Time-lapse Stress Effects in Seismic Data

Predicting time-lapse stress effects in seismic data
JORG HERWANGER, WesternGeco, Gatwick, U.K.
STEVE HORNE, Electromagnetic Instruments, Richmond, California, USA
Time-lapse changes in seismic data are commonly evalu-ated
in terms of changes in reservoir properties such as
pressure, saturation, or temperature. Traditionally, the eval-uation
of time-lapse seismic data has focused on changes of
seismic signatures within the reservoir interval. Recent stud-ies,
however, have shown convincingly that time-lapse seis-mic
changes occur not only in the reservoir, but also in the
overburden and (generally) in the rock mass surrounding
the reservoir. These time-lapse changes can be explained by
production-induced stress changes in the rocks surround-ing
the reservoir.
This article presents a workflow that allows prediction
of stress-induced time-lapse effects in seismic data.
Subsequently, the workflow is applied to investigate stress
effects on observable seismic attributes such as time shifts
in the overburden and shear-wave splitting in the overbur-den.
Both time shifts (Hatchell et al., 2003; Hudson et al.,
2005) and near-surface shear-wave splitting (Olofsson et al.,
2003; Van Dok et al., 2003) have been observed in field data,
providing the motivation for this work. Our work extends
similar workflows of predicting a seismic response from geo-mechanical
modeling (e.g. Olden et al., 2001; Vidal et al.,
2002), by considering the changes in triaxial stress state
instead of changes of mean effective stress. Considering tri-
1234 THE LEADING EDGE DECEMBER 2005
Figure 1. Workflow to predict time-lapse stress effects in seismic data.
Figure 2. Grid geometry and
well locations for reservoir and
geomechanical model. (a) The
model is divided into six geologic
units. Each unit is subdivided
into computational grid cells.
The reservoir interval is finely
discretized. The overburden and
underburden are coarsely dis-cretized.
Note, furthermore, the
grid coarsening toward the side
boundaries of the computational
domain. (b) Three-dimensional
view of grid showing two verti-cal
and one horizontal slice
through the reservoir. (c)
Location of the wells W1-W4.
Note the elongated shape in NE-SE
direction of the reservoir and
the location of the four wells
situated along the shoulders of
the field. (d) Three-dimensional
view showing well positions.

axial stress changes leads necessarily to
changes in anisotropic seismic veloci-ties.
This extension, to include ani-sotropy,
allows the shear-wave splitting
observations to be readily explained.
To investigate observations of time
shifts and shear-wave splitting in the
overburden, we built a realistic struc-tural
model based on a double-dipping
anticlinal structure similar to Valhall and
Ekofisk fields in the North Sea. Using
this fairly simple model, with appro-priate
material properties from pub-lished
data, allows the study of general
features in three-dimensional changes in
the deformation, stress, and velocity
fields.
In field data, significant anomalies
have been observed in the shallow sub-surface.
The most spectacular feature is
a nearly circular subsidence bowl caus-ing
stress-induced shear-wave splitting.
From modeling, we find that in the deep
overburden the vertical ground dis-placement
mirrors the elongated shape
of the reservoir, with the largest values
of displacement encountered around the
wells.
The predicted stress effects in seismic
data are larger than the limit of detectabil-ity;
a slowdown of 4 ms in the overbur-den
and an increase of 2 ms in the
reservoir are predicted for P-waves dur-ing
a three-year production period.
Predicted S-waves show an even larger time-lapse effect of
up to 40 ms and a significant amount of shear-wave splitting,
especially in the shallow overburden.
From coupled reservoir/geomechanical modeling to seismic
attributes: A workflow. The fundamental steps in a work-flow
to estimate stress effects on seismic data are (Figure 1):
1) Build a (static) geomechanical and reservoir model (3D
distribution of Young’s modulus, Poisson’s ratio, density,
porosity, permeability, fluid content, initial stress state
and pore pressure, location of wells and flow rates of
these wells, and other relevant information).
2) Dynamically model the physical behavior (fluid flow,
pressure, deformation, stress, and other properties of
interest) of the reservoir and overburden over time.
3) Calculate changes in the elastic stiffness tensor from
changes in the triaxial stress field using a stress-sen-sitive
rock-physics model.
4) Calculate time-lapse seismic attributes using the modeled
changes in elastic stiffness tensors.
