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Offset-dependence of production-related 4D time-shifts

Citation for published version:Kudarova, A, Hatchell, P, Brain, J & MacBeth, C 2016, 'Offset-dependence of production-related 4D time-shifts: Real data examples and modeling', SEG Technical Program Expanded Abstracts, vol. 35, pp. 5395-5399. https://doi.org/10.1190/segam2016-13611549.1

Digital Object Identifier (DOI):10.1190/segam2016-13611549.1

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Download date: 28. May. 2021

Offset-dependence of production-related 4D time-shifts: real data examples and modeling Asiya Kudarova, Paul Hatchell, Shell Global Solutions International B.V., Jonathan Brain, Shell U.K. Limited,

Colin MacBeth, Heriot-Watt University

Summary

We present examples of 4D time-shifts obtained with offset

and angle sub-stacks of seismic data acquired in deep (Gulf

of Mexico) and shallow water (North Sea) marine

environments. We compare the observations with two

proposed rock-physics models using different linear

relationships between the velocity change and the strain

field induced by reservoir compaction. The model

involving only vertical strain component predicts a similar

time-shift with offset behavior as that observed from the

data. We do not observe a strong decrease of time-shifts

with offset as reported in previous publications.

Introduction

Time-lapse seismic monitoring is an important tool for

interpretation of data acquired over producing fields.

Production-related compaction of a reservoir is visible on

the time-lapse seismic data because it causes deformation

of the subsurface resulting in velocity and path-length

changes that lead to time-shifts that are commonly

observed above the reservoir (Guilbot and Smith, 2000;

Barkved and Kristiansen 2005; Hatchell et al. 2003)

With the recent advancements in long-offset and wide

azimuth data, more attention is being paid to pre-stack data

to have a better understanding of the geomechanical

processes in the field and increase the accuracy of

interpretations.

A simple examination of the components of the stress and

strain tensors resulting from geomechanical models leads to

the expectation that significant offset dependence might

occur. For example, in the rocks above a compacting

reservoir the vertical normal strains are extensional

whereas the horizontal normal strains are compressional.

Waves travelling vertically and horizontally might behave

quite differently if the velocity-strain coupling is

anisotropic. Many previous studies predict such an

anisotropic velocity response (Sayers and Kachanov, 1995;

Prioul et al., 2004) and others predict significant offset-

dependence of 4D time-shifts (Fuck et al., 2009;

Herwanger et al., 2007; Smith and Tsvankin, 2012).

If observed in the data, the offset- and azimuth-dependence

of time-shifts can serve as an additional constraint in

interpretation of 4D signals. Additionally, the model that

describes the data can be used to calibrate parameters of

geomechanical models.

We present examples of high-quality data acquired in deep

and shallow marine environments that do not show

significant offset-dependence. These observations are

analyzed by simple geomechanical modeling to understand

what model best explains the data.

Geomechanical model for offset-dependent time-shifts

We extend the empirical model first proposed by Hatchell

and Bourne (2005) for normal-incidence P-waves to non-

zero offset. The model suggests linear dependence of the

vertical strain component εzz and the fractional velocity

change Δv/v

,zzRv

v

(1)

where the factor R is a dimensionless parameter that

describes the sensitivity of the relative change in vertical

velocity to the normal strain resulting from the

geomechanical changes in the subsurface. This parameter

has different values for rocks under extension (R+) and

compression (R-). The model provides qualitatively correct

predictions of 4D time-shifts observed at many compacting

reservoirs around the world. For normally incident waves,

equation (1) predicts a time-shift, Δt/t = (1+R)zz. We will

study extensions of this approach to non-zero offset by

incorporating offset-dependent strain couplings and by

summing the travel time-shifts along the ray path.

The time-shift is defined as the difference in the two-way

travel time between the base and monitor surveys along the

ray paths l and l0, respectively:

0

0ll v

dl

v

dlt (2)

Following Landrø and Stammeijer (2004), we consider

straight rays and isotropic velocities.

Figure 1: Schematic representation of the ray path change.

In Figure 1, θ is the angle of incidence for the baseline data,

x is the offset and Δz is the depth-shift of the horizon of

interest. We assume small changes in layer thickness and

velocity (Δz/z <<1, Δv/v << 1), and use a straight ray path

assumption for the monitor survey as well as for the base

Page 5395© 2016 SEG SEG International Exposition and 86th Annual Meeting

Offset-dependent time-shifts

line survey to calculate time-shifts - this is justified to the

first order, according to Fermat’s principle of minimum

travel time (Landrø and Stammeijer, 2004).

