Time-lapse Stress Effects in Seismic Data

Time-lapse changes in seismic data are commonly evalu-ated in terms of changes in reservoir properties such aspressure, saturation, or temperature. Traditionally, the eval-uation of time-lapse seismic data has focused on changes ofseismic 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 theoverburden and (generally) in the rock mass surroundingthe reservoir. These time-lapse changes can be explained byproduction-induced stress changes in the rocks surround-ing the reservoir.

This article presents a workflow that allows predictionof stress-induced time-lapse effects in seismic data.Subsequently, the workflow is applied to investigate stresseffects on observable seismic attributes such as time shiftsin 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 extendssimilar 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 stateinstead of changes of mean effective stress. Considering tri-

Predicting time-lapse stress effects in seismic dataJORG HERWANGER, WesternGeco, Gatwick, U.K. STEVE HORNE, Electromagnetic Instruments, Richmond, California, USA

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Figure 1. Workflow to predict time-lapse stress effects in seismic data.

Figure 2. Grid geometry andwell locations for reservoir andgeomechanical model. (a) Themodel is divided into six geologicunits. Each unit is subdividedinto computational grid cells.The reservoir interval is finelydiscretized. The overburden andunderburden are coarsely dis-cretized. Note, furthermore, thegrid coarsening toward the sideboundaries of the computationaldomain. (b) Three-dimensionalview of grid showing two verti-cal and one horizontal slicethrough the reservoir. (c)Location of the wells W1-W4.Note the elongated shape in NE-SE direction of the reservoir andthe location of the four wellssituated along the shoulders ofthe field. (d) Three-dimensionalview showing well positions.

axial stress changes leads necessarily tochanges in anisotropic seismic veloci-ties. This extension, to include ani-sotropy, allows the shear-wave splittingobservations to be readily explained.

To investigate observations of timeshifts and shear-wave splitting in theoverburden, we built a realistic struc-tural model based on a double-dippinganticlinal structure similar to Valhall andEkofisk fields in the North Sea. Usingthis fairly simple model, with appro-priate material properties from pub-lished data, allows the study of generalfeatures in three-dimensional changes inthe deformation, stress, and velocityfields.

In field data, significant anomalieshave been observed in the shallow sub-surface. The most spectacular feature isa nearly circular subsidence bowl caus-ing stress-induced shear-wave splitting.From modeling, we find that in the deepoverburden the vertical ground dis-placement mirrors the elongated shapeof the reservoir, with the largest valuesof displacement encountered around thewells.

The predicted stress effects in seismicdata are larger than the limit of detectabil-ity; a slowdown of 4 ms in the overbur-den and an increase of 2 ms in thereservoir are predicted for P-waves dur-ing a three-year production period.Predicted S-waves show an even larger time-lapse effect ofup to 40 ms and a significant amount of shear-wave splitting,especially in the shallow overburden.

From coupled reservoir/geomechanical modeling to seismicattributes: 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 (3Ddistribution of Young’s modulus, Poisson’s ratio, density,porosity, permeability, fluid content, initial stress stateand pore pressure, location of wells and flow rates ofthese wells, and other relevant information).

2) Dynamically model the physical behavior (fluid flow,pressure, deformation, stress, and other properties ofinterest) of the reservoir and overburden over time.

3) Calculate changes in the elastic stiffness tensor fromchanges in the triaxial stress field using a stress-sen-sitive rock-physics model.

4) Calculate time-lapse seismic attributes using the modeledchanges in elastic stiffness tensors.

This article describes use of the workflow to predicttime-lapse seismic attributes for a synthetic oilfield. Usingrealistic parameters, this workflow can carry out a feasibil-ity study to determine whether stress effects are likely to beobserved in seismic data. Asecond application for this work-flow is as a survey evaluation and design tool to determinewhich seismic attributes will show the strongest stress effectsfor a specific acquisition type and geometry. This, in turn,enables decisions about the feasibility of monitoring of stresschanges for use in geomechanical studies.

Building a reservoir and geomechanical model. The firststep in dynamic reservoir geomechanical modeling is thecreation of a geometric model of the reservoir and the over-burden. Within the geometric framework, a computationalgrid is defined. Finally, material properties describing theflow and geomechanical properties can be assigned withineach grid block of the model.