This article describes use of the workflow to predict
time-lapse seismic attributes for a synthetic oilfield. Using
realistic parameters, this workflow can carry out a feasibil-ity
study to determine whether stress effects are likely to be
observed in seismic data. Asecond application for this work-flow
is as a survey evaluation and design tool to determine
which seismic attributes will show the strongest stress effects
for a specific acquisition type and geometry. This, in turn,
enables decisions about the feasibility of monitoring of stress
changes for use in geomechanical studies.
Building a reservoir and geomechanical model. The first
step in dynamic reservoir geomechanical modeling is the
creation of a geometric model of the reservoir and the over-burden.
Within the geometric framework, a computational
grid is defined. Finally, material properties describing the
flow and geomechanical properties can be assigned within
each grid block of the model.
Geometric description of model. The geometry of the reser-voir
and geomechanical model is loosely based on Valhall
and Ekofisk fields in the North Sea. Based on the published
literature (Cook and Jewell, 1996; Barkved et al., 2003, and
references therein), this model is divided into six geologic
units—two overburden units, one unit representing the seal,
two reservoir units, and one unit representing the under-burden
(Figure 2a). Note that each unit is subdivided into
smaller computational grid blocks. The smallest grid blocks
are used where simulation of fluid-flow processes requires
a dense grid (i.e., in the reservoir units). Moderately sized
grid blocks are used for computations of stresses and strains
in the overburden, and large grid blocks are employed
toward the lateral boundaries of the grid.
The densely gridded reservoir region extends 8 km in
the x direction and 10 km in the y direction (Figure 2a-c).
The field consists of a gently double-dipping anticline, with
a long axis of approximately 10 km and a small axis of
approximately 4 km (Figure 2c). Within the reservoir region,
the grid block size is 250 250 m in the x and y directions,
and approximately 20 m in the z direction.
Physical properties of reservoir and overburden rock. To model
the fluid flow and geomechanical behavior of this model,
rock-physical properties (porosity and permeability for fluid
flow; density, Young’s modulus, Poisson’s ratio, and Biot’s
constant for geomechanics) must be specified. The proper-ties
of the reservoir rock and the overburden rock are given
DECEMBER 2005 THE LEADING EDGE 1235

Figure 3. Predicted three-dimensional subsurface displacement in layers 1, 9, and 12 after three years of reservoir production. Vertical displacement is
plotted as a color-coded map with horizontal displacement vectors superimposed. All three images use the same color scale for vertical displacement.
Also note the arrow at the bottom of each image, indicating 5 cm of horizontal displacement.
Figure 4. Change in effective stress in cell i=15, j=25, k=9. The stress change is triaxial—i.e., stress changes vary dependent on direction and can be
described by a second-rank tensor. The principal directions of the tensor determine the direction of the double arrows and the principal values determine
the length of the arrows. Compressive stress is defined as negative. (a) Three-dimensional view of the tensor of stress change and (b) top view of the
same tensor. Effective stress decreases by approximately 0.3 bar in the subvertical direction (green arrows) and increases (anisotropically) in the subhori-zontal
plane (red arrows). See text for details.
in Table 1. The values given are order-of-magnitude esti-mates
calculated from values reported in the literature and
are constant within each geologic unit.
Of particular relevance are the high porosity (45% in the
upper reservoir formation) and the small Young’s modulus
of 6000 bar (=0.6 GPa) in the reservoir units. This combina-tion
of high porosity and a “soft” rock enables reservoir com-paction
and will result in noticeable reservoir deformation
and overburden subsidence during reservoir production.
The properties describing the geomechanical behavior—
Young’s modulus (E), Poisson’s ratio (ν), Biot constant (α),
and density (ρ)—describe a linearly elastic porous medium.
Reservoir compaction is caused solely by decreasing pore
pressure. In this case, the deformation process is reversible
and re-instating the initial pore pressure (e.g., by injection)
reverses the deformation and stress state to the original val-ues.
Physical properties of pore fluid. Physical properties of the
fluids contained in the pore space can have a strong influ-ence
on the depletion pattern of a reservoir and the pro-duction-
induced stress field. For example, according to
Darcy’s law (relating flow rate with the gradient in pore pres-sure
using viscosity and permeability), a highly viscous
(heavy) oil will result (keeping flow rate and permeability
constant) in a large pressure gradient, whereas a low-vis-cosity
(light) oil will result in a small pressure gradient.
