining 4Dtravel time and amplitude changes, we have devel-oped methods to estimate the thickness of CO2 layers,which makes it possible to estimate volumes. Anotherkey parameter is CO2 saturation, which can be esti-mated using rock physics measurements and models.Although the precision in both 4D seismic methodsand rock physics is increasing, there is no doubtthat precise estimates are hard to achieve, and there-fore we need to improve existing methods and learnhow to combine several methods in order to decreasethe uncertainties associated with these monitoringmethods.

19.11 Future Aspects

The most important issue for further improvement ofthe 4D seismic method, is to improve the repeata-bility. Advances in both seismic acquisition and 4Dprocessing will contribute to this process. As sketchedin Fig. 19.13, it is expected that this will be less pro-nounced than in the past decade. However, it is stilla crucial issue, and even minor improvements mightmean a lot for the value of a 4D seismic study. Furtherimprovements in repeatability will probably involveissues like source stability, source positioning, shottime interval, better handling of various noise sources.Maybe in the future we will see vessels towing asuperdense grid of sensors, in order to obtain perfectrepositioning of the receiver positions.

900

1030

1040

1050

1060

1070

1080

1090

1100

1030

1040

1050

1060

1070

1080

1090

1100

1030

1040

1050

1060

1070

1080

1090

1100

1030

1040

1050

1060

1070

1080

1090

1100

950

1000

1050

1100

1150

Sand

1994 1999 2001 2002

Fig. 19.22 Time-lapse seismic data showing monitoring of the CO2 injection at Sleipner. The strong amplitude increase (shown inblue) is interpreted as a thin CO2 layer (printed with permission from Statoil)

19 4D Seismic 443

Another direction to improve 4D studies could be toconstrain the time-lapse seismic information by othertypes of information, such as geomechanical mod-elling, time-lapse EM, gravimetric data or innovativerock physics measurements.

Our understanding of the relation between changesin the subsurface stress field and the seismic param-eters is still limited, and research within this specificarea will be crucial to advance the 4D. New analysismethods like long offset 4D, might be used as acomplementary technique or as an alternative methodwhere conventional 4D analysis has limited success.However, long offset 4D is limited to reservoirswhere the velocity increases from the cap rock to thereservoir rock.

The link between reservoir simulation (fluid flowsimulation) and time-lapse seismic will continue to bedeveloped. As computer resources increase, the fea-sibility of a joint inversion exploiting both reservoirsimulation and time-lapse seismic data in the samesubsurface model will increase. Despite extra com-puting power, it is reasonable to expect that the non-uniqueness problem (several scenarios will fit the samedatasets) will require that the number of earth mod-els is constrained by models predicting the distributionof rock physical properties based on sedimentology,diagenesis and structural geology.

Acknowledgments Statoil is acknowledged for permission touse and present their data. The Research Council of Norway isacknowledged for financial support to the ROSE (Rock Seismic)project at NTNU. Lasse Amundsen, Lars Pedersen, Lars KristianStrønen, Per Digranes, Eilert Hilde, Odd Arve Solheim, IvarBrevik, Paul Hatchell, Peter Wills, Jan Stammeijer, ThomasRøste, Rodney Calvert, Alexey Stovas, Lyubov Skopintseva,Andreas Evensen, Amir Ghaderi, Dag O. Larsen, KennethDuffaut, Jens Olav Paulsen, Jerome Guilbot, Olav Barkved,Jan Kommedal, Per Gunnar Folstad, Helene Veire, Ola Eiken,Torkjell Stenvold, Jens Olav Paulsen and Alberto Marsala are allacknowledged for co-operation and discussions.

Further Reading

Amundsen, L. and Landrø, M. December 2007. 4D seismic –Status and future challenges, Part II. GeoExpro, 54–58.

Barkved, O. 2004. Continuous seismic monitoring. 74thAnnual International Meeting. The Society of ExplorationGeophysicists, 2537–2540.

Barkved, O., Buer, K., Halleland, K.B., Kjelstadli, R., Kleppan,T. and Kristiansen, T. 2003. 4D seismic response of pri-mary production and waste injection at the Valhall field.

65th Meeting. European Association of Geoscientists andEngineers, Extended Abstracts, A22.

Barkved, O.I. and Kristiansen, T. 2005. Seismic time-lapseeffects and stress changes: Examples from a compactingreservoir. The Leading Edge 24, 1244.

Calvert, R. 2005. Insights and methods for 4D reservoirmonitoring and characterization, EAGE/SEG DistinguishedInstructor Short Course 8.

Christensen, N.I. and Wang, H.F. 1985. The influence of porepressure and confining pressure on dynamic elastic proper-ties of Berea sandstone. Geophysics 50, 207–213.