Geometric description of model. The geometry of the reser-voir and geomechanical model is loosely based on Valhalland Ekofisk fields in the North Sea. Based on the publishedliterature (Cook and Jewell, 1996; Barkved et al., 2003, andreferences therein), this model is divided into six geologicunits—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 intosmaller computational grid blocks. The smallest grid blocksare used where simulation of fluid-flow processes requiresa dense grid (i.e., in the reservoir units). Moderately sizedgrid blocks are used for computations of stresses and strainsin the overburden, and large grid blocks are employedtoward the lateral boundaries of the grid.

The densely gridded reservoir region extends 8 km inthe x direction and 10 km in the y direction (Figure 2a-c).The field consists of a gently double-dipping anticline, witha long axis of approximately 10 km and a small axis ofapproximately 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 modelthe fluid flow and geomechanical behavior of this model,rock-physical properties (porosity and permeability for fluidflow; density, Young’s modulus, Poisson’s ratio, and Biot’sconstant for geomechanics) must be specified. The proper-ties of the reservoir rock and the overburden rock are given

DECEMBER 2005 THE LEADING EDGE 1235

in Table 1. The values given are order-of-magnitude esti-mates calculated from values reported in the literature andare constant within each geologic unit.

Of particular relevance are the high porosity (45% in theupper reservoir formation) and the small Young’s modulusof 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 deformationand 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 porepressure. In this case, the deformation process is reversibleand 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 thefluids 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 toDarcy’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 permeabilityconstant) 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 wellwill show a wider compaction bowl with a lower viscosity ofthe pore-fluid.

Furthermore, the physical properties of the pore fluid are


Figure 3. Predicted three-dimensional subsurface displacement in layers 1, 9, and 12 after three years of reservoir production. Vertical displacement isplotted 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 bedescribed by a second-rank tensor. The principal directions of the tensor determine the direction of the double arrows and the principal values determinethe 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 thesame 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.

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 employinga “compositional simulator” for prediction of fluid flow. Thepore fluid properties (Table 2) are based on published data forValhall 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 2400 m3/day (approximately15 000 b/d) in each well. This production rate is equal to theaverage 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 showsa plan view of the well locations, and Figure 2d shows a three-dimensional representation of the wells and the top reservoirunit. Note the green markers in the reservoir layer, indicatinga perforated and producing well for this layer. The coordinatesof the four wells (W1– W4) in terms of element numbers aregiven in Table 3. The range of cells in the z direction indi-cates the perforated section of the well, comprising the entirereservoir interval.

Coupled reservoir and geomechanical modeling. A com-mercial reservoir simulator, which includes geomechanicalcoupling, was used (Stone et al., 2000). This simulator mod-els both fluid flow and the associated geomechanicalprocesses (pore-pressure depletion and ensuing deforma-tion and triaxial stress changes) within the reservoir and thesurrounding rock. Fluid flow, deformation, and the triaxialstress state are modeled for a three-year production period.

Production-induced subsurface deformation. Perhaps themost visible form of production-induced subsurface defor-mation is surface subsidence—i.e., vertical displacement ofthe earth’s surface. Besides vertical displacement, recentmeasurements with high-precision differential global posi-tioning systems have also shown lateral displacement at theearth’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 stressfields can be predicted in our modeling for each cell of themodel. In the following paragraphs, we discuss the vectordisplacement 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 smoothsubsidence bowl is predicted (Figure 3). Maximum verticalsurface displacement of 28 cm is observed at the center of


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 inevery third cell. Green double arrows indicate a decrease in effective stress and red double arrows indicate an increase in effective stress in the directionof the arrow. See Figure 4 and text for a more detailed explanation.

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 subsidencebowl, 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 10cm/year) compare well with seafloor subsidence observedat Valhall where approximately 4 m of subsidence hasoccurred over a 30-year production period (average subsi-dence rate of 13 cm/year). Note that the shape of the nearlycircular subsidence bowl bears little resemblance to theshape 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 (Figure3b). Within the reservoir, the vertical displacement contoursshow even more topography (Figure 3c). This becomes mostapparent around wells W1–W4, which are all located in thecenter of local maxima of vertical displacement. Maximumvertical 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, inboth amplitude and displacement direction, toward thereservoir. 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, thesmoother the displacement field.