Consequently, reservoir compaction around a producing well
will show a wider compaction bowl with a lower viscosity of
the pore-fluid.
Furthermore, the physical properties of the pore fluid are

Figure 5. Change of effective stress in layers 1, 9 and 12 during three years of reservoir production. The change in triaxial effective stress is plotted in
every third cell. Green double arrows indicate a decrease in effective stress and red double arrows indicate an increase in effective stress in the direction
of the arrow. See Figure 4 and text for a more detailed explanation.
a function of the composition of the fluid in terms of differ-ent
hydrocarbon molecules, temperature, saturation, and pres-sure.
This dependence can be taken into account by employing
a “compositional simulator” for prediction of fluid flow. The
pore fluid properties (Table 2) are based on published data for
Valhall Field.
Well location and production rates. The location of produc-tion
and injection wells and their individual production sched-ules
have a marked influence on the pore-pressure distribution,
and thus on the stress field. To simplify the analysis, produc-tion
from four wells was chosen at a constant production rate
(total hydrocarbons produced) of 2400m3/day (approximately
15 000 b/d) in each well. This production rate is equal to the
average production rate of Valhall Field to date. The four pro-duction
wells are on the upper part of the flanks of the dou-ble-
dipping anticline comprising the reservoir. Figure 2c shows
a plan view of the well locations, and Figure 2d shows a three-dimensional
representation of the wells and the top reservoir
unit. Note the green markers in the reservoir layer, indicating
a perforated and producing well for this layer. The coordinates
of the four wells (W1– W4) in terms of element numbers are
given in Table 3. The range of cells in the z direction indi-cates
the perforated section of the well, comprising the entire
reservoir interval.
Coupled reservoir and geomechanical modeling. A com-mercial
reservoir simulator, which includes geomechanical
coupling, was used (Stone et al., 2000). This simulator mod-els
both fluid flow and the associated geomechanical
processes (pore-pressure depletion and ensuing deforma-tion
and triaxial stress changes) within the reservoir and the
surrounding rock. Fluid flow, deformation, and the triaxial
stress state are modeled for a three-year production period.
Production-induced subsurface deformation. Perhaps the
most visible form of production-induced subsurface defor-mation
is surface subsidence—i.e., vertical displacement of
the earth’s surface. Besides vertical displacement, recent
measurements with high-precision differential global posi-tioning
systems have also shown lateral displacement at the
earth’s surface. Inside the earth, effects of subsurface defor-mation
can be observed in the form of well deformation.
The vector displacement and the resulting strain and stress
fields can be predicted in our modeling for each cell of the
model. In the following paragraphs, we discuss the vector
displacement in three horizons: in the shallow overburden,
in the deep overburden, and within the top reservoir layer.
In the shallow overburden, a nearly circular and smooth
subsidence bowl is predicted (Figure 3). Maximum vertical
surface displacement of 28 cm is observed at the center of

the bowl above the center of the field. Horizontal displace-ments
(indicated by arrows plotted in every third element)
occur in radial directions toward the center of the subsidence
bowl, with a maximum observed displacement of 4.3 cm.
The displacement values (28 cm subsidence in three years;
i.e., approximately an average subsidence rate of 10
cm/year) compare well with seafloor subsidence observed
at Valhall where approximately 4 m of subsidence has
occurred over a 30-year production period (average subsi-dence
rate of 13 cm/year). Note that the shape of the nearly
circular subsidence bowl bears little resemblance to the
shape of the elongated shape of the reservoir.
In the deep overburden, the vertical displacement con-tours
are still smooth but deviate markedly from the near-circular
shape observed in the shallow subsurface (Figure
3b). Within the reservoir, the vertical displacement contours
show even more topography (Figure 3c). This becomes most
apparent around wells W1–W4, which are all located in the
center of local maxima of vertical displacement. Maximum
vertical displacements of 36 cm are observed at well 2.
The horizontal displacement field is smooth in the shal-low
overburden and shows increasingly more variation, in
both amplitude and displacement direction, toward the
reservoir. A simplistic explanation is to consider the reser-voir
deformations as a signal with the earth acting as a low-pass
filter so that the farther away from the source, the
smoother the displacement field.