Davis, K., Li, Y., Batzle, M. and Reynolds, B. 2005. Time-lapsegravity monitoring of an aquifer storage recovery project inLeyden, Colorado. 75th Annual International Meeting. TheSociety of Exploration Geophysicists, GM1.4.

Eiken, O., Zumberge, M., Stenvold, T., Sasagawa, G. and Nooen,S. 2004. Gravimetric monitoring of gas production from theTroll Field. 74th Annual International Meeting. The Societyof Exploration Geophysicists, 2243–2246.

Ellingsrud, S., Eidesmo, T., Johansen, S., Sinha, M.C.,MacGregor, L.M. and Constable, S. 2002. Remote sensingof hydrocarbon layers by seabed logging (SBL): Resultsfrom a cruise offshore Angola. The Leading Edge 21(10),972–982.

Foldstad, P.G., Andorsen, K., Kjørsvik, I. and Landrø, M. 2005.Simulation of 4D seismic signal with noise – Illustrated byWAG injection on the Ula Field. 75th Annual InternationalMeeting. The Society of Exploration Geophysicists,TL2.7.

Furre, A-K., Munkvold, F.R. and Nordby, L.H. 2003. Improvingreservoir understanding using time-lapse seismic at theHeidrun Field, 65th Meeting. European Association ofGeoscientists and Engineers, A20.

Gassmann, F. 1951. Über die elastizität poroser medien.Vierteljahrsschrift der Naturforchenden Gesellschaft inZürich 96, 1–23.

Gosselin, O., Aanonsen, S.I., Aavatsmark, I., Cominelli, A.,Gonard, R., Kolasinski, M., Ferdinandi, F., Kovacic, L. andNeylon, K. 2003. History matching using time-lapse seismic(HUTS), SPE paper 84464.

Guilbot, J. and Smith, B. 2002. 4-D constrained depth con-version for reservoir compaction estimation: Application toEkofisk Field. The Leading Edge 21(3), 302–308.

Hatchell, P.J. and Bourne, S.J. 2005. Rocks under strain: Strain-induced time-lapse time shifts are observed for depletingreservoirs. The Leading Edge 24, 1222–1225.

Hatchell, P.J., Kawar, R.S. and Savitski, A.A. 2005. Integrating4D seismic, geomechanics and reservoir simulation in theValhall oil field. 67th Meeting. European Association ofGeoscientists and Engineers, C012.

Johansen, S.E., Amundsen, H.E.F., Røsten, T., Ellingsrud, S.,Eidesmo, T. and Bhuyian, A.H. 2005. Subsurface hydrocar-bons detected by electromagnetic sounding. First Break 23,31–36.

Kommedal, J.H., Barkved, O.I. and Howe, D.J. 2004. Initialexperience operating a permanent 4D seabed array forreservoir monitoring at Valhall. 74th Annual InternationalMeeting. The Society of Exploration Geophysicists,2239–2242.

Koster, K., Gabriels, P., Hartung, M., Verbeek, J., Deinum, G.and Staples, R. 2000. Time-lapse seismic surveys in the

444 M. Landrø

North Sea and their business impact. The Leading Edge19(03), 286–293.

Kragh, E. and Christie, P. 2002. Seismic repeatability, nor-malized rms, and predictability. The Leading Edge 21,640–647.

Landrø, M. 1999. Repeatability issues of 3-D VSP data.Geophysics 64, 1673–1679.

Landrø, M. 2001. Discrimination between pressure and fluid sat-uration changes from time lapse seismic data. Geophysics66(3), 836–844.

Landrø, M. 2002. Uncertainties in quantitative time-lapse seis-mic analysis. Geophysical Prospecting 50, 527–538.

Landrø, M. 2008. The effect of noise generated by previous shotson seismic reflection data. Geophysics 73, Q9–Q17.

Landrø, M., Digranes, P. and Strønen, L.K. 2001. Mappingreservoir pressure and saturation changes using seismicmethods – Possibilities and limitations. First Break 19,671–677.

Landrø, M., Digranes, P. and Strønen, L.K. 2002. Pressureeffects on seismic data – Possibilities and limitations: Paperpresented at the NPF biannual conference in Kristiansand,Norway, 11–13 March, 2002.

Landrø, M., Digranes, P. and Strønen, L.K. 2005. Pressure deple-tion measured by time-lapse VSP. The Leading Edge 24,1226–1232 (December issue).

Landrø, M. and Duffaut, K. 2004. Vp–Vs ratio versus effec-tive pressure and rock consolidation – A comparisonbetween rock models and time-lapse AVO studies. 74thAnnual International Meeting. The Society of ExplorationGeophysicists, 1519–1522.