Time-lapse stress changes. The stress field inside the earthis principally governed by overburden stress, tectonic stress,and pore pressure. Changing the pore pressure within thereservoir puts the reservoir out of static equilibrium withits surroundings. This results in a transfer of stress to theoverburden, and more generally, to the entire rock mass sur-rounding the reservoir. The resulting stress changes canconsist of either increases or decreases in the stress.Moreover, the stress at a specified location can increase inone direction and decrease in another direction; i.e., thestress changes are triaxial and must be described by a ten-sor. These changes in the state of the triaxial effective stressfield, derived from coupled fluid flow and geomechanicalmodeling, 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 theexamination of the magnitudes and directions of maximum,minimum, and intermediate stress (or stress change). Here wedefine compressive stress (and increase in compressive stress)by negative principal values of the stress tensor. Changes ineffective stress tensor are illustrated graphically in Figure 4.The changes in the stress tensor are depicted by a set of threeorthogonal double arrows. The lengths of the arrows (and sizeof the arrow tip) are proportional to the principal values ofthe tensor and the principal directions of the tensor give thedirections of the double arrows. Directions aligned with thedouble arrows (two pairs of red double arrows pointingtoward each other and one pair of green double arrowspointing away from each other) experience only normalstresses; all other directions also experience a component ofshear 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 doublearrows, 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 thecomputational grid and the results plotted in plan view forthree 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 Figure3. In the near surface, the largest stress increase is observedat the center of the subsidence bowl (above the center of thefield). This observation can be qualitatively explained by theimage of displacement (Figure 3a); all particles of the near-surface rock mass move radially toward the center of thesubsidence bowl. Therefore, the center of the subsidencebowl experiences an isotropic horizontal stress increase.Toward the edges of the subsidence bowl, anisotropic hor-izontal stress changes develop; in radial directions, the stresschanges are small, whereas in tangential directions, there isa marked stress increase. No stress changes are observed inthe vertical direction. Note that the pattern of stress changesis highly symmetric with a nearly circular shape.

In the deep overburden the maximum stress changes areobserved in a subvertical direction. Stress in a subverticaldirection 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 subhorizontalstress changes are compressive, with a marked anisotropybetween the two subhorizontal principal stress changes. Withinthe reservoir, the principal values of change in effective stressare all negative, implying an increase in effective stress in alldirections. The largest increases in effective stresses areobserved in the vertical direction near the wells. Because it ishere that pore pressure decreases most, it follows that the stressin 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 triaxialstress state can cause changes in (anisotropic) seismic veloci-ties. Velocity measurements in laboratory tests on triaxiallystressed rock samples show, as a rule of thumb, that the mainsensitivity of velocity on stress is encountered in directionswhere 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 tolink the changes in stress state and changes in (anisotropic)velocity. Because the changes in stress state are triaxial innature (as shown in the previous section), it is necessary toemploy a rock-physics model that links the changes in theentire stress tensor (predicted from geomechanical model-ing) to changes in the entire elastic stiffness tensor (describ-ing the anisotropic seismic velocity changes). Calculation ofchanges 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 ofa 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 thatthis theory provides a means to compute the stiffness ten-sor, in a particular stress state, from the stiffness tensor atan 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 fromspecialized 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 thisstudy, an isotropic preproduction velocity model is assumed.The (anisotropic) velocity perturbations caused by triaxialstress changes are calculated and subsequently the velocity


perturbations are used to predict time-lapse seismic attrib-utes.

Changes in vertical traveltime. The seismic attribute thatcan arguably be measured most reliably and with greatestaccuracy is the seismic traveltime for vertical incidence.Furthermore, field observations of vertical traveltimechanges in the overburden at a North Sea gas field have beenconclusively linked with stress changes due to overburdenstretching (e.g., Hatchell et al., 2003).

