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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
EDITED REFERENCES Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2016
SEG Technical Program Expanded Abstracts have been copyedited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web.
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