Time-lapse stress changes. The stress field inside the earth
is principally governed by overburden stress, tectonic stress,
and pore pressure. Changing the pore pressure within the
reservoir puts the reservoir out of static equilibrium with
its surroundings. This results in a transfer of stress to the
overburden, and more generally, to the entire rock mass sur-rounding
the reservoir. The resulting stress changes can
consist of either increases or decreases in the stress.
Moreover, the stress at a specified location can increase in
one direction and decrease in another direction; i.e., the
stress changes are triaxial and must be described by a ten-sor.
These changes in the state of the triaxial effective stress
field, derived from coupled fluid flow and geomechanical
modeling, are discussed in this section.
Stress (and stress changes) can be mathematically des-cribed
by a second-order tensor. Computation of principal val-ues
and principal directions of this tensor allows the
examination of the magnitudes and directions of maximum,
minimum, and intermediate stress (or stress change). Here we
define compressive stress (and increase in compressive stress)
by negative principal values of the stress tensor. Changes in
effective stress tensor are illustrated graphically in Figure 4.
The changes in the stress tensor are depicted by a set of three
orthogonal double arrows. The lengths of the arrows (and size
of the arrow tip) are proportional to the principal values of
the tensor and the principal directions of the tensor give the
directions of the double arrows. Directions aligned with the
double arrows (two pairs of red double arrows pointing
toward each other and one pair of green double arrows
pointing away from each other) experience only normal
stresses; all other directions also experience a component of
shear stress. Along the directions of the red double arrows,
the (compressive) stress increases (given by negative prin-cipal
values), and along the direction of the green double
arrows, the stress field decreases (positive principal value).
This analysis of stress change in terms of principal val-ues
and principal directions can be done in each cell of the
computational grid and the results plotted in plan view for
three layers (Figure 5 for layers 1, 9, and 12, respectively).
Note that the stress analysis in Figure 5 is done for the same
layers for which subsurface displacement is plotted in Figure
3. In the near surface, the largest stress increase is observed
at the center of the subsidence bowl (above the center of the
field). This observation can be qualitatively explained by the
image of displacement (Figure 3a); all particles of the near-surface
rock mass move radially toward the center of the
subsidence bowl. Therefore, the center of the subsidence
bowl experiences an isotropic horizontal stress increase.
Toward the edges of the subsidence bowl, anisotropic hor-izontal
stress changes develop; in radial directions, the stress
changes are small, whereas in tangential directions, there is
a marked stress increase. No stress changes are observed in
the vertical direction. Note that the pattern of stress changes
is highly symmetric with a nearly circular shape.
In the deep overburden the maximum stress changes are
observed in a subvertical direction. Stress in a subvertical
direction decreases due to overburden stretching. The con-tours
of the stress change show an ellipsoidal shape, mimic-king
the shape of the underlying reservoir. The subhorizontal
stress changes are compressive, with a marked anisotropy
between the two subhorizontal principal stress changes. Within
the reservoir, the principal values of change in effective stress
are all negative, implying an increase in effective stress in all
directions. The largest increases in effective stresses are
observed in the vertical direction near the wells. Because it is
here that pore pressure decreases most, it follows that the stress
in the rock frame (measured by effective stress) increases, be-cause
parts of the load previously supported by pore pres-sure
must now be supported by the rock frame.
Stress-sensitive rock-physics model. Changes in the triaxial
stress state can cause changes in (anisotropic) seismic veloci-ties.
Velocity measurements in laboratory tests on triaxially
stressed rock samples show, as a rule of thumb, that the main
sensitivity of velocity on stress is encountered in directions
where stress and either polarization or propagation direc-tion
of the seismic wave coincide (e.g., Dillen et al., 1999).
A stress-sensitive rock-physics model provides a theory to
link the changes in stress state and changes in (anisotropic)
velocity. Because the changes in stress state are triaxial in
nature (as shown in the previous section), it is necessary to
employ a rock-physics model that links the changes in the
entire stress tensor (predicted from geomechanical model-ing)
to changes in the entire elastic stiffness tensor (describ-ing
the anisotropic seismic velocity changes). Calculation of
changes in the entire elastic stiffness tensor allows predic-tion
of changes in seismic velocities in arbitrary directions,
prediction of changes in seismic attributes, and creation of
a velocity model for computation of time-lapse synthetic seis-mic
data.