Change in vertical seismic traveltimes due to stress areinvestigated by following the previously described work-flow; after computation of changes in effective stress, astress-sensitive rock-physics model is applied to calculatethe stiffness tensor of the stressed medium in each cell alongthe trajectory of well W1. This allows calculation of verti-cal compressional and shear velocities (Figure 6) along thewell path. Finally, the changes in two-way traveltime toeach interface in the model are calculated for both com-pressional and shear waves (Figure 7). Vertical velocity forcompressional waves is markedly reduced in the near sur-face (layers 1-3) and again noticeably reduced in the deepoverburden (layers 8-11) adjacent to the reservoir. Within thereservoir, the P-wave velocity increases sharply. Verticalshear-wave velocity changes follow a different profile; astrong increase in vertical velocity, together with a markeddevelopment of anisotropy, is predicted in the near surface.In the deep overburden and the reservoir (layers 12-15), adecrease and increase in shear-wave velocity is predicted,respectively. These velocity changes are predicted using arock-physics model that allows computation of anisotropicvelocity changes from triaxial stress changes in the elasticregime. However, the rock-physics model does not accountfor 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-wavevelocities in the reservoir (e.g., by replacing oil with gas andby loosening grain contacts), counteracting the described

stress effect on P-wave velocity.Translating the stress-induced

velocity changes into time-lapsetraveltime changes predicts anincrease in P-wave traveltime ofmore than 3 ms in the overburden,followed by a decrease of 1.5 mswithin the reservoir. Interestingly,the time-lapse effect in the over-burden is predicted to be largerthan the time-lapse effect withinthe reservoir. The same holds truefor the predicted S-wave travel-times; here, time-lapse traveltimechanges are predicted in the over-burden of 30 ms and 40 ms for fastand slow shear waves, respec-tively. Note also, that the majorityof this change occurs in the firstnear-surface layer. Within the reser-voir, the traveltime changes for S-waves are of the order of 1-2 ms.Consequently, the traveltimechange in the overburden is anorder of magnitude larger than inthe reservoir. Thus an effectivestrategy is required to compensatefor these effects in seismic data ifthe time-lapse effects are to bemeaningfully interpreted in terms

of reservoir changes.The above calculations are all based on a synthetic model

making reasonable assumptions and using estimates for allparameters involved. The results strongly suggest that thestress effects are significant enough to be observed in field datausing acquisition technology already in use. The presentedmodel consists of a big field using elastic parameters of acompressive rock. For smaller fields and elastic parametersfor a stiffer rock matrix, the traveltime effects would be smaller.This, in turn, implies that data quality must be excellent, andspecialized data processing may have to be applied to extractthe 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 withinthe reservoir, a top-reservoir and a bottom-reservoir reflectorare required, a situation which is not always given. Therefore,the possibility to infer stress changes within the reservoir fromobservations of traveltime changes above the reservoir is atempting proposition. Traveltime changes in the overburdenhave been observed in some field examples (e.g., Hatchell etal., 2003 and Hudson et al., 2005). We expect that seismic time-lapse traveltime changes in the overburden will become anincreasingly common observation. At present, this time-lapsesignal 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 traveltimechanges can give valuable insight into stress changes withinthe reservoir.

Shear-wave splitting. Azimuthally varying horizontalstress (such as predicted in the shallow surface) will causeazimuthal seismic anisotropy. In azimuthally anisotropicmedia, a vertically emergent shear wave will experienceshear-wave splitting (Figure 8a). If the anisotropy is causedby stress, the fast shear-wave polarization is aligned with


Figure 6. Predicted change in vertical P- and S-velocities along well W1 after three years of reservoirproduction.

the maximum horizontal stress,and the slow shear-wave polar-ization direction indicates thedirection of minimum horizontalstress. The presented workflowallows prediction of the forma-tion of a subsidence bowl (Figure3a), the resulting stress field(Figure 5a), and calculation ofsubsidence-induced shear-wavesplitting (Figure 8).

Two important observableparameters in shear-wave split-ting analysis are (1) the polariza-tion direction of the fast shearwave and (2) the time lag betweenthe fast (qS1) and the slow (qS2)shear waves. The time lag and ori-entation of fast shear waves inevery third cell of our model areplotted for the top 100 m belowseafloor (Figure 8b). The azimuthsof the short lines indicate theazimuths of the fast shear-wavepolarization directions and thelengths of the short lines are pro-portional to the time lag betweenfast and slow shear-wave arrivals.In the center of the subsidencebowl, where stress changes arelargest but nearly isotropic, noshear-wave splitting occurs. Mov-ing away from the center of thesubsidence bowl, the stress chan-ges are azimuthally varying, re-sulting in an azimuthallyanisotropic stiffness tensor andshear-wave splitting. The shear-wave splitting predictions (interms of azimuths and relativeamplitudes) using the workfloware in close agreement with theshear-wave splitting observationsreported in Olofsson et al. (2003).