Model 1: Isotropic velocity change depending on εzz

The simplest extension of the model by Hatchell and

Bourne (2005) to non-zero offset is to assume the velocity

change is isotropic so that the relative change in velocity in

any direction only depends on εzz, according to equation

(1). Substitution of this relation into the integral equation

(2) and using the approximations mentioned above results

in the time-shift

2

1

.)(cos)cos(

1 2

0

z

z

zzdzRV

t

(3)

After that the NMO correction must be applied as we are

modeling post-stack data (Landrø and Stammeijer, 2004):

,02

0

22

0 / tv

xtttNMO

(4)

where t0 = 2z/v is the two-way zero-offset travel time and x

is the offset. Equation (4) suggests that the observed time-

shifts will be magnified as a result of NMO-correction with

the baseline velocity model (standard processing).

Model 2: Isotropic velocity change depending on εpp

There are many ways to include stress-strain anisotropy.

Such models have been considered, for example, by Smith

and Tsvankin (2012), Herwanger et al. (2007), Sayers and

Schutjens (2007), Scott (2007), Herwanger and Horne

(2009) and Fuck et al. (2009). Despite the elegance of

many models presented in the literature, it is still

challenging to use them to explain the observations from

real data. Firstly, it is challenging to build a model that

accurately describes a complicated anisotropic velocity

change introducing only a few parameters. Simplifications

are required to reduce uncertainty in determination of these

parameters. Secondly, it is challenging to define even a few

parameters, because of the difficulties in reproducing the

reservoir stress conditions in the laboratory. The

inconsistency of predictions by some models and the data

can also be explained by the fact that a different physical

mechanism dominates in reality, rather than the one

accounted for in the theory.

We present here a simple heuristic model where all strain

components contribute to the velocity change.

Conceptually, if for vertical waves Δvz/vz = -Rεzz then we

can expect for horizontal waves Δvx/vx = -Rεxx. Rodriguez-

Herrera et al. (2015) generalized this simple concept by

suggesting that the velocity change depends on the strain

along the ray path direction:

,

,

pεp

pp

ppRv

v

(5)

where εpp is the strain component along the ray path

direction, and p is a unit vector of the direction along the

ray path. Then the formula for the time-shifts reads

2

1

.)(cos)cos(

1 2

0

z

z

ppzz dzRV

t

(6)

To compare the offset-dependence predicted by Model 1

and Model 2, we calculate strains in an isotropic half-space

with a compacting reservoir using an analytical solution for

a block-shaped reservoir based on Geertsma (1973) nucleus

of strain solution (Kuvshinov, 2008).

Figure 2 shows the results of applying equations (3) and (6)

to a simple model of a compacting block-shaped reservoir

1.5 km square on the sides, with a thickness of h = 30 m.

The velocity of the unperturbed medium is v = 2000 m/s

and the Poisson ratio is υ = 0.2. We model a pressure drop

that produces 30 cm of compaction in the center of the

block. The depth to top reservoir is 4.1 km. The values for

the R factors for compression and extension are R-=1 and

R+=7, respectively, which has proved reasonable in many

environments (Hatchell and Bourne, 2005).

Incidence angle, degrees

Figure 2: Vertical cross-section through the center of the reservoir area. Time-shifts predicted by Model 1

(upper panel) and Model 2 (lower panel) for different angles of incidence θ.

Page 5396© 2016 SEG SEG International Exposition and 86th Annual Meeting

Time-shifts calculated along a vertical cross section

through the center of the block are depicted in Figure 2 for

angles of incidence from θ = 0 to θ = 50 degrees. The

results for Model 1 are shown in the upper panel and for

Model 2 in the lower panel. In these pictures we modeled

wide-azimuth data and averaged the results of many

calculations at different azimuths. We observe that the

predictions of the offset dependence for the time-shifts by

the two models discussed above are quite different.

Looking first at the region above top reservoir, for Model 1

the time-shifts are flat to slightly increasing with offset (as

a result of the NMO-correction), whereas for Model 2 they

decrease at far offsets (as a result of the flip in polarity of

the horizontal to vertical strain components).

In the region below the reservoir interesting effects happen

including the possibility of raypaths that “undershoot” the

reservoir so that in the deep part of the image the time-

shifts start to vanish at far offsets – an effect that does not

occur at zero offset.