A stress-sensitive rock-physics model based on nonlin-ear
elasticity theory (Prioul et al., 2004) is used. Note that
this theory provides a means to compute the stiffness ten-sor,
in a particular stress state, from the stiffness tensor at
an initial (or reference) stress state, the applied triaxial stress,
and three coupling coefficients. The three coupling coeffi-cients
must be determined from laboratory measurements
(e.g., Prioul and Lebrat, 2004) or can possibly be derived from
specialized long- and short-offset full-waveform sonic logs.
Time-lapse seismic attributes. The final step in the work-flow
is calculation of seismic attributes (such as traveltimes,
amplitudes, polarization directions, AVO parameters, etc.)
for comparison with field data. For the purposes of this
study, an isotropic preproduction velocity model is assumed.
The (anisotropic) velocity perturbations caused by triaxial
stress changes are calculated and subsequently the velocity

Figure 6. Predicted change in vertical P- and S-velocities along well W1 after three years of reservoir
production.
perturbations are used to predict time-lapse seismic attrib-utes.
Changes in vertical traveltime. The seismic attribute that
can arguably be measured most reliably and with greatest
accuracy is the seismic traveltime for vertical incidence.
Furthermore, field observations of vertical traveltime
changes in the overburden at a North Sea gas field have been
conclusively linked with stress changes due to overburden
stretching (e.g., Hatchell et al., 2003).
Change in vertical seismic traveltimes due to stress are
investigated by following the previously described work-flow;
after computation of changes in effective stress, a
stress-sensitive rock-physics model is applied to calculate
the stiffness tensor of the stressed medium in each cell along
the trajectory of well W1. This allows calculation of verti-cal
compressional and shear velocities (Figure 6) along the
well path. Finally, the changes in two-way traveltime to
each interface in the model are calculated for both com-pressional
and shear waves (Figure 7). Vertical velocity for
compressional waves is markedly reduced in the near sur-face
(layers 1-3) and again noticeably reduced in the deep
overburden (layers 8-11) adjacent to the reservoir. Within the
reservoir, the P-wave velocity increases sharply. Vertical
shear-wave velocity changes follow a different profile; a
strong increase in vertical velocity, together with a marked
development of anisotropy, is predicted in the near surface.
In the deep overburden and the reservoir (layers 12-15), a
decrease and increase in shear-wave velocity is predicted,
respectively. These velocity changes are predicted using a
rock-physics model that allows computation of anisotropic
velocity changes from triaxial stress changes in the elastic
regime. However, the rock-physics model does not account
for changes in other reservoir properties such as fluid con-tent
or for nonelastic rock deformation. Both fluid replace-ment
and nonelastic rock deformation can decrease P-wave
velocities in the reservoir (e.g., by replacing oil with gas and
by loosening grain contacts), counteracting the described
stress effect on P-wave velocity.
Translating the stress-induced
velocity changes into time-lapse
traveltime changes predicts an
increase in P-wave traveltime of
more than 3 ms in the overburden,
followed by a decrease of 1.5 ms
within the reservoir. Interestingly,
the time-lapse effect in the over-burden
is predicted to be larger
than the time-lapse effect within
the reservoir. The same holds true
for the predicted S-wave travel-times;
here, time-lapse traveltime
changes are predicted in the over-burden
of 30 ms and 40 ms for fast
and slow shear waves, respec-tively.
Note also, that the majority
of this change occurs in the first
near-surface layer. Within the reser-voir,
the traveltime changes for S-waves
are of the order of 1-2 ms.
Consequently, the traveltime
change in the overburden is an
order of magnitude larger than in
the reservoir. Thus an effective
strategy is required to compensate
for these effects in seismic data if
the time-lapse effects are to be
meaningfully interpreted in terms
of reservoir changes.
The above calculations are all based on a synthetic model
making reasonable assumptions and using estimates for all
parameters involved. The results strongly suggest that the
stress effects are significant enough to be observed in field data
using acquisition technology already in use. The presented
model consists of a big field using elastic parameters of a
compressive rock. For smaller fields and elastic parameters
for a stiffer rock matrix, the traveltime effects would be smaller.
This, in turn, implies that data quality must be excellent, and
specialized data processing may have to be applied to extract
the smaller traveltime effects. Such high quality seismic acqui-sition
and processing techniques have recently become avail-able.