Discussion and conclusions. Aworkflow to estimate effects ofproduction-induced stress chan-ges on seismic data is describedand applied to calculate travel-time changes and near-surfaceshear-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 ameans to model and explore theseeffects.

Special emphasis was givento the triaxial nature of the stresschanges, and we have shown that the principal directionsof the stress changes need not be aligned with the verticalor horizontal directions. The triaxial nature of stress changescauses 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 velocitychanges will also influence other seismic attributes (Her-wanger and Horne, 2005) and must be taken into accountin both time-lapse data processing and reservoir evaluationseismics. If interpreted correctly, the time-lapse changes inthe overburden can give valuable insight into stress changes


Figure 7. Change in traveltimes for vertically traveling P-wave (left) and S-waves (right) along the tra-jectory 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 arethe polarization direction of the fast shear wave (red wavelet) and the time lag between the arrival offast and slow shear waves. (b) Shear-wave splitting predicted for near-surface layer of 100 m. Theazimuth 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 partsof the stress tensor (see Sayers, 2004 for a discussion) andit may be possible to monitor changes in the entire stresstensor from seismic data using suitable acquisition and pro-cessing strategies. Vertically propagating compressionalwaves are predominantly sensitive to changes in verticalstress; vertically propagating shear waves are sensitive tostress changes in horizontal and vertical directions, andwide azimuthal coverage would assist in determining anyrotations of the stress tensor with respect to the coordinateaxes. Running the workflow in an iterative fashion, whileperturbing input model parameters, until observed dataand predicted seismic data match could provide a viableoption to determine as much information about changes inthe stress tensor as possible. The strategy of combiningreservoir modeling, geomechanical modeling, and exami-nation of time-lapse seismic changes could also help dis-criminate between stress effects and saturation changes inthe reservoir.

It is expected that production-induced (anisotropic) stresseffects in seismic data will be more widely observed as soonas seismic specialists look more actively for them. Amongcandidate 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 NileDelta). These fields are also candidates for drilling and well-bore stability problems. Thus, seismic stress monitoringholds promise as a useful geomechanical surveillance tool.

Suggested reading. Geomechanical parameters for Valhall canbe found in “Valhall Field—Still on plateau after 20 years ofproduction” by Barkved et al. (SPE 83957, 2003). Pore fluid,geometry top reservoir are discussed in “Simulation of a NorthSea field experiencing significant compaction drive” by Cookand 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 aColton sandstone under a changing triaxial stress” by Dillen et

al. (GEOPHYSICS, 1999). The link between geomechanics andtime shift in the overburden is presented in “Whole earth 4D:reservoir monitoring geomechanics” by Hatchell et al. (SEG 2003Expanded Abstracts). Stress effects on AVO, shear splitting, andtime 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 stresschange 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 anisotropyfrom 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 3Dsubsurface stress in anisotropic formations: Theory and labo-ratory verification” by Prioul et al. (GEOPHYSICS, 2004). A tableof constants necessary for rock-physics modeling is given in“Calibration of velocity-stress relationships under hydrostaticstress for their use under nonhydrostatic stress conditions” byPrioul and Lebrat (SEG 2004 Expanded Abstracts). A sensitivitystudy about the influence of horizontal/vertical stress on seis-mic attributes is the theme of “Monitoring production-inducedstress changes using seismic waves” by Sayers (SEG 2004Expanded Abstracts). For information on coupled reservoir/geo-mechanical modeling, see “Fully coupled geomechanics in acommercial 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: Ekofisk2D/4C test” by Van Dok et al. (TLE, 2003). Similar workflowfor isotropic data is described by Vidal et al. in “Characterizingreservoir parameters by integrating seismic monitoring andgeomechanics” (TLE, 2002). TLE

Acknowledgments: Steve Horne was with WesternGeco when this workwas performed.

Corresponding author: [email protected]


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Time-lapse Stress Effects in Seismic Data