To investigate the influence of azimuth, Figure 3 shows a

map view of a horizontal slice calculated 50 m above top

reservoir for the angle of incidence θ = 40 degrees and

varying azimuths, for Model 1 (upper panel) and Model 2

(lower panel). Azimuth is defined here as an angle between

the projected ray and the vector pointing east (x axis

direction) at the reference plane (x-y plane). Again, a

drastic difference is observed in the predictions of two

models. Model 2 exhibits a strong azimuth dependence

because of the coupling with horizontal strains that is not

present in Model 1. Azimuth, degrees

Figure 3: Map view, 50 m above the top reservoir. Time-shifts

predicted by Model 1 (upper panel) and Model 2 (lower panel) for

angles on incidence θ = 40 degrees and different azimuths.

Data examples

Data examples showing the offset dependence of time-

shifts at two different fields are given in Figure 4 and

Figure 5. Figure 4 shows the time-shifts obtained from data

acquired with narrow-azimuth streamer surveys in the

Shearwater field of the North Sea. The full stack is depicted

in the leftmost panels, followed by angle stacks to the right.

The vertical cross-sections depicted in the lower panel are

indicated by a dotted line on the maps depicted in the upper

panel. We do not observe any significant offset dependence

of the time-shifts.

Figure 5 shows a similar display of depth shifts obtained

from the data acquired with OBN surveys in the Mars field

in the Gulf of Mexico. Again, no significant offset-

dependence is observed. In this example, we observed the

“undershooting” phenomenon at far offsets below the

reservoir.

The comparison of the data examples with the predictions

by the models given in Figure 2 suggests that the

predictions by Model 1 are consistent with the data, while

Model 2 predicts a significant offset-dependence of time

shifts with increasing offset that is not observed in the data.

There is also no strong azimuthal dependence in the data,

as predicted by Model 2, although these data examples are

not presented here.

These results suggest, firstly, that the R-factor model can

be easily extended to non-zero offset rays. Furthermore, it

is suggested that taking into account lateral components of

the strain tensor leads to significant offset dependence at

far offsets, which was also reported in previous

publications. However, this offset-dependence is not

observed in our data. Model 2 presented in this paper can

be seen as a simplified version of a more general model

where additional parameters can be introduced governing

the sensitivity of the components of the stiffness tensor to

small strains.

We find it very informative to observe the drastic

difference between the two models. Given the fact that it is

hard to estimate the parameters governing stiffness

sensitivities, one must be careful in using the models taking

into account lateral strain components, which are required,

for example, for calibrating geomechanical models.

Page 5397© 2016 SEG SEG International Exposition and 86th Annual Meeting

Offset-dependent time-shifts

Figure 4: Shearwater: observed time-shifts. Upper panel – map of time-shifts for top reservoir; lower panel –

vertical cross-section through the reservoir area.

Full stack 0 – 15 degrees 15 – 30 degrees 30 – 45 degrees

Figure 5: Mars: observed depth shifts. Upper panel – map of depth-shifts for top reservoir; lower panel –

vertical cross-section through the reservoir area.

Conclusions

We have presented two examples of offset-dependent time-

shifts observed in real data acquired in shallow and deep

water marine environments. We do not observe any

significant offset dependence of the time-shifts. This result

is different from expectations based on several models

published in literature.

We compared our results with two different model

predictions. The model that used a linear relationship

between the fractional velocity change and the vertical

strain component worked best for describing the offset-

dependence of the data. This suggests that vertical strains

are dominant in the compaction regime and that the elastic

parameter governing P-wave propagation is sensitive to

small perturbations in the normal strain component induced

by compaction.

The predictions of a second heuristic model where velocity

change is related to the directional strain (the strain

component along the ray path) show a large and clearly

visible offset-dependence of time-shifts which is not

consistent with the observations presented in this paper.

Our results suggest that there is no additional value in

offset-dependence of 4D time-shifts measured in

compacting reservoir environments.

Acknowledgements

We are grateful to our Shell colleagues for providing

processed datasets. We thank Shell International E&P,

Shell Upstream Americas, Esso Exploration & Production

UK, Arco British Limited and BP Exploration and

Production Inc. for permission to publish this paper.

Full stack 0 – 10 degrees 10 – 20 degrees 20 – 30 degrees

Page 5398© 2016 SEG SEG International Exposition and 86th Annual Meeting

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