Furthermore, the observation of changes in traveltimes pre-supposes
that reflections can be observed from horizons at ap-propriate
locations. For example, to measure time shifts within
the reservoir, a top-reservoir and a bottom-reservoir reflector
are required, a situation which is not always given. Therefore,
the possibility to infer stress changes within the reservoir from
observations of traveltime changes above the reservoir is a
tempting proposition. Traveltime changes in the overburden
have been observed in some field examples (e.g., Hatchell et
al., 2003 and Hudson et al., 2005). We expect that seismic time-lapse
traveltime changes in the overburden will become an
increasingly common observation. At present, this time-lapse
signal will (if recognized at all) be commonly regarded as “dif-ferences
in statics” between two surveys and “processed out”
of the data. If recognized as signal, vertical traveltime
changes can give valuable insight into stress changes within
the reservoir.
Shear-wave splitting. Azimuthally varying horizontal
stress (such as predicted in the shallow surface) will cause
azimuthal seismic anisotropy. In azimuthally anisotropic
media, a vertically emergent shear wave will experience
shear-wave splitting (Figure 8a). If the anisotropy is caused
by stress, the fast shear-wave polarization is aligned with

the maximum horizontal stress,
and the slow shear-wave polar-ization
direction indicates the
direction of minimum horizontal
stress. The presented workflow
allows prediction of the forma-tion
of a subsidence bowl (Figure
3a), the resulting stress field
(Figure 5a), and calculation of
subsidence-induced shear-wave
splitting (Figure 8).
Two important observable
parameters in shear-wave split-ting
analysis are (1) the polariza-tion
direction of the fast shear
wave and (2) the time lag between
the fast (qS1) and the slow (qS2)
shear waves. The time lag and ori-entation
of fast shear waves in
every third cell of our model are
plotted for the top 100 m below
seafloor (Figure 8b). The azimuths
of the short lines indicate the
azimuths of the fast shear-wave
polarization directions and the
lengths of the short lines are pro-portional
to the time lag between
fast and slow shear-wave arrivals.
In the center of the subsidence
bowl, where stress changes are
largest but nearly isotropic, no
shear-wave splitting occurs. Mov-ing
away from the center of the
subsidence bowl, the stress chan-ges
are azimuthally varying, re-sulting
in an azimuthally
anisotropic stiffness tensor and
shear-wave splitting. The shear-wave
splitting predictions (in
terms of azimuths and relative
amplitudes) using the workflow
are in close agreement with the
shear-wave splitting observations
reported in Olofsson et al. (2003).
Discussion and conclusions. A
workflow to estimate effects of
production-induced stress chan-ges
on seismic data is described
and applied to calculate travel-time
changes and near-surface
shear-wave splitting for a realis-tic
structural model. Both effects
(traveltime changes in the over-burden
and shear-wave splitting)
have been observed in field data,
and our workflow presents a
means to model and explore these
effects.
Special emphasis was given
Figure 7. Change in traveltimes for vertically traveling P-wave (left) and S-waves (right) along the tra-jectory
to the triaxial nature of the stress
changes, and we have shown that the principal directions
of the stress changes need not be aligned with the vertical
or horizontal directions. The triaxial nature of stress changes
causes anisotropic changes in seismic velocities. This man-ifests
itself spectacularly in near-surface shear-wave split-ting
due to stress-induced azimuthal anisotropy (e.g.,
Olofsson et al., 2003). The anisotropic seismic velocity
changes will also influence other seismic attributes (Her-wanger
and Horne, 2005) and must be taken into account
in both time-lapse data processing and reservoir evaluation
seismics. If interpreted correctly, the time-lapse changes in
the overburden can give valuable insight into stress changes
of well W1.
Figure 8. (a) Sketch of shear-wave splitting. In an azimuthally anisotropic medium, shear waves trav-eling
in a nearly vertical direction experience shear-wave splitting. Observable seismic attributes are
the polarization direction of the fast shear wave (red wavelet) and the time lag between the arrival of
fast and slow shear waves. (b) Shear-wave splitting predicted for near-surface layer of 100 m. The
azimuth of the fast shear-wave polarization direction is indicated by the orientation of the short bars,
and the length of the short bars is proportional to the time lag between fast and slow shear waves.

in the subsurface with implications for geomechanical appli-cations.