Landrø, M., Nguyen, A.K. and Mehdizadeh, H. 2004. Timelapse refraction seismic – A tool for monitoring carbonatefields? 74th Annual International Meeting. The Society ofExploration Geophysicists, 2295–2298.

Landrø, M. and Skopintseva, L. 2008. Potential improvementsin reservoir monitoring using permanent seismic receiverarrays. The Leading Edge 27, 1638–1645.

Landrø, M., Solheim, O.A., Hilde, E., Ekren, B.O. and Strønen,L.K. 1999. The Gullfaks 4D seismic study. PetroleumGeoscience 5, 213–226.

Landrø, M. and Stammeijer, J. 2004. Quantitative estimation ofcompaction and velocity changes using 4D impedance andtraveltime changes. Geophysics, The Society of ExplorationGeophysicists 69, 949–957.

Landrø, M., Veire, H.H., Duffaut, K. and Najjar, N. 2003.Discrimination between pressure and fluid saturationchanges from marine multicomponent time-lapse seismicdata. Geophysics, The Society of Exploration Geophysicists68, 1592–1599.

Larsen, D. and Lie, A. 1990. Monitoring an underground flow byshallow seismic data: A case study. SEG Expanded Abstracts9, 201 pp.

MacLeod, M., Hanson, R.A., Bell, C.R. and McHugo, S. 1999.The Alba Field ocean bottom cable survey: Impact on devel-opment. The Leading Edge 18, 1306–1312.

Mavko, G., Mukerji, T. and Dvorkin, J. 1998. The Rock PhysicsHandbook. Cambridge University Press, Cambridge, ISBN0521 62068 6, 147–161.

Mehdizadeh, H., Landrø, M., Mythen, B.A., Vedanti, N. andSrivastava, R. 2005. Time lapse seismic analysis using longoffset PS data. 75th Annual International Meeting. TheSociety of Exploration Geophysicists, TL3.7.

Mindlin, R.D. 1949. Compliance of elastic bodies in contact.Journal of Applied Mechanics 16, 259–268.

Nes, O.M., Holt, R.M. and Fjær, E. 2000. The reliability of coredata as input to seismic reservoir monitoring studies. SPE65180.

Osdal, B., Husby, O., Aronsen, H.A., Chen, N. and Alsos, T.2006. Mapping the fluid front and pressure buildup using 4Ddata on Norne Field. The Leading Edge 25, 1134–1141.

Parr, R., Marsh, J. and Griffin, T. 2000. Interpretation andintegration of 4-D results into reservoir management,Schiehallion Field, UKCS. 70th Annual InternationalMeeting. The Society of Exploration Geophysicists,1464–1467.

Rogno, H., Duffaut, K., Furre, A.K., Eide, A.L. and Kvamme,L. 1999. Integration, quantification and dynamic updat-ing – Experiences from the Statfjord 4-D case. 69thAnnual International Meeting. The Society of ExplorationGeophysicists, 2051–2054.

Røste, T., Stovas, A. and Landrø, M. 2005. Estimation of layerthickness and velocity changes using 4D prestack seismicdata. 67th Meeting. European Association of Geoscientistsand Engineers, C010.

Sasagawa, G.S., Crawford, W., Eiken, O., Nooner, S., Stenvold,T. and Zumberge, M. 2003. A new sea-floor gravimeter.Geophysics, The Society of Exploration Geophysicists 68,544–553.

Stovas, A. and Landrø, M. 2004. Optimal use of PP and PS time-lapse stacks for fluid pressure discrimination. GeophysicalProspecting, European Association of Geoscientists andEngineers 52, 301–312.

Tura, A. and Lumley, D.E. 1999. Estimating pressureand saturation changes from time-lapse AVO data. 69thAnnual International Meeting, The Society of ExplorationGeophysicists, Expanded Abstracts, 1655–1658.

Tøndel, R. and Eiken, O. 2005. Pressure depletion observationsfrom time-lapse seismic data at the Troll Field. 67th EAGEMeeting, Abstract, C037.

Vasco, D.W., Datta-Gupta, A., Behrens, R., Condon, P.and Rickett, J. 2004. Seismic imaging of reservoir flowproperties: Time-lapse amplitude changes. Geophysics 69,1425–1442.

Watts, G.F.T., Jizba, D., Gawith, D.E. and Gutteridge, P.1996. Reservoir monitoring of the Magnus Field through4D time-lapse seismic analysis. Petroleum Geoscience 2,361–372.

Zimmer, M., Prasad, M. and Baggeroer, A.B. 2002. Pressure andporosity influences on Vp–Vs ratio in unconsolidated sands.The Leading Edge 21(2), 178–183.