Different seismic attributes are sensitive to different parts
of the stress tensor (see Sayers, 2004 for a discussion) and
it may be possible to monitor changes in the entire stress
tensor from seismic data using suitable acquisition and pro-cessing
strategies. Vertically propagating compressional
waves are predominantly sensitive to changes in vertical
stress; vertically propagating shear waves are sensitive to
stress changes in horizontal and vertical directions, and
wide azimuthal coverage would assist in determining any
rotations of the stress tensor with respect to the coordinate
axes. Running the workflow in an iterative fashion, while
perturbing input model parameters, until observed data
and predicted seismic data match could provide a viable
option to determine as much information about changes in
the stress tensor as possible. The strategy of combining
reservoir modeling, geomechanical modeling, and exami-nation
of time-lapse seismic changes could also help dis-criminate
between stress effects and saturation changes in
the reservoir.
It is expected that production-induced (anisotropic) stress
effects in seismic data will be more widely observed as soon
as seismic specialists look more actively for them. Among
candidate fields that are likely to show stress effects in seis-mic
data are deepwater, overpressured, and underconsoli-dated
fields (e.g., the Gulf of Mexico, Niger Delta, or Nile
Delta). These fields are also candidates for drilling and well-bore
stability problems. Thus, seismic stress monitoring
holds promise as a useful geomechanical surveillance tool.
Suggested reading. Geomechanical parameters for Valhall can
be found in “Valhall Field—Still on plateau after 20 years of
production” by Barkved et al. (SPE 83957, 2003). Pore fluid,
geometry top reservoir are discussed in “Simulation of a North
Sea field experiencing significant compaction drive” by Cook
and Jewell (SPE 29132, 1996). Laboratory measurements of seis-mic
velocities in triaxially stressed media are described in
“Ultrasonic velocity and shear-wave splitting behavior of a
Colton sandstone under a changing triaxial stress” by Dillen et
al. (GEOPHYSICS, 1999). The link between geomechanics and
time shift in the overburden is presented in “Whole earth 4D:
reservoir monitoring geomechanics” by Hatchell et al. (SEG 2003
Expanded Abstracts). Stress effects on AVO, shear splitting, and
time shifts are discussed in “Linking geomechanics and seis-mics:
Stress effects on time-lapse multicomponent seismic data”
by Herwanger and Horne (EAGE 2005 Extended Abstracts) and
“Genesis Field, Gulf of Mexico, 4-D project status and prelim-inary
lookback” by Hudson et al. (SEG 2005 Expanded Abstracts).
Linking geomechanical modeling and seismic response in reser-voir
are described in “Modeling combined fluid and stress
change effects in the seismic response of a producing hydro-carbon
reservoir” by Olden et al. (TLE, 2001). Observed shear-wave
splitting at Valhall can be found in “Azimuthal anisotropy
from the Valhall 4C 3D survey” by Olofsson et al. (TLE, 2003).
Stress sensitive rock-physics employed in this study are ana-lyzed
in “Nonlinear rock physics model for estimation of 3D
subsurface stress in anisotropic formations: Theory and labo-ratory
verification” by Prioul et al. (GEOPHYSICS, 2004). A table
of constants necessary for rock-physics modeling is given in
“Calibration of velocity-stress relationships under hydrostatic
stress for their use under nonhydrostatic stress conditions” by
Prioul and Lebrat (SEG 2004 Expanded Abstracts). A sensitivity
study about the influence of horizontal/vertical stress on seis-mic
attributes is the theme of “Monitoring production-induced
stress changes using seismic waves” by Sayers (SEG 2004
Expanded Abstracts). For information on coupled reservoir/geo-mechanical
modeling, see “Fully coupled geomechanics in a
commercial reservoir simulator” by Stone et al. (SPE 65107,
2000). Shear-wave splitting at Ekofisk is described by “Near-surface
shear-wave birefringence in the North Sea: Ekofisk
2D/4C test” by Van Dok et al. (TLE, 2003). Similar workflow
for isotropic data is described by Vidal et al. in “Characterizing
reservoir parameters by integrating seismic monitoring and
geomechanics” (TLE, 2002). TLE
Acknowledgments: Steve Horne was with WesternGeco when this work
was performed.
Corresponding author: jherwanger@gatwick.westerngeco.slb.com

Time-lapse Stress Effects in Seismic Data

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